diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/DOC/GATBXA1.PS" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/DOC/GATBXA1.PS" index a2730447874a78d2b25f3285e64c2c381c1cfcb2..f9d7ae95bdd5aa26975bbff936e9821e68ce9ec9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/DOC/GATBXA1.PS" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/DOC/GATBXA1.PS" @@ -1,3 +1,7342 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f9ad22259c732168b5ba5fa45e60067c187dfacf874ed4aff805f3948f7797f4 -size 204230 +%! +%%BoundingBox: (atend) +%%Pages: (atend) +%%DocumentFonts: (atend) +%%EndComments +% +% FrameMaker PostScript Prolog 3.0, for use with FrameMaker 3.0 +% Copyright (c) 1986,87,89,90,91 by Frame Technology Corporation. +% All rights reserved. +% +% Known Problems: +% Due to bugs in Transcript, the 'PS-Adobe-' is omitted from line 1 +/FMversion (3.0) def +% Set up Color vs. Black-and-White + /FMPrintInColor systemdict /colorimage known + systemdict /currentcolortransfer known or def +% Uncomment this line to force b&w on color printer +% /FMPrintInColor false def +/FrameDict 195 dict def +systemdict /errordict known not {/errordict 10 dict def + errordict /rangecheck {stop} put} if +% The readline in 23.0 doesn't recognize cr's as nl's on AppleTalk +FrameDict /tmprangecheck errordict /rangecheck get put +errordict /rangecheck {FrameDict /bug true put} put +FrameDict /bug false put +mark +% Some PS machines read past the CR, so keep the following 3 lines together! +currentfile 5 string readline +00 +0000000000 +cleartomark +errordict /rangecheck FrameDict /tmprangecheck get put +FrameDict /bug get { + /readline { + /gstring exch def + /gfile exch def + /gindex 0 def + { + gfile read pop + dup 10 eq {exit} if + dup 13 eq {exit} if + gstring exch gindex exch put + /gindex gindex 1 add def + } loop + pop + gstring 0 gindex getinterval true + } def + } if +/FMVERSION { + FMversion ne { + /Times-Roman findfont 18 scalefont setfont + 100 100 moveto + (FrameMaker version does not match postscript_prolog!) + dup = + show showpage + } if + } def +/FMLOCAL { + FrameDict begin + 0 def + end + } def + /gstring FMLOCAL + /gfile FMLOCAL + /gindex FMLOCAL + /orgxfer FMLOCAL + /orgproc FMLOCAL + /organgle FMLOCAL + /orgfreq FMLOCAL + /yscale FMLOCAL + /xscale FMLOCAL + /manualfeed FMLOCAL + /paperheight FMLOCAL + /paperwidth FMLOCAL +/FMDOCUMENT { + array /FMfonts exch def + /#copies exch def + FrameDict begin + 0 ne dup {setmanualfeed} if + /manualfeed exch def + /paperheight exch def + /paperwidth exch def + /yscale exch def + /xscale exch def + currenttransfer cvlit /orgxfer exch def + currentscreen cvlit /orgproc exch def + /organgle exch def /orgfreq exch def + setpapername + manualfeed {true} {papersize} ifelse + {manualpapersize} {false} ifelse + {desperatepapersize} if + end + } def + /pagesave FMLOCAL + /orgmatrix FMLOCAL + /landscape FMLOCAL +/FMBEGINPAGE { + FrameDict begin + /pagesave save def + 3.86 setmiterlimit + /landscape exch 0 ne def + landscape { + 90 rotate 0 exch neg translate pop + } + {pop pop} + ifelse + xscale yscale scale + /orgmatrix matrix def + gsave + } def +/FMENDPAGE { + grestore + pagesave restore + end + showpage + } def +/FMFONTDEFINE { + FrameDict begin + findfont + ReEncode + 1 index exch + definefont + FMfonts 3 1 roll + put + end + } def +/FMFILLS { + FrameDict begin + array /fillvals exch def + end + } def +/FMFILL { + FrameDict begin + fillvals 3 1 roll put + end + } def +/FMNORMALIZEGRAPHICS { + newpath + 0.0 0.0 moveto + 1 setlinewidth + 0 setlinecap + 0 0 0 sethsbcolor + 0 setgray + } bind def + /fx FMLOCAL + /fy FMLOCAL + /fh FMLOCAL + /fw FMLOCAL + /llx FMLOCAL + /lly FMLOCAL + /urx FMLOCAL + /ury FMLOCAL +/FMBEGINEPSF { + end + /FMEPSF save def + /showpage {} def + FMNORMALIZEGRAPHICS + [/fy /fx /fh /fw /ury /urx /lly /llx] {exch def} forall + fx fy translate + rotate + fw urx llx sub div fh ury lly sub div scale + llx neg lly neg translate + } bind def +/FMENDEPSF { + FMEPSF restore + FrameDict begin + } bind def +FrameDict begin +/setmanualfeed { +%%BeginFeature *ManualFeed True + statusdict /manualfeed true put +%%EndFeature + } def +/max {2 copy lt {exch} if pop} bind def +/min {2 copy gt {exch} if pop} bind def +/inch {72 mul} def +/pagedimen { + paperheight sub abs 16 lt exch + paperwidth sub abs 16 lt and + {/papername exch def} {pop} ifelse + } def + /papersizedict FMLOCAL +/setpapername { + /papersizedict 14 dict def + papersizedict begin + /papername /unknown def + /Letter 8.5 inch 11.0 inch pagedimen + /LetterSmall 7.68 inch 10.16 inch pagedimen + /Tabloid 11.0 inch 17.0 inch pagedimen + /Ledger 17.0 inch 11.0 inch pagedimen + 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papersizedict begin + /Letter {letter} def + /LetterSmall {lettersmall} def + /Tabloid {11x17} def + /Ledger {ledger} def + /Legal {legal} def + /Statement {statement} def + /Executive {executive} def + /A3 {a3} def + /A4 {a4} def + /A4Small {a4small} def + /B4 {b4} def + /B5 {b5} def + /unknown {unknown} def + papersizedict dup papername known {papername} {/unknown} ifelse get + end + stopped + } def +/desperatepapersize { + statusdict /setpageparams known + { + paperwidth paperheight 0 1 + statusdict begin + {setpageparams} stopped pop + end + } if + } def +/savematrix { + orgmatrix currentmatrix pop + } bind def +/restorematrix { + orgmatrix setmatrix + } bind def +/dmatrix matrix def +/dpi 72 0 dmatrix defaultmatrix dtransform + dup mul exch dup mul add sqrt def +/freq dpi 18.75 div 8 div round dup 0 eq {pop 1} if 8 mul dpi exch div def +/sangle 1 0 dmatrix defaultmatrix dtransform exch atan def +/DiacriticEncoding [ +/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/.notdef /.notdef /.notdef /.notdef /space /exclam /quotedbl +/numbersign /dollar /percent /ampersand /quotesingle /parenleft +/parenright /asterisk /plus /comma /hyphen /period /slash /zero /one +/two /three /four /five /six /seven /eight /nine /colon /semicolon +/less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K +/L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash +/bracketright /asciicircum /underscore /grave /a /b /c /d /e /f /g /h +/i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar +/braceright /asciitilde /.notdef /Adieresis /Aring /Ccedilla /Eacute +/Ntilde /Odieresis /Udieresis /aacute /agrave /acircumflex /adieresis +/atilde /aring /ccedilla /eacute /egrave /ecircumflex /edieresis +/iacute /igrave /icircumflex /idieresis /ntilde /oacute /ograve +/ocircumflex /odieresis /otilde /uacute /ugrave /ucircumflex +/udieresis /dagger /.notdef /cent /sterling /section /bullet +/paragraph /germandbls /registered /copyright /trademark /acute +/dieresis /.notdef /AE /Oslash /.notdef /.notdef /.notdef /.notdef +/yen /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/ordfeminine /ordmasculine /.notdef /ae /oslash /questiondown +/exclamdown /logicalnot /.notdef /florin /.notdef /.notdef +/guillemotleft /guillemotright /ellipsis /.notdef /Agrave /Atilde +/Otilde /OE /oe /endash /emdash /quotedblleft /quotedblright +/quoteleft /quoteright /.notdef /.notdef /ydieresis /Ydieresis +/fraction /currency /guilsinglleft /guilsinglright /fi /fl /daggerdbl +/periodcentered /quotesinglbase /quotedblbase /perthousand +/Acircumflex /Ecircumflex /Aacute /Edieresis /Egrave /Iacute +/Icircumflex /Idieresis /Igrave /Oacute /Ocircumflex /.notdef /Ograve +/Uacute /Ucircumflex /Ugrave /dotlessi /circumflex /tilde /macron +/breve /dotaccent /ring /cedilla /hungarumlaut /ogonek /caron +] def +/ReEncode { + dup + length + dict begin + { + 1 index /FID ne + {def} + {pop pop} ifelse + } forall + 0 eq {/Encoding DiacriticEncoding def} if + currentdict + end + } bind def +/graymode true def + /bwidth FMLOCAL + /bpside FMLOCAL + /bstring FMLOCAL + /onbits FMLOCAL + /offbits FMLOCAL + /xindex FMLOCAL + /yindex FMLOCAL + /x FMLOCAL + /y FMLOCAL +/setpattern { + /bwidth exch def + /bpside exch def + /bstring exch def + /onbits 0 def /offbits 0 def + freq sangle landscape {90 add} if + {/y exch def + /x exch def + /xindex x 1 add 2 div bpside mul cvi def + /yindex y 1 add 2 div bpside mul cvi def + bstring yindex bwidth mul xindex 8 idiv add get + 1 7 xindex 8 mod sub bitshift and 0 ne + {/onbits onbits 1 add def 1} + {/offbits offbits 1 add def 0} + ifelse + } + setscreen + {} settransfer + offbits offbits onbits add div FMsetgray + /graymode false def + } bind def +/grayness { + FMsetgray + graymode not { + /graymode true def + orgxfer cvx settransfer + orgfreq organgle orgproc cvx setscreen + } if + } bind def + /HUE FMLOCAL + /SAT FMLOCAL + /BRIGHT FMLOCAL + /Colors FMLOCAL +FMPrintInColor + + { + /HUE 0 def + /SAT 0 def + /BRIGHT 0 def + % array of arrays Hue and Sat values for the separations [HUE BRIGHT] + /Colors + [[0 0 ] % black + [0 0 ] % white + [0.00 1.0] % red + [0.37 1.0] % green + [0.60 1.0] % blue + [0.50 1.0] % cyan + [0.83 1.0] % magenta + [0.16 1.0] % comment / yellow + ] def + + /BEGINBITMAPCOLOR { + BITMAPCOLOR} def + /BEGINBITMAPCOLORc { + BITMAPCOLORc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUECOLOR } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUECOLORc } def + /K { + Colors exch get dup + 0 get /HUE exch store + 1 get /BRIGHT exch store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } def + /FMsetgray { + /SAT exch 1.0 exch sub store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } bind def + } + + { + /BEGINBITMAPCOLOR { + BITMAPGRAY} def + /BEGINBITMAPCOLORc { + BITMAPGRAYc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUEGRAY } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUEGRAYc } def + /FMsetgray {setgray} bind def + /K { + pop + } def + } +ifelse +/normalize { + transform round exch round exch itransform + } bind def +/dnormalize { + dtransform round exch round exch idtransform + } bind def +/lnormalize { + 0 dtransform exch cvi 2 idiv 2 mul 1 add exch idtransform pop + } bind def +/H { + lnormalize setlinewidth + } bind def +/Z { + setlinecap + } bind def + /fillvals FMLOCAL +/X { + fillvals exch get + dup type /stringtype eq + {8 1 setpattern} + {grayness} + ifelse + } bind def +/V { + gsave eofill grestore + } bind def +/N { + stroke + } bind def +/M {newpath moveto} bind def +/E {lineto} bind def +/D {curveto} bind def +/O {closepath} bind def + /n FMLOCAL +/L { + /n exch def + newpath + normalize + moveto + 2 1 n {pop normalize lineto} for + } bind def +/Y { + L + closepath + } bind def + /x1 FMLOCAL + /x2 FMLOCAL + /y1 FMLOCAL + /y2 FMLOCAL + /rad FMLOCAL +/R { + /y2 exch def + /x2 exch def + /y1 exch def + /x1 exch def + x1 y1 + x2 y1 + x2 y2 + x1 y2 + 4 Y + } bind def +/RR { + /rad exch def + normalize + /y2 exch def + /x2 exch def + normalize + /y1 exch def + /x1 exch def + newpath + x1 y1 rad add moveto + x1 y2 x2 y2 rad arcto + x2 y2 x2 y1 rad arcto + x2 y1 x1 y1 rad arcto + x1 y1 x1 y2 rad arcto + closepath + 16 {pop} repeat + } bind def +/C { + grestore + gsave + R + clip + } bind def + /FMpointsize FMLOCAL +/F { + FMfonts exch get + FMpointsize scalefont + setfont + } bind def +/Q { + /FMpointsize exch def + F + } bind def +/T { + moveto show + } bind def +/RF { + rotate + 0 ne {-1 1 scale} if + } bind def +/TF { + gsave + moveto + RF + show + grestore + } bind def +/P { + moveto + 0 32 3 2 roll widthshow + } bind def +/PF { + gsave + moveto + RF + 0 32 3 2 roll widthshow + grestore + } bind def +/S { + moveto + 0 exch ashow + } bind def +/SF { + gsave + moveto + RF + 0 exch ashow + grestore + } bind def +/B { + moveto + 0 32 4 2 roll 0 exch awidthshow + } bind def +/BF { + gsave + moveto + RF + 0 32 4 2 roll 0 exch awidthshow + grestore + } bind def +/G { + gsave + newpath + normalize translate 0.0 0.0 moveto + dnormalize scale + 0.0 0.0 1.0 5 3 roll arc + closepath fill + grestore + } bind def +/A { + gsave + savematrix + newpath + 2 index 2 div add exch 3 index 2 div sub exch + normalize 2 index 2 div sub exch 3 index 2 div add exch + translate + scale + 0.0 0.0 1.0 5 3 roll arc + restorematrix + stroke + grestore + } bind def + /x FMLOCAL + /y FMLOCAL + /w FMLOCAL + /h FMLOCAL + /xx FMLOCAL + /yy FMLOCAL + /ww FMLOCAL + /hh FMLOCAL + /FMsaveobject FMLOCAL + /FMoptop FMLOCAL + /FMdicttop FMLOCAL +/BEGINPRINTCODE { + /FMdicttop countdictstack 1 add def + /FMoptop count 4 sub def + /FMsaveobject save def + userdict begin + /showpage {} def + FMNORMALIZEGRAPHICS + 3 index neg 3 index neg translate + } bind def +/ENDPRINTCODE { + count -1 FMoptop {pop pop} for + countdictstack -1 FMdicttop {pop end} for + FMsaveobject restore + } bind def +/gn { + 0 + { 46 mul + cf read pop + 32 sub + dup 46 lt {exit} if + 46 sub add + } loop + add + } bind def + /str FMLOCAL +/cfs { + /str sl string def + 0 1 sl 1 sub {str exch val put} for + str def + } bind def +/ic [ + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 + {0 hx} {1 hx} {2 hx} {3 hx} {4 hx} {5 hx} {6 hx} {7 hx} {8 hx} {9 hx} + {10 hx} {11 hx} {12 hx} {13 hx} {14 hx} {15 hx} {16 hx} {17 hx} {18 hx} + {19 hx} {gn hx} {0} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12} + {13} {14} {15} {16} {17} {18} {19} {gn} {0 wh} {1 wh} {2 wh} {3 wh} + {4 wh} {5 wh} {6 wh} {7 wh} {8 wh} {9 wh} {10 wh} {11 wh} {12 wh} + {13 wh} {14 wh} {gn wh} {0 bl} {1 bl} {2 bl} {3 bl} {4 bl} {5 bl} {6 bl} + {7 bl} {8 bl} {9 bl} {10 bl} {11 bl} {12 bl} {13 bl} {14 bl} {gn bl} + {0 fl} {1 fl} {2 fl} {3 fl} {4 fl} {5 fl} {6 fl} {7 fl} {8 fl} {9 fl} + {10 fl} {11 fl} {12 fl} {13 fl} {14 fl} {gn fl} + ] def + /sl FMLOCAL + /val FMLOCAL + /ws FMLOCAL + /im FMLOCAL + /bs FMLOCAL + /cs FMLOCAL + /len FMLOCAL + /pos FMLOCAL +/ms { + /sl exch def + /val 255 def + /ws cfs + /im cfs + /val 0 def + /bs cfs + /cs cfs + } bind def +400 ms +/ip { + is + 0 + cf cs readline pop + { ic exch get exec + add + } forall + pop + + } bind def +/wh { + /len exch def + /pos exch def + ws 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/bl { + /len exch def + /pos exch def + bs 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/s1 1 string def +/fl { + /len exch def + /pos exch def + /val cf s1 readhexstring pop 0 get def + pos 1 pos len add 1 sub {im exch val put} for + pos len + } bind def +/hx { + 3 copy getinterval + cf exch readhexstring pop pop + } bind def + /h FMLOCAL + /w FMLOCAL + /d FMLOCAL + /lb FMLOCAL + /bitmapsave FMLOCAL + /is FMLOCAL + /cf FMLOCAL +/wbytes { + dup + 8 eq {pop} {1 eq {7 add 8 idiv} {3 add 4 idiv} ifelse} ifelse + } bind def +/BEGINBITMAPBWc { + 1 {} COMMONBITMAPc + } bind def +/BEGINBITMAPGRAYc { + 8 {} COMMONBITMAPc + } bind def +/BEGINBITMAP2BITc { + 2 {} COMMONBITMAPc + } bind def +/COMMONBITMAPc { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + r + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} image + bitmapsave restore + grestore + } bind def +/BEGINBITMAPBW { + 1 {} COMMONBITMAP + } bind def +/BEGINBITMAPGRAY { + 8 {} COMMONBITMAP + } bind def +/BEGINBITMAP2BIT { + 2 {} COMMONBITMAP + } bind def +/COMMONBITMAP { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + r + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} image + bitmapsave restore + grestore + } bind def + /proc1 FMLOCAL + /proc2 FMLOCAL + /newproc FMLOCAL +/Fmcc { + /proc2 exch cvlit def + /proc1 exch cvlit def + /newproc proc1 length proc2 length add array def + newproc 0 proc1 putinterval + newproc proc1 length proc2 putinterval + newproc cvx +} bind def +/ngrayt 256 array def +/nredt 256 array def +/nbluet 256 array def +/ngreent 256 array def + /gryt FMLOCAL + /blut FMLOCAL + /grnt FMLOCAL + /redt FMLOCAL + /indx FMLOCAL + /cynu FMLOCAL + /magu FMLOCAL + /yelu FMLOCAL + /k FMLOCAL + /u FMLOCAL +/colorsetup { + currentcolortransfer + /gryt exch def + /blut exch def + /grnt exch def + /redt exch def + 0 1 255 { + /indx exch def + /cynu 1 red indx get 255 div sub def + /magu 1 green indx get 255 div sub def + /yelu 1 blue indx get 255 div sub def + /k cynu magu min yelu min def + /u k currentundercolorremoval exec def + nredt indx 1 0 cynu u sub max sub redt exec put + ngreent indx 1 0 magu u sub max sub grnt exec put + nbluet indx 1 0 yelu u sub max sub blut exec put + ngrayt indx 1 k currentblackgeneration exec sub gryt exec put + } for + {255 mul cvi nredt exch get} + {255 mul cvi ngreent exch get} + {255 mul cvi nbluet exch get} + {255 mul cvi ngrayt exch get} + setcolortransfer + {pop 0} setundercolorremoval + {} setblackgeneration + } bind def + /tran FMLOCAL +/fakecolorsetup { + /tran 256 string def + 0 1 255 {/indx exch def + tran indx + red indx get 77 mul + green indx get 151 mul + blue indx get 28 mul + add add 256 idiv put} for + currenttransfer + {255 mul cvi tran exch get 255.0 div} + exch Fmcc settransfer +} bind def +/BITMAPCOLOR { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + colorsetup + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPCOLORc { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + colorsetup + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLORc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip} {gip} {bip} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLOR { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop } + { cf gis readhexstring pop } + { cf bis readhexstring pop } + true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUEGRAYc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip gip bip w gray} image + bitmapsave restore + grestore + } bind def +/ww FMLOCAL +/r FMLOCAL +/g FMLOCAL +/b FMLOCAL +/i FMLOCAL +/gray { + /ww exch def + /b exch def + /g exch def + /r exch def + 0 1 ww 1 sub { /i exch def r i get .299 mul g i get .587 mul + b i get .114 mul add add r i 3 -1 roll floor cvi put } for + r + } bind def +/BITMAPTRUEGRAY { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop + cf gis readhexstring pop + cf bis readhexstring pop w gray} image + bitmapsave restore + grestore + } bind def +/BITMAPGRAY { + 8 {fakecolorsetup} COMMONBITMAP + } bind def +/BITMAPGRAYc { + 8 {fakecolorsetup} COMMONBITMAPc + } bind def +/ENDBITMAP { + } bind def +end + /ALDsave FMLOCAL + /ALDmatrix matrix def ALDmatrix currentmatrix pop +/StartALD { + /ALDsave save def + savematrix + ALDmatrix setmatrix + } bind def +/InALD { + restorematrix + } bind def +/DoneALD { + ALDsave restore + } bind def +%%EndProlog +%%BeginSetup +(3.0) FMVERSION +1 1 595.3 841.9 0 1 21 FMDOCUMENT +0 0 /Times-Italic FMFONTDEFINE +1 0 /Times-Bold FMFONTDEFINE +2 0 /Times-Roman FMFONTDEFINE +3 0 /Courier FMFONTDEFINE +4 1 /Symbol FMFONTDEFINE +5 0 /Times-BoldItalic FMFONTDEFINE +6 0 /Courier-BoldOblique FMFONTDEFINE +32 FMFILLS +0 0 FMFILL +1 .1 FMFILL +2 .3 FMFILL +3 .5 FMFILL +4 .7 FMFILL +5 .9 FMFILL +6 .97 FMFILL +7 1 FMFILL +8 <0f1e3c78f0e1c387> FMFILL +9 <0f87c3e1f0783c1e> FMFILL +10 FMFILL +11 FMFILL +12 <8142241818244281> FMFILL +13 <03060c183060c081> FMFILL +14 <8040201008040201> FMFILL +16 1 FMFILL +17 .9 FMFILL +18 .7 FMFILL +19 .5 FMFILL +20 .3 FMFILL +21 .1 FMFILL +22 0.03 FMFILL +23 0 FMFILL +24 FMFILL +25 FMFILL +26 <3333333333333333> FMFILL +27 <0000ffff0000ffff> FMFILL +28 <7ebddbe7e7dbbd7e> FMFILL +29 FMFILL +30 <7fbfdfeff7fbfdfe> FMFILL +%%EndSetup +%%Page: "1" 1 +%%BeginPaperSize: A4 +%%EndPaperSize +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-1) 518.33 61.29 T +1 28 Q +(1 T) 63.65 726.29 T +(utorial) 100.75 726.29 T +2 12 Q +4.82 (M) 135.65 692.95 P +2 10 Q +4.02 (A) 146.31 692.95 P +4.02 (TLAB) 152.42 692.95 P +2 12 Q +4.82 ( has a wide variety of functions useful to the genetic algorithm) 178.51 692.95 P +1.63 (practitioner and those wishing to experiment with the genetic algorithm for the) 135.65 678.95 P +-0.03 (\336rst time. Given the versatility of M) 135.65 664.95 P +2 10 Q +-0.02 (A) 309.05 664.95 P +-0.02 (TLAB) 315.16 664.95 P +2 12 Q +-0.03 (\325) 341.26 664.95 P +-0.03 (s high-level language, problems can be) 344.59 664.95 P +0.58 (coded in m-\336les in a fraction of the time that it would take to create C or Fortran) 135.65 650.95 P +3.7 (programs for the same purpose. Couple this with M) 135.65 636.95 P +2 10 Q +3.09 (A) 412.78 636.95 P +3.09 (TLAB) 418.88 636.95 P +2 12 Q +3.7 (\325) 444.98 636.95 P +3.7 (s advanced data) 448.31 636.95 P +0.17 (analysis, visualisation tools and special purpose application domain toolboxes and) 135.65 622.95 P +2.91 (the user is presented with a uniform environment with which to explore the) 135.65 608.95 P +(potential of genetic algorithms.) 135.65 594.95 T +1.02 (The Genetic Algorithm T) 135.65 568.95 P +1.02 (oolbox uses M) 260.1 568.95 P +2 10 Q +0.85 (A) 332.76 568.95 P +0.85 (TLAB) 338.87 568.95 P +2 12 Q +1.02 ( matrix functions to build a set of) 364.97 568.95 P +0.87 (versatile tools for implementing a wide range of genetic algorithm methods. The) 135.65 554.95 P +1.04 (Genetic Algorithm T) 135.65 540.95 P +1.04 (oolbox is a collection of routines, written mostly in m-\336les,) 237.48 540.95 P +(which implement the most important functions in genetic algorithms.) 135.65 526.95 T +FMENDPAGE +%%EndPage: "1" 2 +%%Page: "2" 2 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-2) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Installation) 63.65 732.95 T +2 12 Q +2.37 (Instructions for installing the Genetic Algorithm T) 135.65 694.95 P +2.37 (oolbox can be found in the) 391.55 694.95 P +0.36 (M) 135.65 680.95 P +2 10 Q +0.3 (A) 146.31 680.95 P +0.3 (TLAB) 152.42 680.95 P +2 12 Q +0.36 ( installation instructions. It is recommended that the \336les for this toolbox) 178.51 680.95 P +(are stored in a directory named genetic of) 135.65 666.95 T +(f the main matlab/toolbox directory) 334.93 666.95 T +(.) 504.71 666.95 T +3.33 (A number of demonstrations are available. A single-population binary-coded) 135.65 640.95 P +-0.13 (genetic algorithm to solve a numerical optimization problem is implemented in the) 135.65 626.95 P +-0.25 (m-\336le) 135.65 612.95 P +3 F +-0.61 (sga.m) 167.04 612.95 P +2 F +-0.25 (. The demonstration m-\336le) 203.02 612.95 P +3 F +-0.61 (mpga.m) 332.93 612.95 P +2 F +-0.25 ( implements a real-valued multi-) 376.1 612.95 P +1.29 (population genetic algorithm to solve a dynamic control problem. Both of these) 135.65 598.95 P +(demonstration m-\336les are discussed in detail in the) 135.65 584.95 T +0 F +(Examples) 382.16 584.95 T +2 F +( Section.) 428.79 584.95 T +1.06 (Additionally) 135.65 558.95 P +1.06 (, a set of test functions, drawn from the genetic algorithm literature,) 195.51 558.95 P +2.55 (are supplied in a separate directory) 135.65 544.95 P +2.55 (,) 315.12 544.95 P +3 F +6.11 (test_fns) 323.66 544.95 P +2 F +2.55 (, from the Genetic Algorithm) 381.23 544.95 P +0.05 (T) 135.65 530.95 P +0.05 (oolbox functions. A brief description of these test functions is given at the end of) 142.14 530.95 P +0.93 (the) 135.65 516.95 P +0 F +0.93 (Examples) 154.23 516.95 P +2 F +0.93 ( Section. A further document describes the implementation and use) 200.86 516.95 P +(of these functions.) 135.65 502.95 T +FMENDPAGE +%%EndPage: "2" 3 +%%Page: "3" 3 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-3) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(An Overview of Genetic Algorithms) 63.65 732.95 T +2 12 Q +-0.06 (In this Section we give a tutorial introduction to the basic Genetic Algorithm \050GA\051) 135.65 694.95 P +(and outline the procedures for solving problems using the GA.) 135.65 680.95 T +1 16 Q +(What ar) 135.65 652.29 T +(e Genetic Algorithms?) 192.66 652.29 T +2 12 Q +0.56 (The GA is a stochastic global search method that mimics the metaphor of natural) 135.65 624.95 P +0.66 (biological evolution. GAs operate on a population of potential solutions applying) 135.65 610.95 P +2.41 (the principle of survival of the \336ttest to produce \050hopefully\051 better and better) 135.65 596.95 P +0.86 (approximations to a solution. At each generation, a new set of approximations is) 135.65 582.95 P +0.15 (created by the process of selecting individuals according to their level of \336tness in) 135.65 568.95 P +1.29 (the problem domain and breeding them together using operators borrowed from) 135.65 554.95 P +0.63 (natural genetics. This process leads to the evolution of populations of individuals) 135.65 540.95 P +2.41 (that are better suited to their environment than the individuals that they were) 135.65 526.95 P +(created from, just as in natural adaptation.) 135.65 512.95 T +3.17 (Individuals, or current approximations, are encoded as strings,) 135.65 486.95 P +0 F +3.17 (chr) 463.14 486.95 P +3.17 (omosomes) 478.68 486.95 P +2 F +3.17 (,) 528.65 486.95 P +0.8 (composed over some alphabet\050s\051, so that the) 135.65 472.95 P +0 F +0.8 (genotypes) 357.07 472.95 P +2 F +0.8 ( \050chromosome values\051 are) 405.03 472.95 P +3.66 (uniquely mapped onto the decision variable \050) 135.65 458.95 P +0 F +3.66 (phenotypic) 374.11 458.95 P +2 F +3.66 (\051 domain. The most) 426.73 458.95 P +0.03 (commonly used representation in GAs is the binary alphabet {0, 1} although other) 135.65 444.95 P +1.05 (representations can be used, e.g. ternary) 135.65 430.95 P +1.05 (, integer) 331.97 430.95 P +1.05 (, real-valued etc. For example, a) 371.85 430.95 P +2.13 (problem with two variables,) 135.65 416.95 P +0 F +2.13 (x) 281.76 416.95 P +0 10 Q +1.78 (1) 287.08 413.95 P +2 12 Q +2.13 ( and) 292.08 416.95 P +0 F +2.13 (x) 319.66 416.95 P +0 10 Q +1.78 (2) 324.98 413.95 P +2 12 Q +2.13 (, may be mapped onto the chromosome) 329.98 416.95 P +(structure in the following way:) 135.65 402.95 T +-0.3 (where) 135.65 299.98 P +0 F +-0.3 (x) 167.65 299.98 P +0 10 Q +-0.25 (1) 172.98 296.98 P +2 12 Q +-0.3 ( is encoded with 10 bits and) 177.97 299.98 P +0 F +-0.3 (x) 312.82 299.98 P +0 10 Q +-0.25 (2) 318.14 296.98 P +2 12 Q +-0.3 ( with 15 bits, possibly re\337ecting the level of) 323.14 299.98 P +-0.2 (accuracy or range of the individual decision variables. Examining the chromosome) 135.65 285.98 P +0.43 (string in isolation yields no information about the problem we are trying to solve.) 135.65 271.98 P +0.11 (It is only with the decoding of the chromosome into its phenotypic values that any) 135.65 257.98 P +1.35 (meaning can be applied to the representation. However) 135.65 243.98 P +1.35 (, as described below) 409.1 243.98 P +1.35 (, the) 509.64 243.98 P +0.55 (search process will operate on this encoding of the decision variables, rather than) 135.65 229.98 P +0.8 (the decision variables themselves, except, of course, where real-valued genes are) 135.65 215.98 P +(used.) 135.65 201.98 T +-0.19 (Having decoded the chromosome representation into the decision variable domain,) 135.65 175.98 P +1.94 (it is possible to assess the performance, or) 135.65 161.98 P +0 F +1.94 (\336tness) 356.04 161.98 P +2 F +1.94 (, of individual members of a) 386.03 161.98 P +3.53 (population. This is done through an objective function that characterises an) 135.65 147.98 P +0.6 (individual\325) 135.65 133.98 P +0.6 (s performance in the problem domain. In the natural world, this would) 187.63 133.98 P +0.08 (be an individual\325) 135.65 119.98 P +0.08 (s ability to survive in its present environment. Thus, the objective) 216.42 119.98 P +63.65 96.95 531.65 744.95 C +135.65 321.98 531.65 398.95 C +146.65 328.95 520.65 391.95 C +146.65 328.95 520.65 391.95 R +7 X +0 K +V +3 12 Q +0 X +(1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1) 157.35 369.97 T +170.49 343.64 158.95 346.95 170.49 350.26 170.49 346.95 4 Y +V +282.42 350.26 293.95 346.95 282.42 343.64 282.42 346.95 4 Y +V +170.49 346.95 282.42 346.95 2 L +0.5 H +0 Z +N +297.08 382.95 297.08 337.95 2 L +2 Z +11 X +N +311.49 343.64 299.95 346.95 311.49 350.26 311.49 346.95 4 Y +0 X +V +495.42 350.26 506.95 346.95 495.42 343.64 495.42 346.95 4 Y +V +311.49 346.95 495.42 346.95 2 L +0 Z +N +0 F +(x) 221.29 353.75 T +0 10 Q +(1) 226.62 350.75 T +0 12 Q +(x) 398.29 353.75 T +0 10 Q +(2) 403.61 350.75 T +135.65 321.98 531.65 398.95 C +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "3" 4 +%%Page: "4" 4 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-4) 518.33 61.29 T +2 12 Q +2.35 (function establishes the basis for selection of pairs of individuals that will be) 135.65 736.95 P +(mated together during reproduction.) 135.65 722.95 T +0.45 (During the reproduction phase, each individual is assigned a \336tness value derived) 135.65 696.95 P +0.94 (from its raw performance measure given by the objective function. This value is) 135.65 682.95 P +1.18 (used in the selection to bias towards more \336t individuals. Highly \336t individuals,) 135.65 668.95 P +2.11 (relative to the whole population, have a high probability of being selected for) 135.65 654.95 P +2.56 (mating whereas less \336t individuals have a correspondingly low probability of) 135.65 640.95 P +(being selected.) 135.65 626.95 T +0.54 (Once the individuals have been assigned a \336tness value, they can be chosen from) 135.65 600.95 P +5.22 (the population, with a probability according to their relative \336tness, and) 135.65 586.95 P +2.85 (recombined to produce the next generation. Genetic operators manipulate the) 135.65 572.95 P +0.61 (characters \050genes\051 of the chromosomes directly) 135.65 558.95 P +0.61 (, using the assumption that certain) 364.71 558.95 P +0.18 (individual\325) 135.65 544.95 P +0.18 (s gene codes, on average, produce \336tter individuals. The recombination) 187.63 544.95 P +0.68 (operator is used to exchange genetic information between pairs, or lar) 135.65 530.95 P +0.68 (ger groups,) 477.01 530.95 P +4.62 (of individuals. The simplest recombination operator is that of single-point) 135.65 516.95 P +(crossover) 135.65 502.95 T +(.) 180.95 502.95 T +(Consider the two parent binary strings:) 135.65 476.95 T +3 F +(P) 171.65 450.95 T +3 10 Q +(1) 178.84 447.95 T +3 12 Q +( = 1 0 0 1 0 1 1 0) 184.84 450.95 T +2 F +(, and) 314.37 450.95 T +3 F +(P) 171.65 424.95 T +3 10 Q +(2) 178.84 421.95 T +3 12 Q +( = 1 0 1 1 1 0 0 0) 184.84 424.95 T +2 F +(.) 314.37 424.95 T +0.59 (If an integer position,) 135.65 398.95 P +0 F +0.59 (i) 244.27 398.95 P +2 F +0.59 (, is selected uniformly at random between 1 and the string) 247.6 398.95 P +0.97 (length,) 135.65 384.95 P +0 F +0.97 (l) 172.6 384.95 P +2 F +0.97 (, minus one [1,) 175.93 384.95 P +0 F +0.97 (l) 254.42 384.95 P +2 F +0.97 (-1], and the genetic information exchanged between the) 257.76 384.95 P +0.15 (individuals about this point, then two new of) 135.65 370.95 P +0.15 (fspring strings are produced. The two) 351.03 370.95 P +(of) 135.65 356.95 T +(fspring below are produced when the crossover point) 145.42 356.95 T +0 F +(i = 5) 403.22 356.95 T +2 F +( is selected,) 426.64 356.95 T +3 F +(O) 171.65 330.95 T +3 10 Q +(1) 178.84 327.95 T +3 12 Q +( = 1 0 0 1 0 0 0 0) 184.84 330.95 T +2 F +(, and) 314.37 330.95 T +3 F +(O) 171.65 304.95 T +3 10 Q +(2) 178.84 301.95 T +3 12 Q +( = 1 0 1 1 1 1 1 0) 184.84 304.95 T +2 F +(.) 314.37 304.95 T +3.99 (This crossover operation is not necessarily performed on all strings in the) 135.65 278.95 P +0.87 (population. Instead, it is applied with a probability) 135.65 264.95 P +0 F +0.87 (Px) 387.77 264.95 P +2 F +0.87 ( when the pairs are chosen) 400.42 264.95 P +-0.2 (for breeding. A further genetic operator) 135.65 250.95 P +-0.2 (, called mutation, is then applied to the new) 324.02 250.95 P +1.8 (chromosomes, again with a set probability) 135.65 236.95 P +1.8 (,) 347.08 236.95 P +0 F +1.8 (Pm) 354.88 236.95 P +2 F +1.8 (. Mutation causes the individual) 370.87 236.95 P +1.06 (genetic representation to be changed according to some probabilistic rule. In the) 135.65 222.95 P +0.41 (binary) 135.65 208.95 P +0.41 (string) 172.7 208.95 P +0.41 ( representation,) 206.01 208.95 P +0.41 ( mutation will cause a single bit to change its state,) 283.36 208.95 P +0.74 (0) 135.65 194.95 P +4 F +0.74 (\336) 145.38 194.95 P +2 F +0.74 (1 or 1) 160.96 194.95 P +4 F +0.74 (\336) 194.15 194.95 P +2 F +0.74 ( 0. So, for example, mutating the fourth bit of) 205.99 194.95 P +3 F +1.77 (O) 434.89 194.95 P +3 10 Q +1.48 (1) 442.09 191.95 P +2 12 Q +0.74 ( leads to the new) 448.09 194.95 P +(string,) 135.65 180.95 T +3 F +(O) 171.65 154.95 T +3 10 Q +(1m) 178.84 151.95 T +3 12 Q +( = 1 0 0 0 0 0 0 0) 190.84 154.95 T +2 F +(.) 320.37 154.95 T +0.19 (Mutation is generally considered to be a background operator that ensures that the) 135.65 128.95 P +0.61 (probability of searching a particular subspace of the problem space is never zero.) 135.65 114.95 P +FMENDPAGE +%%EndPage: "4" 5 +%%Page: "5" 5 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-5) 518.33 61.29 T +2 12 Q +1.57 (This has the ef) 135.65 736.95 P +1.57 (fect of tending to inhibit the possibility of conver) 210.43 736.95 P +1.57 (ging to a local) 458.64 736.95 P +(optimum, rather than the global optimum.) 135.65 722.95 T +1.87 (After recombination and mutation, the individual strings are then, if necessary) 135.65 696.95 P +1.87 (,) 528.65 696.95 P +4.09 (decoded, the objective function evaluated, a \336tness value assigned to each) 135.65 682.95 P +-0.01 (individual and individuals selected for mating according to their \336tness, and so the) 135.65 668.95 P +4.08 (process continues through subsequent generations. In this way) 135.65 654.95 P +4.08 (, the average) 462.55 654.95 P +3.36 (performance of individuals in a population is expected to increase, as good) 135.65 640.95 P +0.1 (individuals are preserved and bred with one another and the less \336t individuals die) 135.65 626.95 P +-0.26 (out. The GA is terminated when some criteria are satis\336ed, e.g. a certain number of) 135.65 612.95 P +0.66 (generations, a mean deviation in the population, or when a particular point in the) 135.65 598.95 P +(search space is encountered.) 135.65 584.95 T +1 16 Q +(GAs versus T) 135.65 556.29 T +(raditional Methods) 226.86 556.29 T +2 12 Q +1.06 (From the above discussion, it can be seen that the GA dif) 135.65 528.95 P +1.06 (fers substantially from) 421.6 528.95 P +3.43 (more traditional search and optimization methods. The four most signi\336cant) 135.65 514.95 P +(dif) 135.65 500.95 T +(ferences are:) 148.76 500.95 T +(\245) 157.25 474.95 T +(GAs search a population of points in parallel, not a single point.) 171.65 474.95 T +(\245) 157.25 454.95 T +1.32 (GAs do not require derivative information or other auxiliary knowledge;) 171.65 454.95 P +1.1 (only the objective function and corresponding \336tness levels in\337uence the) 171.65 440.95 P +(directions of search.) 171.65 426.95 T +(\245) 157.25 406.95 T +(GAs use probabilistic transition rules, not deterministic ones.) 171.65 406.95 T +(\245) 157.25 386.95 T +-0.26 (GAs work on an encoding of the parameter set rather than the parameter set) 171.65 386.95 P +(itself \050except in where real-valued individuals are used\051.) 171.65 372.95 T +1.06 (It is important to note that the GA provides a number of potential solutions to a) 135.65 346.95 P +0.5 (given problem and the choice of \336nal solution is left to the user) 135.65 332.95 P +0.5 (. In cases where a) 444.75 332.95 P +0.44 (particular problem does not have one individual solution, for example a family of) 135.65 318.95 P +4.61 (Pareto-optimal solutions, as is the case in multiobjective optimization and) 135.65 304.95 P +3.39 (scheduling problems, then the GA is potentially useful for identifying these) 135.65 290.95 P +(alternative solutions simultaneously) 135.65 276.95 T +(.) 307.44 276.95 T +FMENDPAGE +%%EndPage: "5" 6 +%%Page: "6" 6 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-6) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Major Elements of the Genetic Algorithm) 63.65 732.95 T +2 12 Q +0.01 (The simple genetic algorithm \050SGA\051 is described by Goldber) 135.65 694.95 P +0.01 (g [1] and is used here) 428.67 694.95 P +0.09 (to illustrate the basic components of the GA. A pseudo-code outline of the SGA is) 135.65 680.95 P +1.58 (shown in Fig. 1. The population at time) 135.65 666.95 P +0 F +1.58 (t) 340.87 666.95 P +2 F +1.58 ( is represented by the time-dependent) 344.21 666.95 P +0.74 (variable) 135.65 652.95 P +0 F +0.74 (P) 178.02 652.95 P +2 F +0.74 (, with the initial population of random estimates being) 184.02 652.95 P +0 F +0.74 (P\0500\051) 453.87 652.95 P +2 F +0.74 (. Using this) 475.19 652.95 P +0.28 (outline of a GA, the remainder of this Section describes the major elements of the) 135.65 638.95 P +(GA.) 135.65 624.95 T +1 16 Q +(Population Repr) 135.65 336.01 T +(esentation and Initialisation) 248.64 336.01 T +2 12 Q +0.3 (GAs operate on a number of potential solutions, called a population, consisting of) 135.65 308.67 P +2.4 (some encoding of the parameter set simultaneously) 135.65 294.67 P +2.4 (. T) 395.08 294.67 P +2.4 (ypically) 409.97 294.67 P +2.4 (, a population is) 447.83 294.67 P +0.25 (composed of between 30 and 100 individuals, although, a variant called the micro) 135.65 280.67 P +1.11 (GA uses very small populations, ~10 individuals, with a restrictive reproduction) 135.65 266.67 P +(and replacement strategy in an attempt to reach real-time execution [2].) 135.65 252.67 T +0.4 (The most commonly used representation of chromosomes in the GA is that of the) 135.65 226.67 P +2.36 (single-level binary string. Here, each decision variable in the parameter set is) 135.65 212.67 P +0.23 (encoded as a binary string and these are concatenated to form a chromosome. The) 135.65 198.67 P +1.64 (use of Gray coding has been advocated as a method of overcoming the hidden) 135.65 184.67 P +4.2 (representational bias in conventional binary representation as the Hamming) 135.65 170.67 P +1.13 (distance between adjacent values is constant [3]. Empirical evidence of Caruana) 135.65 156.67 P +1.94 (and Schaf) 135.65 142.67 P +1.94 (fer [4] suggests that lar) 185 142.67 P +1.94 (ge Hamming distances in the representational) 303.11 142.67 P +5.36 (mapping between adjacent values, as is the case in the standard binary) 135.65 128.67 P +3.42 (representation, can result in the search process being deceived or unable to) 135.65 114.67 P +63.65 96.95 531.65 744.95 C +133.38 360.67 531.65 620.95 C +162.43 380.97 502.59 600.65 R +7 X +0 K +V +2 12 Q +0 X +(procedure GA) 198.43 592.65 T +(begin) 198.43 577.65 T +(t = 0;) 243.43 562.65 T +(initialize P\050t\051;) 243.43 547.65 T +(evaluate P\050t\051;) 243.43 532.65 T +(while not finished do) 243.43 517.65 T +(begin) 243.43 502.65 T +(t = t + 1;) 315.43 487.65 T +(select P\050t\051 from P\050t-1\051;) 315.43 472.65 T +(reproduce pairs in P\050t\051;) 315.43 457.65 T +(evaluate P\050t\051;) 315.43 442.65 T +(end) 243.43 427.65 T +(end.) 198.43 412.65 T +5 F +(Figure 1: A Simple Genetic Algorithm) 234.43 386.65 T +146.89 370.34 518.14 611.28 R +0.5 H +2 Z +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "6" 7 +%%Page: "7" 7 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-7) 518.33 61.29 T +2 12 Q +0.64 (ef) 135.65 736.95 P +0.64 (\336ciently locate the global minimum. A further approach of Schmitendor) 144.75 736.95 P +0.64 (gf) 496.04 736.95 P +0 F +0.64 (et-al) 509.66 736.95 P +2 F +5.3 ([5], is the use of logarithmic scaling in the conversion of binary-coded) 135.65 722.95 P +3.46 (chromosomes to their real phenotypic values. Although the precision of the) 135.65 708.95 P +1.48 (parameter values is possibly less consistent over the desired range, in problems) 135.65 694.95 P +0.3 (where the spread of feasible parameters is unknown, a lar) 135.65 680.95 P +0.3 (ger search space may be) 413.9 680.95 P +0.51 (covered with the same number of bits than a linear mapping scheme allowing the) 135.65 666.95 P +-0.2 (computational burden of exploring unknown search spaces to be reduced to a more) 135.65 652.95 P +(manageable level.) 135.65 638.95 T +0.33 (Whilst binary-coded GAs are most commonly used, there is an increasing interest) 135.65 612.95 P +0.52 (in alternative encoding strategies, such as integer and real-valued representations.) 135.65 598.95 P +1.37 (For some problem domains, it is ar) 135.65 584.95 P +1.37 (gued that the binary representation is in fact) 311.22 584.95 P +1.28 (deceptive in that it obscures the nature of the search [6]. In the subset selection) 135.65 570.95 P +0.8 (problem [7], for example, the use of an integer representation and look-up tables) 135.65 556.95 P +5.49 (provides a convenient and natural way of expressing the mapping from) 135.65 542.95 P +(representation to problem domain.) 135.65 528.95 T +0.06 (The use of real-valued genes in GAs is claimed by W) 135.65 502.95 P +0.06 (right [8] to of) 392.27 502.95 P +0.06 (fer a number of) 457.2 502.95 P +1.02 (advantages in numerical function optimization over binary encodings. Ef) 135.65 488.95 P +1.02 (\336ciency) 493.68 488.95 P +0.45 (of the GA is increased as there is no need to convert chromosomes to phenotypes) 135.65 474.95 P +-0.02 (before each function evaluation; less memory is required as ef) 135.65 460.95 P +-0.02 (\336cient \337oating-point) 433.38 460.95 P +-0.03 (internal computer representations can be used directly; there is no loss in precision) 135.65 446.95 P +1.89 (by discretisation to binary or other values; and there is greater freedom to use) 135.65 432.95 P +0.23 (dif) 135.65 418.95 P +0.23 (ferent genetic operators. The use of real-valued encodings is described in detail) 148.76 418.95 P +0.08 (by Michalewicz [9] and in the literature on Evolution Strategies \050see, for example,) 135.65 404.95 P +([10]\051.) 135.65 390.95 T +1.85 (Having decided on the representation, the \336rst step in the SGA is to create an) 135.65 364.95 P +0.93 (initial population. This is usually achieved by generating the required number of) 135.65 350.95 P +0.95 (individuals using a random number generator that uniformly distributes numbers) 135.65 336.95 P +1.57 (in the desired range. For example, with a binary population of) 135.65 322.95 P +0 F +1.57 (N) 453 322.95 P +0 10 Q +1.3 (ind) 461 319.95 P +2 12 Q +1.57 ( individuals) 473.77 322.95 P +1.57 (whose chromosomes are) 135.65 308.95 P +0 F +1.57 (L) 261.27 308.95 P +0 10 Q +1.31 (ind) 267.94 305.95 P +2 12 Q +1.57 ( bits long,) 280.71 308.95 P +0 F +1.57 (N) 336.08 308.95 P +0 10 Q +1.31 (ind) 344.08 305.95 P +4 12 Q +1.57 (\264) 361.42 308.95 P +0 F +1.57 (L) 372.58 308.95 P +0 10 Q +1.31 (ind) 379.24 305.95 P +2 12 Q +1.57 ( random numbers uniformly) 392.02 308.95 P +(distributed from the set {0, 1} would be produced.) 135.65 294.95 T +3.16 (A variation is the) 135.65 268.95 P +0 F +3.16 (extended random initialisation) 234.23 268.95 P +2 F +3.16 ( procedure of Bramlette [6]) 387.8 268.95 P +1.02 (whereby a number of random initialisations are tried for each individual and the) 135.65 254.95 P +0.74 (one with the best performance is chosen for the initial population. Other users of) 135.65 240.95 P +-0.01 (GAs have seeded the initial population with some individuals that are known to be) 135.65 226.95 P +2.31 (in the vicinity of the global minimum \050see, for example, [1) 135.65 212.95 P +2.31 (1] and [12]\051. This) 440.12 212.95 P +3.22 (approach is, of course, only applicable if the nature of the problem is well) 135.65 198.95 P +-0.16 (understood beforehand or if the GA is used in conjunction with a knowledge based) 135.65 184.95 P +(system.) 135.65 170.95 T +5.61 (The GA T) 135.65 144.95 P +5.61 (oolbox supports binary) 195.31 144.95 P +5.61 (, integer and \337oating-point chromosome) 316.35 144.95 P +3.8 (representations. Binary and integer populations may be initialised using the) 135.65 130.95 P +1.9 (T) 135.65 116.95 P +1.9 (oolbox function to create binary populations,) 142.14 116.95 P +3 F +4.55 (crtbp) 372.38 116.95 P +2 F +1.9 (. An additional function,) 408.36 116.95 P +3 F +3.25 (crtbase) 135.65 102.95 P +2 F +1.35 (, is provided that builds a vector describing the integer representation) 186.02 102.95 P +FMENDPAGE +%%EndPage: "7" 8 +%%Page: "8" 8 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-8) 518.33 61.29 T +2 12 Q +3.99 (used. Real-valued populations may be initialised with the function) 135.65 736.95 P +3 F +9.57 (crtrp) 492.67 736.95 P +2 F +3.99 (.) 528.65 736.95 P +2.54 (Conversion between binary strings and real values is provided by the routine) 135.65 722.95 P +3 F +(bs2rv) 135.65 708.95 T +2 F +( that supports the use of Gray codes and logarithmic scaling.) 171.63 708.95 T +1 16 Q +(The Objective and Fitness Functions) 135.65 680.29 T +2 12 Q +2.47 (The objective function is used to provide a measure of how individuals have) 135.65 652.95 P +-0.11 (performed in the problem domain. In the case of a minimization problem, the most) 135.65 638.95 P +1.87 (\336t individuals will have the lowest numerical value of the associated objective) 135.65 624.95 P +0.17 (function. This raw measure of \336tness is usually only used as an intermediate stage) 135.65 610.95 P +0.36 (in determining the relative performance of individuals in a GA. Another function,) 135.65 596.95 P +0.05 (the) 135.65 582.95 P +0 F +0.05 (\336tness function) 153.35 582.95 P +2 F +0.05 (, is normally used to transform the objective function value into) 225.7 582.95 P +(a measure of relative \336tness [13], thus:) 135.65 568.95 T +-0.29 (where) 135.65 514.76 P +0 F +-0.29 (f) 167.66 514.76 P +2 F +-0.29 ( is the objective function,) 170.99 514.76 P +0 F +-0.29 (g) 294.13 514.76 P +2 F +-0.29 ( transforms the value of the objective function to) 300.13 514.76 P +2.1 (a non-negative number and) 135.65 500.76 P +0 F +2.1 (F) 277.95 500.76 P +2 F +2.1 ( is the resulting relative \336tness. This mapping is) 285.28 500.76 P +1.97 (always necessary when the objective function is to be minimized as the lower) 135.65 486.76 P +3.03 (objective function values correspond to \336tter individuals. In many cases, the) 135.65 472.76 P +-0.29 (\336tness function value corresponds to the number of of) 135.65 458.76 P +-0.29 (fspring that an individual can) 392.24 458.76 P +0.33 (expect to produce in the next generation. A commonly used transformation is that) 135.65 444.76 P +1.03 (of proportional \336tness assignment \050see, for example, [1]\051. The individual \336tness,) 135.65 430.76 P +0 F +1.4 (F\050x) 135.65 416.76 P +0 10 Q +1.17 (i) 152.29 413.76 P +0 12 Q +1.4 (\051) 155.07 416.76 P +2 F +1.4 (, of each individual is computed as the individual\325) 159.07 416.76 P +1.4 (s raw performance,) 409.79 416.76 P +0 F +1.4 (f\050x) 509.22 416.76 P +0 10 Q +1.17 (i) 521.88 413.76 P +0 12 Q +1.4 (\051) 524.66 416.76 P +2 F +1.4 (,) 528.65 416.76 P +(relative to the whole population, i.e.,) 135.65 402.76 T +(,) 380.93 365.33 T +1.36 (where) 135.65 304.51 P +0 F +1.36 (N) 169.3 304.51 P +0 10 Q +1.13 (ind) 177.3 301.51 P +2 12 Q +1.36 ( is the population size and) 190.08 304.51 P +0 F +1.36 (x) 326.15 304.51 P +0 10 Q +1.13 (i) 331.47 301.51 P +2 12 Q +1.36 ( is the phenotypic value of individual) 334.25 304.51 P +0 F +1.36 (i) 525.32 304.51 P +2 F +1.36 (.) 528.65 304.51 P +1.87 (Whilst this \336tness assignment ensures that each individual has a probability of) 135.65 290.51 P +3.54 (reproducing according to its relative \336tness, it fails to account for negative) 135.65 276.51 P +(objective function values.) 135.65 262.51 T +0.15 (A linear transformation which of) 135.65 236.51 P +0.15 (fsets the objective function [1] is often used prior) 293.92 236.51 P +(to \336tness assignment, such that,) 135.65 222.51 T +0.2 (where) 135.65 168.32 P +0 F +0.2 (a) 168.15 168.32 P +2 F +0.2 ( is a positive scaling factor if the optimization is maximizing and negative) 174.14 168.32 P +-0.1 (if we are minimizing. The of) 135.65 154.32 P +-0.1 (fset) 272.83 154.32 P +0 F +-0.1 (b) 293.04 154.32 P +2 F +-0.1 ( is used to ensure that the resulting \336tness values) 299.04 154.32 P +(are non-negative.) 135.65 140.32 T +288.09 536.76 379.21 550.95 C +0 12 Q +0 X +0 K +(F) 289.09 541.75 T +(x) 304.22 541.75 T +4 F +(\050) 299.12 541.75 T +(\051) 310.16 541.75 T +0 F +(g) 334.73 541.75 T +(f) 348.54 541.75 T +(x) 359.68 541.75 T +4 F +(\050) 354.58 541.75 T +(\051) 365.61 541.75 T +(\050) 343.44 541.75 T +(\051) 372.21 541.75 T +(=) 322.15 541.75 T +-8.35 24.95 603.65 816.95 C +283.37 326.51 380.93 384.76 C +0 12 Q +0 X +0 K +(F) 284.37 365.33 T +(x) 299.5 365.33 T +0 9 Q +(i) 305.29 361.55 T +4 12 Q +(\050) 294.4 365.33 T +(\051) 308.4 365.33 T +0 F +(f) 343.44 375.55 T +(x) 354.58 375.55 T +0 9 Q +(i) 360.36 371.77 T +4 12 Q +(\050) 349.48 375.55 T +(\051) 363.47 375.55 T +0 F +(f) 352.9 343.76 T +(x) 364.04 343.76 T +0 9 Q +(i) 369.83 339.98 T +4 12 Q +(\050) 358.94 343.76 T +(\051) 372.93 343.76 T +0 9 Q +(i) 333.98 329.46 T +2 F +(1) 347.41 329.46 T +4 F +(=) 339.47 329.46 T +0 F +(N) 335.47 360.27 T +0 6 Q +(i) 341.82 357.82 T +(n) 343.94 357.82 T +(d) 347.4 357.82 T +4 18 Q +(\345) 336.52 340.55 T +4 12 Q +(=) 320.39 365.33 T +333.98 367.92 378.68 367.92 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +285.65 190.32 381.65 204.51 C +0 12 Q +0 X +0 K +(F) 286.65 195.31 T +(x) 301.79 195.31 T +4 F +(\050) 296.68 195.31 T +(\051) 307.72 195.31 T +0 F +(a) 332.3 195.31 T +(f) 339 195.31 T +(x) 350.14 195.31 T +4 F +(\050) 345.04 195.31 T +(\051) 356.07 195.31 T +0 F +(b) 374.65 195.31 T +4 F +(+) 365.07 195.31 T +(=) 319.71 195.31 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "8" 9 +%%Page: "9" 9 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-9) 518.33 61.29 T +2 12 Q +0.91 (The linear scaling and of) 135.65 736.95 P +0.91 (fsetting outlined above is, however) 258.3 736.95 P +0.91 (, susceptible to rapid) 429.66 736.95 P +6.1 (conver) 135.65 722.95 P +6.1 (gence. The) 168.07 722.95 P +0 F +6.1 (selection) 235.88 722.95 P +2 F +6.1 ( algorithm \050see below\051 selects individuals for) 278.52 722.95 P +3.81 (reproduction on the basis of their relative \336tness. Using linear scaling, the) 135.65 708.95 P +2.09 (expected number of of) 135.65 694.95 P +2.09 (fspring is approximately proportional to that individuals) 249.94 694.95 P +0.83 (performance. As there is no constraint on an individual\325) 135.65 680.95 P +0.83 (s performance in a given) 409.76 680.95 P +6.32 (generation, highly \336t individuals in early generations can dominate the) 135.65 666.95 P +5.59 (reproduction causing rapid conver) 135.65 652.95 P +5.59 (gence to possibly sub-optimal solutions.) 316.4 652.95 P +0.26 (Similarly) 135.65 638.95 P +0.26 (, if there is little deviation in the population, then scaling provides only a) 179.52 638.95 P +(small bias towards the most \336t individuals.) 135.65 624.95 T +0.33 (Baker [14] suggests that by limiting the reproductive range, so that no individuals) 135.65 598.95 P +-0.13 (generate an excessive number of of) 135.65 584.95 P +-0.13 (fspring, prevents premature conver) 304.27 584.95 P +-0.13 (gence. Here,) 471.52 584.95 P +0.97 (individuals are assigned a \336tness according to their rank in the population rather) 135.65 570.95 P +0.72 (than their raw performance. One variable,) 135.65 556.95 P +0 F +0.72 (MAX) 343.76 556.95 P +2 F +0.72 (, is used to determine the bias, or) 368.41 556.95 P +0 F +0.65 (selective pr) 135.65 542.95 P +0.65 (essur) 190.81 542.95 P +0.65 (e) 215.68 542.95 P +2 F +0.65 (, towards the most \336t individuals and the \336tness of the others is) 221.01 542.95 P +(determined by the following rules:) 135.65 528.95 T +(\245) 157.25 502.95 T +0 F +(MIN) 164.44 502.95 T +2 F +( = 2.0 -) 186.43 502.95 T +0 F +(MAX) 224.17 502.95 T +2 F +(\245) 157.25 482.95 T +0 F +(INC) 164.44 482.95 T +2 F +( = 2.0) 184.44 482.95 T +4 F +(\264) 215.19 482.95 T +2 F +( \050) 221.77 482.95 T +0 F +(MAX) 228.76 482.95 T +2 F +( -1.0\051 /) 253.41 482.95 T +0 F +(N) 288.72 482.95 T +0 10 Q +(ind) 296.72 479.95 T +2 12 Q +(\245) 157.25 462.95 T +0 F +(LOW) 164.44 462.95 T +2 F +( =) 189.76 462.95 T +0 F +(INC) 202.52 462.95 T +2 F +( / 2.0) 222.52 462.95 T +2.81 (where) 135.65 442.95 P +0 F +2.81 (MIN) 170.75 442.95 P +2 F +2.81 ( is the lower bound,) 192.74 442.95 P +0 F +2.81 (INC) 304.71 442.95 P +2 F +2.81 ( is the dif) 324.7 442.95 P +2.81 (ference between the \336tness of) 377.88 442.95 P +0.97 (adjacent individuals and) 135.65 428.95 P +0 F +0.97 (LOW) 258.13 428.95 P +2 F +0.97 ( is the expected number of trials \050number of times) 283.45 428.95 P +1.2 (selected\051 of the least \336t individual.) 135.65 414.95 P +0 F +1.2 (MAX) 311.73 414.95 P +2 F +1.2 ( is typically chosen in the interval [1.1,) 336.38 414.95 P +0.66 (2.0]. Hence, for a population size of) 135.65 400.95 P +0 F +0.66 (N) 316.12 400.95 P +0 10 Q +0.55 (ind) 324.11 397.95 P +2 12 Q +0.66 ( = 40 and) 336.89 400.95 P +0 F +0.66 (MAX) 387.59 400.95 P +2 F +0.66 ( = 1.1, we obtain) 412.24 400.95 P +0 F +0.66 (MIN) 499.24 400.95 P +2 F +0.66 ( =) 521.23 400.95 P +-0.18 (0.9,) 135.65 386.95 P +0 F +-0.18 (INC) 156.46 386.95 P +2 F +-0.18 ( = 0.05 and) 176.45 386.95 P +0 F +-0.18 (LOW) 232.81 386.95 P +2 F +-0.18 ( = 0.025. The \336tness of individuals in the population may) 258.13 386.95 P +(also be calculated directly as,) 135.65 372.95 T +(,) 439.73 335.53 T +(where) 135.65 299.28 T +0 F +(x) 167.95 299.28 T +0 10 Q +(i) 173.27 296.28 T +2 12 Q +( is the position in the ordered population of individual) 176.05 299.28 T +0 F +(i) 437.9 299.28 T +2 F +(.) 441.24 299.28 T +-0.04 (Objective functions must be created by the user) 135.65 273.28 P +-0.04 (, although a number of example m-) 363.03 273.28 P +0.7 (\336les are supplied with the T) 135.65 259.28 P +0.7 (oolbox that implement common test functions. These) 271.91 259.28 P +0.98 (objective functions all have the \336lename pre\336x) 135.65 245.28 P +3 F +2.36 (obj) 370.71 245.28 P +2 F +0.98 (. The T) 392.3 245.28 P +0.98 (oolbox supports both) 428.4 245.28 P +1.65 (linear and non-linear ranking methods,) 135.65 231.28 P +3 F +3.97 (ranking) 333.11 231.28 P +2 F +1.65 (, and includes a simple linear) 383.48 231.28 P +1.26 (scaling function,) 135.65 217.28 P +3 F +3.02 (scaling) 221.11 217.28 P +2 F +1.26 (, for completeness. It should be noted that the linear) 271.49 217.28 P +-0.14 (scaling function is not suitable for use with objective functions that return negative) 135.65 203.28 P +(\336tness values.) 135.65 189.28 T +1 16 Q +(Selection) 135.65 160.61 T +2 12 Q +0.46 (Selection is the process of determining the number of times, or) 135.65 133.28 P +0 F +0.46 (trials) 445.13 133.28 P +2 F +0.46 (, a particular) 470.46 133.28 P +1.43 (individual is chosen for reproduction and, thus, the number of of) 135.65 119.28 P +1.43 (fspring that an) 459.51 119.28 P +224.57 321.28 439.73 354.95 C +0 12 Q +0 X +0 K +(F) 225.57 335.53 T +(x) 240.7 335.53 T +0 9 Q +(i) 246.49 331.75 T +4 12 Q +(\050) 235.6 335.53 T +(\051) 249.59 335.53 T +2 F +(2) 274.17 335.53 T +0 F +(M) 292.75 335.53 T +(A) 303.45 335.53 T +(X) 311.48 335.53 T +4 F +(-) 283.17 335.53 T +2 F +(2) 331.39 335.53 T +0 F +(M) 345.2 335.53 T +(A) 355.89 335.53 T +(X) 363.93 335.53 T +2 F +(1) 383.84 335.53 T +4 F +(-) 374.26 335.53 T +(\050) 340.1 335.53 T +(\051) 390.45 335.53 T +0 F +(x) 404.51 345.75 T +0 9 Q +(i) 410.29 341.97 T +2 12 Q +(1) 425.37 345.75 T +4 F +(-) 415.79 345.75 T +0 F +(N) 398.14 327.91 T +0 9 Q +(i) 406.61 324.13 T +(n) 409.63 324.13 T +(d) 414.66 324.13 T +2 12 Q +(1) 431.73 327.91 T +4 F +(-) 422.15 327.91 T +(+) 321.81 335.53 T +(=) 261.59 335.53 T +398.14 338.12 437.48 338.12 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "9" 10 +%%Page: "10" 10 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-10) 513.33 61.29 T +2 12 Q +-0.28 (individual will produce. The selection of individuals can be viewed as two separate) 135.65 736.95 P +(processes:) 135.65 722.95 T +(1\051) 135.65 696.95 T +0.93 (determination of the number of trials an individual can expect to receive,) 171.65 696.95 P +(and) 171.65 682.95 T +(2\051) 135.65 662.95 T +2.6 (conversion of the expected number of trials into a discrete number of) 171.65 662.95 P +(of) 171.65 648.95 T +(fspring.) 181.42 648.95 T +-0.07 (The \336rst part is concerned with the transformation of raw \336tness values into a real-) 135.65 628.95 P +0.47 (valued expectation of an individual\325) 135.65 614.95 P +0.47 (s probability to reproduce and is dealt with in) 310.06 614.95 P +0.51 (the previous subsection as \336tness assignment. The second part is the probabilistic) 135.65 600.95 P +-0.19 (selection of individuals for reproduction based on the \336tness of individuals relative) 135.65 586.95 P +3.05 (to one another and is sometimes known as) 135.65 572.95 P +0 F +3.05 (sampling) 365.89 572.95 P +2 F +3.05 (. The remainder of this) 409.87 572.95 P +2.11 (subsection will review some of the more popular selection methods in current) 135.65 558.95 P +(usage.) 135.65 544.95 T +-0.17 (Baker [15] presented three measures of performance for selection algorithms,) 135.65 518.95 P +0 F +-0.17 (bias) 508.66 518.95 P +2 F +-0.17 (,) 528.65 518.95 P +0 F +3.37 (spr) 135.65 504.95 P +3.37 (ead) 150.53 504.95 P +2 F +3.37 ( and) 167.85 504.95 P +0 F +3.37 (ef\336ciency) 197.9 504.95 P +2 F +3.37 (. Bias is de\336ned as the absolute dif) 242.41 504.95 P +3.37 (ference between an) 432.34 504.95 P +4.34 (individual\325) 135.65 490.95 P +4.34 (s actual and expected selection probability) 187.63 490.95 P +4.34 (. Optimal zero bias is) 412.04 490.95 P +1.03 (therefore achieved when an individual\325) 135.65 476.95 P +1.03 (s selection probability equals its expected) 326.95 476.95 P +(number of trials.) 135.65 462.95 T +-0.05 (Spread is the range in the possible number of trials that an individual may achieve.) 135.65 436.95 P +0.71 (If) 135.65 422.95 P +0 F +0.71 (f\050i\051) 147.34 422.95 P +2 F +0.71 ( is the actual number of trials that individual) 162 422.95 P +0 F +0.71 (i) 383.91 422.95 P +2 F +0.71 ( receives, then the \322minimum) 387.24 422.95 P +(spread\323 is the smallest spread that theoretically permits zero bias, i.e.) 135.65 408.95 T +0.3 (where) 135.65 321.65 P +0 F +0.3 (et\050i\051) 168.24 321.65 P +2 F +0.3 ( is the expected number of trials of individual) 188.23 321.65 P +0 F +0.3 (i) 412.42 321.65 P +2 F +0.3 (,) 415.76 321.65 P +0.3 ( is the \337oor of) 463.16 321.65 P +1.64 (et\050i\051 and) 135.65 307.65 P +1.64 ( is the ceil. Thus, while bias is an indication of accuracy) 223.32 307.65 P +1.64 (, the) 509.36 307.65 P +(spread of a selection method measures its consistency) 135.65 293.65 T +(.) 393.02 293.65 T +0.88 (The desire for ef) 135.65 267.65 P +0.88 (\336cient selection methods is motivated by the need to maintain a) 217.67 267.65 P +1.72 (GAs overall time complexity) 135.65 253.65 P +1.72 (. It has been shown in the literature that the other) 279.61 253.65 P +4.96 (phases of a GA \050excluding the actual objective function evaluations\051 are) 135.65 239.65 P +1 (O\050L) 135.65 225.65 P +2 10 Q +0.83 (ind) 155.63 222.65 P +2 12 Q +1 (.N) 168.4 225.65 P +2 10 Q +0.83 (ind) 180.06 222.65 P +2 12 Q +1 (\051 or better time complexity) 192.83 225.65 P +1 (, where L) 324.64 225.65 P +2 10 Q +0.83 (ind) 372.27 222.65 P +2 12 Q +1 ( is the length of an individual) 385.05 225.65 P +0.71 (and N) 135.65 211.65 P +2 10 Q +0.59 (ind) 165.33 208.65 P +2 12 Q +0.71 ( is the population size. The selection algorithm should thus achieve zero) 178.1 211.65 P +1.51 (bias whilst maintaining a minimum spread and not contributing to an increased) 135.65 197.65 P +(time complexity of the GA.) 135.65 183.65 T +1 14 Q +(Roulette Wheel Selection Methods) 135.65 156.31 T +2 12 Q +8.61 (Many selection techniques employ a \322roulette wheel\323 mechanism to) 135.65 129.65 P +-0.14 (probabilistically select individuals based on some measure of their performance. A) 135.65 115.65 P +2.72 (real-valued interval,) 135.65 101.65 P +0 F +2.72 (Sum) 240.67 101.65 P +2 F +2.72 (, is determined as either the sum of the individuals\325) 261.32 101.65 P +261.26 343.65 406.04 390.95 C +0 12 Q +0 X +0 K +(f) 262.26 364.71 T +(i) 273.4 364.71 T +4 F +(\050) 268.3 364.71 T +(\051) 277.34 364.71 T +0 F +(e) 312.75 365.19 T +(t) 318.78 365.19 T +(i) 329.92 365.19 T +4 F +(\050) 324.82 365.19 T +(\051) 333.86 365.19 T +0 F +(e) 357.85 365.19 T +(t) 363.89 365.19 T +(i) 375.03 365.19 T +4 F +(\050) 369.92 365.19 T +(\051) 378.97 365.19 T +(,) 345.86 365.19 T +(\376) 394.67 350.05 T +(\375) 394.67 362.17 T +(\374) 394.67 374.29 T +(\356) 299.88 350.05 T +(\355) 299.88 362.17 T +(\354) 299.88 374.29 T +(\316) 286.33 364.71 T +307.75 362.2 307.75 373.4 2 L +0.33 H +0 Z +N +307.75 362.2 310.75 362.2 2 L +N +343.86 362.2 343.86 373.4 2 L +N +343.86 362.2 340.86 362.2 2 L +N +352.85 362.2 352.85 373.4 2 L +N +352.85 373.4 355.85 373.4 2 L +N +388.96 362.2 388.96 373.4 2 L +N +388.96 373.4 385.96 373.4 2 L +N +-8.35 24.95 603.65 816.95 C +422.05 316.65 463.16 330.85 C +0 12 Q +0 X +0 K +(e) 429.05 321.65 T +(t) 435.08 321.65 T +(i) 446.23 321.65 T +4 F +(\050) 441.12 321.65 T +(\051) 450.17 321.65 T +424.05 318.65 424.05 329.85 2 L +0.33 H +0 Z +N +424.05 318.65 427.05 318.65 2 L +N +460.16 318.65 460.16 329.85 2 L +N +460.16 318.65 457.16 318.65 2 L +N +-8.35 24.95 603.65 816.95 C +182.22 302.65 223.32 316.85 C +0 12 Q +0 X +0 K +(e) 189.22 307.65 T +(t) 195.25 307.65 T +(i) 206.39 307.65 T +4 F +(\050) 201.29 307.65 T +(\051) 210.33 307.65 T +184.22 304.65 184.22 315.85 2 L +0.33 H +0 Z +N +184.22 315.85 187.22 315.85 2 L +N +220.32 304.65 220.32 315.85 2 L +N +220.32 315.85 217.32 315.85 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "10" 11 +%%Page: "11" 11 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-11) 513.33 61.29 T +2 12 Q +1.17 (expected selection probabilities or the sum of the raw \336tness values over all the) 135.65 736.95 P +0.26 (individuals in the current population. Individuals are then mapped one-to-one into) 135.65 722.95 P +1.69 (contiguous intervals in the range [0,) 135.65 708.95 P +0 F +1.69 (Sum) 321.33 708.95 P +2 F +1.69 (]. The size of each individual interval) 341.98 708.95 P +-0.14 (corresponds to the \336tness value of the associated individual. For example, in Fig. 2) 135.65 694.95 P +1.38 (the circumference of the roulette wheel is the sum of all six individual\325) 135.65 680.95 P +1.38 (s \336tness) 491.95 680.95 P +1.76 (values. Individual 5 is the most \336t individual and occupies the lar) 135.65 666.95 P +1.76 (gest interval,) 467.93 666.95 P +1.97 (whereas individuals 6 and 4 are the least \336t and have correspondingly smaller) 135.65 652.95 P +1.31 (intervals within the roulette wheel. T) 135.65 638.95 P +1.31 (o select an individual, a random number is) 318.59 638.95 P +1.88 (generated in the interval [0,) 135.65 624.95 P +0 F +1.88 (Sum) 280.29 624.95 P +2 F +1.88 (] and the individual whose segment spans the) 300.94 624.95 P +1.11 (random number is selected. This process is repeated until the desired number of) 135.65 610.95 P +(individuals have been selected.) 135.65 596.95 T +-0.04 (The basic roulette wheel selection method is stochastic sampling with replacement) 135.65 570.95 P +4.89 (\050SSR\051. Here, the segment size and selection probability remain the same) 135.65 556.95 P +3.36 (throughout the selection phase and individuals are selected according to the) 135.65 542.95 P +0.48 (procedure outlined above. SSR gives zero bias but a potentially unlimited spread.) 135.65 528.95 P +(Any individual with a segment size > 0 could entirely \336ll the next population.) 135.65 514.95 T +3.91 (Stochastic sampling with partial replacement \050SSPR\051 extends upon SSR by) 135.65 271.94 P +3.1 (resizing an individual\325) 135.65 257.94 P +3.1 (s segment if it is selected. Each time an individual is) 249.12 257.94 P +1.33 (selected, the size of its segment is reduced by 1.0. If the segment size becomes) 135.65 243.94 P +2.15 (negative, then it is set to 0.0. This provides an upper bound on the spread of) 135.65 229.94 P +-0.2 (. However) 176.76 215.94 P +-0.2 (, the lower bound is zero and the bias is higher than that of SSR.) 226.02 215.94 P +1.29 (Remainder sampling methods involve two distinct phases. In the integral phase,) 135.65 189.94 P +2.36 (individuals are selected deterministically according to the integer part of their) 135.65 175.94 P +0.4 (expected trials. The remaining individuals are then selected probabilistically from) 135.65 161.94 P +3.95 (the fractional part of the individuals expected values. Remainder stochastic) 135.65 147.94 P +1.82 (sampling with replacement \050RSSR\051 uses roulette wheel selection to sample the) 135.65 133.94 P +3.42 (individual not assigned deterministically) 135.65 119.94 P +3.42 (. During the roulette wheel selection) 340.02 119.94 P +3.29 (phase, individual\325) 135.65 105.94 P +3.29 (s fractional parts remain unchanged and, thus, compete for) 224.22 105.94 P +63.65 96.95 531.65 744.95 C +133.38 293.94 531.65 510.95 C +0.5 H +2 Z +0 X +0 K +90 450 70.87 70.87 332.51 420.22 A +332.51 491.09 332.51 420.22 2 L +N +332.51 420.22 282.91 370.61 2 L +N +332.51 420.22 384.95 466.76 2 L +N +332.51 420.22 394.88 389.74 2 L +N +2 12 Q +(1) 358.18 462.39 T +90 450 7.09 7.09 361.18 466.48 A +(3) 350.03 366.22 T +90 450 7.09 7.09 353.03 370.31 A +(2) 382.66 416.22 T +90 450 7.09 7.09 385.66 420.31 A +(4) 299.18 370.87 T +90 450 7.09 7.09 302.18 374.96 A +332.51 420.22 303.38 484.74 2 L +N +(5) 278.18 428.87 T +90 450 7.09 7.09 281.18 432.96 A +332.38 418.74 305.38 355.74 2 L +N +(6) 319.18 469.89 T +90 450 7.09 7.09 322.18 473.98 A +5 F +(Figure 2: Roulette Wheel Selection) 245.56 316.24 T +146.49 303.24 518.54 501.66 R +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +135.65 210.95 176.75 225.15 C +0 12 Q +0 X +0 K +(e) 142.65 215.94 T +(t) 148.68 215.94 T +(i) 159.82 215.94 T +4 F +(\050) 154.72 215.94 T +(\051) 163.76 215.94 T +137.65 212.95 137.65 224.15 2 L +0.33 H +0 Z +N +137.65 224.15 140.65 224.15 2 L +N +173.76 212.95 173.76 224.15 2 L +N +173.76 224.15 170.76 224.15 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "11" 12 +%%Page: "12" 12 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-12) 513.33 61.29 T +2 12 Q +2.99 (selection between \322spins\323. RSSR provides zero bias and the spread is lower) 135.65 736.95 P +0.55 (bounded. The upper bound is limited only by the number of fractionally assigned) 135.65 722.95 P +2.87 (samples and the size of the integral part of an individual. For example, any) 135.65 708.95 P +-0.04 (individual with a fractional part > 0 could win all the samples during the fractional) 135.65 694.95 P +2.65 (phase. Remainder stochastic sampling without replacement \050RSSWR\051 sets the) 135.65 680.95 P +0.02 (fractional part of an individual\325) 135.65 666.95 P +0.02 (s expected values to zero if it is sampled during the) 285.62 666.95 P +2.51 (fractional phase. This gives RSSWR minimum spread, although this selection) 135.65 652.95 P +(method is biased in favour of smaller fractions.) 135.65 638.95 T +1 14 Q +(Stochastic Universal Sampling) 135.65 611.62 T +2 12 Q +1.84 (Stochastic universal sampling \050SUS\051 is a single-phase sampling algorithm with) 135.65 584.95 P +0.05 (minimum spread and zero bias. Instead of the single selection pointer employed in) 135.65 570.95 P +2.58 (roulette wheel methods, SUS uses) 135.65 556.95 P +0 F +2.58 (N) 315.09 556.95 P +2 F +2.58 ( equally spaced pointers, where) 323.09 556.95 P +0 F +2.58 (N) 489.84 556.95 P +2 F +2.58 ( is the) 497.84 556.95 P +1.13 (number of selections required. The population is shuf) 135.65 542.95 P +1.13 (\337ed randomly and a single) 399.86 542.95 P +1.43 (random number in the range [0) 135.65 528.95 P +0 F +1.43 (Sum) 296.11 528.95 P +2 F +1.43 (/) 316.77 528.95 P +0 F +1.43 (N) 320.1 528.95 P +2 F +1.43 (] is generated,) 328.1 528.95 P +0 F +1.43 (ptr) 402.99 528.95 P +2 F +1.43 (. The) 416.33 528.95 P +0 F +1.43 (N) 446.84 528.95 P +2 F +1.43 ( individuals are) 454.84 528.95 P +-0.2 (then chosen by generating the) 135.65 514.95 P +0 F +-0.2 (N) 280.87 514.95 P +2 F +-0.2 ( pointers spaced by 1, [) 288.87 514.95 P +0 F +-0.2 (ptr) 399.13 514.95 P +2 F +-0.2 (,) 412.64 514.95 P +0 F +-0.2 (ptr) 418.44 514.95 P +2 F +-0.2 (+1, ...,) 432.44 514.95 P +0 F +-0.2 (ptr) 465.79 514.95 P +2 F +-0.2 (+) 479.78 514.95 P +0 F +-0.2 (N) 486.55 514.95 P +2 F +-0.2 (-1], and) 494.55 514.95 P +1.84 (selecting the individuals whose \336tnesses span the positions of the pointers. An) 135.65 500.95 P +0.78 (individual is thus guaranteed to be selected a minimum of) 135.65 486.95 P +0.78 ( times and no) 465.02 486.95 P +1.34 (more than) 135.65 472.95 P +1.34 (, thus achieving minimum spread. In addition, as individuals) 230.74 472.95 P +(are selected entirely on their position in the population, SUS has zero bias.) 135.65 458.95 T +3.69 (The roulette wheel selection methods can all be implemented as O\050NlogN\051) 135.65 432.95 P +0.4 (although SUS is a simpler algorithm and has time complexity O\050N\051. The T) 135.65 418.95 P +0.4 (oolbox) 498.33 418.95 P +4.7 (supplies a stochastic universal sampling function,) 135.65 404.95 P +3 F +11.28 (sus) 404.69 404.95 P +2 F +4.7 (, and the stochastic) 426.28 404.95 P +(sampling with replacement algorithm,) 135.65 390.95 T +3 F +(rws) 321.2 390.95 T +2 F +(.) 342.79 390.95 T +1 16 Q +(Cr) 135.65 362.29 T +(ossover \050Recombination\051) 154.01 362.29 T +2 12 Q +-0.08 (The basic operator for producing new chromosomes in the GA is that of crossover) 135.65 334.95 P +-0.08 (.) 528.65 334.95 P +0.39 (Like its counterpart in nature, crossover produces new individuals that have some) 135.65 320.95 P +1.05 (parts of both parent\325) 135.65 306.95 P +1.05 (s genetic material. The simplest form of crossover is that of) 235.72 306.95 P +3.04 (single-point crossover) 135.65 292.95 P +3.04 (, described in the Overview of GAs. In this Section, a) 244.47 292.95 P +1.75 (number of variations on crossover are described and discussed and the relative) 135.65 278.95 P +(merits of each reviewed.) 135.65 264.95 T +1 14 Q +(Multi-point Cr) 135.65 237.62 T +(ossover) 224.4 237.62 T +2 12 Q +0.7 (For multi-point crossover) 135.65 210.95 P +0.7 (,) 259.16 210.95 P +0 F +0.7 (m) 265.86 210.95 P +2 F +0.7 ( crossover positions,) 274.52 210.95 P +0.7 (, where) 483.85 210.95 P +0 F +0.7 (k) 523.54 210.95 P +0 10 Q +0.58 (i) 528.87 207.95 P +2 12 Q +2.14 (are the crossover points and) 135.65 196.95 P +0 F +2.14 (l) 283.23 196.95 P +2 F +2.14 ( is the length of the chromosome, are chosen at) 286.57 196.95 P +0.08 (random with no duplicates and sorted into ascending order) 135.65 182.95 P +0.08 (. Then, the bits between) 416.75 182.95 P +-0.18 (successive crossover points are exchanged between the two parents to produce two) 135.65 168.95 P +423.91 481.96 465.02 496.16 C +0 12 Q +0 X +0 K +(e) 430.91 486.95 T +(t) 436.94 486.95 T +(i) 448.08 486.95 T +4 F +(\050) 442.98 486.95 T +(\051) 452.02 486.95 T +425.91 483.96 425.91 495.16 2 L +0.33 H +0 Z +N +425.91 483.96 428.91 483.96 2 L +N +462.02 483.96 462.02 495.16 2 L +N +462.02 483.96 459.02 483.96 2 L +N +-8.35 24.95 603.65 816.95 C +189.63 467.96 230.74 482.16 C +0 12 Q +0 X +0 K +(e) 196.63 472.95 T +(t) 202.66 472.95 T +(i) 213.8 472.95 T +4 F +(\050) 208.7 472.95 T +(\051) 217.74 472.95 T +191.63 469.96 191.63 481.16 2 L +0.33 H +0 Z +N +191.63 481.16 194.63 481.16 2 L +N +227.74 469.96 227.74 481.16 2 L +N +227.74 481.16 224.74 481.16 2 L +N +-8.35 24.95 603.65 816.95 C +377.89 204.32 483.85 220.16 C +0 12 Q +0 X +0 K +(k) 378.89 210.95 T +0 9 Q +(i) 384.68 207.17 T +2 12 Q +(1) 410.59 210.95 T +(2) 422.58 210.95 T +4 F +(\274) 434.58 210.95 T +0 F +(l) 452.57 210.95 T +2 F +(1) 468.49 210.95 T +4 F +(-) 458.91 210.95 T +(,) 416.59 210.95 T +(,) 428.58 210.95 T +(,) 446.57 210.95 T +({) 403.73 210.95 T +(}) 475.09 210.95 T +(\316) 390.17 210.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "12" 13 +%%Page: "13" 13 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-13) 513.33 61.29 T +2 12 Q +0.51 (new of) 135.65 736.95 P +0.51 (fspring. The section between the \336rst allele position and the \336rst crossover) 168.91 736.95 P +(point is not exchanged between individuals. This process is illustrated in Fig. 3.) 135.65 722.95 T +0.94 (The idea behind multi-point, and indeed many of the variations on the crossover) 135.65 557.78 P +0.7 (operator) 135.65 543.78 P +0.7 (, is that the parts of the chromosome representation that contribute to the) 175.13 543.78 P +4.05 (most to the performance of a particular individual may not necessarily be) 135.65 529.78 P +0.41 (contained in adjacent substrings [16]. Further) 135.65 515.78 P +0.41 (, the disruptive nature of multi-point) 355.05 515.78 P +1.73 (crossover appears to encourage the exploration of the search space, rather than) 135.65 501.78 P +0.29 (favoring the conver) 135.65 487.78 P +0.29 (gence to highly \336t individuals early in the search, thus making) 229.93 487.78 P +(the search more robust [17].) 135.65 473.78 T +1 14 Q +(Uniform Cr) 135.65 446.44 T +(ossover) 206.51 446.44 T +2 12 Q +0.42 (Single and multi-point crossover de\336ne cross points as places between loci where) 135.65 419.78 P +1.9 (a chromosome can be split. Uniform crossover [18] generalises this scheme to) 135.65 405.78 P +0.75 (make every locus a potential crossover point. A crossover mask, the same length) 135.65 391.78 P +0.26 (as the chromosome structures is created at random and the parity of the bits in the) 135.65 377.78 P +1.13 (mask indicates which parent will supply the of) 135.65 363.78 P +1.13 (fspring with which bits. Consider) 366.88 363.78 P +(the following two parents, crossover mask and resulting of) 135.65 349.78 T +(fspring:) 416.9 349.78 T +3 F +(P) 143.73 323.78 T +3 10 Q +(1) 150.92 320.78 T +3 12 Q +(= 1 0 1 1 0 0 0 1 1 1) 186.25 323.78 T +(P) 143.73 305.78 T +3 10 Q +(2) 150.92 302.78 T +3 12 Q +(= 0 0 0 1 1 1 1 0 0 0) 186.25 305.78 T +(Mask) 143.73 287.78 T +(= 0 0 1 1 0 0 1 1 0 0) 186.25 287.78 T +(O) 143.73 269.78 T +3 10 Q +(1) 150.92 266.78 T +3 12 Q +(= 0 0 1 1 1 1 0 1 0 0) 186.25 269.78 T +(O) 143.73 251.78 T +3 10 Q +(2) 150.92 248.78 T +3 12 Q +(= 1 0 0 1 0 0 1 0 1 1) 186.25 251.78 T +2 F +3.65 (Here, the \336rst of) 135.65 221.78 P +3.65 (fspring,) 224.98 221.78 P +3 F +8.75 (O) 268.6 221.78 P +3 10 Q +7.29 (1) 275.79 218.78 P +2 12 Q +3.65 (, is produced by taking the bit from) 281.79 221.78 P +3 F +8.75 (P) 483.18 221.78 P +3 10 Q +7.29 (1) 490.38 218.78 P +2 12 Q +3.65 ( if the) 496.38 221.78 P +0.5 (corresponding mask bit is 1 or the bit from) 135.65 207.78 P +3 F +1.21 (P) 348.37 207.78 P +3 10 Q +1 (2) 355.57 204.78 P +2 12 Q +0.5 ( if the corresponding mask bit is 0.) 361.57 207.78 P +-0.28 (Of) 135.65 193.78 P +-0.28 (fspring) 148.09 193.78 P +3 F +-0.67 (O) 184.78 193.78 P +3 10 Q +-0.56 (2) 191.98 190.78 P +2 12 Q +-0.28 ( is created using the inverse of the mask or) 197.97 193.78 P +-0.28 (, equivalently) 399.82 193.78 P +-0.28 (, swapping) 464.05 193.78 P +3 F +-0.67 (P) 518.46 193.78 P +3 10 Q +-0.56 (1) 525.65 190.78 P +2 12 Q +(and) 135.65 179.78 T +3 F +(P) 155.96 179.78 T +3 10 Q +(2) 163.16 176.78 T +2 12 Q +(.) 169.16 179.78 T +0.08 (Uniform crossover) 135.65 153.78 P +0.08 (, like multi-point crossover) 225.51 153.78 P +0.08 (, has been claimed to reduce the bias) 355.21 153.78 P +2.24 (associated with the length of the binary representation used and the particular) 135.65 139.78 P +0.79 (coding for a given parameter set. This helps to overcome the bias in single-point) 135.65 125.78 P +0.58 (crossover towards short substrings without requiring precise understanding of the) 135.65 111.78 P +63.65 96.95 531.65 744.95 C +124.27 579.78 531.65 718.95 C +151.07 674.97 307.83 682.06 R +8 X +0 K +V +0.5 H +2 Z +0 X +N +151.07 646.62 307.83 653.71 R +4 X +V +0 X +N +164.13 689.14 164.13 639.54 2 L +N +190.26 689.14 190.26 639.54 2 L +N +242.51 689.14 242.51 639.54 2 L +N +278.44 689.14 278.44 639.54 2 L +N +301.3 689.14 301.3 639.54 2 L +N +360.08 674.97 373.15 682.06 R +8 X +V +0 X +N +373.15 646.62 399.28 653.71 R +8 X +V +0 X +N +399.27 674.97 451.53 682.06 R +8 X +V +0 X +N +451.53 646.62 487.45 653.71 R +8 X +V +0 X +N +487.45 674.97 510.32 682.06 R +8 X +V +0 X +N +510.32 646.62 516.85 653.71 R +8 X +V +0 X +N +373.15 674.97 399.28 682.06 R +4 X +V +0 X +N +451.53 674.97 487.45 682.06 R +4 X +V +0 X +N +510.32 674.97 516.85 682.06 R +4 X +V +0 X +N +360.08 646.62 373.15 653.71 R +4 X +V +0 X +N +399.27 646.62 451.53 653.71 R +4 X +V +0 X +N +487.45 646.62 510.32 653.71 R +4 X +V +0 X +N +335.49 667.65 347.02 664.34 335.49 661.03 335.49 664.34 4 Y +V +320.89 664.34 335.49 664.34 2 L +N +5 12 Q +(Figure 3: Multi-point Crossover \050m=5\051) 237.91 612.02 T +138 594.44 529.92 704.29 R +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "13" 14 +%%Page: "14" 14 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-14) 513.33 61.29 T +2 12 Q +1.26 (signi\336cance of individual bits in the chromosome representation. Spears and De) 135.65 736.95 P +1.96 (Jong [19] have demonstrated how uniform crossover may be parameterised by) 135.65 722.95 P +0.09 (applying a probability to the swapping of bits. This extra parameter can be used to) 135.65 708.95 P +0.56 (control the amount of disruption during recombination without introducing a bias) 135.65 694.95 P +1.78 (towards the length of the representation used. When uniform crossover is used) 135.65 680.95 P +(with real-valued alleles, it is usually referred to as) 135.65 666.95 T +0 F +(discr) 378.13 666.95 T +(ete r) 401.67 666.95 T +(ecombination) 422.88 666.95 T +2 F +(.) 488.17 666.95 T +1 14 Q +(Other Cr) 135.65 639.62 T +(ossover Operators) 190.96 639.62 T +2 12 Q +-0.05 (A related crossover operator is that of) 135.65 612.95 P +0 F +-0.05 (shuf\337e) 319.45 612.95 P +2 F +-0.05 ( [20]. A single cross-point is selected,) 350.77 612.95 P +-0.24 (but before the bits are exchanged, they are randomly shuf) 135.65 598.95 P +-0.24 (\337ed in both parents. After) 409.03 598.95 P +-0.15 (recombination, the bits in the of) 135.65 584.95 P +-0.15 (fspring are unshuf) 287.92 584.95 P +-0.15 (\337ed. This too removes positional) 374.67 584.95 P +(bias as the bits are randomly reassigned each time crossover is performed.) 135.65 570.95 T +0.72 (The) 135.65 544.95 P +0 F +0.72 (r) 158.02 544.95 P +0.72 (educed surr) 162.24 544.95 P +0.72 (ogate) 219.47 544.95 P +2 F +0.72 ( operator [16] constrains crossover to always produce new) 246.12 544.95 P +2.89 (individuals wherever possible. Usually) 135.65 530.95 P +2.89 (, this is implemented by restricting the) 330.08 530.95 P +2.18 (location of crossover points such that crossover points only occur where gene) 135.65 516.95 P +(values dif) 135.65 502.95 T +(fer) 182.4 502.95 T +(.) 195.05 502.95 T +1 14 Q +(Intermediate Recombination) 135.65 475.62 T +2 12 Q +5.99 (Given a real-valued encoding of the chromosome structure, intermediate) 135.65 448.95 P +0.54 (recombination is a method of producing new phenotypes around and between the) 135.65 434.95 P +1.68 (values of the parents phenotypes [21]. Of) 135.65 420.95 P +1.68 (fspring are produced according to the) 343.71 420.95 P +(rule,) 135.65 406.95 T +(,) 391.24 379.75 T +2.92 (where) 135.65 351.04 P +4 F +2.92 (a) 170.87 351.04 P +2 F +2.92 ( is a scaling factor chosen uniformly at random over some interval,) 178.43 351.04 P +3.3 (typically [-0.25, 1.25] and) 135.65 337.04 P +0 F +3.3 (P) 277.1 337.04 P +0 10 Q +2.75 (1) 284.42 334.04 P +2 12 Q +3.3 ( and) 289.42 337.04 P +0 F +3.3 (P) 319.34 337.04 P +0 10 Q +2.75 (2) 326.67 334.04 P +2 12 Q +3.3 ( are the parent chromosomes \050see, for) 331.67 337.04 P +2.82 (example, [21]\051. Each variable in the of) 135.65 323.04 P +2.82 (fspring is the result of combining the) 337.52 323.04 P +-0.04 (variables in the parents according to the above expression with a new) 135.65 309.04 P +4 F +-0.04 (a) 470.88 309.04 P +2 F +-0.04 ( chosen for) 478.45 309.04 P +3.03 (each pair of parent genes. In geometric terms, intermediate recombination is) 135.65 295.04 P +273.05 373.04 391.24 388.95 C +0 12 Q +0 X +0 K +(O) 274.05 379.75 T +2 9 Q +(1) 283.17 375.99 T +0 12 Q +(P) 306.25 379.75 T +2 9 Q +(1) 314.04 375.99 T +4 12 Q +(a) 331.12 379.75 T +0 F +(P) 346.49 379.75 T +2 9 Q +(2) 354.28 375.99 T +0 12 Q +(P) 371.36 379.75 T +2 9 Q +(1) 379.15 375.99 T +4 12 Q +(-) 361.78 379.75 T +(\050) 341.39 379.75 T +(\051) 384.25 379.75 T +(\264) 321.53 379.75 T +(=) 293.67 379.75 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "14" 15 +%%Page: "15" 15 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-15) 513.33 61.29 T +2 12 Q +1.47 (capable of producing new variables within a slightly lar) 135.65 736.95 P +1.47 (ger hypercube than that) 414.33 736.95 P +(de\336ned by the parents but constrained by the range of) 135.65 722.95 T +4 F +(a) 396.12 722.95 T +2 F +(. as shown in Fig 4.) 403.69 722.95 T +1 14 Q +(Line Recombination) 135.65 481.79 T +2 12 Q +0.13 (Line recombination [21] is similar to intermediate recombination, except that only) 135.65 455.12 P +0.29 (one value of) 135.65 441.12 P +4 F +0.29 (a) 198.79 441.12 P +2 F +0.29 ( is used in the recombination. Fig. 5 shows how line recombination) 206.36 441.12 P +0.88 (can generate any point on the line de\336ned by the parents within the limits of the) 135.65 427.12 P +(perturbation,) 135.65 413.12 T +4 F +(a,) 200.27 413.12 T +2 F +(for a recombination in two variables.) 213.83 413.12 T +1 14 Q +(Discussion) 135.65 165.83 T +2 12 Q +2.58 (The binary operators discussed in this Section have all, to some extent, used) 135.65 139.16 P +0.03 (disruption in the representation to help improve exploration during recombination.) 135.65 125.16 P +1.99 (Whilst these operators may be used with real-valued populations, the resulting) 135.65 111.16 P +63.65 96.95 531.65 744.95 C +133.38 505.12 531.65 718.95 C +205.79 685.03 209.1 696.57 212.41 685.03 209.1 685.03 4 Y +0 X +0 K +V +209.1 565.46 209.1 685.03 2 L +0.5 H +2 Z +N +1 X +90 450 5.32 5.32 249.85 655.82 G +0 X +90 450 5.32 5.32 249.85 655.82 A +230.36 590.27 315.4 675.31 R +8 X +N +325.12 572.18 336.66 568.87 325.12 565.56 325.12 568.87 4 Y +0 X +V +205.56 568.87 325.12 568.87 2 L +N +1 X +90 450 5.32 5.32 295.91 609.75 G +0 X +90 450 5.32 5.32 295.91 609.75 A +4 X +90 450 5.32 5.32 271.11 662.9 G +0 X +90 450 5.32 5.32 271.11 662.9 A +4 X +90 450 5.32 5.32 260.48 631.01 G +0 X +90 450 5.32 5.32 260.48 631.01 A +4 X +90 450 5.32 5.32 242.76 602.67 G +0 X +90 450 5.32 5.32 242.76 602.67 A +4 X +90 450 5.32 5.32 285.28 641.64 G +0 X +90 450 5.32 5.32 285.28 641.64 A +1 X +90 450 5.32 5.32 356.15 634.56 G +0 X +90 450 5.32 5.32 356.15 634.56 A +4 X +90 450 5.32 5.32 356.15 609.75 G +0 X +90 450 5.32 5.32 356.15 609.75 A +2 12 Q +(Gene1) 255.46 553.89 T +(Gene 2) 0 -270 197.02 611.53 TF +(Parents) 368.55 630.47 T +(Potential of) 368.55 605.66 T +(fspring) 423.97 605.66 T +(Area of possible of) 350.83 656.65 T +(fspring) 442.21 656.65 T +330.48 657.43 318.94 660.74 330.48 664.05 330.48 660.74 4 Y +V +347.29 660.74 330.48 660.74 2 L +N +5 F +(Figure 4: Geometric Ef) 186.7 529.94 T +(fect of Intermediate Recombination) 302.75 529.94 T +141.18 514.6 523.85 709.48 R +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +63.65 96.95 531.65 744.95 C +133.38 189.16 531.65 409.12 C +196.34 372.12 199.64 383.66 202.95 372.12 199.64 372.12 4 Y +0 X +0 K +V +199.64 252.55 199.64 372.12 2 L +0.5 H +2 Z +N +1 X +90 450 5.32 5.32 228.24 352.09 G +0 X +90 450 5.32 5.32 228.24 352.09 A +315.67 259.27 327.2 255.96 315.67 252.65 315.67 255.96 4 Y +V +196.1 255.96 315.67 255.96 2 L +N +1 X +90 450 5.32 5.32 299.08 281.22 G +0 X +90 450 5.32 5.32 299.08 281.22 A +4 X +90 450 5.32 5.32 221.15 359.14 G +0 X +90 450 5.32 5.32 221.15 359.14 A +4 X +90 450 5.32 5.32 255.87 324.45 G +0 X +90 450 5.32 5.32 255.87 324.45 A +4 X +90 450 5.32 5.32 239.55 340.03 G +0 X +90 450 5.32 5.32 239.55 340.03 A +1 X +90 450 5.32 5.32 346.69 321.65 G +0 X +90 450 5.32 5.32 346.69 321.65 A +4 X +90 450 5.32 5.32 346.69 296.85 G +0 X +90 450 5.32 5.32 346.69 296.85 A +2 12 Q +(Gene1) 246 240.98 T +(Gene 2) 0 -270 187.56 298.62 TF +(Parents) 359.09 317.56 T +(Potential of) 359.09 292.76 T +(fspring) 414.51 292.76 T +5 F +(Figure 5: Geometric Ef) 197.57 217.03 T +(fect of Line Recombination) 313.62 217.03 T +141.18 201.7 523.85 396.58 R +N +4 X +90 450 5.32 5.32 270.76 309.57 G +0 X +90 450 5.32 5.32 270.76 309.57 A +4 X +90 450 5.32 5.32 286.33 293.94 G +0 X +90 450 5.32 5.32 286.33 293.94 A +4 X +90 450 5.32 5.32 306.88 273.42 G +0 X +90 450 5.32 5.32 306.88 273.42 A +4 X +90 450 5.32 5.32 314.68 265.62 G +0 X +90 450 5.32 5.32 314.68 265.62 A +4 X +90 450 5.32 5.32 214.04 366.26 G +0 X +90 450 5.32 5.32 214.04 366.26 A +213.69 366.6 312.9 267.39 2 L +V +8 X +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "15" 16 +%%Page: "16" 16 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-16) 513.33 61.29 T +2 12 Q +0.19 (changes in the genetic material after recombination would not extend to the actual) 135.65 736.95 P +0.54 (values of the decision variables, although of) 135.65 722.95 P +0.54 (fspring may) 350.19 722.95 P +0.54 (, of course, contain genes) 407.58 722.95 P +1.14 (from either parent. The intermediate and line recombination operators overcome) 135.65 708.95 P +3.39 (this limitation by acting on the decision variables themselves. Like uniform) 135.65 694.95 P +-0.23 (crossover) 135.65 680.95 P +-0.23 (, the real-valued operators may also be parameterised to provide a control) 181.13 680.95 P +4.94 (over the level of disruption introduced into of) 135.65 666.95 P +4.94 (fspring. For discrete-valued) 388.87 666.95 P +-0.07 (representations, variations on the recombination operators may be used that ensure) 135.65 652.95 P +(that only valid values are produced as a result of crossover [22].) 135.65 638.95 T +1.04 (The GA T) 135.65 612.95 P +1.04 (oolbox provides a number of crossover routines incorporating most of) 186.18 612.95 P +0.24 (the methods described above. Single-point, double-point and shuf) 135.65 598.95 P +0.24 (\337e crossover are) 452.58 598.95 P +0.73 (implemented in the T) 135.65 584.95 P +0.73 (oolbox functions) 239.92 584.95 P +3 F +1.74 (xovsp) 325.33 584.95 P +2 F +0.73 (,) 361.31 584.95 P +3 F +1.74 (xovdp) 368.03 584.95 P +2 F +0.73 ( and) 404.01 584.95 P +3 F +1.74 (xovsh) 428.77 584.95 P +2 F +0.73 (, respectively) 464.76 584.95 P +0.73 (,) 528.65 584.95 P +0.56 (and can operate on any chromosome representation. Reduced surrogate crossover) 135.65 570.95 P +3.17 (is supported with both single-point,) 135.65 556.95 P +3 F +7.62 (xovsprs) 324.77 556.95 P +2 F +3.17 (, and double-point,) 375.14 556.95 P +3 F +7.62 (xovdprs) 478.28 556.95 P +2 F +3.17 (,) 528.65 556.95 P +2.17 (crossover and with shuf) 135.65 542.95 P +2.17 (\337e crossover) 256.2 542.95 P +2.17 (,) 318.85 542.95 P +3 F +5.22 (xovshrs) 327.02 542.95 P +2 F +2.17 (. A further general multi-point) 377.39 542.95 P +1.09 (crossover routine,) 135.65 528.95 P +3 F +2.61 (xovmp) 226.75 528.95 P +2 F +1.09 (, is also provided. T) 262.73 528.95 P +1.09 (o support real-valued chromosome) 361.51 528.95 P +1.62 (representations, discrete, intermediate and line recombination operators are also) 135.65 514.95 P +1.57 (included. The discrete recombination operator) 135.65 500.95 P +1.57 (,) 362.95 500.95 P +3 F +3.77 (recdis) 370.52 500.95 P +2 F +1.57 (, performs crossover on) 413.69 500.95 P +1.86 (real-valued individuals in a similar manner to the uniform crossover operators.) 135.65 486.95 P +0.37 (Line and intermediate recombination are supported by the functions) 135.65 472.95 P +3 F +0.9 (reclin) 467.78 472.95 P +2 F +0.37 ( and) 510.96 472.95 P +3 F +0.26 (recint) 135.65 458.95 P +2 F +0.11 ( respectively) 178.82 458.95 P +0.11 (. A high-level entry function to all of the crossover operators) 239.1 458.95 P +(is provided by the function) 135.65 444.95 T +3 F +(recombin) 267.9 444.95 T +2 F +(.) 325.47 444.95 T +1 16 Q +(Mutation) 135.65 416.29 T +2 12 Q +1.09 (In natural evolution, mutation is a random process where one allele of a gene is) 135.65 388.95 P +2.75 (replaced by another to produce a new genetic structure. In GAs, mutation is) 135.65 374.95 P +0.53 (randomly applied with low probability) 135.65 360.95 P +0.53 (, typically in the range 0.001 and 0.01, and) 322.21 360.95 P +3.36 (modi\336es elements in the chromosomes. Usually considered as a background) 135.65 346.95 P +2.57 (operator) 135.65 332.95 P +2.57 (, the role of mutation is often seen as providing a guarantee that the) 175.13 332.95 P +0.45 (probability of searching any given string will never be zero and acting as a safety) 135.65 318.95 P +3.12 (net to recover good genetic material that may be lost through the action of) 135.65 304.95 P +(selection and crossover [1].) 135.65 290.95 T +2.61 (The ef) 135.65 264.95 P +2.61 (fect of mutation on a binary string is illustrated in Fig. 6 for a 10-bit) 169.01 264.95 P +0.05 (chromosome representing a real value decoded over the interval [0, 10] using both) 135.65 250.95 P +1.59 (standard and Gray coding and a mutation point of 3 in the binary string. Here,) 135.65 236.95 P +1.41 (binary mutation \337ips the value of the bit at the loci selected to be the mutation) 135.65 222.95 P +-0.23 (point. Given that mutation is generally applied uniformly to an entire population of) 135.65 208.95 P +FMENDPAGE +%%EndPage: "16" 17 +%%Page: "17" 17 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-17) 513.33 61.29 T +2 12 Q +0.82 (strings, it is possible that a given binary string may be mutated at more than one) 135.65 736.95 P +(point.) 135.65 722.95 T +2.23 (W) 135.65 580.82 P +2.23 (ith non-binary representations, mutation is achieved by either perturbing the) 146.49 580.82 P +0.87 (gene values or random selection of new values within the allowed range. W) 135.65 566.82 P +0.87 (right) 508.99 566.82 P +-0 ([8] and Janikow and Michalewicz [23] demonstrate how real-coded GAs may take) 135.65 552.82 P +0.21 (advantage of higher mutation rates than binary-coded GAs, increasing the level of) 135.65 538.82 P +5.94 (possible exploration of the search space without adversely af) 135.65 524.82 P +5.94 (fecting the) 474.74 524.82 P +1.62 (conver) 135.65 510.82 P +1.62 (gence characteristics. Indeed, T) 168.07 510.82 P +1.62 (ate and Smith [24] ar) 323.63 510.82 P +1.62 (gue that for codings) 431.17 510.82 P +-0.22 (more complex than binary) 135.65 496.82 P +-0.22 (, high mutation rates can be both desirable and necessary) 260.46 496.82 P +0.57 (and show how) 135.65 482.82 P +0.57 (, for a complex combinatorial optimization problem, high mutation) 205.29 482.82 P +0.62 (rates and non-binary coding yielded signi\336cantly better solutions than the normal) 135.65 468.82 P +(approach.) 135.65 454.82 T +2.89 (Many variations on the mutation operator have been proposed. For example,) 135.65 428.82 P +0.6 (biasing the mutation towards individuals with lower \336tness values to increase the) 135.65 414.82 P +-0.25 (exploration in the search without losing information from the \336tter individuals [25]) 135.65 400.82 P +2.48 (or parameterising the mutation such that the mutation rate decreases with the) 135.65 386.82 P +0.13 (population conver) 135.65 372.82 P +0.13 (gence [26]. M\237hlenbein [21] has introduced a mutation operator) 222.5 372.82 P +0.5 (for the real-coded GA that uses a non-linear term for the distribution of the range) 135.65 358.82 P +0.38 (of mutation applied to gene values. It is claimed that by biasing mutation towards) 135.65 344.82 P +3.96 (smaller changes in gene values, mutation can be used in conjunction with) 135.65 330.82 P +0.7 (recombination as a foreground search process. Other mutation operations include) 135.65 316.82 P +2.66 (that of) 135.65 302.82 P +0 F +2.66 (trade mutation) 174.94 302.82 P +2 F +2.66 ( [7], whereby the contribution of individual genes in a) 248.57 302.82 P +3.95 (chromosome is used to direct mutation towards weaker terms, and) 135.65 288.82 P +0 F +3.95 (r) 495.89 288.82 P +3.95 (eor) 500.12 288.82 P +3.95 (der) 515.66 288.82 P +0.71 (mutation) 135.65 274.82 P +2 F +0.71 ( [7], that swaps the positions of bits or genes to increase diversity in the) 178.3 274.82 P +(decision variable space.) 135.65 260.82 T +1.82 (Binary and integer mutation are provided in the T) 135.65 234.82 P +1.82 (oolbox by the function) 387.85 234.82 P +3 F +4.36 (mut) 507.06 234.82 P +2 F +1.82 (.) 528.65 234.82 P +0.54 (Real-valued mutation is available using the function) 135.65 220.82 P +3 F +1.29 (mutbga) 392.92 220.82 P +2 F +0.54 (. A high-level entry) 436.1 220.82 P +(function to the mutation operators is provided by the function) 135.65 206.82 T +3 F +(mutate) 434.13 206.82 T +2 F +(.) 477.3 206.82 T +63.65 96.95 531.65 744.95 C +133.42 602.82 531.65 718.95 C +5 12 Q +0 X +0 K +(Figure 6: Binary Mutation) 266.07 625.61 T +141.21 613.74 523.89 708.01 R +0.5 H +2 Z +N +2 F +( Original string -) 170.1 671.56 T +( Mutated string -) 170.1 653.69 T +(binary) 413.58 689.43 T +(Gray) 466.52 689.43 T +3 F +(0 0 0 1 1 0 0 0 1 0) 255.14 671.91 T +(0 0 1 1 1 0 0 0 1 0) 255.14 654.04 T +2 F +(0.9659) 412.41 671.56 T +(2.2146) 412.41 653.69 T +(0.6634) 462.02 671.56 T +(1.8439) 462.02 653.69 T +281.81 650.83 291.75 681.92 R +8 X +N +0 X +(mutation point) 172.34 690.39 T +279.39 694.94 285.77 684.78 274.98 690.02 277.19 692.48 4 Y +V +248.93 693.96 275.26 694.21 277.19 692.48 3 L +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "17" 18 +%%Page: "18" 18 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-18) 513.33 61.29 T +1 16 Q +(Reinsertion) 135.65 734.29 T +2 12 Q +2.42 (Once a new population has been produced by selection and recombination of) 135.65 706.95 P +2.66 (individuals from the old population, the \336tness of the individuals in the new) 135.65 692.95 P +7.66 (population may be determined. If fewer individuals are produced by) 135.65 678.95 P +4.52 (recombination than the size of the original population, then the fractional) 135.65 664.95 P +1.26 (dif) 135.65 650.95 P +1.26 (ference between the new and old population sizes is termed a generation gap) 148.76 650.95 P +-0.08 ([27]. In the case where the number of new individuals produced at each generation) 135.65 636.95 P +0.43 (is one or two, the GA is said to be steady-state [28] or incremental [29]. If one or) 135.65 622.95 P +0.6 (more of the most \336t individuals is deterministically allowed to propagate through) 135.65 608.95 P +(successive generations then the GA is said to use an) 135.65 594.95 T +0 F +(elitist strategy) 388.13 594.95 T +2 F +(.) 455.66 594.95 T +1.67 (T) 135.65 568.95 P +1.67 (o maintain the size of the original population, the new individuals have to be) 142.14 568.95 P +-0.07 (reinserted into the old population. Similarly) 135.65 554.95 P +-0.07 (, if not all the new individuals are to be) 344.4 554.95 P +0.46 (used at each generation or if more of) 135.65 540.95 P +0.46 (fspring are generated than the size of the old) 314.82 540.95 P +0.17 (population then a reinsertion scheme must be used to determine which individuals) 135.65 526.95 P +2.22 (are to exist in the new population. An important feature of not creating more) 135.65 512.95 P +5.28 (of) 135.65 498.95 P +5.28 (fspring than the current population size at each generation is that the) 145.42 498.95 P +1.12 (generational computational time is reduced, most dramatically in the case of the) 135.65 484.95 P +2.39 (steady-state GA, and that the memory requirements are smaller as fewer new) 135.65 470.95 P +(individuals need to be stored while of) 135.65 456.95 T +(fspring are produced.) 315.98 456.95 T +0.19 (When selecting which members of the old population should be replaced the most) 135.65 430.95 P +0.23 (apparent strategy is to replace the least \336t members deterministically) 135.65 416.95 P +0.23 (. However) 466.39 416.95 P +0.23 (, in) 516.09 416.95 P +2.7 (studies, Fogarty [30] has shown that no signi\336cant dif) 135.65 402.95 P +2.7 (ference in conver) 415.24 402.95 P +2.7 (gence) 503.68 402.95 P +2.15 (characteristics was found when the individuals selected for replacement where) 135.65 388.95 P +0.69 (chosen with inverse proportional selection or deterministically as the least \336t. He) 135.65 374.95 P +0.01 (further asserts that replacing the least \336t members ef) 135.65 360.95 P +0.01 (fectively implements an elitist) 386.69 360.95 P +5.91 (strategy as the most \336t will probabilistically survive through successive) 135.65 346.95 P +-0.23 (generations. Indeed, the most successful replacement scheme was one that selected) 135.65 332.95 P +-0.23 (the oldest members of a population for replacement. This is reported as being more) 135.65 318.95 P +0.03 (in keeping with generational reproduction as every member of the population will,) 135.65 304.95 P +4.87 (at some time, be replaced. Thus, for an individual to survive successive) 135.65 290.95 P +5.74 (generations, it must be suf) 135.65 276.95 P +5.74 (\336ciently \336t to ensure propagation into future) 284.66 276.95 P +(generations.) 135.65 262.95 T +-0.23 (The GA T) 135.65 236.95 P +-0.23 (oolbox provides a function for reinserting individuals into the population) 183.63 236.95 P +1.89 (after recombination,) 135.65 222.95 P +3 F +4.55 (reins) 239.69 222.95 P +2 F +1.89 (. Optional input parameters allow the use of either) 275.67 222.95 P +0.3 (uniform random or \336tness-based reinsertion. Additionally) 135.65 208.95 P +0.3 (, this routine can also be) 413.54 208.95 P +(selected to reinsert fewer of) 135.65 194.95 T +(fspring than those produced at recombination.) 268.64 194.95 T +1 16 Q +(T) 135.65 166.29 T +(ermination of the GA) 144.84 166.29 T +2 12 Q +1.32 (Because the GA is a stochastic search method, it is dif) 135.65 138.95 P +1.32 (\336cult to formally specify) 408.77 138.95 P +-0.06 (conver) 135.65 124.95 P +-0.06 (gence criteria. As the \336tness of a population may remain static for a number) 168.07 124.95 P +5.99 (of generations before a superior individual is found, the application of) 135.65 110.95 P +FMENDPAGE +%%EndPage: "18" 19 +%%Page: "19" 19 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-19) 513.33 61.29 T +2 12 Q +1.07 (conventional termination criteria becomes problematic. A common practice is to) 135.65 736.95 P +2.19 (terminate the GA after a prespeci\336ed number of generations and then test the) 135.65 722.95 P +0.17 (quality of the best members of the population against the problem de\336nition. If no) 135.65 708.95 P +-0.22 (acceptable solutions are found, the GA may be restarted or a fresh search initiated.) 135.65 694.95 P +FMENDPAGE +%%EndPage: "19" 20 +%%Page: "20" 20 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-20) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Data Structur) 63.65 732.95 T +(es) 170.74 732.95 T +2 12 Q +1.25 (M) 135.65 694.95 P +2 10 Q +1.04 (A) 146.31 694.95 P +1.04 (TLAB) 152.42 694.95 P +2 12 Q +1.25 ( essentially supports only one data type, a rectangular matrix of real or) 178.51 694.95 P +1.93 (complex numeric elements. The main data structures in the Genetic Algorithm) 135.65 680.95 P +(toolbox are:) 135.65 666.95 T +(\245) 157.25 640.95 T +(chromosomes) 171.65 640.95 T +(\245) 157.25 620.95 T +(phenotypes) 171.65 620.95 T +(\245) 157.25 600.95 T +(objective function values) 171.65 600.95 T +(\245) 157.25 580.95 T +(\336tness values) 171.65 580.95 T +(These data structures are discussed in the following subsections.) 135.65 560.95 T +1 16 Q +(Chr) 135.65 532.29 T +(omosomes) 162.9 532.29 T +2 12 Q +1.24 (The chromosome data structure stores an entire population in a single matrix of) 135.65 504.95 P +1.17 (size) 135.65 490.95 P +3 F +2.81 (Nind) 158.47 490.95 P +4 F +1.17 (\264) 191.42 490.95 P +3 F +2.81 (Lind) 202.18 490.95 P +2 F +1.17 (, where) 230.96 490.95 P +3 F +2.81 (Nind) 271.6 490.95 P +2 F +1.17 ( is the number of individuals in the population) 300.39 490.95 P +0.48 (and) 135.65 476.95 P +3 F +1.16 (Lind) 156.45 476.95 P +2 F +0.48 ( is the length of the genotypic representation of those individuals. Each) 185.23 476.95 P +-0.26 (row corresponds to an individual\325) 135.65 462.95 P +-0.26 (s genotype, consisting of base-) 295.83 462.95 P +0 F +-0.26 (n) 442.34 462.95 P +2 F +-0.26 (, typically binary) 448.34 462.95 P +-0.26 (,) 528.65 462.95 P +(values.) 135.65 448.95 T +(An example of the chromosome data structure is shown below) 135.65 422.95 T +(.) 434.32 422.95 T +1 (This data representation does not force a structure on the chromosome structure,) 135.65 262.48 P +4.56 (only requiring that all chromosomes are of equal length. Thus, structured) 135.65 248.48 P +2.9 (populations or populations with varying genotypic bases may be used in the) 135.65 234.48 P +1.08 (Genetic Algorithm T) 135.65 220.48 P +1.08 (oolbox provided that a suitable decoding function, mapping) 237.58 220.48 P +0.48 (chromosomes onto phenotypes, is employed. The role of the decoding function is) 135.65 206.48 P +(described below) 135.65 192.48 T +(.) 213.14 192.48 T +1 16 Q +(Phenotypes) 135.65 163.81 T +2 12 Q +1.57 (The decision variables, or phenotypes, in the genetic algorithm are obtained by) 135.65 136.48 P +2.06 (applying some mapping from the chromosome representation into the decision) 135.65 122.48 P +0.9 (variable space. Here, each string contained in the chromosome structure decodes) 135.65 108.48 P +154.05 284.48 513.25 404.95 C +3 12 Q +0 X +0 K +(C) 155.05 341.98 T +(h) 162.95 341.98 T +(r) 170.85 341.98 T +(o) 178.76 341.98 T +(m) 186.66 341.98 T +0 F +(g) 224.47 376.28 T +2 9 Q +(1) 230.93 372.52 T +(1) 239.92 372.52 T +4 F +(,) 235.43 372.52 T +0 12 Q +(g) 263.48 376.28 T +2 9 Q +(1) 269.94 372.52 T +(2) 278.93 372.52 T +4 F +(,) 274.44 372.52 T +0 12 Q +(g) 304.29 376.28 T +2 9 Q +(1) 310.75 372.52 T +(3) 319.74 372.52 T +4 F +(,) 315.25 372.52 T +4 12 Q +(\274) 337.57 376.28 T +0 F +(g) 362.89 376.28 T +2 9 Q +(1) 369.35 372.52 T +3 F +(L) 378.34 372.52 T +(i) 384.27 372.52 T +(n) 390.19 372.52 T +(d) 396.11 372.52 T +4 F +(,) 373.85 372.52 T +0 12 Q +(g) 224.47 358.37 T +2 9 Q +(2) 230.93 354.6 T +(1) 239.92 354.6 T +4 F +(,) 235.43 354.6 T +0 12 Q +(g) 263.48 358.37 T +2 9 Q +(2) 269.94 354.6 T +(2) 278.93 354.6 T +4 F +(,) 274.44 354.6 T +0 12 Q +(g) 304.29 358.37 T +2 9 Q +(2) 310.75 354.6 T +(3) 319.74 354.6 T +4 F +(,) 315.25 354.6 T +4 12 Q +(\274) 337.57 358.37 T +0 F +(g) 362.89 358.37 T +2 9 Q +(2) 369.35 354.6 T +3 F +(L) 378.34 354.6 T +(i) 384.27 354.6 T +(n) 390.19 354.6 T +(d) 396.11 354.6 T +4 F +(,) 373.85 354.6 T +0 12 Q +(g) 224.47 340.45 T +2 9 Q +(3) 230.93 336.69 T +(1) 239.92 336.69 T +4 F +(,) 235.43 336.69 T +0 12 Q +(g) 263.48 340.45 T +2 9 Q +(3) 269.94 336.69 T +(2) 278.93 336.69 T +4 F +(,) 274.44 336.69 T +0 12 Q +(g) 304.29 340.45 T +2 9 Q +(3) 310.75 336.69 T +(3) 319.74 336.69 T +4 F +(,) 315.25 336.69 T +4 12 Q +(\274) 337.57 340.45 T +0 F +(g) 362.89 340.45 T +2 9 Q +(3) 369.35 336.69 T +3 F +(L) 378.34 336.69 T +(i) 384.27 336.69 T +(n) 390.19 336.69 T +(d) 396.11 336.69 T +4 F +(,) 373.85 336.69 T +2 12 Q +(.) 232.45 322.56 T +(.) 271.46 322.56 T +(.) 312.27 322.56 T +4 F +(\274) 337.57 322.56 T +2 F +(.) 380.2 322.56 T +0 F +(g) 216.94 306.36 T +2 9 Q +(N) 223.4 302.6 T +(i) 230.41 302.6 T +(n) 233.44 302.6 T +(d) 238.47 302.6 T +(1) 247.46 302.6 T +4 F +(,) 242.96 302.6 T +0 12 Q +(g) 255.95 306.36 T +2 9 Q +(N) 262.41 302.6 T +(i) 269.43 302.6 T +(n) 272.45 302.6 T +(d) 277.48 302.6 T +(2) 286.47 302.6 T +4 F +(,) 281.97 302.6 T +0 12 Q +(g) 294.96 306.36 T +3 9 Q +(N) 301.42 302.6 T +(i) 307.34 302.6 T +(n) 313.26 302.6 T +(d) 319.19 302.6 T +2 F +(3) 329.08 302.6 T +4 F +(,) 324.58 302.6 T +4 12 Q +(\274) 337.57 306.36 T +0 F +(g) 353.56 306.36 T +3 9 Q +(N) 360.02 302.74 T +(i) 365.94 302.74 T +(n) 371.86 302.74 T +(d) 377.79 302.74 T +(L) 387.67 302.74 T +(i) 393.6 302.74 T +(n) 399.52 302.74 T +(d) 405.44 302.74 T +4 F +(,) 383.18 302.74 T +2 12 Q +(i) 432.35 376.89 T +(n) 435.68 376.89 T +(d) 441.68 376.89 T +(i) 447.67 376.89 T +(v) 451.01 376.89 T +(i) 457 376.89 T +(d) 460.34 376.89 T +(u) 466.33 376.89 T +(a) 472.33 376.89 T +(l) 477.66 376.89 T +(\021) 480.99 376.89 T +(1) 483.99 376.89 T +(i) 432.35 359.09 T +(n) 435.68 359.09 T +(d) 441.68 359.09 T +(i) 447.67 359.09 T +(v) 451.01 359.09 T +(i) 457 359.09 T +(d) 460.34 359.09 T +(u) 466.33 359.09 T +(a) 472.33 359.09 T +(l) 477.66 359.09 T +(\021) 480.99 359.09 T +(2) 483.99 359.09 T +(i) 432.35 341.29 T +(n) 435.68 341.29 T +(d) 441.68 341.29 T +(i) 447.67 341.29 T +(v) 451.01 341.29 T +(i) 457 341.29 T +(d) 460.34 341.29 T +(u) 466.33 341.29 T +(a) 472.33 341.29 T +(l) 477.66 341.29 T +(\021) 480.99 341.29 T +(3) 483.99 341.29 T +(.) 459.67 323.49 T +(i) 419.54 305.69 T +(n) 422.87 305.69 T +(d) 428.87 305.69 T +(i) 434.87 305.69 T +(v) 438.2 305.69 T +(i) 444.2 305.69 T +(d) 447.53 305.69 T +(u) 453.53 305.69 T +(a) 459.52 305.69 T +(l) 464.85 305.69 T +(\021) 468.18 305.69 T +3 F +(N) 472.89 305.69 T +(i) 480.79 305.69 T +(n) 488.69 305.69 T +(d) 496.6 305.69 T +4 F +(=) 199.85 341.98 T +218.44 300.65 214.44 300.65 2 L +0.33 H +0 Z +N +214.44 300.65 214.44 388.49 2 L +N +214.44 388.49 218.44 388.49 2 L +N +408.33 300.65 412.33 300.65 2 L +N +412.33 300.65 412.33 388.49 2 L +N +412.33 388.49 408.33 388.49 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "20" 21 +%%Page: "21" 21 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-21) 513.33 61.29 T +2 12 Q +1.97 (to a row vector of order) 135.65 736.95 P +3 F +4.73 (Nvar) 264.05 736.95 P +2 F +1.97 (, according to the number of dimensions in the) 292.35 736.95 P +(search space and corresponding to the decision variable vector value.) 135.65 722.95 T +1.7 (The decision variables are stored in a numerical matrix of size) 135.65 696.95 P +3 F +4.08 (Nind) 455.76 696.95 P +4 F +1.7 (\264) 489.24 696.95 P +3 F +4.08 (Nvar) 500.52 696.95 P +2 F +1.7 (.) 528.65 696.95 P +0.96 (Again, each row corresponds to a particular individual\325) 135.65 682.95 P +0.96 (s phenotype. An example) 406.85 682.95 P +-0.11 (of the phenotype data structure is given below) 135.65 668.95 P +-0.11 (, where) 355.59 668.95 P +3 F +-0.27 (DECODE) 393.66 668.95 P +2 F +-0.11 ( is used to represent) 436.83 668.95 P +0.25 (an arbitrary function, possibly from the GA T) 135.65 654.95 P +0.25 (oolbox, mapping the genotypes onto) 355.74 654.95 P +(the phenotypes.) 135.65 640.95 T +0.29 (The actual mapping between the chromosome representation and their phenotypic) 135.65 456.66 P +0.39 (values depends upon the) 135.65 442.66 P +3 F +0.94 (DECODE) 257.8 442.66 P +2 F +0.39 ( function used. It is perfectly feasible using this) 300.98 442.66 P +4.22 (representation to have vectors of decision variables of dif) 135.65 428.66 P +4.22 (ferent types. For) 444.28 428.66 P +2.81 (example, it is possible to mix integer) 135.65 414.66 P +2.81 (, real-valued and alphanumeric decision) 328.91 414.66 P +(variables in the same) 135.65 400.66 T +3 F +(Phen) 239.57 400.66 T +2 F +( data structure.) 268.36 400.66 T +1 16 Q +(Objective function values) 135.65 372 T +2 12 Q +0.05 (An objective function is used to evaluate the performance of the phenotypes in the) 135.65 344.66 P +3.4 (problem domain. Objective function values can be scalar or) 135.65 330.66 P +3.4 (, in the case of) 448.45 330.66 P +2.36 (multiobjective problems, vectorial. Note that objective function values are not) 135.65 316.66 P +(necessarily the same as the \336tness values.) 135.65 302.66 T +0.47 (Objective function values are stored in a numerical matrix of size) 135.65 276.66 P +3 F +1.12 (Nind) 457.56 276.66 P +4 F +0.47 (\264) 489.81 276.66 P +3 F +1.12 (Nobj) 499.86 276.66 P +2 F +0.47 (,) 528.65 276.66 P +1.65 (where) 135.65 262.66 P +3 F +3.96 (Nobj) 169.6 262.66 P +2 F +1.65 ( is the number of objectives. Each row corresponds to a particular) 198.38 262.66 P +1.86 (individual\325) 135.65 248.66 P +1.86 (s objective vector) 187.63 248.66 P +1.86 (. An example of the objective function values data) 275.29 248.66 P +3.98 (structure is shown below) 135.65 234.66 P +3.98 (, with) 266.4 234.66 P +3 F +9.56 (OBJFUN) 304.68 234.66 P +2 F +3.98 ( representing an arbitrary objective) 347.86 234.66 P +(function.) 135.65 220.66 T +144.97 478.66 522.32 622.95 C +3 12 Q +0 X +0 K +(P) 146.97 613.96 T +(h) 153.87 613.96 T +(e) 161.78 613.96 T +(n) 169.68 613.96 T +(D) 195.46 613.96 T +(E) 203.36 613.96 T +(C) 211.26 613.96 T +(O) 219.16 613.96 T +(D) 227.07 613.96 T +(E) 234.97 613.96 T +(C) 249.97 613.96 T +(h) 257.87 613.96 T +(r) 265.77 613.96 T +(o) 273.68 613.96 T +(m) 281.58 613.96 T +4 F +(\050) 244.87 613.96 T +(\051) 289.38 613.96 T +3 F +(%) 309.08 613.96 T +(\021) 316.28 613.96 T +(M) 323.47 613.96 T +(a) 330.67 613.96 T +(p) 337.86 613.96 T +(\021) 345.06 613.96 T +(G) 352.26 613.96 T +(e) 359.45 613.96 T +(n) 366.65 613.96 T +(o) 373.85 613.96 T +(t) 381.04 613.96 T +(y) 388.24 613.96 T +(p) 395.43 613.96 T +(e) 402.63 613.96 T +(\021) 409.83 613.96 T +(t) 417.02 613.96 T +(o) 424.22 613.96 T +(\021) 431.41 613.96 T +(P) 438.61 613.96 T +(h) 445.81 613.96 T +(e) 453 613.96 T +(n) 460.2 613.96 T +(o) 467.39 613.96 T +(t) 474.59 613.96 T +(y) 481.79 613.96 T +(p) 488.98 613.96 T +(e) 496.18 613.96 T +4 F +(=) 182.87 613.96 T +0 F +(x) 207.38 568.27 T +2 9 Q +(1) 213.17 564.51 T +(1) 222.16 564.51 T +4 F +(,) 217.67 564.51 T +0 12 Q +(x) 249.32 568.27 T +2 9 Q +(1) 255.11 564.51 T +(2) 264.1 564.51 T +4 F +(,) 259.6 564.51 T +0 12 Q +(x) 291.26 568.27 T +2 9 Q +(1) 297.04 564.51 T +(3) 306.03 564.51 T +4 F +(,) 301.54 564.51 T +4 12 Q +(\274) 323.86 568.27 T +0 F +(x) 349.18 568.27 T +2 9 Q +(1) 354.97 564.51 T +3 F +(N) 363.96 564.51 T +(v) 369.88 564.51 T +(a) 375.8 564.51 T +(r) 381.73 564.51 T +4 F +(,) 359.46 564.51 T +0 12 Q +(x) 207.38 550.35 T +2 9 Q +(2) 213.17 546.59 T +(1) 222.16 546.59 T +4 F +(,) 217.67 546.59 T +0 12 Q +(x) 249.32 550.35 T +2 9 Q +(2) 255.11 546.59 T +(2) 264.1 546.59 T +4 F +(,) 259.6 546.59 T +0 12 Q +(x) 291.26 550.35 T +2 9 Q +(2) 297.04 546.59 T +(3) 306.03 546.59 T +4 F +(,) 301.54 546.59 T +4 12 Q +(\274) 323.86 550.35 T +0 F +(x) 349.18 550.35 T +2 9 Q +(2) 354.97 546.59 T +3 F +(N) 363.96 546.59 T +(v) 369.88 546.59 T +(a) 375.8 546.59 T +(r) 381.73 546.59 T +4 F +(,) 359.46 546.59 T +0 12 Q +(x) 207.38 532.44 T +2 9 Q +(3) 213.17 528.68 T +(1) 222.16 528.68 T +4 F +(,) 217.67 528.68 T +0 12 Q +(x) 249.32 532.44 T +2 9 Q +(3) 255.11 528.68 T +(2) 264.1 528.68 T +4 F +(,) 259.6 528.68 T +0 12 Q +(x) 291.26 532.44 T +2 9 Q +(3) 297.04 528.68 T +(3) 306.03 528.68 T +4 F +(,) 301.54 528.68 T +4 12 Q +(\274) 323.86 532.44 T +0 F +(x) 349.18 532.44 T +2 9 Q +(3) 354.97 528.68 T +3 F +(N) 363.96 528.68 T +(v) 369.88 528.68 T +(a) 375.8 528.68 T +(r) 381.73 528.68 T +4 F +(,) 359.46 528.68 T +2 12 Q +(.) 215.02 514.55 T +(.) 256.96 514.55 T +(.) 298.89 514.55 T +4 F +(\274) 323.86 514.55 T +2 F +(.) 366.15 514.55 T +0 F +(x) 198.05 498.35 T +3 9 Q +(N) 203.84 494.59 T +(i) 209.76 494.59 T +(n) 215.68 494.59 T +(d) 221.6 494.59 T +2 F +(1) 231.49 494.59 T +4 F +(,) 227 494.59 T +0 12 Q +(x) 239.99 498.35 T +3 9 Q +(N) 245.77 494.59 T +(i) 251.7 494.59 T +(n) 257.62 494.59 T +(d) 263.54 494.59 T +2 F +(2) 273.43 494.59 T +4 F +(,) 268.93 494.59 T +0 12 Q +(x) 281.92 498.35 T +3 9 Q +(N) 287.71 494.59 T +(i) 293.63 494.59 T +(n) 299.55 494.59 T +(d) 305.48 494.59 T +2 F +(3) 315.36 494.59 T +4 F +(,) 310.87 494.59 T +4 12 Q +(\274) 323.86 498.35 T +0 F +(x) 339.85 498.35 T +3 9 Q +(N) 345.64 494.73 T +(i) 351.56 494.73 T +(n) 357.48 494.73 T +(d) 363.4 494.73 T +(N) 373.29 494.73 T +(v) 379.21 494.73 T +(a) 385.14 494.73 T +(r) 391.06 494.73 T +4 F +(,) 368.8 494.73 T +2 12 Q +(i) 417.96 568.88 T +(n) 421.3 568.88 T +(d) 427.29 568.88 T +(i) 433.29 568.88 T +(v) 436.62 568.88 T +(i) 442.62 568.88 T +(d) 445.96 568.88 T +(u) 451.95 568.88 T +(a) 457.95 568.88 T +(l) 463.27 568.88 T +(\021) 466.61 568.88 T +(1) 469.61 568.88 T +(i) 417.96 551.08 T +(n) 421.3 551.08 T +(d) 427.29 551.08 T +(i) 433.29 551.08 T +(v) 436.62 551.08 T +(i) 442.62 551.08 T +(d) 445.96 551.08 T +(u) 451.95 551.08 T +(a) 457.95 551.08 T +(l) 463.27 551.08 T +(\021) 466.61 551.08 T +(2) 469.61 551.08 T +(i) 417.96 533.28 T +(n) 421.3 533.28 T +(d) 427.29 533.28 T +(i) 433.29 533.28 T +(v) 436.62 533.28 T +(i) 442.62 533.28 T +(d) 445.96 533.28 T +(u) 451.95 533.28 T +(a) 457.95 533.28 T +(l) 463.27 533.28 T +(\021) 466.61 533.28 T +(3) 469.61 533.28 T +(.) 445.28 515.48 T +(i) 405.16 497.68 T +(n) 408.49 497.68 T +(d) 414.49 497.68 T +(i) 420.48 497.68 T +(v) 423.82 497.68 T +(i) 429.82 497.68 T +(d) 433.15 497.68 T +(u) 439.15 497.68 T +(a) 445.14 497.68 T +(l) 450.47 497.68 T +(\021) 453.8 497.68 T +3 F +(N) 458.51 497.68 T +(i) 466.41 497.68 T +(n) 474.31 497.68 T +(d) 482.21 497.68 T +4 F +(=) 180.97 533.96 T +199.55 492.64 195.55 492.64 2 L +0.33 H +0 Z +N +195.55 492.64 195.55 580.48 2 L +N +195.55 580.48 199.55 580.48 2 L +N +393.95 492.64 397.95 492.64 2 L +N +397.95 492.64 397.95 580.48 2 L +N +397.95 580.48 393.95 580.48 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "21" 22 +%%Page: "22" 22 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-22) 513.33 61.29 T +1 16 Q +(Fitness values) 135.65 577.51 T +2 12 Q +2.12 (Fitness values are derived from objective function values through a scaling or) 135.65 550.18 P +2.59 (ranking function. Fitnesses are non-negative scalars and are stored in column) 135.65 536.18 P +0.07 (vectors of length) 135.65 522.18 P +3 F +0.17 (Nind) 219.46 522.18 P +2 F +0.07 (, an example of which is shown below) 248.25 522.18 P +0.07 (. Again, FITNESS is) 431.82 522.18 P +(an arbitrary \336tness function.) 135.65 508.18 T +1.6 (Note that for multiobjective functions, the \336tness of a particular individual is a) 135.65 335.63 P +2.33 (function of a vector of objective function values. Multiobjective problems are) 135.65 321.62 P +2.49 (characterised by having no single unique solution, but a family of equally \336t) 135.65 307.62 P +2.42 (solutions with dif) 135.65 293.62 P +2.42 (ferent values of decision variables. Care should therefore be) 224.23 293.62 P +0.26 (taken to adopt some mechanism to ensure that the population is able to evolve the) 135.65 279.62 P +1.35 (set of Pareto optimal solutions, for example by using \336tness sharing [31] in the) 135.65 265.62 P +-0.04 (selection method. Although not supported in this version of the Genetic Algorithm) 135.65 251.62 P +1.73 (T) 135.65 237.62 P +1.73 (oolbox, it is planned that multiobjective search will be implemented in future) 142.14 237.62 P +(versions.) 135.65 223.62 T +152.42 602.18 514.87 744.95 C +3 12 Q +0 X +0 K +(O) 162.01 735.96 T +(b) 169.91 735.96 T +(j) 177.82 735.96 T +(V) 185.72 735.96 T +(O) 211.5 735.96 T +(B) 219.4 735.96 T +(J) 227.3 735.96 T +(F) 235.2 735.96 T +(U) 243.1 735.96 T +(N) 251.01 735.96 T +(P) 266.01 735.96 T +(h) 273.91 735.96 T +(e) 281.81 735.96 T +(n) 289.72 735.96 T +4 F +(\050) 260.91 735.96 T +(\051) 297.52 735.96 T +3 F +(%) 317.22 735.96 T +(\021) 324.42 735.96 T +(O) 331.61 735.96 T +(b) 338.81 735.96 T +(j) 346 735.96 T +(e) 353.2 735.96 T +(c) 360.39 735.96 T +(t) 367.59 735.96 T +(i) 374.79 735.96 T +(v) 381.98 735.96 T +(e) 389.18 735.96 T +(\021) 396.38 735.96 T +(F) 403.57 735.96 T +(u) 410.77 735.96 T +(n) 417.96 735.96 T +(c) 425.16 735.96 T +(t) 432.36 735.96 T +(i) 439.55 735.96 T +(o) 446.75 735.96 T +(n) 453.94 735.96 T +4 F +(=) 198.91 735.96 T +0 F +(y) 223.43 690.27 T +2 9 Q +(1) 229.21 686.51 T +(1) 238.2 686.51 T +4 F +(,) 233.71 686.51 T +0 12 Q +(y) 265.36 690.27 T +2 9 Q +(1) 271.15 686.51 T +(2) 280.14 686.51 T +4 F +(,) 275.64 686.51 T +0 12 Q +(y) 307.3 690.27 T +2 9 Q +(1) 313.08 686.51 T +(3) 322.07 686.51 T +4 F +(,) 317.58 686.51 T +4 12 Q +(\274) 339.9 690.27 T +0 F +(y) 365.22 690.27 T +2 9 Q +(1) 371.01 686.51 T +3 F +(N) 380 686.51 T +(v) 385.92 686.51 T +(a) 391.85 686.51 T +(r) 397.77 686.51 T +4 F +(,) 375.5 686.51 T +0 12 Q +(y) 223.43 672.36 T +2 9 Q +(2) 229.21 668.59 T +(1) 238.2 668.59 T +4 F +(,) 233.71 668.59 T +0 12 Q +(y) 265.36 672.36 T +2 9 Q +(2) 271.15 668.59 T +(2) 280.14 668.59 T +4 F +(,) 275.64 668.59 T +0 12 Q +(y) 307.3 672.36 T +2 9 Q +(2) 313.08 668.59 T +(3) 322.07 668.59 T +4 F +(,) 317.58 668.59 T +4 12 Q +(\274) 339.9 672.36 T +0 F +(y) 365.22 672.36 T +2 9 Q +(2) 371.01 668.59 T +3 F +(N) 380 668.59 T +(v) 385.92 668.59 T +(a) 391.85 668.59 T +(r) 397.77 668.59 T +4 F +(,) 375.5 668.59 T +0 12 Q +(y) 223.43 654.44 T +2 9 Q +(3) 229.21 650.68 T +(1) 238.2 650.68 T +4 F +(,) 233.71 650.68 T +0 12 Q +(y) 265.36 654.44 T +2 9 Q +(3) 271.15 650.68 T +(2) 280.14 650.68 T +4 F +(,) 275.64 650.68 T +0 12 Q +(y) 307.3 654.44 T +2 9 Q +(3) 313.08 650.68 T +(3) 322.07 650.68 T +4 F +(,) 317.58 650.68 T +4 12 Q +(\274) 339.9 654.44 T +0 F +(y) 365.22 654.44 T +2 9 Q +(3) 371.01 650.68 T +3 F +(N) 380 650.68 T +(v) 385.92 650.68 T +(a) 391.85 650.68 T +(r) 397.77 650.68 T +4 F +(,) 375.5 650.68 T +2 12 Q +(.) 231.06 636.55 T +(.) 273 636.55 T +(.) 314.93 636.55 T +4 F +(\274) 339.9 636.55 T +2 F +(.) 382.19 636.55 T +0 F +(y) 214.09 620.35 T +3 9 Q +(N) 219.88 616.59 T +(i) 225.8 616.59 T +(n) 231.72 616.59 T +(d) 237.65 616.59 T +2 F +(1) 247.53 616.59 T +4 F +(,) 243.04 616.59 T +0 12 Q +(y) 256.03 620.35 T +3 9 Q +(N) 261.82 616.59 T +(i) 267.74 616.59 T +(n) 273.66 616.59 T +(d) 279.58 616.59 T +2 F +(2) 289.47 616.59 T +4 F +(,) 284.97 616.59 T +0 12 Q +(y) 297.96 620.35 T +3 9 Q +(N) 303.75 616.59 T +(i) 309.67 616.59 T +(n) 315.59 616.59 T +(d) 321.52 616.59 T +2 F +(3) 331.4 616.59 T +4 F +(,) 326.91 616.59 T +4 12 Q +(\274) 339.9 620.35 T +0 F +(y) 355.89 620.35 T +3 9 Q +(N) 361.68 616.73 T +(i) 367.6 616.73 T +(n) 373.52 616.73 T +(d) 379.44 616.73 T +(N) 389.33 616.73 T +(v) 395.26 616.73 T +(a) 401.18 616.73 T +(r) 407.1 616.73 T +4 F +(,) 384.84 616.73 T +2 12 Q +(i) 434 690.88 T +(n) 437.34 690.88 T +(d) 443.33 690.88 T +(i) 449.33 690.88 T +(v) 452.66 690.88 T +(i) 458.66 690.88 T +(d) 461.99 690.88 T +(u) 467.99 690.88 T +(a) 473.99 690.88 T +(l) 479.31 690.88 T +(\021) 482.65 690.88 T +(1) 485.65 690.88 T +(i) 434 673.08 T +(n) 437.34 673.08 T +(d) 443.33 673.08 T +(i) 449.33 673.08 T +(v) 452.66 673.08 T +(i) 458.66 673.08 T +(d) 461.99 673.08 T +(u) 467.99 673.08 T +(a) 473.99 673.08 T +(l) 479.31 673.08 T +(\021) 482.65 673.08 T +(2) 485.65 673.08 T +(i) 434 655.28 T +(n) 437.34 655.28 T +(d) 443.33 655.28 T +(i) 449.33 655.28 T +(v) 452.66 655.28 T +(i) 458.66 655.28 T +(d) 461.99 655.28 T +(u) 467.99 655.28 T +(a) 473.99 655.28 T +(l) 479.31 655.28 T +(\021) 482.65 655.28 T +(3) 485.65 655.28 T +(.) 461.32 637.48 T +(i) 421.2 619.68 T +(n) 424.53 619.68 T +(d) 430.53 619.68 T +(i) 436.52 619.68 T +(v) 439.86 619.68 T +(i) 445.86 619.68 T +(d) 449.19 619.68 T +(u) 455.19 619.68 T +(a) 461.18 619.68 T +(l) 466.51 619.68 T +(\021) 469.84 619.68 T +3 F +(N) 474.55 619.68 T +(i) 482.45 619.68 T +(n) 490.35 619.68 T +(d) 498.25 619.68 T +4 F +(=) 197.01 655.96 T +215.59 614.64 211.59 614.64 2 L +0.33 H +0 Z +N +211.59 614.64 211.59 702.48 2 L +N +211.59 702.48 215.59 702.48 2 L +N +409.99 614.64 413.99 614.64 2 L +N +413.99 614.64 413.99 702.48 2 L +N +413.99 702.48 409.99 702.48 2 L +N +-8.35 24.95 603.65 816.95 C +182.59 357.63 484.7 488.74 C +3 12 Q +0 X +0 K +(F) 195.87 479.75 T +(i) 203.77 479.75 T +(t) 211.68 479.75 T +(n) 219.58 479.75 T +(F) 245.36 479.75 T +(I) 253.26 479.75 T +(T) 261.16 479.75 T +(N) 269.07 479.75 T +(E) 276.97 479.75 T +(S) 284.87 479.75 T +(S) 292.77 479.75 T +(O) 307.77 479.75 T +(b) 315.68 479.75 T +(j) 323.58 479.75 T +(V) 331.48 479.75 T +4 F +(\050) 302.67 479.75 T +(\051) 339.28 479.75 T +3 F +(\021) 345.98 479.75 T +(%) 353.18 479.75 T +(\021) 360.37 479.75 T +(F) 367.57 479.75 T +(i) 374.77 479.75 T +(t) 381.96 479.75 T +(n) 389.16 479.75 T +(e) 396.36 479.75 T +(s) 403.55 479.75 T +(s) 410.75 479.75 T +(\021) 417.94 479.75 T +(F) 425.14 479.75 T +(u) 432.33 479.75 T +(n) 439.53 479.75 T +(c) 446.73 479.75 T +(t) 453.92 479.75 T +(i) 461.12 479.75 T +(o) 468.32 479.75 T +(n) 475.51 479.75 T +4 F +(=) 232.77 479.75 T +0 F +(f) 259.74 442.24 T +2 9 Q +(1) 263.54 438.48 T +0 12 Q +(f) 259.74 424.33 T +2 9 Q +(2) 263.54 420.56 T +0 12 Q +(f) 259.74 406.41 T +2 9 Q +(3) 263.54 402.65 T +2 12 Q +(.) 261.89 388.52 T +0 F +(f) 250.41 373.71 T +3 9 Q +(N) 254.2 370.09 T +(i) 260.13 370.09 T +(n) 266.05 370.09 T +(d) 271.97 370.09 T +2 12 Q +(i) 298.32 442.15 T +(n) 301.65 442.15 T +(d) 307.64 442.15 T +(i) 313.64 442.15 T +(v) 316.98 442.15 T +(i) 322.97 442.15 T +(d) 326.31 442.15 T +(u) 332.3 442.15 T +(a) 338.3 442.15 T +(l) 343.63 442.15 T +(\021) 346.96 442.15 T +(1) 349.96 442.15 T +(i) 298.32 424.35 T +(n) 301.65 424.35 T +(d) 307.64 424.35 T +(i) 313.64 424.35 T +(v) 316.98 424.35 T +(i) 322.97 424.35 T +(d) 326.31 424.35 T +(u) 332.3 424.35 T +(a) 338.3 424.35 T +(l) 343.63 424.35 T +(\021) 346.96 424.35 T +(2) 349.96 424.35 T +(i) 298.32 406.55 T +(n) 301.65 406.55 T +(d) 307.64 406.55 T +(i) 313.64 406.55 T +(v) 316.98 406.55 T +(i) 322.97 406.55 T +(d) 326.31 406.55 T +(u) 332.3 406.55 T +(a) 338.3 406.55 T +(l) 343.63 406.55 T +(\021) 346.96 406.55 T +(3) 349.96 406.55 T +(.) 328.11 388.75 T +(i) 286.07 373.97 T +(n) 289.4 373.97 T +(d) 295.4 373.97 T +(i) 301.39 373.97 T +(v) 304.73 373.97 T +(i) 310.73 373.97 T +(d) 314.06 373.97 T +(u) 320.06 373.97 T +(a) 326.05 373.97 T +(l) 331.38 373.97 T +(\021) 334.71 373.97 T +3 F +(N) 339.42 373.97 T +(i) 346.61 373.97 T +(n) 353.81 373.97 T +(d) 361.01 373.97 T +4 F +(=) 233.32 408.75 T +251.91 368.23 247.91 368.23 2 L +0.33 H +0 Z +N +247.91 368.23 247.91 454.45 2 L +N +247.91 454.45 251.91 454.45 2 L +N +274.86 368.23 278.86 368.23 2 L +N +278.86 368.23 278.86 454.45 2 L +N +278.86 454.45 274.86 454.45 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "22" 23 +%%Page: "23" 23 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-23) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Support for Multiple Populations) 63.65 732.95 T +2 12 Q +0.49 (The GA T) 135.65 694.95 P +0.49 (oolbox provides support for multiple subpopulations through the use of) 185.09 694.95 P +2.44 (high-level genetic operator functions and a routine for exchanging individuals) 135.65 680.95 P +0.12 (between subpopulations. In the literature, the use of multiple populations has been) 135.65 666.95 P +1.48 (shown, in most cases, to improve the quality of the results obtained using GAs) 135.65 652.95 P +(compared to the single population GA \050see, for example, [32] and [33]\051.) 135.65 638.95 T +0.36 (The GA T) 135.65 612.95 P +0.36 (oolbox supports the use of a single population divided into a number of) 184.83 612.95 P +3.75 (subpopulations or) 135.65 598.95 P +0 F +3.75 (demes) 231.76 598.95 P +2 F +3.75 ( by modifying the use of data structures such that) 261.74 598.95 P +4.05 (subpopulations are stored in contiguous blocks within a single matrix. For) 135.65 584.95 P +5.76 (example, the chromosome data structure,) 135.65 570.95 P +3 F +13.81 (Chrom) 364.61 570.95 P +2 F +5.76 (, composed of) 400.59 570.95 P +3 F +13.81 (SUBPOP) 488.47 570.95 P +2 F +(subpopulations each of length) 135.65 556.95 T +3 F +(N) 282.22 556.95 T +2 F +( individuals is stored as:) 289.42 556.95 T +2.16 (This is known as the) 135.65 242.2 P +0 F +2.16 (Migration) 248.04 242.2 P +2 F +2.16 (, or) 296.69 242.2 P +0 F +2.16 (Island) 319.99 242.2 P +2 F +2.16 (, model [34]. Each subpopulation is) 349.97 242.2 P +1.3 (evolved over generations by a traditional GA and from time to time individuals) 135.65 228.2 P +5.19 (migrate from one subpopulation to another) 135.65 214.2 P +5.19 (. The amount of migration of) 366.46 214.2 P +3.82 (individuals and the pattern of that migration determines how much genetic) 135.65 200.2 P +(diversity can occur) 135.65 186.2 T +(.) 226.25 186.2 T +2.83 (T) 135.65 160.2 P +2.83 (o allow the T) 142.14 160.2 P +2.83 (oolbox routines to operate independently on subpopulations, a) 213.4 160.2 P +-0.29 (number of high-level entry functions are provided that accept an optional ar) 135.65 146.2 P +-0.29 (gument) 495.67 146.2 P +1.24 (that determines the number of subpopulations contained in a data structure. The) 135.65 132.2 P +0.5 (low-level routines are then called independently) 135.65 118.2 P +0.5 (, in turn, with each subpopulation) 368.22 118.2 P +238.13 264.2 429.16 548.95 C +3 12 Q +0 X +0 K +(C) 239.13 402.93 T +(h) 246.33 402.93 T +(r) 253.52 402.93 T +(o) 260.72 402.93 T +(m) 267.92 402.93 T +(I) 317.18 515.29 T +(n) 324.38 515.29 T +(d) 331.58 515.29 T +(1) 340.23 509.8 T +(S) 349.14 515.29 T +(u) 356.33 515.29 T +(b) 363.53 515.29 T +(P) 370.73 515.29 T +(o) 377.92 515.29 T +(p) 385.12 515.29 T +(1) 393.77 509.8 T +(I) 317.68 495.33 T +(n) 324.88 495.33 T +(d) 332.08 495.33 T +(2) 340.73 489.85 T +(S) 348.64 495.33 T +(u) 355.83 495.33 T +(b) 363.03 495.33 T +(P) 370.23 495.33 T +(o) 377.42 495.33 T +(p) 384.62 495.33 T +(1) 393.27 489.85 T +4 F +(\274) 353.58 475.38 T +3 F +(I) 317.18 459.4 T +(n) 324.38 459.4 T +(d) 331.58 459.4 T +(N) 340.23 453.92 T +(S) 349.14 459.4 T +(u) 356.33 459.4 T +(b) 363.53 459.4 T +(P) 370.73 459.4 T +(o) 377.92 459.4 T +(p) 385.12 459.4 T +(1) 393.77 453.92 T +(I) 317.68 439.45 T +(n) 324.88 439.45 T +(d) 332.08 439.45 T +(1) 340.73 433.96 T +(S) 349.64 439.45 T +(u) 356.83 439.45 T +(b) 364.03 439.45 T +(P) 371.23 439.45 T +(o) 378.42 439.45 T +(p) 385.62 439.45 T +(2) 394.27 433.96 T +(I) 317.68 419.49 T +(n) 324.88 419.49 T +(d) 332.08 419.49 T +(2) 340.73 414.01 T +(S) 348.64 419.49 T +(u) 355.83 419.49 T +(b) 363.03 419.49 T +(P) 370.23 419.49 T +(o) 377.42 419.49 T +(p) 384.62 419.49 T +(2) 393.27 414.01 T +4 F +(\274) 353.58 399.54 T +3 F +(I) 317.18 383.56 T +(n) 324.38 383.56 T +(d) 331.58 383.56 T +(N) 340.23 378.07 T +(S) 349.14 383.56 T +(u) 356.33 383.56 T +(b) 363.53 383.56 T +(P) 370.73 383.56 T +(o) 377.92 383.56 T +(p) 385.12 383.56 T +(2) 393.77 378.07 T +4 F +(\274) 353.58 363.6 T +3 F +(I) 299.2 347.62 T +(n) 306.39 347.62 T +(d) 313.59 347.62 T +(1) 322.24 342.14 T +(S) 331.15 347.62 T +(u) 338.34 347.62 T +(b) 345.54 347.62 T +(P) 352.73 347.62 T +(o) 359.93 347.62 T +(p) 367.13 347.62 T +(S) 375.79 342.14 T +(U) 382.98 342.14 T +(B) 390.18 342.14 T +(P) 397.37 342.14 T +(O) 404.57 342.14 T +(P) 411.77 342.14 T +(I) 299.7 327.67 T +(n) 306.89 327.67 T +(d) 314.09 327.67 T +(2) 322.74 322.18 T +(S) 330.65 327.67 T +(u) 337.84 327.67 T +(b) 345.04 327.67 T +(P) 352.23 327.67 T +(o) 359.43 327.67 T +(p) 366.63 327.67 T +(S) 375.29 322.18 T +(U) 382.48 322.18 T +(B) 389.68 322.18 T +(P) 396.87 322.18 T +(O) 404.07 322.18 T +(P) 411.27 322.18 T +4 F +(\274) 353.58 307.72 T +3 F +(I) 299.2 291.73 T +(n) 306.39 291.73 T +(d) 313.59 291.73 T +(N) 322.24 286.25 T +(S) 331.15 291.73 T +(u) 338.34 291.73 T +(b) 345.54 291.73 T +(P) 352.73 291.73 T +(o) 359.93 291.73 T +(p) 367.13 291.73 T +(S) 375.79 286.25 T +(U) 382.98 286.25 T +(B) 390.18 286.25 T +(P) 397.37 286.25 T +(O) 404.57 286.25 T +(P) 411.77 286.25 T +2 F +(.) 424.17 402.93 T +4 F +(=) 282.11 402.93 T +300.7 283.77 296.7 283.77 2 L +0.33 H +0 Z +N +296.7 283.77 296.7 527.27 2 L +N +296.7 527.27 300.7 527.27 2 L +N +417.46 283.77 421.46 283.77 2 L +N +421.46 283.77 421.46 527.27 2 L +N +421.46 527.27 417.46 527.27 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "23" 24 +%%Page: "24" 24 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-24) 513.33 61.29 T +2 12 Q +0.1 (to perform functions such as selection, crossover and reinsertion. These high-level) 135.65 736.95 P +(functions are listed in the T) 135.65 722.95 T +(able below) 266.39 722.95 T +(.) 317.9 722.95 T +1 F +(Note:) 135.65 570.95 T +2 F +( As currently implemented, all subpopulations must be of equal size.) 163.62 570.95 T +0.04 (The transfer of individuals between subpopulations is implemented in the T) 135.65 544.95 P +0.04 (oolbox) 498.33 544.95 P +0.57 (function) 135.65 530.95 P +3 F +1.37 (migrate) 179.19 530.95 P +2 F +0.57 (. A single scalar is used to determine the amount of migration) 229.56 530.95 P +3.62 (of individuals from one subpopulation to another) 135.65 516.95 P +3.62 (. Thus, given a population) 391.9 516.95 P +1.6 (comprised of a number of subpopulations, the same number of individuals will) 135.65 502.95 P +1.86 (always be transferred from a subpopulation as the number it will receive from) 135.65 488.95 P +0.15 (another subpopulation. A second parameter to the function) 135.65 474.95 P +3 F +0.37 (migrate) 421.67 474.95 P +2 F +0.15 ( controls the) 472.05 474.95 P +3.59 (manner in which individuals are selected for migration, either uniformly or) 135.65 460.95 P +4.25 (according to \336tness. Uniform selection picks individuals for migration and) 135.65 446.95 P +2.52 (replaces individuals in a subpopulation with immigrants in a random manner) 135.65 432.95 P +2.52 (.) 528.65 432.95 P +2.4 (Fitness-based migration selects individuals according to their \336tness level, the) 135.65 418.95 P +0.08 (most \336t individuals being the ones selected for migration, and replaces individuals) 135.65 404.95 P +(in a subpopulation uniformly at random.) 135.65 390.95 T +1.09 (A further parameter speci\336es the population topology over which migration will) 135.65 364.95 P +-0.26 (take place. Fig. 7 shows the most basic migration paths implemented in) 135.65 350.95 P +3 F +-0.63 (migrate) 478.28 350.95 P +2 F +-0.26 (,) 528.65 350.95 P +0.71 (the ring topology) 135.65 336.95 P +0.71 (. Here individuals are transferred between directionally adjacent) 218.92 336.95 P +1.69 (subpopulations. For example, individuals from subpopulation 6 migrate only to) 135.65 322.95 P +6.65 (subpopulation 1 and individuals from subpopulation 1 only migrate to) 135.65 308.95 P +(subpopulation 2.) 135.65 294.95 T +(SUBPOPULA) 222.4 690.95 T +(TION SUPPOR) 291.04 690.95 T +(T FUNCTIONS) 367.28 690.95 T +3 F +(mutate) 141.65 666.95 T +2 F +(mutation operators) 249.65 666.95 T +3 F +(recombin) 141.65 644.95 T +2 F +(crossover and recombination operators) 249.65 644.95 T +3 F +(reins) 141.65 622.95 T +2 F +(uniform random and \336tness-based reinsertion) 249.65 622.95 T +3 F +(select) 141.65 600.95 T +2 F +(independent subpopulation selection) 249.65 600.95 T +135.65 706.7 135.65 593.2 2 L +V +0.5 H +0 Z +N +243.65 679.45 243.65 592.7 2 L +V +N +531.65 706.7 531.65 593.2 2 L +V +N +135.4 706.95 531.9 706.95 2 L +V +N +135.9 682.2 531.4 682.2 2 L +V +N +135.9 679.7 531.4 679.7 2 L +V +N +135.4 592.95 531.9 592.95 2 L +V +N +63.65 96.95 531.65 744.95 C +133.38 126.4 531.65 290.95 C +314.34 259.94 354.02 279.78 9.92 RR +7 X +0 K +V +0.5 H +2 Z +0 X +N +2 9 Q +(SubPop 1) 316.82 266.16 T +373.86 190.49 413.55 210.33 9.92 RR +7 X +V +0 X +N +(SubPop 3) 376.35 196.71 T +254.81 190.49 294.49 210.33 9.92 RR +7 X +V +0 X +N +(SubPop 5) 257.3 196.71 T +254.81 230.17 294.49 250.02 9.92 RR +7 X +V +0 X +N +(SubPop 6) 257.3 236.4 T +373.86 230.17 413.55 250.02 9.92 RR +7 X +V +0 X +N +(SubPop 2) 376.35 236.4 T +314.34 160.72 354.02 180.57 9.92 RR +7 X +V +0 X +N +(SubPop 4) 316.82 166.95 T +308.7 272.85 314.34 269.86 308.93 266.48 308.81 269.67 4 Y +V +98 180 39.68 19.84 314.34 250.02 A +395.27 255.94 393.69 250.02 389.35 254.35 392.31 255.15 4 Y +V +15 90 39.68 19.84 354.02 250.02 A +273.07 184.57 274.65 190.49 278.99 186.17 276.03 185.37 4 Y +V +195 270 39.68 19.84 314.34 190.49 A +359.65 167.65 354.02 170.65 359.43 174.03 359.54 170.84 4 Y +V +278 360 39.68 19.84 354.02 190.49 A +396.7 215.53 393.7 210.33 390.7 215.53 393.7 215.53 4 Y +V +393.7 230.17 393.7 215.53 2 L +N +271.65 224.98 274.65 230.17 277.65 224.98 274.65 224.98 4 Y +V +274.65 210.33 274.65 224.98 2 L +N +5 12 Q +(Figure 7: Ring Migration T) 246.77 143.55 T +(opology) 382.95 143.55 T +142.84 130.96 525.52 287.44 R +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "24" 25 +%%Page: "25" 25 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-25) 513.33 61.29 T +2 12 Q +1.18 (A similar strategy to the ring topology is the neighbourhood migration of Fig.8.) 135.65 736.95 P +3.3 (Like the ring topology) 135.65 722.95 P +3.3 (, migration is made only between nearest neighbours,) 252.38 722.95 P +2.19 (however) 135.65 708.95 P +2.19 (, migration may occur in either direction between subpopulations. For) 176.46 708.95 P +2.73 (each subpopulation, the possible immigrants are determined, according to the) 135.65 694.95 P +0.13 (desired selection method, from adjacent subpopulations and a \336nal selection made) 135.65 680.95 P +0.07 (from this pool of individuals. This ensures that individuals will not migrate from a) 135.65 666.95 P +(subpopulation to the same subpopulation.) 135.65 652.95 T +-0.1 (The most general migration strategy supported by) 135.65 458.75 P +3 F +-0.25 (migrate) 377.1 458.75 P +2 F +-0.1 ( is that of unrestricted) 427.47 458.75 P +3.36 (migration, Fig. 9. Here, individuals may migrate from any subpopulation to) 135.65 444.75 P +2.16 (another) 135.65 430.75 P +2.16 (. For each subpopulation, a pool of potential immigrants is constructed) 170.96 430.75 P +3.58 (from the other subpopulations. The individual migrants are then determined) 135.65 416.75 P +(according to the appropriate selection strategy) 135.65 402.75 T +(.) 356.36 402.75 T +0.63 (An example of a GA with multiple subpopulations is considered in the) 135.65 215.11 P +0 F +0.63 (Examples) 485.02 215.11 P +2 F +(Section.) 135.65 201.11 T +63.65 96.95 531.65 744.95 C +133.38 470.75 531.65 648.95 C +312.67 609.34 352.35 629.18 9.92 RR +7 X +0 K +V +0.5 H +0 Z +0 X +N +2 9 Q +(SubPop 1) 315.16 615.56 T +372.2 539.9 411.88 559.74 9.92 RR +7 X +V +0 X +N +(SubPop 3) 374.68 546.12 T +253.14 539.9 292.83 559.74 9.92 RR +7 X +V +0 X +N +(SubPop 5) 255.63 546.12 T +253.14 579.58 292.83 599.42 9.92 RR +7 X +V +0 X +N +(SubPop 6) 255.63 585.8 T +372.2 579.58 411.88 599.42 9.92 RR +7 X +V +0 X +N +(SubPop 2) 374.68 585.8 T +312.67 510.13 352.35 529.97 9.92 RR +7 X +V +0 X +N +(SubPop 4) 315.16 516.35 T +277.32 603.75 272.98 599.42 271.4 605.35 274.36 604.55 4 Y +V +307.04 622.26 312.67 619.26 307.26 615.88 307.15 619.07 4 Y +V +98 165 39.68 19.84 312.67 599.42 A +357.77 615.88 352.36 619.26 357.99 622.26 357.88 619.07 4 Y +V +393.6 605.35 392.03 599.42 387.68 603.75 390.64 604.55 4 Y +V +15 82 39.68 19.84 352.35 599.42 A +307.26 523.43 312.67 520.05 307.04 517.06 307.15 520.25 4 Y +V +271.4 533.98 272.98 539.9 277.32 535.57 274.36 534.77 4 Y +V +195 262 39.68 19.84 312.67 539.9 A +387.68 535.57 392.03 539.9 393.6 533.98 390.64 534.77 4 Y +V +357.99 517.06 352.36 520.05 357.77 523.43 357.88 520.25 4 Y +V +278 345 39.68 19.84 352.35 539.9 A +389.04 574.38 392.04 579.58 395.04 574.38 392.04 574.38 4 Y +V +395.04 564.93 392.04 559.74 389.04 564.93 392.04 564.93 4 Y +V +392.04 574.38 392.04 564.93 2 L +N +275.99 564.93 272.99 559.74 269.99 564.93 272.99 564.93 4 Y +V +269.99 574.38 272.99 579.58 275.99 574.38 272.99 574.38 4 Y +V +272.99 564.93 272.99 574.38 2 L +N +5 12 Q +(Figure 8: Neighbourhood Migration T) 218.12 492.95 T +(opology) 408.27 492.95 T +141.18 481.15 523.85 638.55 R +2 Z +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +63.65 96.95 531.65 744.95 C +133.38 227.11 531.65 398.75 C +311.25 362.42 353.77 382.26 9.92 RR +7 X +0 K +V +0.5 H +0 Z +0 X +N +2 9 Q +(SubPop 1) 315.16 369.28 T +382.12 291.56 424.64 311.4 9.92 RR +7 X +V +0 X +N +(SubPop 3) 386.02 298.41 T +311.25 263.21 353.77 283.05 9.92 RR +7 X +V +0 X +N +(SubPop 4) 315.16 270.07 T +240.39 334.08 282.91 353.92 9.92 RR +7 X +V +0 X +N +(SubPop 6) 244.29 340.93 T +382.12 334.08 424.64 353.92 9.92 RR +7 X +V +0 X +N +(SubPop 2) 386.02 340.93 T +240.39 291.56 282.91 311.4 9.92 RR +7 X +V +0 X +N +(SubPop 5) 244.29 298.41 T +288.1 339.74 282.91 342.74 288.1 345.74 288.1 342.74 4 Y +V +376.92 345.74 382.12 342.74 376.92 339.74 376.92 342.74 4 Y +V +288.1 342.74 376.92 342.74 2 L +N +288.1 297.22 282.91 300.22 288.1 303.22 288.1 300.22 4 Y +V +376.92 303.22 382.12 300.22 376.92 297.22 376.92 300.22 4 Y +V +288.1 300.22 376.92 300.22 2 L +N +259.27 328.82 262.45 333.91 265.27 328.61 262.27 328.72 4 Y +V +264.83 316.48 261.64 311.4 258.83 316.7 261.83 316.59 4 Y +V +262.27 328.71 261.83 316.59 2 L +N +400.7 328.77 403.79 333.91 406.69 328.66 403.69 328.71 4 Y +V +406.47 316.54 403.38 311.4 400.47 316.65 403.47 316.59 4 Y +V +403.7 328.71 403.48 316.59 2 L +N +335.55 288.23 332.51 283.05 329.55 288.27 332.55 288.25 4 Y +V +330.08 357.4 333.12 362.57 336.08 357.36 333.08 357.38 4 Y +V +332.55 288.25 333.08 357.38 2 L +N +265.7 357.93 261.12 353.91 259.92 359.88 262.81 358.91 4 Y +V +304.36 376.57 310.45 373.24 304.52 369.63 304.44 373.1 4 Y +V +97 165 49.33 19.33 310.46 353.91 A +358.95 369.45 353.79 372.57 359.07 375.49 359.01 372.47 4 Y +V +404.8 360.17 403.78 353.91 398.86 357.93 401.83 359.05 4 Y +V +16 84 50 18.67 353.79 353.91 A +398.23 287.21 403.12 291.24 404.17 284.99 401.2 286.1 4 Y +V +359.87 269.25 353.78 272.58 359.71 276.19 359.79 272.72 4 Y +V +277 344 49.33 18.67 353.79 291.24 A +305.19 275.53 311.12 271.91 305.02 268.58 305.11 272.05 4 Y +V +260.59 285.27 261.79 291.24 266.36 287.22 263.48 286.24 4 Y +V +195 263 49.33 19.33 311.12 291.24 A +377.29 310.28 382.45 306.58 376.66 303.96 376.97 307.12 4 Y +V +339.96 356.6 343.12 362.57 346.72 356.84 343.34 356.72 4 Y +V +186 262 39.33 56 382.46 362.57 A +314.84 356.76 318.45 362.57 321.68 356.54 318.26 356.65 4 Y +V +289.05 303.42 283.12 305.91 288.24 309.8 288.64 306.61 4 Y +V +279 354 35.33 56.67 283.12 362.57 A +286.86 334.27 281.79 337.91 287.48 340.48 287.17 337.37 4 Y +V +323.54 289.08 320.45 283.24 316.94 288.83 320.24 288.96 4 Y +V +6 82 38.67 54.67 281.79 283.24 A +343.9 289.35 340.45 283.91 337.47 289.62 340.69 289.49 4 Y +V +378.27 339.89 383.78 337.24 378.73 333.79 378.5 336.84 4 Y +V +97 174 43.33 53.33 383.79 283.91 A +5 12 Q +(Figure 9: Unrestricted Migration T) 226.45 246.03 T +(opology) 399.93 246.03 T +141.18 238.52 523.85 387.34 R +2 Z +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "25" 26 +%%Page: "26" 26 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-26) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Examples) 63.65 732.95 T +2 12 Q +2.91 (This Section contains two detailed examples using the GA T) 135.65 694.95 P +2.91 (oolbox to solve) 451.86 694.95 P +(optimization problems:) 135.65 680.95 T +(\245) 157.25 654.95 T +(A simple binary GA to solve De Jong\325) 171.65 654.95 T +(s \336rst test function [13].) 355.87 654.95 T +(\245) 157.25 634.95 T +(A real-valued multi-population GA to solve the Harvest problem [9].) 171.65 634.95 T +1 16 Q +(The Simple GA) 135.65 598.29 T +2 12 Q +1.33 (This example demonstrates how a simple GA can be constructed using routines) 135.65 570.95 P +0.28 (from the GA T) 135.65 556.95 P +0.28 (oolbox to solve an optimization problem. The objective function to) 207.28 556.95 P +(be minimized is an extended version of De Jong\325) 135.65 542.95 T +(s \336rst test function [13]:) 370.15 542.95 T +(,) 315.32 503.13 T +0.97 (where) 135.65 463.88 P +0 F +0.97 (n) 168.91 463.88 P +2 F +0.97 ( de\336nes the number of dimensions of the problem. For this example, we) 174.91 463.88 P +(choose) 135.65 449.88 T +0 F +(n) 171.95 449.88 T +2 F +( = 20. The minimum of this function is, of course, located at) 177.95 449.88 T +0 F +(x) 469.87 449.88 T +0 10 Q +(i) 475.19 446.88 T +2 12 Q +( = 0.) 477.97 449.88 T +1 (The computational element of the M) 135.65 423.88 P +2 10 Q +0.84 (A) 316.21 423.88 P +0.84 (TLAB) 322.32 423.88 P +2 12 Q +1 ( objective function is encapsulated in) 348.42 423.88 P +(the code segment below) 135.65 409.88 T +(.) 250.45 409.88 T +3 F +(function ObjVal = objfun1\050 Phen \051) 171.65 383.88 T +(ObjVal = sum\050\050Phen .* Phen\051\325\051\325;) 171.65 363.88 T +2 F +1.32 (An m-\336le implementing this objective function,) 135.65 337.88 P +3 F +3.15 (objfun1) 375.74 337.88 P +2 F +1.32 (, is included with the) 426.11 337.88 P +(GA T) 135.65 323.88 T +(oolbox software.) 162.45 323.88 T +1.92 (Having written an m-\336le for the objective function, the GA code may now be) 135.65 297.88 P +-0.07 (constructed. This can be done directly from the M) 135.65 283.88 P +2 10 Q +-0.06 (A) 375.22 283.88 P +-0.06 (TLAB) 381.33 283.88 P +2 12 Q +-0.07 ( command line, in a script) 407.42 283.88 P +2.05 (\336le or as a M) 135.65 269.88 P +2 10 Q +1.71 (A) 207.13 269.88 P +1.71 (TLAB) 213.24 269.88 P +2 12 Q +2.05 ( function. Fig. 10 shows an outline of the script \336le) 239.33 269.88 P +3 F +4.92 (sga) 510.06 269.88 P +2 F +(supplied with the toolbox that implements a simple GA to solve this problem.) 135.65 255.88 T +3.3 (The \336rst \336ve lines describe the major variables of the GA. The number of) 135.65 229.88 P +1.5 (individuals is set to) 135.65 215.88 P +3 F +3.6 (NIND = 40) 237.61 215.88 P +2 F +1.5 ( and the number of generations) 309.58 215.88 P +3 F +3.6 (MAXGEN =) 470.48 215.88 P +-0.31 (300) 135.65 201.88 P +2 F +-0.13 (. The number of variables used is) 157.24 201.88 P +3 F +-0.31 (NVAR = 20) 318.87 201.88 P +2 F +-0.13 ( and each variable uses a 20 bit) 383.01 201.88 P +1.58 (representation,) 135.65 187.88 P +3 F +3.8 (PRECI = 20) 211.17 187.88 P +2 F +1.58 (. This example uses a generation gap,) 290.73 187.88 P +3 F +3.8 (GGAP =) 484.67 187.88 P +4.4 (0.9) 135.65 173.88 P +2 F +1.83 (, and \336tness-based reinsertion to implement an elitist strategy whereby the) 157.24 173.88 P +2.92 (four most \336t individuals always propagate through to successive generations.) 135.65 159.88 P +(Thus, 36 \050) 135.65 145.88 T +3 F +(NIND) 184.62 145.88 T +4 F +(\264) 216.4 145.88 T +3 F +(GGAP) 225.98 145.88 T +2 F +(\051 new individuals are produced at each generation.) 254.77 145.88 T +237.51 485.88 315.32 524.95 C +0 12 Q +0 X +0 K +(f) 238.51 503.13 T +2 9 Q +(1) 242.31 499.36 T +0 12 Q +(x) 254.61 503.13 T +4 F +(\050) 249.51 503.13 T +(\051) 260.54 503.13 T +0 F +(x) 304.04 503.13 T +0 9 Q +(i) 309.83 499.35 T +2 F +(2) 309.83 509.24 T +0 F +(i) 285.12 488.83 T +2 F +(1) 298.55 488.83 T +4 F +(=) 290.62 488.83 T +0 F +(n) 291.83 517.81 T +4 18 Q +(\345) 287.67 499.93 T +4 12 Q +(=) 272.53 503.13 T +-8.35 24.95 603.65 816.95 C +351.3 496.49 429.79 512.33 C +2 12 Q +0 X +0 K +(5) 359.35 503.13 T +(1) 365.35 503.13 T +(2) 371.34 503.13 T +4 F +(-) 352.3 503.13 T +0 F +(x) 389.92 503.13 T +0 9 Q +(i) 395.71 499.35 T +2 12 Q +(5) 410.8 503.13 T +(1) 416.79 503.13 T +(2) 422.79 503.13 T +4 F +(\243) 380.34 503.13 T +(\243) 401.21 503.13 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "26" 27 +%%Page: "27" 27 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-27) 513.33 61.29 T +2 12 Q +1.06 (The \336eld descriptor is constructed using the matrix replication function,) 135.65 178.42 P +3 F +2.54 (rep) 493.67 178.42 P +2 F +1.06 (, to) 515.26 178.42 P +3.96 (build the matrix,) 135.65 164.42 P +3 F +9.51 (FieldD) 230.16 164.42 P +2 F +3.96 (, describing the chromosomes\325 representation and) 273.34 164.42 P +-0.2 (interpretation. In this case,) 135.65 150.42 P +3 F +-0.49 (FieldD) 265.41 150.42 P +2 F +-0.2 ( describes 20 variables, each Gray coded using) 308.59 150.42 P +0.35 (20 bits over the interval [-512, 512]. An initial population is then created with the) 135.65 136.42 P +(function) 135.65 122.42 T +3 F +(crtbp) 178.62 122.42 T +2 F +( thus,) 214.6 122.42 T +63.65 96.95 531.65 744.95 C +136.44 200.42 531.65 732.95 C +142.71 234 525.38 722.98 R +7 X +0 K +V +3 12 Q +0 X +(NIND = 40;) 142.71 714.98 T +(% Number of individuals) 305.86 714.98 T +(MAXGEN = 300;) 142.71 700.98 T +(% Maximum no. of generations) 305.86 700.98 T +(NVAR = 20;) 142.71 686.98 T +(% No. of variables) 305.86 686.98 T +(PRECI = 20;) 142.71 672.98 T +(% Precision of variables) 305.86 672.98 T +(GGAP = 0.9;) 142.71 658.98 T +(% Generation gap) 305.86 658.98 T +(% Build f) 142.71 639.98 T +(ield descriptor) 207.47 639.98 T +(FieldD = [rep\050[PRECI],[1,NVAR]\051;...) 142.71 625.98 T +(rep\050[-512;512],[1,NVAR]\051; rep\050[1;0;1;1],[1,NVAR]\051];) 157.1 611.98 T +(% Initialise population) 142.71 592.98 T +(Chrom = crtbp\050NIND, NVAR*PRECI\051;) 142.71 578.98 T +(gen = 0;) 142.71 559.98 T +(% Counter) 305.86 559.98 T +(% Evaluate initial population) 142.71 540.98 T +(ObjV = objfun1\050bs2rv\050Chrom,FieldD\051\051;) 142.71 526.98 T +(% Generational loop) 142.71 507.98 T +(while gen < MAXGEN,) 142.71 493.98 T +(% Assign f) 167.91 474.98 T +(itness values to entire population) 239.87 474.98 T +(FitnV = ranking\050ObjV\051;) 167.91 460.98 T +(% Select individuals for breeding) 167.91 441.98 T +(SelCh = select\050\325sus\325, Chrom, FitnV, GGAP\051;) 167.91 427.98 T +(% Recombine individuals \050crossover\051) 167.91 408.98 T +(SelCh = recombin\050\325xovsp\325,SelCh,0.7\051;) 167.91 394.98 T +(% Apply mutation) 167.91 375.98 T +(SelCh = mut\050SelCh\051;) 167.91 361.98 T +(% Evaluate offspring, call objective function) 167.91 342.98 T +(ObjVSel = objfun1\050bs2rv\050SelCh,FieldD\051\051;) 167.91 328.98 T +(% Reinsert offspring into population) 167.91 309.98 T +([Chrom ObjV]=reins\050Chrom,SelCh,1,1,ObjV,ObjVSel\051;) 167.91 295.98 T +(% Increment counter) 167.91 276.98 T +(gen = gen+1;) 167.91 262.98 T +(end) 142.71 243.98 T +139.16 204.48 528.92 728.89 R +0.5 H +2 Z +N +5 F +(Figure 10: The Simple GA in M) 238.91 212.83 T +5 10 Q +(A) 397.51 212.83 T +(TLAB) 403.63 212.83 T +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "27" 28 +%%Page: "28" 28 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-28) 513.33 61.29 T +3 12 Q +(Chrom = crtbp\050NIND, NVAR*PRECI\051;) 171.65 736.95 T +2 F +0.14 (producing a matrix,) 135.65 710.95 P +3 F +0.35 (Chrom) 233.35 710.95 P +2 F +0.14 (, of) 269.33 710.95 P +3 F +0.35 (NIND) 288.6 710.95 P +2 F +0.14 ( uniformly distributed random binary strings) 317.39 710.95 P +(of length) 135.65 696.95 T +3 F +(NVAR) 181.62 696.95 T +4 F +(\264) 213.4 696.95 T +3 F +(PRECI) 222.98 696.95 T +2 F +(.) 258.96 696.95 T +0.86 (The generation counter) 135.65 670.95 P +0.86 (,) 248.12 670.95 P +3 F +2.06 (gen) 254.98 670.95 P +2 F +0.86 (, is set to zero. The following line then converts the) 276.57 670.95 P +0.12 (binary strings to real-values using the function) 135.65 656.95 P +3 F +0.28 (bs2rv) 362.64 656.95 P +2 F +0.12 ( and evaluates the objective) 398.62 656.95 P +1.26 (function,) 135.65 642.95 P +3 F +3.03 (objfun1) 182.88 642.95 P +2 F +1.26 (, for all of the individuals in the initial population as shown) 233.25 642.95 P +(below) 135.65 628.95 T +(.) 164.18 628.95 T +3 F +(ObjV = objfun1\050bs2rv\050Chrom, FieldD\051\051;) 171.65 602.95 T +2 F +2.08 (The function) 135.65 576.95 P +3 F +4.98 (bs2rv) 204.42 576.95 P +2 F +2.08 ( converts the binary strings in the matrix) 240.4 576.95 P +3 F +4.98 (Chrom) 454.22 576.95 P +2 F +2.08 ( to real-) 490.2 576.95 P +1.74 (values according to the \336eld descriptor) 135.65 562.95 P +1.74 (,) 330.07 562.95 P +3 F +4.18 (FieldD) 337.81 562.95 P +2 F +1.74 (, and returns a matrix of real-) 380.99 562.95 P +1.05 (valued phenotypes. The return value matrix of) 135.65 548.95 P +3 F +2.52 (bs2rv) 368.17 548.95 P +2 F +1.05 ( is then passed directly as) 404.15 548.95 P +4.34 (the input ar) 135.65 534.95 P +4.34 (gument to the objective function,) 198.74 534.95 P +3 F +10.41 (objfun1) 382.32 534.95 P +2 F +4.34 (, and the resulting) 432.69 534.95 P +0.18 (objective function values are returned in the matrix) 135.65 520.95 P +3 F +0.44 (ObjV) 385.59 520.95 P +2 F +0.18 (. The GA then enters the) 412.83 520.95 P +(generational) 135.65 506.95 T +3 F +(while) 197.93 506.95 T +2 F +( loop.) 233.91 506.95 T +1.49 (The \336rst step in the generational loop is the assignment of \336tness values to the) 135.65 480.95 P +3.02 (individuals. In this example, rank-based \336tness assignment is used as shown) 135.65 466.95 P +(below) 135.65 452.95 T +(,) 164.18 452.95 T +3 F +(FitnV = ranking\050ObjV\051;) 171.65 426.95 T +2 F +2.36 (Here, the objective function values, ObjV) 135.65 400.95 P +2.36 (, are passed to the T) 346.1 400.95 P +2.36 (oolbox function) 452.99 400.95 P +3 F +1.32 (ranking) 135.65 386.95 P +2 F +0.55 ( with no other ar) 186.02 386.95 P +0.55 (guments. The default setting for the ranking algorithm) 267.29 386.95 P +-0.1 (assume a selective pressure of 2 and linear ranking, giving the most \336t individual a) 135.65 372.95 P +1.62 (\336tness value of 2 and the least \336t individual a \336tness value of 0. Note that the) 135.65 358.95 P +1.78 (ranking algorithm assumes that the objective function is to be) 135.65 344.95 P +1 F +1.78 (minimised) 451.91 344.95 P +2 F +1.78 (. The) 505.22 344.95 P +(resulting \336tness values are returned in the vector) 135.65 330.95 T +3 F +(FitnV) 371.47 330.95 T +2 F +(.) 405.91 330.95 T +2.13 (The selection stage uses the high-level function) 135.65 304.95 P +3 F +5.1 (select) 381.37 304.95 P +2 F +2.13 ( to call the low-level) 424.55 304.95 P +(stochastic universal sampling routine,) 135.65 290.95 T +3 F +(sus) 319.87 290.95 T +2 F +(, as follows,) 341.45 290.95 T +3 F +(SelCh = select\050\325sus\325, Chrom, FitnV, GGAP\051;) 171.65 264.95 T +2 F +2.64 (After selection,) 135.65 238.95 P +3 F +6.33 (SelCh) 217.86 238.95 P +2 F +2.64 ( contains) 253.84 238.95 P +3 F +6.33 (GGAP) 305.09 238.95 P +4 F +2.64 (\264) 339.51 238.95 P +3 F +6.33 (NIND) 351.73 238.95 P +2 F +2.64 ( individuals from the original) 380.51 238.95 P +1.73 (population) 135.65 224.95 P +3 F +4.16 (Chrom) 191.68 224.95 P +2 F +1.73 (. These individuals are now recombined using the high-level) 227.67 224.95 P +(function) 135.65 210.95 T +3 F +(recombin) 178.62 210.95 T +2 F +( as shown below) 236.19 210.95 T +(.) 315.02 210.95 T +3 F +(SelCh = recombin\050\325xovsp\325, SelCh, 0.7\051;) 171.65 184.95 T +1.76 (recombin) 135.65 158.95 P +2 F +0.73 ( takes the individuals selected for reproduction,) 193.22 158.95 P +3 F +1.76 (SelCh) 428.85 158.95 P +2 F +0.73 (, and uses the) 464.83 158.95 P +-0.27 (single-point crossover routine,) 135.65 144.95 P +3 F +-0.65 (xovsp) 284.07 144.95 P +2 F +-0.27 (, to perform crossover with probability) 320.05 144.95 P +-0.27 (,) 503.78 144.95 P +0 F +-0.27 (Px) 509.5 144.95 P +2 F +-0.27 ( =) 522.16 144.95 P +-0.21 (0.7. The individuals in the input matrix) 135.65 130.95 P +3 F +-0.51 (SelCh) 325.06 130.95 P +2 F +-0.21 ( are ordered such that individuals in) 361.04 130.95 P +2.9 (odd numbered positions are crossed with the individual in the adjacent even) 135.65 116.95 P +1.66 (numbered position. If the number of individuals in) 135.65 102.95 P +3 F +3.98 (SelCh) 394.43 102.95 P +2 F +1.66 ( is odd then the last) 430.41 102.95 P +FMENDPAGE +%%EndPage: "28" 29 +%%Page: "29" 29 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-29) 513.33 61.29 T +2 12 Q +0.28 (individual is always returned uncrossed. The of) 135.65 736.95 P +0.28 (fspring produced by this crossover) 364.63 736.95 P +-0.05 (are returned in the same matrix,) 135.65 722.95 P +3 F +-0.13 (SelCh) 290.87 722.95 P +2 F +-0.05 (. The actual crossover routine used may be) 326.85 722.95 P +5.34 (changed by supplying a dif) 135.65 708.95 P +5.34 (ferent function name in the string passed to) 286.72 708.95 P +3 F +(recombin) 135.65 694.95 T +2 F +(.) 193.22 694.95 T +2.79 (Having produced a set of of) 135.65 668.95 P +2.79 (fspring, mutation may now be applied using the) 282.93 668.95 P +(mutation function) 135.65 654.95 T +3 F +(mut) 224.27 654.95 T +2 F +(:) 245.85 654.95 T +3 F +(SelCh = mut\050SelCh\051;) 171.65 628.95 T +2 F +2.71 (Again, the of) 135.65 602.95 P +2.71 (fspring are returned in the matrix) 203.8 602.95 P +3 F +6.49 (SelCh) 381.91 602.95 P +2 F +2.71 (. As no probability of) 417.89 602.95 P +-0.08 (mutation has been speci\336ed in the function call, the default value of) 135.65 588.95 P +0 F +-0.08 (Pm) 462.74 588.95 P +2 F +-0.08 ( = 0.7/) 478.73 588.95 P +0 F +-0.08 (Lind) 509.65 588.95 P +2 F +(= 0.0017, where) 135.65 574.95 T +0 F +(Lind) 216.69 574.95 T +2 F +( is the length of an individual, is assumed.) 238.68 574.95 T +-0.02 (The objective function values for the of) 135.65 548.95 P +-0.02 (fspring,) 325.16 548.95 P +3 F +-0.05 (ObjVSel) 365.12 548.95 P +2 F +-0.02 (, may now be calculated) 415.49 548.95 P +(thus:) 135.65 534.95 T +3 F +(ObjVSel = objfun1\050bs2rv\050SelCh, FieldD\051\051;) 171.65 508.95 T +2 F +0.92 (Because we have used a generation gap, the number of of) 135.65 482.95 P +0.92 (fspring is less than the) 420.71 482.95 P +1.1 (size of the population. Therefore, we must reinsert the of) 135.65 468.95 P +1.1 (fspring into the current) 418.1 468.95 P +(population. This is achieved using the reinsertion function,) 135.65 454.95 T +3 F +(reins) 420.8 454.95 T +2 F +(, as follows:) 456.78 454.95 T +3 F +([Chrom,ObjV]=reins\050Chrom, SelCh,1,1,ObjV,ObjVSel\051;) 171.65 428.95 T +2 F +0.57 (Here,) 135.65 402.95 P +3 F +1.37 (Chrom) 165.52 402.95 P +2 F +0.57 ( and) 201.5 402.95 P +3 F +1.37 (SelCh) 225.95 402.95 P +2 F +0.57 ( are matrices containing the original population and the) 261.93 402.95 P +1.36 (resulting of) 135.65 388.95 P +1.36 (fspring. The two occurrences of the numeral) 191.76 388.95 P +3 F +3.26 (1) 417.09 388.95 P +2 F +1.36 ( indicate that a single) 424.28 388.95 P +2.69 (population is used and that \336tness-based reinsertion be applied. Fitness-based) 135.65 374.95 P +3.38 (reinsertion replaces the least \336t members of) 135.65 360.95 P +3 F +8.12 (Chrom) 371.51 360.95 P +2 F +3.38 ( with the individuals in) 407.49 360.95 P +3 F +2.11 (SelCh) 135.65 346.95 P +2 F +0.88 (. The objective function values of the original population,) 171.63 346.95 P +3 F +2.11 (ObjV) 459.02 346.95 P +2 F +0.88 (, are thus) 486.26 346.95 P +2.41 (required as a parameter to) 135.65 332.95 P +3 F +5.79 (reins) 275.25 332.95 P +2 F +2.41 (. In addition, so that the objective function) 311.23 332.95 P +1.58 (values of the new population can be returned without having to re-evaluate the) 135.65 318.95 P +0.74 (objective function for the entire population, the objective values of the of) 135.65 304.95 P +0.74 (fspring,) 494.67 304.95 P +3 F +-0.64 (ObjVSel) 135.65 290.95 P +2 F +-0.27 (, are also supplied.) 186.02 290.95 P +3 F +-0.64 (reins) 277.56 290.95 P +2 F +-0.27 ( returns the new population with the of) 313.54 290.95 P +-0.27 (fspring) 497.67 290.95 P +(inserted,) 135.65 276.95 T +3 F +(Chrom) 179.62 276.95 T +2 F +(, and the objective function values for this population,) 215.6 276.95 T +3 F +(ObjV) 477.76 276.95 T +2 F +(.) 505 276.95 T +0.09 (Finally) 135.65 250.95 P +0.09 (, the generational counter) 168.86 250.95 P +0.09 (,) 290.54 250.95 P +3 F +0.21 (gen) 296.62 250.95 P +2 F +0.09 (, is incremented. The GA iterates around the) 318.21 250.95 P +0.49 (loop until) 135.65 236.95 P +3 F +1.17 (gen = MAXGEN) 185.94 236.95 P +2 F +0.49 (, in this case 300, and then terminates. The results of) 274.62 236.95 P +1.28 (the genetic optimization are contained in the matrix ObjV and the values of the) 135.65 222.95 P +(decision variables may be obtained by:) 135.65 208.95 T +3 F +(Phen = bs2rv\050Chrom, FieldD\051;) 171.65 182.95 T +FMENDPAGE +%%EndPage: "29" 30 +%%Page: "30" 30 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-30) 513.33 61.29 T +1 16 Q +(A Multi-population GA) 135.65 734.29 T +2 12 Q +3.7 (This example shows how functions from the GA T) 135.65 706.95 P +3.7 (oolbox may be used to) 408.25 706.95 P +1.76 (implement a real-valued, multi-population GA. A M) 135.65 692.95 P +2 10 Q +1.47 (A) 398.07 692.95 P +1.47 (TLAB) 404.18 692.95 P +2 12 Q +1.76 ( m-\336le script) 430.27 692.95 P +3 F +4.24 (mpga) 499.86 692.95 P +2 F +1.76 (,) 528.65 692.95 P +0.49 (supplied with the T) 135.65 678.95 P +0.49 (oolbox, implements the code described in this subsection. The) 229.23 678.95 P +2.82 (objective function chosen is that of the harvest problem [9] which is a one-) 135.65 664.95 P +(dimensional equation of growth:) 135.65 650.95 T +(,) 378.2 623.75 T +(with one equality constraint,) 135.65 595.02 T +(,) 353.47 567.81 T +0.35 (where) 135.65 539.1 P +0 F +0.35 (x) 168.29 539.1 P +0 10 Q +0.29 (0) 173.62 536.1 P +2 12 Q +0.35 ( is the initial condition of the state,) 178.62 539.1 P +0 F +0.35 (a) 350.98 539.1 P +2 F +0.35 ( is a scalar constant, and) 356.98 539.1 P +0 F +0.35 (x) 478.65 539.1 P +0 10 Q +0.29 (k) 483.97 536.1 P +4 12 Q +0.35 (\316) 491.76 539.1 P +0 F +0.35 (R) 503.65 539.1 P +2 F +0.35 (and) 514.33 539.1 P +0 F +0.25 (u) 135.65 525.1 P +0 10 Q +0.21 (k) 141.65 522.1 P +4 12 Q +0.25 (\316) 149.33 525.1 P +0 F +0.25 ( R) 157.88 525.1 P +0 10 Q +0.21 (+) 168.46 529.9 P +2 12 Q +0.25 ( are the state and nonnegative control respectively) 175.2 525.1 P +0.25 (. The objective function) 416.31 525.1 P +(is de\336ned as:) 135.65 511.1 T +(,) 375.47 471.18 T +0.04 (where) 135.65 431.93 P +0 F +0.04 (N) 167.98 431.93 P +2 F +0.04 ( is the number of control steps over which the problem is to be solved. An) 175.98 431.93 P +1.19 (m-\336le implementing this objective function,) 135.65 417.93 P +3 F +2.86 (objharv) 356.16 417.93 P +2 F +1.19 (, is supplied with the GA) 405.75 417.93 P +1.41 (T) 135.65 403.93 P +1.41 (oolbox software. Note that as this is a maximisation problem and the T) 142.14 403.93 P +1.41 (oolbox) 498.33 403.93 P +5.62 (routines are implemented to minimise, the objective function,) 135.65 389.93 P +3 F +13.48 (objharv) 479.06 389.93 P +2 F +5.62 (,) 528.65 389.93 P +-0.25 (multiplies) 135.65 375.93 P +0 F +-0.25 (J) 186.38 375.93 P +2 F +-0.25 ( by -1 to produce a minimisation problem. The initial condition is set to) 191.71 375.93 P +0 F +2.3 (x) 135.65 361.93 P +0 10 Q +1.92 (0) 140.97 358.93 P +2 12 Q +2.3 ( = 100 and the scalar is chosen as) 145.97 361.93 P +0 F +2.3 (a) 329.64 361.93 P +2 F +2.3 ( = 1.1. Additionally) 335.64 361.93 P +2.3 (, the exact optimal) 436.14 361.93 P +(solution for this problem can be determined analytically as:) 135.65 347.93 T +(.) 384.8 299.39 T +2.08 (The number of control steps for this problem is) 135.65 260.73 P +0 F +2.08 (N) 383.86 260.73 P +2 F +2.08 ( = 20, thus,) 391.86 260.73 P +3 F +4.99 (NVAR = 20) 456.91 260.73 P +2 F +2.9 (decision variables will be used, one for each control input,) 135.65 246.73 P +0 F +2.9 (u) 447.79 246.73 P +0 10 Q +2.42 (k) 453.79 243.73 P +2 12 Q +2.9 (. The decision) 458.23 246.73 P +-0.02 (variables are bounded in the range) 135.65 232.73 P +3 F +-0.04 (RANGE = [0, 200]) 303.4 232.73 P +2 F +-0.02 (, limiting the maximum) 418.41 232.73 P +0.99 (control input, at any time-step, to 200. The \336eld descriptor) 135.65 218.73 P +0.99 (,) 424.54 218.73 P +3 F +2.37 (FieldD) 431.52 218.73 P +2 F +0.99 (, describing) 474.7 218.73 P +1.46 (the decision variables may be constructed using the matrix replication function,) 135.65 204.73 P +3 F +(rep) 135.65 190.73 T +2 F +(, thus:) 157.24 190.73 T +3 F +(NVAR = 20;) 171.65 164.73 T +(RANGE = [0; 200];) 171.65 149.73 T +(FieldD = rep\050RANGE,[1,NVAR]\051;) 171.65 134.73 T +286.1 617.02 378.2 632.95 C +0 12 Q +0 X +0 K +(x) 287.1 623.75 T +0 9 Q +(k) 292.89 619.97 T +2 F +(1) 306.31 619.97 T +4 F +(+) 299.13 619.97 T +0 12 Q +(a) 329.39 623.75 T +(x) 344.39 623.75 T +4 F +(\327) 338.39 623.75 T +0 9 Q +(k) 350.17 619.97 T +0 12 Q +(u) 366.75 623.75 T +0 9 Q +(k) 373.21 619.97 T +4 12 Q +(-) 357.16 623.75 T +(=) 316.81 623.75 T +-8.35 24.95 603.65 816.95 C +310.83 561.1 353.47 577.02 C +0 12 Q +0 X +0 K +(x) 311.83 567.81 T +2 9 Q +(0) 317.61 564.05 T +0 12 Q +(x) 340.69 567.81 T +0 9 Q +(N) 346.48 564.03 T +4 12 Q +(=) 328.11 567.81 T +-8.35 24.95 603.65 816.95 C +288.83 453.93 375.47 493.1 C +0 12 Q +0 X +0 K +(J) 289.83 471.18 T +2 F +(m) 313.74 471.18 T +(a) 323.07 471.18 T +(x) 328.39 471.18 T +0 F +(u) 364.02 471.18 T +0 9 Q +(k) 370.48 467.4 T +(k) 336.35 456.88 T +2 F +(0) 351.27 456.88 T +4 F +(=) 343.34 456.88 T +0 F +(N) 336.1 485.95 T +2 F +(1) 351.53 485.95 T +4 F +(-) 344.34 485.95 T +4 18 Q +(\345) 339.64 467.97 T +4 12 Q +(=) 301.15 471.18 T +374.47 482.38 364.02 482.38 2 L +0.33 H +0 Z +N +364.02 482.38 361.02 467.54 2 L +N +361.02 467.54 359.02 471.75 2 L +N +359.02 471.75 358.02 469.65 2 L +N +-8.35 24.95 603.65 816.95 C +279.49 282.73 384.8 329.93 C +0 12 Q +0 X +0 K +(J) 280.49 299.39 T +2 9 Q +(*) 285.82 305.5 T +0 12 Q +(x) 320.47 309.69 T +2 9 Q +(0) 326.26 305.93 T +0 12 Q +(a) 338.56 309.69 T +0 9 Q +(N) 344.56 315.75 T +2 12 Q +(1) 363.14 309.69 T +4 F +(-) 353.55 309.69 T +(\050) 333.46 309.69 T +(\051) 369.74 309.69 T +2 9 Q +(2) 375.73 319.8 T +0 12 Q +(a) 317.9 287.73 T +0 9 Q +(N) 323.89 293.83 T +2 F +(1) 339.32 293.83 T +4 F +(-) 332.14 293.83 T +0 12 Q +(a) 351.62 287.73 T +2 F +(1) 370.2 287.73 T +4 F +(-) 360.62 287.73 T +(\050) 346.52 287.73 T +(\051) 376.81 287.73 T +(=) 297.31 299.39 T +317.9 301.98 382.55 301.98 2 L +0.33 H +0 Z +N +383.8 328.93 316.9 328.93 2 L +N +316.9 328.93 313.9 285.73 2 L +N +313.9 285.73 311.9 297.03 2 L +N +311.9 297.03 310.9 291.38 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "30" 31 +%%Page: "31" 31 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-31) 513.33 61.29 T +2 12 Q +1.59 (The parameters for the GA may be speci\336ed using M) 135.65 736.95 P +2 10 Q +1.32 (A) 405.4 736.95 P +1.32 (TLAB) 411.51 736.95 P +2 12 Q +1.59 ( variables. For this) 437.61 736.95 P +(example the following parameters are de\336ned:) 135.65 722.95 T +3 F +(% Def) 171.65 696.95 T +(ine GA Parameters) 207.63 696.95 T +(GGAP = 0.8;) 171.65 681.95 T +(% Generation gap) 315.65 681.95 T +(XOVR = 1;) 171.65 666.95 T +(% Crossover rate) 315.65 666.95 T +(MUTR = 1/NVAR;) 171.65 651.95 T +(% Mutation rate) 315.65 651.95 T +(MAXGEN = 1200;) 171.65 636.95 T +(% Maximum no. of generations) 315.65 636.95 T +(INSR = 0.9;) 171.65 621.95 T +(% Insertion rate) 315.65 621.95 T +(SUBPOP = 8;) 171.65 606.95 T +(% No. of subpopulations) 315.65 606.95 T +(MIGR = 0.2;) 171.65 591.95 T +(% Migration rate) 315.65 591.95 T +(MIGGEN = 20;) 171.65 576.95 T +(% No. of gens / migration) 315.65 576.95 T +(NIND = 20;) 171.65 561.95 T +(% No. of individuals / subpop) 315.65 561.95 T +2 F +1.04 (As well as the conventional GA parameters, such as generation gap \050) 135.65 535.95 P +3 F +2.5 (GGAP) 477.51 535.95 P +2 F +1.04 (\051 and) 506.3 535.95 P +3.32 (crossover rate \050) 135.65 521.95 P +3 F +7.96 (XOVR) 216.21 521.95 P +2 F +3.32 (\051, a number of other parameters associated with multi-) 244.99 521.95 P +0.71 (population GAs are de\336ned. Here,) 135.65 507.95 P +3 F +1.71 (INSR = 0.9) 306.75 507.95 P +2 F +0.71 ( speci\336es that only 90% of the) 382.13 507.95 P +4.47 (individuals produced at each generation are reinserted into the population,) 135.65 493.95 P +3 F +2.2 (SUBPOP = 8) 135.65 479.95 P +2 F +0.92 ( subpopulations are to be used with a migration rate of) 212.01 479.95 P +3 F +2.2 (MIGR =) 486.27 479.95 P +1.31 (0.2) 135.65 465.95 P +2 F +0.55 (, or 20%, between subpopulations and migration occurring at every) 157.24 465.95 P +3 F +1.31 (MIGGEN) 488.47 465.95 P +(= 20) 135.65 451.95 T +2 F +(generations. Each subpopulation contains) 171.63 451.95 T +3 F +(NIND = 20) 373.83 451.95 T +2 F +( individuals.) 438.59 451.95 T +(The functions used by the script-\336le are speci\336ed using M) 135.65 425.95 T +2 10 Q +(A) 414.46 425.95 T +(TLAB) 420.57 425.95 T +2 12 Q +( strings:) 446.66 425.95 T +3 F +(% Specify other functions as strings) 171.65 399.95 T +(SEL_F = \325sus\325;) 171.65 384.95 T +(% Name of selection function) 315.65 384.95 T +(XOV_F = \325recdis\325;) 171.65 369.95 T +(% Name of recombination fun.) 315.65 369.95 T +(MUT_F = \325mutbga\325;) 171.65 354.95 T +(% Name of mutation function) 315.65 354.95 T +(OBJ_F = \325objharv\325;) 171.65 339.95 T +(% Name of objective function) 315.65 339.95 T +2 F +3.51 (Because we are using discrete recombination,) 135.65 313.95 P +3 F +8.42 (recdis) 378.85 313.95 P +2 F +3.51 (, for the breeding of) 422.03 313.95 P +(of) 135.65 299.95 T +(fspring, the crossover rate is not used and, hence) 145.42 299.95 T +3 F +(XOVR = 1) 381.57 299.95 T +2 F +( above.) 439.14 299.95 T +2.11 (The initial population is created using the function) 135.65 273.95 P +3 F +5.07 (crtrp) 397.73 273.95 P +2 F +2.11 ( and the generation) 433.71 273.95 P +(counter) 135.65 259.95 T +(,) 171.14 259.95 T +3 F +(gen) 177.13 259.95 T +2 F +(, set to zero:) 198.72 259.95 T +3 F +(Chrom = crtrp\050SUBPOP*NIND,FieldD\051;) 171.65 233.95 T +(gen = 0;) 171.65 218.95 T +2 F +4.09 (This will consist of) 135.65 192.95 P +3 F +9.82 (SUBPOP) 247.3 192.95 P +4 F +4.09 (\264) 297.57 192.95 P +3 F +9.82 (NIND) 311.25 192.95 P +2 F +4.09 ( individuals with individual decision) 340.03 192.95 P +2.1 (variables chosen uniformly at random in the range speci\336ed by) 135.65 178.95 P +3 F +5.03 (FieldD) 461.73 178.95 P +2 F +2.1 (. The) 504.9 178.95 P +3 F +-0.02 (Chrom) 135.65 164.95 P +2 F +-0.01 ( matrix contains all of the subpopulations and the objective function values) 171.63 164.95 P +(for all the individuals in all the subpopulations may be calculated directly) 135.65 150.95 T +(,) 487.64 150.95 T +3 F +(ObjV = feval\050OBJ_F, Chrom\051;) 171.65 124.95 T +FMENDPAGE +%%EndPage: "31" 32 +%%Page: "32" 32 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-32) 513.33 61.29 T +2 12 Q +0 (using the M) 135.65 736.95 P +2 10 Q +0 (A) 192.96 736.95 P +0 (TLAB) 199.07 736.95 P +3 12 Q +0.01 (feval) 228.16 736.95 P +2 F +0 ( command.) 264.14 736.95 P +3 F +0.01 (feval) 320.45 736.95 P +2 F +0 ( performs function evaluation taking) 356.42 736.95 P +-0.19 (the \336rst input ar) 135.65 722.95 P +-0.19 (gument, in this case the name of our objective function,) 211.15 722.95 P +3 F +-0.46 (objharv) 479.06 722.95 P +2 F +-0.19 (,) 528.65 722.95 P +-0.13 (contained in) 135.65 708.95 P +3 F +-0.3 (OBJ_F) 197.35 708.95 P +2 F +-0.13 (, as the function to be evaluated and calls that function with all) 232.37 708.95 P +(the remaining parameters as its input ar) 135.65 694.95 T +(guments. In this case, the function call is:) 324.63 694.95 T +3 F +(ObjV = objharv\050Chrom\051;) 171.65 668.95 T +2 F +0.28 (As a real-valued coding is used, there is no need to convert the chromosomes into) 135.65 642.95 P +2.3 (a phenotypic representation. Like the previous example, the GA now enters a) 135.65 628.95 P +(generational) 135.65 614.95 T +3 F +(while) 197.93 614.95 T +2 F +( loop.) 233.91 614.95 T +0.39 (The M) 135.65 588.95 P +2 10 Q +0.33 (A) 168.35 588.95 P +0.33 (TLAB) 174.46 588.95 P +2 12 Q +0.39 ( code for the generational loop of the multi-population GA is shown) 200.55 588.95 P +(in Fig. 1) 135.65 574.95 T +(1 below) 175.53 574.95 T +(.) 213.05 574.95 T +63.65 96.95 531.65 744.95 C +136.44 123.46 531.65 570.95 C +142.71 164.04 525.38 558 R +7 X +0 K +V +3 12 Q +0 X +(% Generational loop) 142.71 550 T +(while gen < MAXGEN,) 142.71 536 T +(% Fitness assignment to whole population) 167.91 514 T +(FitnV = ranking\050ObjV,2,SUBPOP\051;) 167.91 500 T +(% Select individuals from population) 167.91 478 T +-0.39 (SelCh = select\050SEL_F, Chrom, FitnV, GGAP, SUBPOP\051;) 167.91 464 P +(% Recombine selected individuals) 167.91 442 T +(SelCh=recombin\050XOV_F, SelCh, XOVR, SUBPOP\051;) 167.91 428 T +(% Mutate offspring) 167.91 406 T +(SelCh = mutate\050MUT_F,SelCh,FieldD,[MUTR],SUBPOP\051;) 167.91 392 T +(% Calculate objective function for offsprings) 167.91 370 T +(ObjVOff = feval\050OBJ_F,SelCh\051;) 167.91 356 T +(% Insert best offspring replacing worst parents) 167.91 334 T +([Chrom, ObjV] = reins\050Chrom, SelCh, SUBPOP, ...) 167.91 320 T +([1 INSR], ObjV, ObjVOff\051;) 203.89 306 T +(% Increment counter) 167.91 284 T +(gen=gen+1;) 167.91 270 T +(% Migrate individuals between subpopulations) 167.91 248 T +(if \050rem\050gen,MIGGEN\051 == 0\051) 167.91 234 T +([Chrom, ObjV] = ...) 189.49 220 T +-0.47 (migrate\050Chrom, SUBPOP, [MIGR, 1, 1], ObjV\051;) 218.28 206 P +(end) 167.91 192 T +(end) 142.71 170 T +139.16 129.55 528.92 564.86 R +0.5 H +2 Z +N +5 F +(Figure 1) 196.93 138.85 T +(1: Generational Loop of a Multipopulation GA) 239.25 138.85 T +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "32" 33 +%%Page: "33" 33 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-33) 513.33 61.29 T +2 12 Q +2.91 (The \336rst step of the generational loop is the assignment of \336tness values to) 135.65 736.95 P +(individuals:) 135.65 722.95 T +3 F +(FitnV = ranking\050ObjV, 2, SUBPOP\051;) 171.65 696.95 T +2 F +1.22 (Because we are using multiple subpopulations,) 135.65 670.95 P +3 F +2.92 (ranking) 371.15 670.95 P +2 F +1.22 ( requires us to specify) 421.52 670.95 P +2.2 (the selective pressure required, here we use a selective pressure of 2, and the) 135.65 656.95 P +0.96 (number of subpopulations,) 135.65 642.95 P +3 F +2.3 (SUBPOP) 269.77 642.95 P +2 F +0.96 (. Each subpopulation\325) 311.62 642.95 P +0.96 (s individuals\325 objective) 417.8 642.95 P +2.68 (values in) 135.65 628.95 P +3 F +6.43 (ObjV) 186.97 628.95 P +2 F +2.68 ( are ranked separately and the resulting sets of \336tness values) 215.76 628.95 P +(returned in the vector) 135.65 614.95 T +3 F +(FitnV) 241.56 614.95 T +2 F +(.) 275.99 614.95 T +1.97 (W) 135.65 588.95 P +1.97 (ithin each subpopulation, individuals are selected for breeding independently) 146.49 588.95 P +(using the high-level selection function,) 135.65 574.95 T +3 F +(select) 325.53 574.95 T +2 F +(:) 368.7 574.95 T +3 F +(SelCh = select\050SEL_F, Chrom, FitnV, GGAP, SUBPOP\051;) 171.65 548.95 T +5.96 (select) 135.65 522.95 P +2 F +2.48 ( calls the low-level selection function,) 178.82 522.95 P +3 F +5.96 (SEL_F = \325sus\325) 379.26 522.95 P +2 F +2.48 ( for each) 484.73 522.95 P +0.23 (subpopulation and builds the matrix) 135.65 508.95 P +3 F +0.56 (SelCh) 312.38 508.95 P +2 F +0.23 ( containing all the pairs of individuals) 348.36 508.95 P +0.24 (to be recombined. Like the previous example, the generation gap,) 135.65 494.95 P +3 F +0.59 (GGAP = 0.8) 455.52 494.95 P +2 F +0.24 (,) 528.65 494.95 P +2.22 (means that 0.8) 135.65 480.95 P +4 F +2.22 (\264) 214.92 480.95 P +2 F +2.22 ( 20 = 16,) 221.5 480.95 P +3 F +5.32 (GGAP) 276.11 480.95 P +4 F +2.22 (\264) 310.11 480.95 P +3 F +5.32 (NIND) 321.92 480.95 P +2 F +2.22 (, individuals are selected from each) 350.7 480.95 P +-0.03 (subpopulation. Thus,) 135.65 466.95 P +3 F +-0.07 (SelCh) 239.54 466.95 P +2 F +-0.03 ( contains a total of) 275.52 466.95 P +3 F +-0.07 (GGAP) 366.98 466.95 P +4 F +-0.03 (\264) 398.73 466.95 P +3 F +-0.07 (NIND) 408.29 466.95 P +4 F +-0.03 (\264) 440.04 466.95 P +3 F +-0.07 (SUBPOP) 449.59 466.95 P +-0.07 (= 128) 495.74 466.95 P +2 F +(individuals.) 135.65 452.95 T +0.04 (In a similar manner) 135.65 426.95 P +0.04 (, the high-level recombination function,) 228.89 426.95 P +3 F +0.1 (recombin) 422.64 426.95 P +2 F +0.04 (, is used to) 480.21 426.95 P +(recombine the pairs of individuals within each subpopulation of) 135.65 412.95 T +3 F +(SelCh) 445.11 412.95 T +2 F +(:) 481.09 412.95 T +3 F +(SelCh = recombin\050XOV_F, SelCh, XOVR, SUBPOP\051;) 171.65 386.95 T +2 F +5.24 (The recombination function,) 135.65 360.95 P +3 F +12.58 (XOV_F = \325recdis\325) 291.28 360.95 P +2 F +5.24 (, performs discrete) 431.57 360.95 P +1.73 (recombination between pairs of individuals for each subpopulation. As discrete) 135.65 346.95 P +0.6 (recombination does not require the speci\336cation of a conventional crossover rate,) 135.65 332.95 P +(the variable) 135.65 318.95 T +3 F +(XOVR = 1.0) 194.93 318.95 T +2 F +( is used only for compatibility) 266.89 318.95 T +(.) 410.37 318.95 T +(The of) 135.65 292.95 T +(fspring are now mutated:) 167.07 292.95 T +3 F +(SelCh = mutate\050MUT_F,SelCh,FieldD,MUTR,SUBPOP\051;) 171.65 266.95 T +2 F +0.16 (Here, the breeder genetic algorithm mutation function,) 135.65 240.95 P +3 F +0.39 (MUT_F = \325mutbga\325) 401.58 240.95 P +2 F +0.16 (, is) 517.49 240.95 P +2 (called using the high-level mutation routine,) 135.65 226.95 P +3 F +4.81 (mutate) 363.2 226.95 P +2 F +2 (, with a mutation rate of) 406.38 226.95 P +3 F +1.94 (MUTR = 1/NIND = 0.05) 135.65 212.95 P +2 F +0.81 (. The breeder genetic algorithm mutation function) 287.31 212.95 P +2.68 (requires the \336eld descriptor) 135.65 198.95 P +2.68 (,) 274.78 198.95 P +3 F +6.43 (FieldD) 283.45 198.95 P +2 F +2.68 (, so that the result of mutation will not) 326.63 198.95 P +(produce values outside the bounds of the decision variables.) 135.65 184.95 T +0.23 (The objective values of all the of) 135.65 158.95 P +0.23 (fspring,) 294.7 158.95 P +3 F +0.55 (ObjVOff) 334.9 158.95 P +2 F +0.23 ( may now be calculated, again) 385.28 158.95 P +(using) 135.65 144.95 T +3 F +(feval) 164.64 144.95 T +2 F +(:) 200.62 144.95 T +3 F +(ObjVOff = feval\050OBJ_F, SelCh\051;) 171.65 118.95 T +FMENDPAGE +%%EndPage: "33" 34 +%%Page: "34" 34 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-34) 513.33 61.29 T +2 12 Q +(Of) 135.65 736.95 T +(fspring may now be reinserted into the appropriate subpopulations:) 148.09 736.95 T +3 F +([Chrom, ObjV] = reins\050Chrom, SelCh, SUBPOP,...) 171.65 710.95 T +([1, INSR], ObjV, ObjVOff\051;) 337.16 695.95 T +2 F +1.72 (Fitness-based reinsertion is used, but the addition of the extra parameter to the) 135.65 669.95 P +1.81 (fourth ar) 135.65 655.95 P +1.81 (gument of) 178.87 655.95 P +3 F +4.34 (reins) 234.46 655.95 P +2 F +1.81 ( speci\336es an insertion rate of) 270.44 655.95 P +3 F +4.34 (INSR = 0.9) 421.87 655.95 P +2 F +1.81 (. This) 502.52 655.95 P +3.04 (means that for each subpopulation the least-\336t 10% of the of) 135.65 641.95 P +3.04 (fspring are not) 455.62 641.95 P +(reinserted.) 135.65 627.95 T +4.78 (Individuals in Multi-population GAs migrate between populations at some) 135.65 601.95 P +2.63 (interval. The T) 135.65 587.95 P +2.63 (oolbox routine) 211.69 587.95 P +3 F +6.32 (migrate) 290.25 587.95 P +2 F +2.63 ( is used to swap individuals between) 340.62 587.95 P +1.84 (subpopulations according to some migration strategy) 135.65 573.95 P +1.84 (. In this example, at every) 398.23 573.95 P +3 F +(MIGGEN = 20) 135.65 559.95 T +2 F +( generations, migration takes place between subpopulations.) 214.8 559.95 T +3 F +(% Migration between subpopulations) 171.65 533.95 T +(if\050rem\050gen, MIGGEN\051 == 0\051) 171.65 518.95 T +([Chrom, ObjV] = migrate\050Chrom, SUBPOP, ...) 200.43 503.95 T +([MIGR, 1, 1], ObjV\051;) 380.33 488.95 T +(end) 171.65 473.95 T +2 F +1.79 (Here, the most \336t 20%,) 135.65 447.95 P +3 F +4.29 (MIGR = 0.2) 258.85 447.95 P +2 F +1.79 (, of each subpopulation is selected for) 339.39 447.95 P +3.37 (migration. Nearest neighbour subpopulations then exchange these individuals) 135.65 433.95 P +2.79 (amongst their subpopulations, uniformly reinserting the immigrant individuals) 135.65 419.95 P +0.32 (\050see the) 135.65 405.95 P +0 F +0.32 (Support for Multiple Populations) 176.26 405.95 P +2 F +0.32 ( Section\051. The return matrix) 336.83 405.95 P +3 F +0.78 (Chrom) 475.02 405.95 P +2 F +0.32 ( and) 511.01 405.95 P +0.24 (vector) 135.65 391.95 P +3 F +0.58 (ObjV) 168.86 391.95 P +2 F +0.24 ( re\337ect the changes of individuals in the subpopulations as a result of) 197.64 391.95 P +(migration.) 135.65 377.95 T +1.39 (The GA iterates around the generational loop until) 135.65 351.95 P +3 F +3.33 (gen = MAXGEN) 391.9 351.95 P +2 F +1.39 ( and then) 484.91 351.95 P +1.41 (terminates. Fig. 12 shows a typical solution of the harvest problem obtained by) 135.65 337.95 P +3 F +(mpga) 135.65 323.95 T +2 F +(.) 164.43 323.95 T +63.65 96.95 531.65 744.95 C +133.38 101.21 531.65 319.95 C +0 77 211 550 590 191.56 153.49 240.81 153.36 FMBEGINEPSF +%%BeginDocument: +%!PS-Adobe-2.0 EPSF-1.2 +%%Creator: MATLAB, The Mathworks, Inc. +%%Title: MATLAB graph +%%CreationDate: 04/13/94 22:48:14 +%%DocumentFonts: Times-Roman +%%DocumentNeededFonts: Times-Roman +%%DocumentProcessColors: Cyan Magenta Yellow Black +%%Pages: 1 +%%BoundingBox: 77 211 550 590 +%%EndComments + +%%BeginProlog + +% MathWorks dictionary +/MathWorks 120 dict begin + +% definition operators +/bdef {bind def} bind def +/ldef {load def} bind def +/xdef {exch def} bdef +/xstore {exch store} bdef + +% operator abbreviations +/c /clip ldef +/cc /concat ldef +/cp /closepath ldef +/gr /grestore ldef +/gs /gsave ldef +/mt /moveto ldef +/np /newpath ldef +/cm /currentmatrix ldef +/sm /setmatrix ldef +/rc {rectclip} bdef 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bdef +/MP { + 3 1 roll moveto + 1 sub {rlineto} repeat + } bdef +/AP { + {rlineto} repeat + } bdef +/PP { + closepath fill + } bdef +/DP { + closepath stroke + } bdef +/MR { + 4 -2 roll moveto + dup 0 exch rlineto + exch 0 rlineto + neg 0 exch rlineto + closepath + } bdef +/FR { + MR stroke + } bdef +/PR { + MR fill + } bdef +/L1i { + { currentfile picstr readhexstring pop } image + } bdef + +/tMatrix matrix def +/MakeOval { + newpath + tMatrix currentmatrix pop + translate scale + 0 0 1 0 360 arc + tMatrix setmatrix + } bdef +/FO { + MakeOval + stroke + } bdef +/PO { + MakeOval + fill + } bdef + +/PD { + 2 copy moveto lineto stroke + } bdef + + +currentdict end def +%%EndProlog + +%%BeginSetup +MathWorks begin + +% fonts for text, standard numbers and exponents +%%IncludeFont: Times-Roman + +%line width, line cap, and joint spec +0 cap 1 setlinejoin + +end +%%EndSetup + +%%Page: 1 1 +%%BeginPageSetup +%%PageBoundingBox: 77 211 550 590 +MathWorks begin +bpage +%%EndPageSetup + +%%BeginObject: graph1 1 +bplot + +/dpi2point 12 def +portraitMode 0216 7344 csm + + 710 260 5677 4549 MR c np +76 dict begin %Colortable dictionary +/c0 { 0 0 0 sc} bdef +/c1 { 1 1 1 sc} bdef +/c2 { 1 0 0 sc} bdef +/c3 { 0 1 0 sc} bdef +/c4 { 0 0 1 sc} bdef +/c5 { 1 1 0 sc} bdef +/c6 { 1 0 1 sc} bdef +/c7 { 0 1 1 sc} bdef + +/Helvetica 144 FMS + +c1 + 0 0 6917 5187 PR +6 w +DO +4 w +SO +6 w +c0 + 899 4615 mt 6258 4615 L + 899 389 mt 6258 389 L + 899 4615 mt 899 389 L +6258 4615 mt 6258 389 L + 899 4615 mt 899 4615 L +6258 4615 mt 6258 4615 L + 899 4615 mt 6258 4615 L + 899 4615 mt 899 389 L + 899 4615 mt 899 4615 L + 899 4615 mt 899 4561 L + 899 389 mt 899 443 L + 859 4776 mt +(0) s +1435 4615 mt 1435 4561 L +1435 389 mt 1435 443 L +1395 4776 mt +(2) s +1971 4615 mt 1971 4561 L +1971 389 mt 1971 443 L +1931 4776 mt +(4) s +2507 4615 mt 2507 4561 L +2507 389 mt 2507 443 L +2467 4776 mt +(6) s +3043 4615 mt 3043 4561 L +3043 389 mt 3043 443 L +3003 4776 mt +(8) s +3579 4615 mt 3579 4561 L +3579 389 mt 3579 443 L +3499 4776 mt +(10) s +4114 4615 mt 4114 4561 L +4114 389 mt 4114 443 L +4034 4776 mt +(12) s +4650 4615 mt 4650 4561 L +4650 389 mt 4650 443 L +4570 4776 mt +(14) s +5186 4615 mt 5186 4561 L +5186 389 mt 5186 443 L +5106 4776 mt +(16) s +5722 4615 mt 5722 4561 L +5722 389 mt 5722 443 L +5642 4776 mt +(18) s +6258 4615 mt 6258 4561 L +6258 389 mt 6258 443 L +6178 4776 mt +(20) s + 899 4615 mt 953 4615 L +6258 4615 mt 6204 4615 L + 792 4668 mt +(0) s + 899 3911 mt 953 3911 L +6258 3911 mt 6204 3911 L + 712 3964 mt +(10) s + 899 3206 mt 953 3206 L +6258 3206 mt 6204 3206 L + 712 3259 mt +(20) s + 899 2502 mt 953 2502 L +6258 2502 mt 6204 2502 L + 712 2555 mt +(30) s + 899 1798 mt 953 1798 L +6258 1798 mt 6204 1798 L + 712 1851 mt +(40) s + 899 1093 mt 953 1093 L +6258 1093 mt 6204 1093 L + 712 1146 mt +(50) s + 899 389 mt 953 389 L +6258 389 mt 6204 389 L + 712 442 mt +(60) s + 899 4615 mt 6258 4615 L + 899 389 mt 6258 389 L + 899 4615 mt 899 389 L +6258 4615 mt 6258 389 L + 899 389 mt 899 389 L +6258 389 mt 6258 389 L +gs 899 389 5360 4227 MR c np +268 -498 268 -691 268 -535 268 -415 268 -274 268 -381 268 -226 268 -159 +268 -204 267 -157 268 -95 268 -80 268 -95 268 -56 268 -33 268 -59 +268 -34 268 -28 268 -21 1167 4500 20 MP stroke +gr +gs 0 0 256 192 MR c np + +end + +eplot +%%EndObject graph 1 + +epage +end + +showpage + +%%Trailer +%%EOF + +%%EndDocument +FMENDEPSF +0 12 Q +0 X +0 K +(u) 334.85 146.66 T +0 10 Q +(k) 340.85 143.66 T +0 12 Q +(J) 232.65 228.4 T +5 F +(Figure 12: Optimal Solution Obtained by) 214.83 124 T +6 F +(mpga) 421.42 124 T +137.63 114.44 527.4 313.33 R +0.5 H +2 Z +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "34" 35 +%%Page: "35" 35 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-35) 513.33 61.29 T +2 12 Q +0.02 (Again, like the previous example, the results of the GA search are contained in the) 135.65 736.95 P +0.13 (matrix) 135.65 722.95 P +3 F +0.31 (ObjV) 170.09 722.95 P +2 F +0.13 (. The objective value and index of the best individual are found using) 197.33 722.95 P +(the function) 135.65 708.95 T +3 F +(min) 196.27 708.95 T +2 F +(, for example:) 217.86 708.95 T +3 F +([Y, I] = min\050ObjV\051) 171.65 682.95 T +(Y =) 171.65 667.95 T +(-73.2370) 200.43 652.95 T +(I =) 171.65 637.95 T +(50) 200.43 622.95 T +2 F +0.87 (Remembering that the sign of the objective function has been changed to form a) 135.65 596.95 P +0.99 (minimisation problem, these results correspond to an objective function value of) 135.65 582.95 P +2.46 (73.2370. The exact solution is given as 73.2376. The GA optimal solution is) 135.65 568.95 P +1.59 (therefore accurate within a 10) 135.65 554.95 P +2 10 Q +1.32 (-5) 285.2 559.75 P +2 12 Q +1.59 (error bound on the exact optimal solution. The) 297.35 554.95 P +(chromosome values are displayed in Fig. 12 using:) 135.65 540.95 T +3 F +(plot\050Chrom\050I,:\051\051) 171.65 514.95 T +FMENDPAGE +%%EndPage: "35" 36 +%%Page: "36" 36 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-36) 513.33 61.29 T +1 16 Q +(Demonstration Scripts) 135.65 734.29 T +2 12 Q +-0.03 (A number of test functions have been implemented for use with the GA script \336les) 135.65 706.95 P +4.04 (supplied with the T) 135.65 692.95 P +4.04 (oolbox. These test functions are supplied in a separate) 239.87 692.95 P +1.62 (directory) 135.65 678.95 P +1.62 (,) 178.16 678.95 P +3 F +3.89 (test_fns) 185.78 678.95 P +2 F +1.62 (, from the main demonstrations and T) 243.35 678.95 P +1.62 (oolbox routines and) 433.13 678.95 P +1.58 (are accompanied by a postscript \336le,) 135.65 664.95 P +3 F +3.79 (test_fns.ps) 323.33 664.95 P +2 F +1.58 (, giving full details of the) 402.48 664.95 P +1.23 (problems implemented. The T) 135.65 650.95 P +1.23 (able below summarises the test functions supplied) 283.74 650.95 P +(with the T) 135.65 636.95 T +(oolbox.) 184.11 636.95 T +(No.) 179.02 604.95 T +(m-\336le name) 232.83 604.95 T +(Description) 379.47 604.95 T +(1) 163.25 580.95 T +3 F +(objfun1) 224.45 580.95 T +2 F +(De Jong\325) 310.85 580.95 T +(s function 1) 353.82 580.95 T +(2) 163.25 558.95 T +3 F +(objfun1a) 224.45 558.95 T +2 F +(axis parallel hyper) 310.85 558.95 T +(-ellipsoid) 399.2 558.95 T +(3) 163.25 536.95 T +3 F +(objfun1b) 224.45 536.95 T +2 F +(rotated hyper) 310.85 536.95 T +(-ellipsoid) 374.22 536.95 T +(4) 163.25 514.95 T +3 F +(objfun2) 224.45 514.95 T +2 F +(Rosenbrock\325) 310.85 514.95 T +(s valley \050banana function\051) 371.48 514.95 T +(5) 163.25 492.95 T +3 F +(objfun6) 224.45 492.95 T +2 F +(Rastrigin\325) 310.85 492.95 T +(s function) 358.16 492.95 T +(6) 163.25 470.95 T +3 F +(objfun7) 224.45 470.95 T +2 F +(Schwefel\325) 310.85 470.95 T +(s function) 358.81 470.95 T +(7) 163.25 448.95 T +3 F +(objfun8) 224.45 448.95 T +2 F +(Griewangk\325) 310.85 448.95 T +(s function) 367.47 448.95 T +(8) 163.25 426.95 T +3 F +(objfun9) 224.45 426.95 T +2 F +(sum of dif) 310.85 426.95 T +(ferent powers) 359.94 426.95 T +(9) 163.25 404.95 T +3 F +(objdopi) 224.45 404.95 T +2 F +(double integrator) 310.85 404.95 T +(10) 163.25 382.95 T +3 F +(objharv) 224.45 382.95 T +2 F +(harvest problem) 310.85 382.95 T +(1) 163.25 360.95 T +(1) 168.8 360.95 T +3 F +(objlinq) 224.45 360.95 T +2 F +(discrete linear) 310.85 360.95 T +(-quadratic problem) 378.21 360.95 T +(12) 163.25 338.95 T +3 F +(objlinq2) 224.45 338.95 T +2 F +(continuous linear) 310.85 338.95 T +(-quadratic problem) 393.55 338.95 T +(13) 163.25 316.95 T +3 F +(objpush) 224.45 316.95 T +2 F +(push-cart problem) 310.85 316.95 T +157.25 620.7 157.25 309.2 2 L +V +0.5 H +0 Z +N +218.45 621.2 218.45 308.7 2 L +V +N +304.85 621.2 304.85 308.7 2 L +V +N +510.05 620.7 510.05 309.2 2 L +V +N +157 620.95 510.3 620.95 2 L +V +N +157.5 596.2 509.8 596.2 2 L +V +N +157.5 593.7 509.8 593.7 2 L +V +N +157 572.95 510.3 572.95 2 L +V +N +157 550.95 510.3 550.95 2 L +V +N +157 528.95 510.3 528.95 2 L +V +N +157 506.95 510.3 506.95 2 L +V +N +157 484.95 510.3 484.95 2 L +V +N +157 462.95 510.3 462.95 2 L +V +N +157 440.95 510.3 440.95 2 L +V +N +157 418.95 510.3 418.95 2 L +V +2 H +N +157 396.95 510.3 396.95 2 L +V +0.5 H +N +157 374.95 510.3 374.95 2 L +V +N +157 352.95 510.3 352.95 2 L +V +N +157 330.95 510.3 330.95 2 L +V +N +157 308.95 510.3 308.95 2 L +V +N +FMENDPAGE +%%EndPage: "36" 37 +%%Page: "37" 37 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-37) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Refer) 63.65 732.95 T +(ences) 106.27 732.95 T +2 12 Q +2.36 ([1] D. E. Goldber) 135.65 694.95 P +2.36 (g,) 226.77 694.95 P +0 F +2.36 (Genetic Algorithms in Sear) 241.12 694.95 P +2.36 (ch, Optimization and Machine) 378.67 694.95 P +(Learning) 150.05 680.95 T +2 F +(, Addison W) 194.03 680.95 T +(esley Publishing Company) 254.03 680.95 T +(, January 1989.) 381.86 680.95 T +1.14 ([2] C. L. Karr) 135.65 658.95 P +1.14 (, \322Design of an Adaptive Fuzzy Logic Controller Using a Genetic) 204.85 658.95 P +(Algorithm\323,) 150.05 644.95 T +0 F +(Pr) 211.35 644.95 T +(oc. ICGA 4) 222.9 644.95 T +2 F +(, pp. 450-457, 1991.) 277.19 644.95 T +1.8 ([3] R. B. Holstien,) 135.65 622.95 P +0 F +1.8 (Arti\336cial Genetic Adaptation in Computer Contr) 234.46 622.95 P +1.8 (ol Systems) 476.55 622.95 P +2 F +1.8 (,) 528.65 622.95 P +7.26 (PhD Thesis, Department of Computer and Communication Sciences,) 150.05 608.95 P +(University of Michigan, Ann Arbor) 150.05 594.95 T +(, 1971.) 320.45 594.95 T +0.67 ([4] R. A. Caruana and J. D. Schaf) 135.65 572.95 P +0.67 (fer) 301.64 572.95 P +0.67 (, \322Representation and Hidden Bias: Gray vs.) 314.47 572.95 P +(Binary Coding\323,) 150.05 558.95 T +0 F +(Pr) 232.34 558.95 T +(oc. 6) 243.88 558.95 T +274.98 562.79 267.2 562.79 2 L +V +0.48 H +0 Z +N +0 10 Q +(th) 267.2 563.75 T +0 12 Q +( Int. Conf. Machine Learning) 274.98 558.95 T +2 F +(, pp153-161, 1988.) 415.56 558.95 T +2.14 ([5] W) 135.65 536.95 P +2.14 (. E. Schmitendor) 164.99 536.95 P +2.14 (gf, O. Shaw) 249.67 536.95 P +2.14 (, R. Benson and S. Forrest, \322Using Genetic) 310.46 536.95 P +1.16 (Algorithms for Controller Design: Simultaneous Stabilization and Eigenvalue) 150.05 522.95 P +4.21 (Placement in a Region\323,) 150.05 508.95 P +0 F +4.21 (T) 286.49 508.95 P +4.21 (echnical Report No. CS92-9) 292.05 508.95 P +2 F +4.21 (, Dept. Computer) 439.94 508.95 P +(Science, College of Engineering, University of New Mexico, 1992.) 150.05 494.95 T +1.52 ([6] M. F) 135.65 472.95 P +1.52 (. Bramlette, \322Initialization, Mutation and Selection Methods in Genetic) 178.04 472.95 P +(Algorithms for Function Optimization\323,) 150.05 458.95 T +0 F +(Pr) 344.94 458.95 T +(oc ICGA 4) 356.49 458.95 T +2 F +(, pp. 100-107, 1991.) 407.79 458.95 T +0.31 ([7] C. B. Lucasius and G. Kateman, \322T) 135.65 436.95 P +0.31 (owards Solving Subset Selection Problems) 324.51 436.95 P +2.37 (with the Aid of the Genetic Algorithm\323, In) 150.05 422.95 P +0 F +2.37 (Parallel Pr) 377.18 422.95 P +2.37 (oblem Solving fr) 433.41 422.95 P +2.37 (om) 516.99 422.95 P +2.89 (Natur) 150.05 408.95 P +2.89 (e 2) 177.6 408.95 P +2 F +2.89 (, R. M\212nner and B. Manderick, \050Eds.\051, pp. 239-247, Amsterdam:) 194.81 408.95 P +(North-Holland, 1992.) 150.05 394.95 T +2.88 ([8] A. H. W) 135.65 372.95 P +2.88 (right, \322Genetic Algorithms for Real Parameter Optimization\323, In) 201.41 372.95 P +0 F +-0.29 (Foundations of Genetic Algorithms) 150.05 358.95 P +2 F +-0.29 (, J. E. Rawlins \050Ed.\051, Mor) 318.74 358.95 P +-0.29 (gan Kaufmann, pp.) 440.31 358.95 P +(205-218, 1991.) 150.05 344.95 T +-0.01 ([9] Z. Michalewicz,) 135.65 322.95 P +0 F +-0.01 (Genetic Algorithms + Data Structur) 233.88 322.95 P +-0.01 (es = Evolution Pr) 407.41 322.95 P +-0.01 (ograms) 492.67 322.95 P +2 F +-0.01 (,) 528.65 322.95 P +(Springer V) 150.05 308.95 T +(erlag, 1992.) 201.68 308.95 T +4.12 ([10] T) 135.65 286.95 P +4.12 (. B\212ck, F) 169.19 286.95 P +4.12 (. Hof) 219.77 286.95 P +4.12 (fmeister and H.-P) 248.32 286.95 P +4.12 (. Schwefel, \322A Survey of Evolution) 340.17 286.95 P +(Strategies\323,) 150.05 272.95 T +0 F +(Pr) 208.67 272.95 T +(oc. ICGA 4) 220.22 272.95 T +2 F +(, pp. 2-10, 1991.) 274.52 272.95 T +1.27 ([1) 135.65 250.95 P +1.27 (1] J. J. Grefenstette, \322Incorporating Problem Speci\336c Knowledge into Genetic) 145.2 250.95 P +1.83 (Algorithms\323, In) 150.05 236.95 P +0 F +1.83 (Genetic Algorithms and Simulated Annealing) 232.66 236.95 P +2 F +1.83 (, pp. 42-60, L.) 457.86 236.95 P +(Davis \050Ed.\051, Mor) 150.05 222.95 T +(gan Kaufmann, 1987.) 231.77 222.95 T +0.89 ([12] D. Whitley) 135.65 200.95 P +0.89 (, K. Mathias and P) 212.93 200.95 P +0.89 (. Fitzhorn, \322Delta Coding: An Iterative Search) 304.45 200.95 P +(Strategy for Genetic Algorithms\323,) 150.05 186.95 T +0 F +(Pr) 316.27 186.95 T +(oc. ICGA 4) 327.81 186.95 T +2 F +(, pp. 77-84, 1991.) 382.11 186.95 T +1.8 ([13] K. A. De Jong,) 135.65 164.95 P +0 F +1.8 (Analysis of the Behaviour of a Class of Genetic Adaptive) 242.59 164.95 P +4.64 (Systems) 150.05 150.95 P +2 F +4.64 (, PhD Thesis, Dept. of Computer and Communication Sciences,) 188.02 150.95 P +(University of Michigan, Ann Arbor) 150.05 136.95 T +(, 1975.) 320.45 136.95 T +2.09 ([14] J. E. Baker) 135.65 114.95 P +2.09 (, \322Adaptive Selection Methods for Genetic Algorithms\323,) 217.03 114.95 P +0 F +2.09 (Pr) 505.78 114.95 P +2.09 (oc.) 517.33 114.95 P +(ICGA 1) 150.05 100.95 T +2 F +(, pp. 101-1) 187.02 100.95 T +(1) 238.55 100.95 T +(1, 1985.) 244.1 100.95 T +FMENDPAGE +%%EndPage: "37" 38 +%%Page: "38" 38 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-38) 513.33 61.29 T +2 12 Q +-0.08 ([15] J. E. Baker) 135.65 736.95 P +-0.08 (, \322Reducing bias and inef) 210.55 736.95 P +-0.08 (\336ciency in the selection algorithm\323,) 331.61 736.95 P +0 F +-0.08 (Pr) 505.78 736.95 P +-0.08 (oc.) 517.33 736.95 P +(ICGA 2) 150.05 722.95 T +2 F +(, pp. 14-21, 1987.) 187.02 722.95 T +0.71 ([16] L. Booker) 135.65 700.95 P +0.71 (, \322Improving search in genetic algorithms,\323 In) 208.2 700.95 P +0 F +0.71 (Genetic Algorithms) 437.33 700.95 P +4.04 (and Simulated Annealing) 150.05 686.95 P +2 F +4.04 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 279.4 686.95 P +4.04 (gan Kaufmann) 456.66 686.95 P +(Publishers, 1987.) 150.05 672.95 T +0 ([17] W) 135.65 650.95 P +0 (. M. Spears and K. A. De Jong, \322An Analysis of Multi-Point Crossover\323, In) 168.85 650.95 P +0 F +(Foundations of Genetic Algorithms) 150.05 636.95 T +2 F +(, J. E. Rawlins \050Ed.\051, pp. 301-315, 1991.) 319.62 636.95 T +0.66 ([18] G. Syswerda, \322Uniform crossover in genetic algorithms\323, Proc. ICGA 3, pp.) 135.65 614.95 P +(2-9, 1989.) 150.05 600.95 T +0.46 ([19] W) 135.65 578.95 P +0.46 (. M. Spears and K. A. De Jong, \322On the V) 169.31 578.95 P +0.46 (irtues of Parameterised Uniform) 375.38 578.95 P +(Crossover\323,) 150.05 564.95 T +0 F +(Pr) 210 564.95 T +(oc. ICGA 4) 221.55 564.95 T +2 F +(, pp.230-236, 1991.) 275.85 564.95 T +1.05 ([20] R. A. Caruana, L. A. Eshelman, J. D. Schaf) 135.65 542.95 P +1.05 (fer) 376.42 542.95 P +1.05 (, \322Representation and hidden) 389.25 542.95 P +-0.3 (bias II: Eliminating de\336ning length bias in genetic search via shuf) 150.05 528.95 P +-0.3 (\337e crossover\323,) 462.67 528.95 P +2.77 (In) 150.05 514.95 P +0 F +2.77 (Eleventh International Joint Confer) 165.81 514.95 P +2.77 (ence on Arti\336cial Intelligence) 345.24 514.95 P +2 F +2.77 (, N. S.) 495.79 514.95 P +(Sridharan \050Ed.\051, V) 150.05 500.95 T +(ol. 1, pp. 750-755, Mor) 237.1 500.95 T +(gan Kaufmann Publishers, 1989.) 348.82 500.95 T +3.24 ([21] H. M\237hlenbein and D. Schlierkamp-V) 135.65 478.95 P +3.24 (oosen, \322Predictive Models for the) 357.14 478.95 P +0.37 (Breeder Genetic Algorithm\323,) 150.05 464.95 P +0 F +0.37 (Evolutionary Computation) 293.72 464.95 P +2 F +0.37 (, V) 422.36 464.95 P +0.37 (ol. 1, No. 1, pp. 25-) 435.84 464.95 P +(49, 1993.) 150.05 450.95 T +1.26 ([22] H. Furuya and R. T) 135.65 428.95 P +1.26 (. Haftka, \322Genetic Algorithms for Placing Actuators on) 257.33 428.95 P +(Space Structures\323,) 150.05 414.95 T +0 F +(Pr) 241.64 414.95 T +(oc. ICGA 5) 253.19 414.95 T +2 F +(, pp. 536-542, 1993.) 307.48 414.95 T +0.3 ([23] C. Z. Janikow and Z. Michalewicz, \322An Experimental Comparison of Binary) 135.65 392.95 P +0.49 (and Floating Point Representations in Genetic Algorithms\323,) 150.05 378.95 P +0 F +0.49 (Pr) 443.33 378.95 P +0.49 (oc. ICGA 4) 454.89 378.95 P +2 F +0.49 (, pp.) 510.17 378.95 P +(31-36, 1991.) 150.05 364.95 T +0.74 ([24] D. M. T) 135.65 342.95 P +0.74 (ate and A. E. Smith, \322Expected Allele Conver) 198.65 342.95 P +0.74 (gence and the Role of) 424.11 342.95 P +(Mutation in Genetic Algorithms\323,) 150.05 328.95 T +0 F +(Pr) 315.62 328.95 T +(oc. ICGA) 327.17 328.95 T +2 F +( 5, pp.31-37, 1993.) 372.47 328.95 T +2.12 ([25] L. Davis, \322Adapting Operator Probabilities in Genetic Algorithms\323,) 135.65 306.95 P +0 F +2.12 (Pr) 505.78 306.95 P +2.12 (oc.) 517.33 306.95 P +(ICGA 3) 150.05 292.95 T +2 F +(, pp. 61-69, 1989.) 187.02 292.95 T +5.14 ([26] T) 135.65 270.95 P +5.14 (. C. Fogarty) 170.21 270.95 P +5.14 (, \322V) 237.02 270.95 P +5.14 (arying the Probability of Mutation in the Genetic) 260.81 270.95 P +(Algorithm\323,) 150.05 256.95 T +0 F +(Pr) 211.35 256.95 T +(oc. ICGA 3) 222.9 256.95 T +2 F +(, pp. 104-109, 1989.) 277.19 256.95 T +0.12 ([27] K. A. De Jong and J. Sarma, \322Generation Gaps Revisited\323, In) 135.65 234.95 P +0 F +0.12 ( Foundations of) 455.43 234.95 P +2.86 (Genetic Algorithms 2) 150.05 220.95 P +2 F +2.86 (, L. D. Whitley \050Ed.\051, Mor) 258.37 220.95 P +2.86 (gan Kaufmann Publishers,) 399.02 220.95 P +(1993.) 150.05 206.95 T +2.13 ([28] D. Whitley) 135.65 184.95 P +2.13 (, \322The GENIT) 215.4 184.95 P +2.13 (OR algorithm and selection pressure: why rank-) 288.38 184.95 P +1.7 (based allocations of reproductive trials is best\323,) 150.05 170.95 P +0 F +1.7 ( Pr) 387.77 170.95 P +1.7 (oc. ICGA 3) 404.02 170.95 P +2 F +1.7 (, pp. 1) 461.73 170.95 P +1.7 (16-121,) 494.67 170.95 P +(1989.) 150.05 156.95 T +2.82 ([29] R. Huang and T. C. Fogarty, \322Adaptive Classification and Control-Rule) 135.65 134.95 P +1.46 (Optimization Via a Learning Algorithm for Controlling a Dynamic System\323,) 150.05 120.95 P +0 F +(Proc. 30th Conf. Decision and Control) 150.05 106.95 T +2 F +(, Brighton, England, pp. 867-868, 1991.) 336.95 106.95 T +FMENDPAGE +%%EndPage: "38" 39 +%%Page: "39" 39 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-39) 513.33 61.29 T +2 12 Q +0.5 ([30] T) 135.65 736.95 P +0.5 (. C. Fogarty) 165.57 736.95 P +0.5 (, \322An Incremental Genetic Algorithm for Real-T) 223.11 736.95 P +0.5 (ime Learning\323,) 458.53 736.95 P +0 F +(Pr) 150.05 722.95 T +(oc. 6th Int. W) 161.6 722.95 T +(orkshop on Machine Learning) 225.45 722.95 T +2 F +(, pp. 416-419, 1989.) 371.03 722.95 T +2.13 ([31] D. E. Goldber) 135.65 700.95 P +2.13 (g and J. Richardson, \322Genetic Algorithms with Sharing for) 232.1 700.95 P +(Multimodal Function Optimization\323,) 150.05 686.95 T +0 F +(Pr) 329.96 686.95 T +(oc. ICGA 2) 341.51 686.95 T +2 F +(, pp.41-49, 1987.) 395.8 686.95 T +0.39 ([32] H. M\237hlenbein, M. Schomisch and J. Born, \322The Parallel Genetic Algorithm) 135.65 664.95 P +(as a Function Optimizer\323,) 150.05 650.95 T +0 F +(Parallel Computing) 276.96 650.95 T +2 F +(, No. 17, pp. 619-632, 1991.) 372.59 650.95 T +-0.14 ([33] T) 135.65 628.95 P +-0.14 (. Starkweather) 164.93 628.95 P +-0.14 (, D. Whitley and K. Mathias, \322Optimization Using Distributed) 233.59 628.95 P +0.85 (Genetic Algorithms\323,) 150.05 614.95 P +0 F +0.85 (Pr) 258 614.95 P +0.85 (oc. Parallel Pr) 269.55 614.95 P +0.85 (oblem Solving Fr) 342.43 614.95 P +0.85 (om Natur) 426.96 614.95 P +0.85 (e 1) 473.01 614.95 P +2 F +0.85 (, Lecture) 488.18 614.95 P +(Notes in Computer Science No. 496, pp. 176-185, Springer) 150.05 600.95 T +(-V) 434.29 600.95 T +(erlag, 1990.) 445.61 600.95 T +0.22 ([34] M. Geor) 135.65 578.95 P +0.22 (ges-Schleuter) 199.48 578.95 P +0.22 (, \322Comparison of Local Mating Strategies in Massively) 264.28 578.95 P +1.35 (Parallel Genetic Algorithms\323, In) 150.05 564.95 P +0 F +1.35 ( Parallel Pr) 309.98 564.95 P +1.35 (oblem Solving fr) 369.54 564.95 P +1.35 (om Natur) 451.08 564.95 P +1.35 (e 2) 497.64 564.95 P +2 F +1.35 (, R.) 513.3 564.95 P +1.77 (M\212nner and B. Manderick, \050Eds.\051, pp. 553-562, Amsterdam: North-Holland,) 150.05 550.95 P +(1992.) 150.05 536.95 T +FMENDPAGE +%%EndPage: "39" 40 +%%Trailer +%%BoundingBox: 0 0 595.3 841.9 +%%Pages: 39 1 +%%DocumentFonts: Times-Italic +%%+ Times-Bold +%%+ Times-Roman +%%+ Courier +%%+ Symbol +%%+ Times-BoldItalic +%%+ Courier-BoldOblique diff --git 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/ring /cedilla /hungarumlaut /ogonek /caron +] def +/ReEncode { + dup + length + dict begin + { + 1 index /FID ne + {def} + {pop pop} ifelse + } forall + 0 eq {/Encoding DiacriticEncoding def} if + currentdict + end + } bind def +/graymode true def + /bwidth FMLOCAL + /bpside FMLOCAL + /bstring FMLOCAL + /onbits FMLOCAL + /offbits FMLOCAL + /xindex FMLOCAL + /yindex FMLOCAL + /x FMLOCAL + /y FMLOCAL +/setpattern { + /bwidth exch def + /bpside exch def + /bstring exch def + /onbits 0 def /offbits 0 def + freq sangle landscape {90 add} if + {/y exch def + /x exch def + /xindex x 1 add 2 div bpside mul cvi def + /yindex y 1 add 2 div bpside mul cvi def + bstring yindex bwidth mul xindex 8 idiv add get + 1 7 xindex 8 mod sub bitshift and 0 ne + {/onbits onbits 1 add def 1} + {/offbits offbits 1 add def 0} + ifelse + } + setscreen + {} settransfer + offbits offbits onbits add div FMsetgray + /graymode false def + } bind def +/grayness { + FMsetgray + graymode not { + /graymode true def + orgxfer cvx settransfer + orgfreq organgle orgproc cvx setscreen + } if + } bind def + /HUE FMLOCAL + /SAT FMLOCAL + /BRIGHT FMLOCAL + /Colors FMLOCAL +FMPrintInColor + + { + /HUE 0 def + /SAT 0 def + /BRIGHT 0 def + % array of arrays Hue and Sat values for the separations [HUE BRIGHT] + /Colors + [[0 0 ] % black + [0 0 ] % white + [0.00 1.0] % red + [0.37 1.0] % green + [0.60 1.0] % blue + [0.50 1.0] % cyan + [0.83 1.0] % magenta + [0.16 1.0] % comment / yellow + ] def + + /BEGINBITMAPCOLOR { + BITMAPCOLOR} def + /BEGINBITMAPCOLORc { + BITMAPCOLORc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUECOLOR } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUECOLORc } def + /K { + Colors exch get dup + 0 get /HUE exch store + 1 get /BRIGHT exch store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } def + /FMsetgray { + /SAT exch 1.0 exch sub store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } bind def + } + + { + /BEGINBITMAPCOLOR { + BITMAPGRAY} def + /BEGINBITMAPCOLORc { + BITMAPGRAYc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUEGRAY } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUEGRAYc } def + /FMsetgray {setgray} bind def + /K { + pop + } def + } +ifelse +/normalize { + transform round exch round exch itransform + } bind def +/dnormalize { + dtransform round exch round exch idtransform + } bind def +/lnormalize { + 0 dtransform exch cvi 2 idiv 2 mul 1 add exch idtransform pop + } bind def +/H { + lnormalize setlinewidth + } bind def +/Z { + setlinecap + } bind def + /fillvals FMLOCAL +/X { + fillvals exch get + dup type /stringtype eq + {8 1 setpattern} + {grayness} + ifelse + } bind def +/V { + gsave eofill grestore + } bind def +/N { + stroke + } bind def +/M {newpath moveto} bind def +/E {lineto} bind def +/D {curveto} bind def +/O {closepath} bind def + /n FMLOCAL +/L { + /n exch def + newpath + normalize + moveto + 2 1 n {pop normalize lineto} for + } bind def +/Y { + L + closepath + } bind def + /x1 FMLOCAL + /x2 FMLOCAL + /y1 FMLOCAL + /y2 FMLOCAL + /rad FMLOCAL +/R { + /y2 exch def + /x2 exch def + /y1 exch def + /x1 exch def + x1 y1 + x2 y1 + x2 y2 + x1 y2 + 4 Y + } bind def +/RR { + /rad exch def + normalize + /y2 exch def + /x2 exch def + normalize + /y1 exch def + /x1 exch def + newpath + x1 y1 rad add moveto + x1 y2 x2 y2 rad arcto + x2 y2 x2 y1 rad arcto + x2 y1 x1 y1 rad arcto + x1 y1 x1 y2 rad arcto + closepath + 16 {pop} repeat + } bind def +/C { + grestore + gsave + R + clip + } bind def + /FMpointsize FMLOCAL +/F { + FMfonts exch get + FMpointsize scalefont + setfont + } bind def +/Q { + /FMpointsize exch def + F + } bind def +/T { + moveto show + } bind def +/RF { + rotate + 0 ne {-1 1 scale} if + } bind def +/TF { + gsave + moveto + RF + show + grestore + } bind def +/P { + moveto + 0 32 3 2 roll widthshow + } bind def +/PF { + gsave + moveto + RF + 0 32 3 2 roll widthshow + grestore + } bind def +/S { + moveto + 0 exch ashow + } bind def +/SF { + gsave + moveto + RF + 0 exch ashow + grestore + } bind def +/B { + moveto + 0 32 4 2 roll 0 exch awidthshow + } bind def +/BF { + gsave + moveto + RF + 0 32 4 2 roll 0 exch awidthshow + grestore + } bind def +/G { + gsave + newpath + normalize translate 0.0 0.0 moveto + dnormalize scale + 0.0 0.0 1.0 5 3 roll arc + closepath fill + grestore + } bind def +/A { + gsave + savematrix + newpath + 2 index 2 div add exch 3 index 2 div sub exch + normalize 2 index 2 div sub exch 3 index 2 div add exch + translate + scale + 0.0 0.0 1.0 5 3 roll arc + restorematrix + stroke + grestore + } bind def + /x FMLOCAL + /y FMLOCAL + /w FMLOCAL + /h FMLOCAL + /xx FMLOCAL + /yy FMLOCAL + /ww FMLOCAL + /hh FMLOCAL + /FMsaveobject FMLOCAL + /FMoptop FMLOCAL + /FMdicttop FMLOCAL +/BEGINPRINTCODE { + /FMdicttop countdictstack 1 add def + /FMoptop count 4 sub def + /FMsaveobject save def + userdict begin + /showpage {} def + FMNORMALIZEGRAPHICS + 3 index neg 3 index neg translate + } bind def +/ENDPRINTCODE { + count -1 FMoptop {pop pop} for + countdictstack -1 FMdicttop {pop end} for + FMsaveobject restore + } bind def +/gn { + 0 + { 46 mul + cf read pop + 32 sub + dup 46 lt {exit} if + 46 sub add + } loop + add + } bind def + /str FMLOCAL +/cfs { + /str sl string def + 0 1 sl 1 sub {str exch val put} for + str def + } bind def +/ic [ + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 + {0 hx} {1 hx} {2 hx} {3 hx} {4 hx} {5 hx} {6 hx} {7 hx} {8 hx} {9 hx} + {10 hx} {11 hx} {12 hx} {13 hx} {14 hx} {15 hx} {16 hx} {17 hx} {18 hx} + {19 hx} {gn hx} {0} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12} + {13} {14} {15} {16} {17} {18} {19} {gn} {0 wh} {1 wh} {2 wh} {3 wh} + {4 wh} {5 wh} {6 wh} {7 wh} {8 wh} {9 wh} {10 wh} {11 wh} {12 wh} + {13 wh} {14 wh} {gn wh} {0 bl} {1 bl} {2 bl} {3 bl} {4 bl} {5 bl} {6 bl} + {7 bl} {8 bl} {9 bl} {10 bl} {11 bl} {12 bl} {13 bl} {14 bl} {gn bl} + {0 fl} {1 fl} {2 fl} {3 fl} {4 fl} {5 fl} {6 fl} {7 fl} {8 fl} {9 fl} + {10 fl} {11 fl} {12 fl} {13 fl} {14 fl} {gn fl} + ] def + /sl FMLOCAL + /val FMLOCAL + /ws FMLOCAL + /im FMLOCAL + /bs FMLOCAL + /cs FMLOCAL + /len FMLOCAL + /pos FMLOCAL +/ms { + /sl exch def + /val 255 def + /ws cfs + /im cfs + /val 0 def + /bs cfs + /cs cfs + } bind def +400 ms +/ip { + is + 0 + cf cs readline pop + { ic exch get exec + add + } forall + pop + + } bind def +/wh { + /len exch def + /pos exch def + ws 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/bl { + /len exch def + /pos exch def + bs 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/s1 1 string def +/fl { + /len exch def + /pos exch def + /val cf s1 readhexstring pop 0 get def + pos 1 pos len add 1 sub {im exch val put} for + pos len + } bind def +/hx { + 3 copy getinterval + cf exch readhexstring pop pop + } bind def + /h FMLOCAL + /w FMLOCAL + /d FMLOCAL + /lb FMLOCAL + /bitmapsave FMLOCAL + /is FMLOCAL + /cf FMLOCAL +/wbytes { + dup + 8 eq {pop} {1 eq {7 add 8 idiv} {3 add 4 idiv} ifelse} ifelse + } bind def +/BEGINBITMAPBWc { + 1 {} COMMONBITMAPc + } bind def +/BEGINBITMAPGRAYc { + 8 {} COMMONBITMAPc + } bind def +/BEGINBITMAP2BITc { + 2 {} COMMONBITMAPc + } bind def +/COMMONBITMAPc { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + r + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} image + bitmapsave restore + grestore + } bind def +/BEGINBITMAPBW { + 1 {} COMMONBITMAP + } bind def +/BEGINBITMAPGRAY { + 8 {} COMMONBITMAP + } bind def +/BEGINBITMAP2BIT { + 2 {} COMMONBITMAP + } bind def +/COMMONBITMAP { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + r + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} image + bitmapsave restore + grestore + } bind def + /proc1 FMLOCAL + /proc2 FMLOCAL + /newproc FMLOCAL +/Fmcc { + /proc2 exch cvlit def + /proc1 exch cvlit def + /newproc proc1 length proc2 length add array def + newproc 0 proc1 putinterval + newproc proc1 length proc2 putinterval + newproc cvx +} bind def +/ngrayt 256 array def +/nredt 256 array def +/nbluet 256 array def +/ngreent 256 array def + /gryt FMLOCAL + /blut FMLOCAL + /grnt FMLOCAL + /redt FMLOCAL + /indx FMLOCAL + /cynu FMLOCAL + /magu FMLOCAL + /yelu FMLOCAL + /k FMLOCAL + /u FMLOCAL +/colorsetup { + currentcolortransfer + /gryt exch def + /blut exch def + /grnt exch def + /redt exch def + 0 1 255 { + /indx exch def + /cynu 1 red indx get 255 div sub def + /magu 1 green indx get 255 div sub def + /yelu 1 blue indx get 255 div sub def + /k cynu magu min yelu min def + /u k currentundercolorremoval exec def + nredt indx 1 0 cynu u sub max sub redt exec put + ngreent indx 1 0 magu u sub max sub grnt exec put + nbluet indx 1 0 yelu u sub max sub blut exec put + ngrayt indx 1 k currentblackgeneration exec sub gryt exec put + } for + {255 mul cvi nredt exch get} + {255 mul cvi ngreent exch get} + {255 mul cvi nbluet exch get} + {255 mul cvi ngrayt exch get} + setcolortransfer + {pop 0} setundercolorremoval + {} setblackgeneration + } bind def + /tran FMLOCAL +/fakecolorsetup { + /tran 256 string def + 0 1 255 {/indx exch def + tran indx + red indx get 77 mul + green indx get 151 mul + blue indx get 28 mul + add add 256 idiv put} for + currenttransfer + {255 mul cvi tran exch get 255.0 div} + exch Fmcc settransfer +} bind def +/BITMAPCOLOR { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + colorsetup + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPCOLORc { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + colorsetup + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLORc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip} {gip} {bip} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLOR { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop } + { cf gis readhexstring pop } + { cf bis readhexstring pop } + true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUEGRAYc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip gip bip w gray} image + bitmapsave restore + grestore + } bind def +/ww FMLOCAL +/r FMLOCAL +/g FMLOCAL +/b FMLOCAL +/i FMLOCAL +/gray { + /ww exch def + /b exch def + /g exch def + /r exch def + 0 1 ww 1 sub { /i exch def r i get .299 mul g i get .587 mul + b i get .114 mul add add r i 3 -1 roll floor cvi put } for + r + } bind def +/BITMAPTRUEGRAY { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop + cf gis readhexstring pop + cf bis readhexstring pop w gray} image + bitmapsave restore + grestore + } bind def +/BITMAPGRAY { + 8 {fakecolorsetup} COMMONBITMAP + } bind def +/BITMAPGRAYc { + 8 {fakecolorsetup} COMMONBITMAPc + } bind def +/ENDBITMAP { + } bind def +end + /ALDsave FMLOCAL + /ALDmatrix matrix def ALDmatrix currentmatrix pop +/StartALD { + /ALDsave save def + savematrix + ALDmatrix setmatrix + } bind def +/InALD { + restorematrix + } bind def +/DoneALD { + ALDsave restore + } bind def +%%EndProlog +%%BeginSetup +(3.0) FMVERSION +1 1 595.3 841.9 0 1 15 FMDOCUMENT +0 0 /Times-Italic FMFONTDEFINE +1 0 /Times-Bold FMFONTDEFINE +2 0 /Courier FMFONTDEFINE +3 0 /Times-Roman FMFONTDEFINE +4 1 /Symbol FMFONTDEFINE +32 FMFILLS +0 0 FMFILL +1 .1 FMFILL +2 .3 FMFILL +3 .5 FMFILL +4 .7 FMFILL +5 .9 FMFILL +6 .97 FMFILL +7 1 FMFILL +8 <0f1e3c78f0e1c387> FMFILL +9 <0f87c3e1f0783c1e> FMFILL +10 FMFILL +11 FMFILL +12 <8142241818244281> FMFILL +13 <03060c183060c081> FMFILL +14 <8040201008040201> FMFILL +16 1 FMFILL +17 .9 FMFILL +18 .7 FMFILL +19 .5 FMFILL +20 .3 FMFILL +21 .1 FMFILL +22 0.03 FMFILL +23 0 FMFILL +24 FMFILL +25 FMFILL +26 <3333333333333333> FMFILL +27 <0000ffff0000ffff> FMFILL +28 <7ebddbe7e7dbbd7e> FMFILL +29 FMFILL +30 <7fbfdfeff7fbfdfe> FMFILL +%%EndSetup +%%Page: "1" 1 +%%BeginPaperSize: A4 +%%EndPaperSize +595.3 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...................................................................................................) 186.02 612.95 T +(2-1) 486.65 612.95 T +(1) 502.19 612.95 T +2 F +(mut) 135.65 592.95 T +3 F +( ............................................................................................................) 157.24 592.95 T +(2-14) 486.65 592.95 T +2 F +(mutate) 135.65 572.95 T +3 F +( .....................................................................................................) 178.82 572.95 T +(2-16) 486.65 572.95 T +2 F +(mutbga) 135.65 552.95 T +3 F +( .....................................................................................................) 178.82 552.95 T +(2-17) 486.65 552.95 T +2 F +(ranking) 135.65 532.95 T +3 F +( ...................................................................................................) 186.02 532.95 T +(2-20) 486.65 532.95 T +2 F +(recdis) 135.65 512.95 T +3 F +( .....................................................................................................) 178.82 512.95 T +(2-24) 486.65 512.95 T +2 F +(recint) 135.65 492.95 T +3 F +( .....................................................................................................) 178.82 492.95 T +(2-26) 486.65 492.95 T +2 F +(reclin) 135.65 472.95 T +3 F +( .....................................................................................................) 178.82 472.95 T +(2-28) 486.65 472.95 T +2 F +(recmut) 135.65 452.95 T +3 F +( .....................................................................................................) 178.82 452.95 T +(2-30) 486.65 452.95 T +2 F +(recombin) 135.65 432.95 T +3 F +( .................................................................................................) 193.22 432.95 T +(2-33) 487.05 432.95 T +2 F +(reins) 135.65 412.95 T +3 F +( ........................................................................................................) 171.63 412.95 T +(2-34) 486.65 412.95 T +2 F +(rep) 135.65 392.95 T +3 F +( .............................................................................................................) 157.24 392.95 T +(2-37) 487.05 392.95 T +2 F +(rws) 135.65 372.95 T +3 F +( .............................................................................................................) 157.24 372.95 T +(2-38) 487.05 372.95 T +2 F +(scaling) 135.65 352.95 T +3 F +( ...................................................................................................) 186.02 352.95 T +(2-40) 486.65 352.95 T +2 F +(select) 135.65 332.95 T +3 F +( .....................................................................................................) 178.82 332.95 T +(2-41) 486.65 332.95 T +2 F +(sus) 135.65 312.95 T +3 F +( ............................................................................................................) 157.24 312.95 T +(2-44) 486.65 312.95 T +2 F +(xovdp) 135.65 292.95 T +3 F +( ........................................................................................................) 171.63 292.95 T +(2-46) 486.65 292.95 T +2 F +(xovdprs) 135.65 272.95 T +3 F +( ...................................................................................................) 186.02 272.95 T +(2-47) 486.65 272.95 T +2 F +(xovmp) 135.65 252.95 T +3 F +( ........................................................................................................) 171.63 252.95 T +(2-48) 486.65 252.95 T +2 F +(xovsh) 135.65 232.95 T +3 F +( ........................................................................................................) 171.63 232.95 T +(2-49) 486.65 232.95 T +2 F +(xovshrs) 135.65 212.95 T +3 F +( ...................................................................................................) 186.02 212.95 T +(2-50) 486.65 212.95 T +2 F +(xovsp) 135.65 192.95 T +3 F +( ........................................................................................................) 171.63 192.95 T +(2-51) 486.65 192.95 T +2 F +(xovsprs) 135.65 172.95 T +3 F +( ...................................................................................................) 186.02 172.95 T +(2-52) 486.65 172.95 T +FMENDPAGE +%%EndPage: "1" 2 +%%Page: "2" 2 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-2) 518.33 61.29 T +1 28 Q +(2 Refer) 63.65 726.29 T +(ence) 150.98 726.29 T +3 12 Q +1.19 (This Section contains detailed descriptions of all of the functions in the Genetic) 135.65 692.95 P +0.55 (Algorithm T) 135.65 678.95 P +0.55 (oolbox. It begins with a list of functions grouped by subject area and) 195.66 678.95 P +5.8 (continues with) 135.65 664.95 P +0 F +5.8 (Refer) 220.53 664.95 P +5.8 (ence) 246.07 664.95 P +3 F +5.8 (entries in alphabetical order) 276.83 664.95 P +5.8 (. Information about) 427.12 664.95 P +(individual functions is also available through the on-line) 135.65 650.95 T +2 F +(Help) 409.48 650.95 T +3 F +( facility) 438.27 650.95 T +(.) 474.46 650.95 T +FMENDPAGE +%%EndPage: "2" 3 +%%Page: "3" 3 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-3) 518.33 61.29 T +3 12 Q +(CREA) 262.19 696.95 T +(TING POPULA) 292.85 696.95 T +(TIONS) 369.8 696.95 T +2 F +(crtbase) 141.65 672.95 T +3 F +(create a base vector) 249.65 672.95 T +2 F +(crtbp) 141.65 650.95 T +3 F +(create arbitrary discrete random populations) 249.65 650.95 T +2 F +(crtrp) 141.65 628.95 T +3 F +(create real-valued initial population) 249.65 628.95 T +(FITNESS ASSIGNMENT) 269.85 558.95 T +2 F +(ranking) 141.65 534.95 T +3 F +(generalised rank-based \336tness assignment) 249.65 534.95 T +2 F +(scaling) 141.65 512.95 T +3 F +(proportional \336tness scaling) 249.65 512.95 T +(SELECTION FUNCTIONS) 265.86 442.95 T +2 F +(reins) 141.65 418.95 T +3 F +(uniform random and \336tness-based reinsertion) 249.65 418.95 T +2 F +(rws) 141.65 396.95 T +3 F +(roulette wheel selection) 249.65 396.95 T +2 F +(select) 141.65 374.95 T +3 F +(high-level selection routine) 249.65 374.95 T +2 F +(sus) 141.65 352.95 T +3 F +(stochastic universal sampling) 249.65 352.95 T +(MUT) 267.11 282.95 T +(A) 292.8 282.95 T +(TION OPERA) 300.13 282.95 T +(T) 369.75 282.95 T +(ORS) 376.86 282.95 T +2 F +(mut) 141.65 258.95 T +3 F +(discrete mutation) 249.65 258.95 T +2 F +(mutate) 141.65 236.95 T +3 F +(high-level mutation function) 249.65 236.95 T +2 F +(mutbga) 141.65 214.95 T +3 F +(real-value mutation) 249.65 214.95 T +135.65 712.7 135.65 621.2 2 L +V +0.5 H +0 Z +N +243.65 685.45 243.65 620.7 2 L +V +N +531.65 712.7 531.65 621.2 2 L +V +N +135.4 712.95 531.9 712.95 2 L +V +N +135.9 688.2 531.4 688.2 2 L +V +N +135.9 685.7 531.4 685.7 2 L +V +N +135.4 620.95 531.9 620.95 2 L +V +N +135.65 574.7 135.65 505.2 2 L +V +N +243.65 547.45 243.65 504.7 2 L +V +N +531.65 574.7 531.65 505.2 2 L +V +N +135.4 574.95 531.9 574.95 2 L +V +N +135.9 550.2 531.4 550.2 2 L +V +N +135.9 547.7 531.4 547.7 2 L +V +N +135.4 504.95 531.9 504.95 2 L +V +N +135.65 458.7 135.65 345.2 2 L +V +N +243.65 431.45 243.65 344.7 2 L +V +N +531.65 458.7 531.65 345.2 2 L +V +N +135.4 458.95 531.9 458.95 2 L +V +N +135.9 434.2 531.4 434.2 2 L +V +N +135.9 431.7 531.4 431.7 2 L +V +N +135.4 344.95 531.9 344.95 2 L +V +N +135.65 298.7 135.65 207.2 2 L +V +N +243.65 271.45 243.65 206.7 2 L +V +N +531.65 298.7 531.65 207.2 2 L +V +N +135.4 298.95 531.9 298.95 2 L +V +N +135.9 274.2 531.4 274.2 2 L +V +N +135.9 271.7 531.4 271.7 2 L +V +N +135.4 206.95 531.9 206.95 2 L +V +N +FMENDPAGE +%%EndPage: "3" 4 +%%Page: "4" 4 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-4) 518.33 61.29 T +3 12 Q +(CROSSOVER OPERA) 262.62 696.95 T +(T) 374.24 696.95 T +(ORS) 381.35 696.95 T +2 F +(recdis) 141.65 672.95 T +3 F +(discrete recombination) 249.65 672.95 T +2 F +(recint) 141.65 650.95 T +3 F +(intermediate recombination) 249.65 650.95 T +2 F +(reclin) 141.65 628.95 T +3 F +(line recombination) 249.65 628.95 T +2 F +(recmut) 141.65 606.95 T +3 F +(line recombination with mutation features) 249.65 606.95 T +2 F +(recombin) 141.65 584.95 T +3 F +(high-level recombination operator) 249.65 584.95 T +2 F +(xovdp) 141.65 562.95 T +3 F +(double-point crossover) 249.65 562.95 T +2 F +(xovdprs) 141.65 540.95 T +3 F +(double-point reduced surrogate crossover) 249.65 540.95 T +2 F +(xovmp) 141.65 518.95 T +3 F +(general multi-point crossover) 249.65 518.95 T +2 F +(xovsh) 141.65 496.95 T +3 F +(shuf) 249.65 496.95 T +(\337e crossover) 270.08 496.95 T +2 F +(xovshrs) 141.65 474.95 T +3 F +(shuf) 249.65 474.95 T +(\337e reduced surrogate crossover) 270.08 474.95 T +2 F +(xovsp) 141.65 452.95 T +3 F +(single-point crossover) 249.65 452.95 T +2 F +(xovsprs) 141.65 430.95 T +3 F +(single-point reduced surrogate crossover) 249.65 430.95 T +(SUBPOPULA) 257.54 360.95 T +(TION SUPPOR) 326.18 360.95 T +(T) 402.42 360.95 T +2 F +(migrate) 141.65 336.95 T +3 F +(exchange individuals between subpopulations) 249.65 336.95 T +(UTILITY FUNCTIONS) 274.86 266.95 T +2 F +(bs2rv) 141.65 242.95 T +3 F +(binary string to real-value conversion) 249.65 242.95 T +2 F +(rep) 141.65 220.95 T +3 F +(matrix replication) 249.65 220.95 T +135.65 712.7 135.65 423.2 2 L +V +0.5 H +0 Z +N +243.65 685.45 243.65 422.7 2 L +V +N +531.65 712.7 531.65 423.2 2 L +V +N +135.4 712.95 531.9 712.95 2 L +V +N +135.9 688.2 531.4 688.2 2 L +V +N +135.9 685.7 531.4 685.7 2 L +V +N +135.4 422.95 531.9 422.95 2 L +V +N +135.65 376.7 135.65 329.2 2 L +V +N +243.65 349.45 243.65 328.7 2 L +V +N +531.65 376.7 531.65 329.2 2 L +V +N +135.4 376.95 531.9 376.95 2 L +V +N +135.9 352.2 531.4 352.2 2 L +V +N +135.9 349.7 531.4 349.7 2 L +V +N +135.4 328.95 531.9 328.95 2 L +V +N +135.65 282.7 135.65 213.2 2 L +V +N +243.65 255.45 243.65 212.7 2 L +V +N +531.65 282.7 531.65 213.2 2 L +V +N +135.4 282.95 531.9 282.95 2 L +V +N +135.9 258.2 531.4 258.2 2 L +V +N +135.9 255.7 531.4 255.7 2 L +V +N +135.4 212.95 531.9 212.95 2 L +V +N +FMENDPAGE +%%EndPage: "4" 5 +%%Page: "5" 5 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-5) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(bs2rv) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(binary string to real value conversion) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(Phen = bs2rv\050Chrom, FieldD\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +1.31 (Phen = bs2rv\050Chrom, FieldD\051) 135.65 588.95 P +3 F +0.55 ( decodes the binary representation of the) 333.87 588.95 P +5.26 (population,) 135.65 574.95 P +2 F +12.62 (Chrom) 198.21 574.95 P +3 F +5.26 (, into vectors of reals. The chromosomes are seen as) 234.19 574.95 P +0.28 (concatenated binary strings of given length, and decoded into real numbers over a) 135.65 560.95 P +1.93 (speci\336ed interval using either standard binary or Gray coding according to the) 135.65 546.95 P +8.28 (decoding matrix,) 135.65 532.95 P +2 F +19.86 (FieldD) 236.48 532.95 P +3 F +8.28 (. The resulting matrix,) 279.65 532.95 P +2 F +19.86 (Phen) 422.69 532.95 P +3 F +8.28 (, contains the) 451.47 532.95 P +(corresponding population phenotypes.) 135.65 518.95 T +0.12 (The use of Gray coding for binary chromosome representation is recommended as) 135.65 492.95 P +-0.23 (the regular Hamming distance between quantization intervals reportedly makes the) 135.65 478.95 P +-0.12 (genetic search less deceptive \050see, for example, [1, 2]\051. An option to set the scaling) 135.65 464.95 P +2.54 (between quantization points can be used to select either linear or logarithmic) 135.65 450.95 P +-0.17 (decoding to real values from binary strings. Logarithmic scaling is useful when the) 135.65 436.95 P +0.26 (range of decision variable is unknown at the outset as a wider range of parametric) 135.65 422.95 P +3.55 (values can be searched with fewer bits [3], thus reducing the memory and) 135.65 408.95 P +(computational requirements of the GA.) 135.65 394.95 T +(The matrix) 135.65 368.95 T +2 F +(FieldD) 191.61 368.95 T +3 F +( has the following structure:) 234.79 368.95 T +(,) 356.55 294.72 T +(where the rows of the matrix are composed as follows:) 135.65 221.66 T +2 F +3.26 (len) 135.65 195.66 P +3 F +1.36 (, a row vector containing the length of each substring in) 157.24 195.66 P +2 F +3.26 (Chrom) 442.65 195.66 P +3 F +1.36 (. Note that) 478.63 195.66 P +2 F +(sum\050len\051) 135.65 181.66 T +3 F +( should equal) 193.22 181.66 T +2 F +(length\050Chrom\051) 260.18 181.66 T +3 F +(.) 353.72 181.66 T +2 F +-0.15 (lb) 135.65 155.66 P +3 F +-0.06 ( and) 150.04 155.66 P +2 F +-0.15 (ub) 173.23 155.66 P +3 F +-0.06 ( are row vectors containing the lower and upper bounds respectively for) 187.62 155.66 P +(each variable used.) 135.65 141.66 T +2 F +4.76 (code) 135.65 115.66 P +3 F +1.98 ( is a binary row vector indicating how each substring is decoded. Select) 164.43 115.66 P +2 F +(code\050i\051 = 0) 135.65 101.66 T +3 F +( for standard binary and) 214.8 101.66 T +2 F +(code\050i\051 = 1) 332.38 101.66 T +3 F +( for Gray coding.) 411.53 101.66 T +307.75 243.66 356.55 350.95 C +2 12 Q +0 X +0 K +(l) 321.15 335.96 T +(e) 329.05 335.96 T +(n) 336.95 335.96 T +(l) 325.1 321.49 T +(b) 333 321.49 T +(u) 325.1 307.02 T +(b) 333 307.02 T +(c) 317.2 292.55 T +(o) 325.1 292.55 T +(d) 333 292.55 T +(e) 340.9 292.55 T +(s) 313.25 278.08 T +(c) 321.15 278.08 T +(a) 329.05 278.08 T +(l) 336.95 278.08 T +(e) 344.86 278.08 T +(l) 317.2 263.61 T +(b) 325.1 263.61 T +(i) 333 263.61 T +(n) 340.9 263.61 T +(u) 317.2 249.14 T +(b) 325.1 249.14 T +(i) 333 249.14 T +(n) 340.9 249.14 T +314.75 246.66 310.75 246.66 2 L +0.33 H +0 Z +N +310.75 246.66 310.75 347.95 2 L +N +310.75 347.95 314.75 347.95 2 L +N +349.55 246.66 353.55 246.66 2 L +N +353.55 246.66 353.55 347.95 2 L +N +353.55 347.95 349.55 347.95 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "5" 6 +%%Page: "6" 6 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-6) 518.33 61.29 T +2 12 Q +9.44 (scale) 135.65 736.95 P +3 F +3.93 ( is a binary row vector indicating whether to use arithmetic and/or) 171.63 736.95 P +1.68 (logarithmic scaling for each substring. Select) 135.65 722.95 P +2 F +4.03 (scale\050i\051 = 0) 365.25 722.95 P +3 F +1.68 ( for arithmetic) 459.67 722.95 P +(scaling and) 135.65 708.95 T +2 F +(scale\050i\051 = 1) 192.94 708.95 T +3 F +( for logarithmic scaling.) 279.29 708.95 T +2 F +0.93 (lbin) 135.65 682.95 P +3 F +0.39 ( and) 164.43 682.95 P +2 F +0.93 (ubin) 188.52 682.95 P +3 F +0.39 ( are binary row vectors indicating whether or not to include each) 217.3 682.95 P +2.86 (bound in the representation range. Select) 135.65 668.95 P +2 F +6.86 ({l|u}bin\050i\051 = 0) 351.65 668.95 P +3 F +2.86 ( to exclude) 473.3 668.95 P +2 F +0.9 ({l|u}b\050i\051) 135.65 654.95 P +3 F +0.38 ( from the representation range and) 200.41 654.95 P +2 F +0.9 ({l|u}bin\050i\051 = 1) 370.52 654.95 P +3 F +0.38 ( to include) 480.26 654.95 P +2 F +({l|u}b\050i\051) 135.65 640.95 T +3 F +( in the representation range.) 200.41 640.95 T +1 16 Q +(Example) 117.65 612.29 T +3 12 Q +2.8 (Consider the following binary population, created using the) 135.65 594.95 P +2 F +6.73 (crtbp) 446.89 594.95 P +3 F +2.8 ( function,) 482.87 594.95 P +2.25 (representing a set of single decision variables in the range [-1, 10]. The code) 135.65 580.95 P +1.74 (extract shows how the function) 135.65 566.95 P +2 F +4.17 (bs2rv) 297.24 566.95 P +3 F +1.74 ( may be used to convert the Gray code) 333.22 566.95 P +(binary representation to real-valued phenotypes using arithmetic scaling.) 135.65 552.95 T +2 F +(Chrom = crtbp\0504,8\051 % create random chromosomes) 135.65 532.95 T +(Chrom =) 135.65 512.95 T +(0 0 0 0 0 1 1 1) 153.65 498.95 T +(1 0 0 0 1 0 0 1) 153.65 484.95 T +(0 0 1 0 1 0 0 0) 153.65 470.95 T +(1 1 0 1 1 0 1 1) 153.65 456.95 T +(FieldD = [8; -1; 10; 1; 0; 1; 1]; % representation) 135.65 436.95 T +(Phen = bs2rv\050Chrom,FieldD\051 % convert binary to real) 135.65 416.95 T +(Phen =) 135.65 396.95 T +(-0.7843) 153.65 382.95 T +(9.3961) 160.84 368.95 T +(1.0706) 160.84 354.95 T +(5.2980) 160.84 340.95 T +1 16 Q +(Algorithm) 117.65 318.29 T +2 12 Q +2.04 (bs2rv) 135.65 300.95 P +3 F +0.85 ( is implemented as an m-\336le in the GA T) 171.63 300.95 P +0.85 (oolbox. If logarithmic scaling is) 374.67 300.95 P +(used then the range must not include zero.) 135.65 286.95 T +1 16 Q +(Refer) 117.65 258.29 T +(ence) 155.53 258.29 T +3 12 Q +1.8 ([1] R. B. Holstien,) 135.65 240.95 P +0 F +1.8 (Arti\336cial Genetic Adaptation in Computer Contr) 234.46 240.95 P +1.8 (ol Systems) 476.55 240.95 P +3 F +1.8 (,) 528.65 240.95 P +0.7 (Ph.D. Thesis, Department of Computer and Communication Sciences, University) 135.65 226.95 P +(of Michigan, Ann Arbor) 135.65 212.95 T +(, 1971.) 252.42 212.95 T +0.67 ([2] R. A. Caruana and J. D. Schaf) 135.65 186.95 P +0.67 (fer) 301.64 186.95 P +0.67 (, \322Representation and Hidden Bias: Gray vs.) 314.47 186.95 P +(Binary Coding\323,) 135.65 172.95 T +0 F +(Pr) 217.93 172.95 T +(oc. 6) 229.48 172.95 T +260.58 176.79 252.8 176.79 2 L +V +0.48 H +0 Z +N +0 10 Q +(th) 252.8 177.75 T +0 12 Q +( Int. Conf. Machine Learning) 260.58 172.95 T +3 F +(, pp153-161, 1988.) 401.16 172.95 T +2.14 ([3] W) 135.65 146.95 P +2.14 (. E. Schmitendor) 164.99 146.95 P +2.14 (gf, O. Shaw) 249.67 146.95 P +2.14 (, R. Benson and S. Forrest, \322Using Genetic) 310.46 146.95 P +3.22 (Algorithms for Controller Design: Simultaneous Stabilization and Eigenvalue) 135.65 132.95 P +0.9 (Placement in a Region\323,) 135.65 118.95 P +0 F +0.9 (T) 258.84 118.95 P +0.9 (echnical Report No. CS92-9) 264.41 118.95 P +3 F +0.9 (, Dept. Computer Science,) 402.36 118.95 P +(College of Engineering, University of New Mexico, 1992.) 135.65 104.95 T +FMENDPAGE +%%EndPage: "6" 7 +%%Page: "7" 7 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-7) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(crtbase) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Create a base vector) 135.65 674.95 T +(.) 231.9 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(BaseVec = crtbase\050Lind, Base\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.66 (crtbase) 135.65 588.95 P +3 F +0.27 ( produces a vector whose elements correspond to the base of the loci of) 186.02 588.95 P +1.48 (a chromosome structure. This function can be used in conjunction with) 135.65 574.95 P +2 F +3.55 (crtbp) 495.67 574.95 P +3 F +(when creating populations using representations in dif) 135.65 560.95 T +(ferent bases.) 395.26 560.95 T +2 F +-0.28 (BaseVec = crtbase\050Lind, Base\051) 135.65 534.95 P +3 F +-0.12 ( creates a vector of length) 343.49 534.95 P +2 F +-0.28 (Lind) 469.34 534.95 P +3 F +-0.12 ( whose) 498.12 534.95 P +8.25 (individual elements are of base) 135.65 520.95 P +2 F +19.8 (Base) 329.13 520.95 P +3 F +8.25 (. If) 357.91 520.95 P +2 F +19.8 (Lind) 391.4 520.95 P +3 F +8.25 ( is a vector) 420.18 520.95 P +8.25 (, then) 496.75 520.95 P +2 F +13.9 (length\050BaseVec\051 = sum\050Lind\051) 135.65 506.95 P +3 F +5.79 (. If) 357.74 506.95 P +2 F +13.9 (Base) 386.31 506.95 P +3 F +5.79 ( is also a vector of) 415.09 506.95 P +2 F +7.3 (length\050Lind\051) 135.65 492.95 P +3 F +3.04 (, then) 222 492.95 P +2 F +7.3 (BaseVec) 257.73 492.95 P +3 F +3.04 ( is composed of groups of bases of length) 308.11 492.95 P +1.43 (determined by the elements of) 135.65 478.95 P +2 F +3.44 (Lind) 291.04 478.95 P +3 F +1.43 ( and base) 319.83 478.95 P +2 F +3.44 (Base) 371.76 478.95 P +3 F +1.43 (. This last option is useful) 400.54 478.95 P +(when describing populations with structure.) 135.65 464.95 T +1 16 Q +(Example) 117.65 436.29 T +3 12 Q +0.03 (T) 135.65 418.95 P +0.03 (o create a basevector for a population containing four elements in base 8 and \336ve) 142.14 418.95 P +(elements in base four:) 135.65 404.95 T +2 F +(BaseV = crtbase\050[4 5], [8 4]\051) 135.65 384.95 T +(BaseV =) 135.65 364.95 T +(8 8 8 8 4 4 4 4 4) 153.65 350.95 T +1 16 Q +(See Also) 117.65 328.29 T +2 12 Q +(crtbp) 135.65 310.95 T +3 F +(,) 171.63 310.95 T +2 F +(bs2rv) 177.62 310.95 T +FMENDPAGE +%%EndPage: "7" 8 +%%Page: "8" 8 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-8) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(crtbp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Create an initial population.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +([Chrom, Lind, BaseV] = crtbp\050Nind, Lind\051) 135.65 628.95 T +([Chrom, Lind, BaseV] = crtbp\050Nind, Lind, Base\051) 135.65 608.95 T +([Chrom, Lind, BaseV] = crtbp\050Nind, BaseV\051) 135.65 588.95 T +1 16 Q +(Description) 117.65 566.29 T +3 12 Q +0.45 (The \336rst step in a genetic algorithm is to create an initial population consisting of) 135.65 548.95 P +2.57 (random chromosomes.) 135.65 534.95 P +2 F +6.18 (crtbp) 253.05 534.95 P +3 F +2.57 ( produces a matrix,) 289.03 534.95 P +2 F +6.18 (Chrom) 394.25 534.95 P +3 F +2.57 (, containing random) 430.23 534.95 P +(values in its elements.) 135.65 520.95 T +2 F +4.94 (Chrom = crtbp\050Nind, Lind\051) 135.65 494.95 P +3 F +2.06 ( creates a random binary matrix of size) 330.38 494.95 P +-0.26 (, where) 212.04 480.95 P +2 F +-0.64 (Nind) 249.8 480.95 P +3 F +-0.26 ( speci\336es the number of individuals in the population) 278.58 480.95 P +8.37 (and) 135.65 466.95 P +2 F +20.1 (Lind) 164.34 466.95 P +3 F +8.37 ( the length of the individuals. Additionally) 193.12 466.95 P +8.37 (,) 446.81 466.95 P +2 F +20.1 (Chrom =) 461.18 466.95 P +9.35 (crtbp\050[Nind, Lind]\051) 135.65 452.95 P +3 F +3.9 ( can be used to specify the dimensions of the) 281.73 452.95 P +(chromosome matrix.) 135.65 438.95 T +2 F +0.99 (Chrom = crtbp\050Nind, Lind, Base\051) 135.65 412.95 P +3 F +0.41 ( produces a chromosome matrix of) 362.7 412.95 P +-0.27 (base) 135.65 398.95 P +2 F +-0.64 (Base) 159.69 398.95 P +3 F +-0.27 (. If) 188.48 398.95 P +2 F +-0.64 (Base) 204.92 398.95 P +3 F +-0.27 ( is a vector) 233.71 398.95 P +-0.27 (, then the value of the elements of) 284.71 398.95 P +2 F +-0.64 (Base) 448.11 398.95 P +3 F +-0.27 ( specify the) 476.89 398.95 P +2.26 (base of the loci of the chromosomes. In this case, the second right hand side) 135.65 384.95 P +(ar) 135.65 370.95 T +(gument may be omitted,) 144.75 370.95 T +2 F +(Chrom = crtbp\050Nind, BaseV\051) 264.35 370.95 T +3 F +(.) 451.45 370.95 T +2 F +3.95 ([Chrom, Lind, BaseV] = crtbp\050Nind, BaseV\051) 135.65 344.95 P +3 F +1.65 ( also returns the) 450.43 344.95 P +-0.27 (length of the chromosome structure,) 135.65 330.95 P +2 F +-0.65 (Lind) 310.83 330.95 P +3 F +-0.27 (, and the base of the chromosome loci in) 339.62 330.95 P +(the vector) 135.65 316.95 T +2 F +(BaseV) 186.27 316.95 T +3 F +(.) 220.71 316.95 T +1 16 Q +(Example) 117.65 288.29 T +3 12 Q +0.05 (T) 135.65 270.95 P +0.05 (o create a random population of 6 individuals of length 8 where the \336rst four loci) 142.14 270.95 P +(are base eight and the last \336ve loci are base four:) 135.65 256.95 T +2 F +(BaseV = crtbase\050[4 5], [8 4]\051) 135.65 236.95 T +(Chrom = crtbp\0506, BaseV\051) 135.65 216.95 T +3 F +(or) 135.65 196.95 T +2 F +(Chrom = crtbp\050[6,8],[8 8 8 8 4 4 4 4 4]\051) 135.65 176.95 T +135.65 477.47 212.04 489.94 C +2 12 Q +0 X +0 K +(N) 136.65 480.95 T +(i) 144.55 480.95 T +(n) 152.45 480.95 T +(d) 160.35 480.95 T +(L) 180.13 480.95 T +(i) 188.04 480.95 T +(n) 195.94 480.95 T +(d) 203.84 480.95 T +4 F +(\264) 170.55 480.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "8" 9 +%%Page: "9" 9 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-9) 518.33 61.29 T +2 12 Q +(Chrom =) 135.65 736.95 T +(4 3 1 1 2 0 2 0 3) 153.65 722.95 T +(1 4 7 5 2 1 1 1 0) 153.65 708.95 T +(1 3 0 1 0 0 0 0 2) 153.65 694.95 T +(1 5 5 7 2 0 2 3 1) 153.65 680.95 T +(4 5 7 7 0 1 3 0 3) 153.65 666.95 T +(4 2 4 0 3 3 1 1 0) 153.65 652.95 T +1 16 Q +(Algorithm) 117.65 630.29 T +2 12 Q +(crtbp) 135.65 612.95 T +3 F +( is an m-\336le in the GA T) 171.63 612.95 T +(oolbox that uses the M) 288.38 612.95 T +3 10 Q +(A) 397.66 612.95 T +(TLAB) 403.76 612.95 T +3 12 Q +( function) 429.86 612.95 T +2 F +(rand) 475.83 612.95 T +3 F +(.) 504.61 612.95 T +1 16 Q +(See Also) 117.65 584.29 T +2 12 Q +(crtbase) 135.65 566.95 T +3 F +(,) 186.02 566.95 T +2 F +(crtrp) 192.02 566.95 T +FMENDPAGE +%%EndPage: "9" 10 +%%Page: "10" 10 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-10) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(crtrp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Create a real-valued initial population) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(Chrom = crtrp\050Nind, FieldDR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +3 12 Q +0.45 (The \336rst step in a genetic algorithm is to create an initial population consisting of) 135.65 588.95 P +2.82 (random individuals.) 135.65 574.95 P +2 F +6.77 (crtrp) 240.23 574.95 P +3 F +2.82 ( produces a matrix,) 276.21 574.95 P +2 F +6.77 (Chrom) 382.42 574.95 P +3 F +2.82 (, containing uniformly) 418.4 574.95 P +(distributed random values in its elements.) 135.65 560.95 T +2 F +2.4 (Chrom = crtrp\050Nind, FiedDR\051) 135.65 534.95 P +3 F +1 ( creates a random real-valued matrix of) 337.14 534.95 P +3 (size) 135.65 520.95 P +3 (, where) 236.68 520.95 P +2 F +7.2 (Nind) 280.98 520.95 P +3 F +3 ( speci\336es the number of individuals in the) 309.77 520.95 P +0.14 (population and) 135.65 506.95 P +2 F +0.33 (Nvar) 210.55 506.95 P +3 F +0.14 ( the number of variables of each individual.) 239.33 506.95 P +2 F +0.33 (Nvar) 452.62 506.95 P +3 F +0.14 ( is derived) 481.4 506.95 P +(from) 135.65 492.95 T +2 F +(FieldDR) 161.96 492.95 T +3 F +( with) 212.33 492.95 T +2 F +(Nvar = size\050FieldDR,2\051) 239.65 492.95 T +3 F +(.) 397.97 492.95 T +2 F +0 (FieldDR) 135.65 466.95 P +3 F +0 ( \050FieldDescriptionRealvalue\051 is a matrix of size) 186.02 466.95 P +0 ( and contains) 468.35 466.95 P +0.64 (the boundaries of each variable of an individual. The \336rst row contains the lower) 135.65 452.95 P +(bounds, the second row the upper bounds.) 135.65 438.95 T +2 F +(FieldDR) 135.65 412.95 T +3 F +( is used in other functions \050mutation\051.) 186.02 412.95 T +1 16 Q +(Example) 117.65 384.29 T +3 12 Q +(T) 135.65 366.95 T +(o create a random population of 6 individuals with 4 variables each:) 142.14 366.95 T +(De\336ne boundaries on the variables,) 135.65 346.95 T +2 F +(FieldDR = [) 135.65 326.95 T +(-100 -50 -30 -20;) 153.65 312.95 T +( % lower bound) 283.18 312.95 T +( 100) 153.65 298.95 T +(50) 196.82 298.95 T +(30) 225.61 298.95 T +(20]; % upper bound) 254.39 298.95 T +3 F +(Create initial population) 135.65 278.95 T +2 F +(Chrom = crtrp\0506, FieldDR\051) 135.65 258.95 T +(Chrom =) 135.65 238.95 T +(40.23 -17.17) 168.04 224.95 T +(28.95) 268.79 224.95 T +(15.38) 319.16 224.95 T +(82.06) 168.04 210.95 T +(13.26) 218.41 210.95 T +(13.35) 268.79 210.95 T +(-9.09) 319.16 210.95 T +(52.43) 168.04 196.95 T +(25.64) 218.41 196.95 T +(15.20) 268.79 196.95 T +(-2.54) 319.16 196.95 T +( -47.50) 153.65 182.95 T +( 49.10) 211.22 182.95 T +( 9.09) 268.79 182.95 T +(10.65) 319.16 182.95 T +( -90.50 -13.46 -25.63) 153.65 168.95 T +(-0.89) 319.16 168.95 T +(47.21 -25.29) 168.04 154.95 T +( 7.89 -10.48) 268.79 154.95 T +1 16 Q +(See Also) 117.65 132.29 T +2 12 Q +(mutbga) 138.65 114.95 T +3 F +(,) 181.82 114.95 T +2 F +(recdis) 187.82 114.95 T +3 F +(,) 231 114.95 T +2 F +(recint) 236.99 114.95 T +3 F +(,) 280.17 114.95 T +2 F +(reclin) 286.17 114.95 T +160.3 517.47 236.68 529.94 C +2 12 Q +0 X +0 K +(N) 161.3 520.95 T +(i) 169.2 520.95 T +(n) 177.1 520.95 T +(d) 185 520.95 T +(N) 204.78 520.95 T +(v) 212.68 520.95 T +(a) 220.59 520.95 T +(r) 228.49 520.95 T +4 F +(\264) 195.2 520.95 T +-8.35 24.95 603.65 816.95 C +416.87 463.35 468.35 476.13 C +3 12 Q +0 X +0 K +(2) 417.87 466.95 T +2 F +(N) 436.45 466.95 T +(v) 444.35 466.95 T +(a) 452.26 466.95 T +(r) 460.16 466.95 T +4 F +(\264) 426.87 466.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "10" 11 +%%Page: "11" 11 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-11) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(migrate) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +( Migrate individuals between subpopulations) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(Chrom = migrate\050Chrom, SUBPOP\051) 135.65 628.95 T +(Chrom = migrate\050Chrom, SUBPOP, MigOpt\051) 135.65 608.95 T +(Chrom = migrate\050Chrom, SUBPOP, MigOpt, ObjV\051) 135.65 588.95 T +([Chrom, ObjV] = migrate\050Chrom, SUBPOP, MigOpt, ObjV\051) 135.65 568.95 T +1 16 Q +(Description) 117.65 546.29 T +2 12 Q +9.55 (migrate) 135.65 528.95 P +3 F +3.98 ( performs migration of individuals between subpopulations in the) 186.02 528.95 P +1.62 (current population,) 135.65 514.95 P +2 F +3.89 (Chrom) 233.16 514.95 P +3 F +1.62 (, and returns the population after migration,) 269.14 514.95 P +2 F +3.89 (Chrom) 492.67 514.95 P +3 F +1.62 (.) 528.65 514.95 P +0.02 (Each row of) 135.65 500.95 P +2 F +0.06 (Chrom) 197.33 500.95 P +3 F +0.02 ( corresponds to one individual. The number of subpopulations) 233.31 500.95 P +0.88 (is indicated by) 135.65 486.95 P +2 F +2.12 (SUBPOP) 211.26 486.95 P +3 F +0.88 (. The subpopulations in) 253.1 486.95 P +2 F +2.12 (Chrom) 372.24 486.95 P +3 F +0.88 ( are ordered according to) 408.22 486.95 P +(the following scheme:) 135.65 472.95 T +(All subpopulations must have the same number of individuals.) 135.65 146.46 T +2 F +(MigOpt) 135.65 120.46 T +3 F +( is an optional vector with a maximum of 3 parameters:) 178.82 120.46 T +230.9 168.46 436.39 454.95 C +2 12 Q +0 X +0 K +(C) 239.23 312.73 T +(h) 246.42 312.73 T +(r) 253.62 312.73 T +(o) 260.82 312.73 T +(m) 268.01 312.73 T +(I) 317.28 425.09 T +(n) 324.48 425.09 T +(d) 331.67 425.09 T +(1) 340.33 419.61 T +(S) 349.23 425.09 T +(u) 356.43 425.09 T +(b) 363.63 425.09 T +(P) 370.82 425.09 T +(o) 378.02 425.09 T +(p) 385.21 425.09 T +(1) 393.87 419.61 T +(I) 317.78 405.14 T +(n) 324.98 405.14 T +(d) 332.17 405.14 T +(2) 340.83 399.65 T +(S) 348.73 405.14 T +(u) 355.93 405.14 T +(b) 363.13 405.14 T +(P) 370.32 405.14 T +(o) 377.52 405.14 T +(p) 384.71 405.14 T +(1) 393.37 399.65 T +4 F +(\274) 353.68 385.18 T +2 F +(I) 317.28 369.2 T +(n) 324.48 369.2 T +(d) 331.67 369.2 T +(N) 340.33 363.72 T +(S) 349.23 369.2 T +(u) 356.43 369.2 T +(b) 363.63 369.2 T +(P) 370.82 369.2 T +(o) 378.02 369.2 T +(p) 385.21 369.2 T +(1) 393.87 363.72 T +(I) 317.78 349.25 T +(n) 324.98 349.25 T +(d) 332.17 349.25 T +(1) 340.83 343.77 T +(S) 349.73 349.25 T +(u) 356.93 349.25 T +(b) 364.13 349.25 T +(P) 371.32 349.25 T +(o) 378.52 349.25 T +(p) 385.71 349.25 T +(2) 394.37 343.77 T +(I) 317.78 329.3 T +(n) 324.98 329.3 T +(d) 332.17 329.3 T +(2) 340.83 323.81 T +(S) 348.73 329.3 T +(u) 355.93 329.3 T +(b) 363.13 329.3 T +(P) 370.32 329.3 T +(o) 377.52 329.3 T +(p) 384.71 329.3 T +(2) 393.37 323.81 T +4 F +(\274) 353.68 309.34 T +2 F +(I) 317.28 293.36 T +(n) 324.48 293.36 T +(d) 331.67 293.36 T +(N) 340.33 287.88 T +(S) 349.23 293.36 T +(u) 356.43 293.36 T +(b) 363.63 293.36 T +(P) 370.82 293.36 T +(o) 378.02 293.36 T +(p) 385.21 293.36 T +(2) 393.87 287.88 T +4 F +(\274) 353.68 273.41 T +2 F +(I) 299.29 257.43 T +(n) 306.49 257.43 T +(d) 313.68 257.43 T +(1) 322.34 251.94 T +(S) 331.24 257.43 T +(u) 338.44 257.43 T +(b) 345.64 257.43 T +(P) 352.83 257.43 T +(o) 360.03 257.43 T +(p) 367.22 257.43 T +(S) 375.88 251.94 T +(U) 383.08 251.94 T +(B) 390.27 251.94 T +(P) 397.47 251.94 T +(O) 404.67 251.94 T +(P) 411.86 251.94 T +(I) 299.79 237.47 T +(n) 306.99 237.47 T +(d) 314.18 237.47 T +(2) 322.84 231.99 T +(S) 330.74 237.47 T +(u) 337.94 237.47 T +(b) 345.14 237.47 T +(P) 352.33 237.47 T +(o) 359.53 237.47 T +(p) 366.72 237.47 T +(S) 375.38 231.99 T +(U) 382.58 231.99 T +(B) 389.77 231.99 T +(P) 396.97 231.99 T +(O) 404.17 231.99 T +(P) 411.36 231.99 T +4 F +(\274) 353.68 217.52 T +2 F +(I) 299.29 201.54 T +(n) 306.49 201.54 T +(d) 313.68 201.54 T +(N) 322.34 196.05 T +(S) 331.24 201.54 T +(u) 338.44 201.54 T +(b) 345.64 201.54 T +(P) 352.83 201.54 T +(o) 360.03 201.54 T +(p) 367.22 201.54 T +(S) 375.88 196.05 T +(U) 383.08 196.05 T +(B) 390.27 196.05 T +(P) 397.47 196.05 T +(O) 404.67 196.05 T +(P) 411.86 196.05 T +4 F +(=) 282.21 312.73 T +300.79 193.57 296.79 193.57 2 L +0.33 H +0 Z +N +296.79 193.57 296.79 437.08 2 L +N +296.79 437.08 300.79 437.08 2 L +N +417.56 193.57 421.56 193.57 2 L +N +421.56 193.57 421.56 437.08 2 L +N +421.56 437.08 417.56 437.08 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "11" 12 +%%Page: "12" 12 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-12) 513.33 61.29 T +2 12 Q +(MigOpt\0501\051) 135.65 736.95 T +3 F +(:) 200.41 736.95 T +8.11 (scalar containing the rate of migration of individuals between) 171.65 722.95 P +(subpopulations in the range) 171.65 708.95 T +2 F +([0, 1]) 306.9 708.95 T +3 F +(If omitted or) 171.65 694.95 T +2 F +(NaN) 235.27 694.95 T +3 F +(,) 256.86 694.95 T +2 F +(MigOpt\0501\051 = 0.2) 262.86 694.95 T +3 F +( \05020%\051 is assumed.) 370.8 694.95 T +4.74 (If the migration rate is greater than 0 at least one individual per) 171.65 680.95 P +(subpopulation will migrate.) 171.65 666.95 T +2 F +(MigOpt\0502\051) 135.65 646.95 T +3 F +(:) 200.41 646.95 T +(scalar specifying the migration selection method) 171.65 632.95 T +(0 - uniform migration) 171.65 618.95 T +(1 - \336tness-based migration) 171.65 604.95 T +(If omitted or NaN,) 171.65 590.95 T +2 F +(MigOpt\0502\051 = 0) 263.91 590.95 T +3 F +( is assumed.) 357.46 590.95 T +2 F +(MigOpt\0503\051) 135.65 570.95 T +3 F +(:) 200.41 570.95 T +(scalar indicating the structure of the subpopulations for migration) 171.65 556.95 T +(0 - complete net structure) 171.65 542.95 T +(1 - neighbourhood structure) 171.65 528.95 T +(2 - ring structure) 171.65 514.95 T +(If omitted or) 171.65 500.95 T +2 F +(NaN,) 235.27 500.95 T +(MigOpt\0503\051 = 0) 267.06 500.95 T +3 F +( is assumed) 360.6 500.95 T +(If) 135.65 480.95 T +2 F +(MigOpt) 146.63 480.95 T +3 F +( is omitted or) 189.81 480.95 T +2 F +(NaN) 256.45 480.95 T +3 F +(, then the default values are assumed.) 278.03 480.95 T +2 F +0.25 (ObjV) 135.65 454.95 P +3 F +0.1 ( is an optional column vector with as many rows as) 164.43 454.95 P +2 F +0.25 (Chrom) 414.41 454.95 P +3 F +0.1 ( and contains the) 450.39 454.95 P +2.17 (corresponding objective values for all individuals in) 135.65 440.95 P +2 F +5.22 (Chrom) 403.71 440.95 P +3 F +2.17 (. For \336tness-based) 439.69 440.95 P +1.14 (selection of individuals \050) 135.65 426.95 P +2 F +2.73 (MigOpt\0502\051 = 1) 257.99 426.95 P +3 F +1.14 (\051) 356.99 426.95 P +2 F +2.73 (ObjV) 365.12 426.95 P +3 F +1.14 ( is necessary) 393.9 426.95 P +1.14 (. If) 456.01 426.95 P +2 F +2.73 (ObjV) 475.27 426.95 P +3 F +1.14 ( is an) 504.05 426.95 P +2.98 (input and output parameter) 135.65 412.95 P +2.98 (, the objective values are copied according to the) 273.68 412.95 P +0.45 (migration of the individuals. This saves the recomputation of the objective values) 135.65 398.95 P +(for the whole population.) 135.65 384.95 T +1 16 Q +(Example) 117.65 356.29 T +2 12 Q +2.59 (Chrom = migrate\050Chrom, SUBPOP\051) 135.65 338.95 P +3 F +1.08 ( chooses 20% of the individuals of) 359.29 338.95 P +6.2 (one subpopulation and replaces these individuals with uniformly chosen) 135.65 324.95 P +5.26 (individuals from all other subpopulations. This process is done for each) 135.65 310.95 P +(subpopulation. \050) 135.65 296.95 T +2 F +(MigOpt = [0.2, 0, 0]) 213.6 296.95 T +3 F +(\051) 357.53 296.95 T +2 F +-0.64 (Chrom = migrate\050Chrom, SUBPOP, [NaN 1 NaN], ObjV]\051) 135.65 270.95 P +3 F +-0.27 ( chooses) 490.95 270.95 P +0.3 (20% of the individuals of one subpopulation and replaces these individuals with a) 135.65 256.95 P +1.11 (selection of the \336ttest individuals \050smaller) 135.65 242.95 P +2 F +2.66 (ObjV) 346.85 242.95 P +3 F +1.11 (\051 from all other subpopulations.) 375.64 242.95 P +(\050net structure\051 This process is repeated for each subpopulation.) 135.65 228.95 T +2 F +5.45 ([Chrom,ObjV] = migrate\050Chrom,SUBPOP,[0.3 1 2],ObjV]\051) 135.65 202.95 P +3 F +5.16 (chooses 30% of the individuals of one subpopulation and replaces these) 135.65 188.95 P +5.9 (individuals with the \336ttest individuals \050smaller) 135.65 174.95 P +2 F +14.15 (ObjV) 397.58 174.95 P +3 F +5.9 (\051 from an adjacent) 426.37 174.95 P +0.69 (subpopulation in a unidirectional ring structure. This process is repeated for each) 135.65 160.95 P +1.12 (subpopulation. The \336rst subpopulation receives its new individuals from the last) 135.65 146.95 P +4.69 (subpopulation \050) 135.65 132.95 P +2 F +11.26 (SUBPOP) 215.3 132.95 P +3 F +4.69 (\051.) 258.48 132.95 P +2 F +11.26 (ObjV) 273.16 132.95 P +3 F +4.69 ( is returned according to the migration of) 301.94 132.95 P +(individuals.) 135.65 118.95 T +FMENDPAGE +%%EndPage: "12" 13 +%%Page: "13" 13 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-13) 513.33 61.29 T +3 12 Q +(The migration scheme employed:) 135.65 736.95 T +(subpop1-->subpop2-->subpop3-->...-->subpop) 135.65 722.95 T +2 F +(SUBPOP) 360.24 722.95 T +3 F +(--> subpop1) 403.41 722.95 T +2 F +1.85 ([Chrom,ObjV] = migrate\050Chrom,SUBPOP,[NaN NaN 1],ObjV]\051) 135.65 696.95 P +3 F +5.16 (chooses 20% of the individuals of one subpopulation and replaces these) 135.65 682.95 P +0.69 (individuals with uniformly chosen individuals from both adjacent subpopulations) 135.65 668.95 P +1.18 (in an one dimensional neighborhood structure. This process is repeated for each) 135.65 654.95 P +1.12 (subpopulation. The \336rst subpopulation receives its new individuals from the last) 135.65 640.95 P +2.3 (\050) 135.65 626.95 P +2 F +5.53 (SUBPOP) 139.64 626.95 P +3 F +2.3 (\051 and second subpopulation the last subpopulation from the \336rst and) 182.82 626.95 P +2 F +9.55 (SUBPOP-1) 135.65 612.95 P +3 F +3.98 ( subpopulation.) 193.22 612.95 P +2 F +9.55 (ObjV) 278.14 612.95 P +3 F +3.98 ( is returned according to the migration of) 306.92 612.95 P +(individuals.) 135.65 598.95 T +(The migration scheme employed:) 135.65 584.95 T +(subpop) 135.65 570.95 T +2 F +(SUBPOP) 170.3 570.95 T +3 F +(-->subpop1<-->subpop2<-->...<-->subpop) 213.47 570.95 T +2 F +(SUBPOP) 417.71 570.95 T +3 F +(<--subpop1) 460.89 570.95 T +1 16 Q +(See Also) 117.65 542.29 T +2 12 Q +(select) 135.65 524.95 T +3 F +(,) 178.82 524.95 T +2 F +(recombin) 184.82 524.95 T +3 F +(,) 242.39 524.95 T +2 F +(mutate) 248.39 524.95 T +3 F +(,) 291.56 524.95 T +2 F +(reins) 297.56 524.95 T +1 16 Q +(Refer) 117.65 502.29 T +(ence) 155.53 502.29 T +3 12 Q +-0.23 ([1] H. M) 135.65 484.95 P +-0.23 (\237) 177.49 484.95 P +-0.23 (hlenbein, M. Schomisch and J. Born, \322The Parallel Genetic Algorithm as) 183.49 484.95 P +(a Function Optimizer\323,) 135.65 470.95 T +0 F +(Parallel Computing) 249.57 470.95 T +3 F +(, No. 17, pp.619-632, 1991.) 345.2 470.95 T +0.73 ([2] T) 135.65 444.95 P +0.73 (. Starkweather) 159.8 444.95 P +0.73 (, D. Whitley and K. Mathias, \322Optimization using Distributed) 229.32 444.95 P +0.29 (Genetic Algorithms\323, In) 135.65 430.95 P +0 F +0.29 (Parallel Pr) 255.77 430.95 P +0.29 (oblems Solving fr) 309.93 430.95 P +0.29 (om Natur) 394.02 430.95 P +0.29 (e) 439.52 430.95 P +3 F +0.29 (, Lecture Notes in) 444.84 430.95 P +(Computer Science, V) 135.65 416.95 T +(ol. 496, pp. 176-185, Springer) 237.03 416.95 T +(, 1991.) 381.13 416.95 T +2.45 ([3] R. T) 135.65 390.95 P +2.45 (anese, \322Distributed Genetic Algorithms\323,) 178.02 390.95 P +0 F +2.45 (Pr) 389.03 390.95 P +2.45 (oc. ICGA 3) 400.58 390.95 P +3 F +2.45 (, pp. 434-439,) 459.78 390.95 P +(Mor) 135.65 376.95 T +(gan Kaufmann Publishers, 1989.) 156.09 376.95 T +1.1 ([4] H.-M. V) 135.65 350.95 P +1.1 (oigt, J. Born and I. Santibanez-Koref, \322Modelling and Simulation of) 194.26 350.95 P +2.04 (Distributed Evolutionary Search Processes for Function Optimization\323, Parallel) 135.65 336.95 P +0.35 (Problems Solving from Nature, Lecture Notes in Computer Science, V) 135.65 322.95 P +0.35 (ol. 496, pp.) 476.65 322.95 P +(373-380, Springer V) 135.65 308.95 T +(erlag, 1991.) 233.25 308.95 T +FMENDPAGE +%%EndPage: "13" 14 +%%Page: "14" 14 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-14) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(mut) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Discrete mutation operator) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = mut\050OldChrom, Pm, BaseV\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +2.12 (mut) 135.65 588.95 P +3 F +0.88 ( takes the representation of the current population and mutates each element) 157.24 588.95 P +2.74 (with a given probability) 135.65 574.95 P +2.74 (. T) 258.02 574.95 P +2.74 (o allow for varying bases in the chromosome and) 273.24 574.95 P +1.06 (structured populations,) 135.65 560.95 P +2 F +2.54 (mut) 250.69 560.95 P +3 F +1.06 ( allows an additional ar) 272.28 560.95 P +1.06 (gument) 388.22 560.95 P +2 F +2.54 (BaseV) 428.26 560.95 P +3 F +1.06 ( that speci\336es) 464.24 560.95 P +(the base of the individual elements of a chromosome.) 135.65 546.95 T +2 F +11.77 (NewChrom = mut\050OldChrom, Pm\051) 135.65 520.95 P +3 F +4.91 ( takes the current population,) 372.46 520.95 P +2 F +5.12 (OldChrom) 135.65 506.95 P +3 F +2.13 (, with each row corresponding to an individuals, and mutates each) 193.22 506.95 P +-0.17 (element with probability) 135.65 492.95 P +2 F +-0.41 (Pm) 256.07 492.95 P +3 F +-0.17 (. If the mutation probability) 270.46 492.95 P +-0.17 (,) 401.92 492.95 P +2 F +-0.41 (Pm) 407.75 492.95 P +3 F +-0.17 (, is omitted,) 422.14 492.95 P +2 F +-0.41 (Pm=0.7/) 481.27 492.95 P +3.06 (Lind) 135.65 478.95 P +3 F +1.28 ( is assumed, where) 164.43 478.95 P +2 F +3.06 (Lind) 263.13 478.95 P +3 F +1.28 ( is the length of the chromosome structure. This) 291.92 478.95 P +3.3 (value is selected as it implies that the probability of any one element of a) 135.65 464.95 P +1.07 (chromosome being mutated is approximately 0.5 \050see [1]\051. W) 135.65 450.95 P +1.07 (ithout a third input) 438.82 450.95 P +(ar) 135.65 436.95 T +(gument,) 144.75 436.95 T +2 F +(mut) 186.73 436.95 T +3 F +( assumes that the population is binary coded.) 208.32 436.95 T +2 F +1.55 (NewChrom = \050OldChrom, Pm, BaseV\051) 135.65 410.95 P +3 F +0.64 ( uses a third ar) 372.11 410.95 P +0.64 (gument to specify) 444.41 410.95 P +1.25 (the base of the mutation of the individual elements of the chromosomes. In this) 135.65 396.95 P +0.08 (case,) 135.65 382.95 P +2 F +0.2 (length\050BaseV\051 = Lind) 162.37 382.95 P +3 F +0.08 (, where) 306.68 382.95 P +2 F +0.2 (Lind) 345.14 382.95 P +3 F +0.08 ( is the length of the chromosome) 373.92 382.95 P +(structure.) 135.65 368.95 T +2 F +(mut) 135.65 342.95 T +3 F +( is a low-level mutation function normally called by) 157.24 342.95 T +2 F +(mutate) 409.41 342.95 T +3 F +(.) 452.59 342.95 T +1 16 Q +(Example) 117.65 314.29 T +3 12 Q +(Consider a binary population) 135.65 296.95 T +2 F +(OldChrom) 278.23 296.95 T +3 F +( with 4 individuals each of length 8:) 335.79 296.95 T +2 F +(OldChrom =[) 135.65 276.95 T +(0 0 0 0 0 1 1 1;) 153.65 262.95 T +(1 0 0 0 1 0 0 1;) 153.65 248.95 T +(0 0 1 0 1 0 0 0;) 153.65 234.95 T +(1 1 0 1 1 0 1 1]) 153.65 220.95 T +3 F +(Mutate) 135.65 200.95 T +2 F +(OldChrom) 172.62 200.95 T +3 F +( with default probability:) 230.19 200.95 T +2 F +(NewChrom = mut\050OldChrom\051) 135.65 180.95 T +3 F +(Thus,) 135.65 160.95 T +2 F +(NewChrom) 165.63 160.95 T +3 F +( can become:) 223.2 160.95 T +FMENDPAGE +%%EndPage: "14" 15 +%%Page: "15" 15 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-15) 513.33 61.29 T +2 12 Q +(NewChrom =) 135.65 736.95 T +(0 0 1 0 0 1 1 1) 153.65 722.95 T +(1 1 0 0 0 0 0 1) 153.65 708.95 T +(0 0 0 0 1 0 0 0) 153.65 694.95 T +(1 1 0 1 1 0 1 1) 153.65 680.95 T +3 F +4.05 (The complement of a binary string is obtained by applying mutation with) 135.65 660.95 P +(probability 1.) 135.65 646.95 T +2 F +(mut\050[1 0 1 0 1 1 1 0], 1\051) 135.65 626.95 T +(ans =) 135.65 606.95 T +(0 1 0 1 0 0 0 1) 153.65 592.95 T +1 16 Q +(See Also) 117.65 570.29 T +2 12 Q +(mutate) 135.65 552.95 T +3 F +(,) 178.82 552.95 T +2 F +(mutbga) 184.82 552.95 T +1 16 Q +(Refer) 117.65 530.29 T +(ence) 155.53 530.29 T +3 12 Q +2.35 ([1] J\237r) 135.65 512.95 P +2.35 (gen Hesser and Reinhard M\212nner) 169.42 512.95 P +2.35 (, \322T) 338.86 512.95 P +2.35 (owards an Optimal Mutation Rate) 359.02 512.95 P +1.91 (Probability for Genetic Algorithms\323, In) 135.65 498.95 P +0 F +1.91 (Parallel Pr) 337.76 498.95 P +1.91 (oblem Solving fr) 393.54 498.95 P +1.91 (om Natur) 476.21 498.95 P +1.91 (e) 523.32 498.95 P +3 F +1.91 (,) 528.65 498.95 P +(Lecture Notes in Computer Science, V) 135.65 484.95 T +(ol. 496, pp23-32, 1990.) 319.96 484.95 T +FMENDPAGE +%%EndPage: "15" 16 +%%Page: "16" 16 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-16) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(mutate) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Mutation of individuals \050high-level function\051.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = mutate\050MUT_F, OldChrom, FieldDR\051) 135.65 628.95 T +(NewChrom = mutate\050MUT_F, OldChrom, FieldDR, MutOpt\051) 135.65 608.95 T +(NewChrom = mutate\050MUT_F, OldChrom, FieldDR, MutOpt,) 135.65 588.95 T +(SUBPOP\051) 153.65 574.95 T +1 16 Q +(Description) 117.65 552.29 T +2 12 Q +4.2 (mutate) 135.65 534.95 P +3 F +1.75 ( performs mutation of individuals from a population,) 178.82 534.95 P +2 F +4.2 (OldChrom) 449.01 534.95 P +3 F +1.75 (, and) 506.58 534.95 P +1.91 (returns the mutated individuals in a new population,) 135.65 520.95 P +2 F +4.58 (NewChrom) 403.75 520.95 P +3 F +1.91 (. Each row of) 461.32 520.95 P +2 F +(OldChrom) 135.65 506.95 T +3 F +( and) 193.22 506.95 T +2 F +(NewChrom) 216.53 506.95 T +3 F +( corresponds to one individual.) 274.1 506.95 T +2 F +1.64 (MUT_F) 135.65 480.95 P +3 F +0.69 ( is a string that contains the name of the low-level mutation function, e.g.) 171.63 480.95 P +2 F +(mutbga) 135.65 466.95 T +3 F +( or) 178.82 466.95 T +2 F +(mut) 194.81 466.95 T +3 F +(.) 216.4 466.95 T +2 F +0.87 (FieldDR) 135.65 440.95 P +3 F +0.36 ( is a matrix of size) 186.02 440.95 P +0.36 ( and contains the bounds of each variable) 330.94 440.95 P +3.43 (of an individual \050real-valued variables\051 or a matrix of size) 135.65 426.95 P +3.43 ( and) 507.9 426.95 P +2.56 (contains the base of each variable \050discrete-valued variables\051. If) 135.65 412.95 P +2 F +6.14 (FieldDR) 467.72 412.95 P +3 F +2.56 ( is) 518.09 412.95 P +(omitted, empty or) 135.65 398.95 T +2 F +(NaN) 224.27 398.95 T +3 F +(, a binary representation of the variables is assumed) 245.85 398.95 T +2 F +(.) 494 398.95 T +1.54 (MutOpt) 135.65 372.95 P +3 F +0.64 ( is an optional parameter containing the mutation rate, the probability of) 178.82 372.95 P +1.35 (mutating a variable of an individual. If) 135.65 358.95 P +2 F +3.23 (MutOpt) 333.62 358.95 P +3 F +1.35 ( is omitted) 376.79 358.95 P +2 F +3.23 (,) 430.14 358.95 P +3 F +1.35 ( a default mutation) 437.33 358.95 P +0.34 (rate is assumed. For real-value mutation) 135.65 344.95 P +2 F +0.82 (MutOpt) 333.23 344.95 P +3 F +0.34 ( can contain a second parameter) 376.41 344.95 P +(specifying a scalar for shrinking the mutation range \050see) 135.65 330.95 T +2 F +(mutbga) 408.44 330.95 T +3 F +(\051.) 451.61 330.95 T +2 F +0.01 (SUBPOP) 135.65 304.95 P +3 F +0.01 ( is an optional parameter and determines the number of subpopulations in) 178.82 304.95 P +2 F +5.07 (OldChrom) 135.65 290.95 P +3 F +2.11 (. If) 193.22 290.95 P +2 F +5.07 (SUBPOP) 214.42 290.95 P +3 F +2.11 ( is omitted or) 257.6 290.95 P +2 F +5.07 (NaN,) 332.69 290.95 P +5.07 (SUBPOP = 1) 366.58 290.95 P +3 F +2.11 ( is assumed. All) 448.68 290.95 P +(subpopulations in) 135.65 276.95 T +2 F +(OldChrom) 223.61 276.95 T +3 F +( must have the same size.) 281.18 276.95 T +1 16 Q +(Example) 117.65 248.29 T +3 12 Q +4.98 (For examples, see) 135.65 230.95 P +2 F +11.94 (mutbga) 239.84 230.95 P +3 F +4.98 ( \050real-value mutation\051 and) 283.02 230.95 P +2 F +11.94 (mut) 430.82 230.95 P +3 F +4.98 ( \050discrete-value) 452.41 230.95 P +(mutation\051.) 135.65 216.95 T +1 16 Q +(Algorithm) 117.65 194.29 T +2 12 Q +3.36 (mutate) 135.65 176.95 P +3 F +1.4 ( checks the consistency of the input parameters and calls the low-level) 178.82 176.95 P +-0.05 (mutation function. If) 135.65 162.95 P +2 F +-0.12 (mutate) 238.1 162.95 P +3 F +-0.05 ( is called with more than one subpopulation then the) 281.27 162.95 P +(low-level mutation function is called separately for each subpopulation.) 135.65 148.95 T +1 16 Q +(See Also) 117.65 126.29 T +2 12 Q +(mutbga) 135.65 108.95 T +3 F +(,) 178.82 108.95 T +2 F +(mut) 184.82 108.95 T +3 F +(,) 206.41 108.95 T +2 F +(recombin) 212.41 108.95 T +3 F +(,) 269.97 108.95 T +2 F +(select) 275.97 108.95 T +279.46 437.35 330.94 450.13 C +3 12 Q +0 X +0 K +(2) 280.46 440.95 T +2 F +(N) 299.04 440.95 T +(v) 306.94 440.95 T +(a) 314.84 440.95 T +(r) 322.74 440.95 T +4 F +(\264) 289.45 440.95 T +-8.35 24.95 603.65 816.95 C +450.42 423.35 507.9 436.13 C +3 12 Q +0 X +0 K +(1) 454.42 426.95 T +2 F +(N) 473 426.95 T +(v) 480.9 426.95 T +(a) 488.8 426.95 T +(r) 496.7 426.95 T +4 F +(\264) 463.41 426.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "16" 17 +%%Page: "17" 17 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-17) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(mutbga) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +3.11 (Mutation of real-valued population \050mutation operator of the breeder genetic) 135.65 674.95 P +(algorithm\051.) 135.65 660.95 T +1 16 Q +(Synopsis) 117.65 632.29 T +2 12 Q +(NewChrom = mutbga\050OldChrom, FieldDR\051) 135.65 614.95 T +(NewChrom = mutbga\050OldChrom, FieldDR, MutOpt\051) 135.65 594.95 T +1 16 Q +(Description) 117.65 572.29 T +2 12 Q +-0.41 (mutbga) 135.65 554.95 P +3 F +-0.17 ( takes the real-valued population,) 178.82 554.95 P +2 F +-0.41 (OldChrom) 340.52 554.95 P +3 F +-0.17 (, mutates each variable with) 398.09 554.95 P +(given probability and returns the population after mutation,) 135.65 540.95 T +2 F +(NewChrom) 423.13 540.95 T +3 F +(.) 480.7 540.95 T +2 F +-0.55 (NewChrom = mutbga\050OldChrom, FieldDR, MutOpt\051) 135.65 514.95 P +3 F +-0.23 ( takes the current) 450.07 514.95 P +3.3 (population, stored in the matrix) 135.65 500.95 P +2 F +7.91 (OldChrom) 306.05 500.95 P +3 F +3.3 ( and mutates each variable with) 363.61 500.95 P +0.1 (probability) 135.65 486.95 P +2 F +0.24 (MutOpt\0501\051) 191.39 486.95 P +3 F +0.1 ( by addition of small random values \050size of the mutation) 256.15 486.95 P +(step\051. The mutation step can be shrunk with) 135.65 472.95 T +2 F +(MutOpt\0502\051) 348.51 472.95 T +3 F +(.) 413.27 472.95 T +2 F +1.31 (FieldDR) 135.65 446.95 P +3 F +0.55 ( is a matrix containing the boundaries of each variable of an individual) 186.02 446.95 P +(\050see) 135.65 432.95 T +2 F +(crtrp) 157.96 432.95 T +3 F +(\051.) 193.94 432.95 T +2 F +(MutOpt) 135.65 406.95 T +3 F +( is an optional vector with a maximum of two parameters:) 178.82 406.95 T +2 F +(MutOpt\0501\051) 135.65 386.95 T +3 F +(:) 200.41 386.95 T +(scalar containing the mutation rate in the range) 171.65 372.95 T +2 F +([0, 1].) 400.15 372.95 T +3 F +0.43 (If omitted or) 171.65 358.95 P +2 F +1.02 (NaN) 236.55 358.95 P +3 F +0.43 (,) 258.14 358.95 P +2 F +1.02 (MutOpt\0501\051 = 1/Nvar) 264.56 358.95 P +3 F +0.43 ( is assumed, where) 396.14 358.95 P +2 F +1.02 (Nvar) 491.44 358.95 P +3 F +0.43 ( is) 520.22 358.95 P +0.63 (the number of variables per individual de\336ned by) 171.65 344.95 P +2 F +1.51 (size\050FieldDR,2\051.) 416.51 344.95 P +3 F +3.35 (This value is selected as it implies that the number of variables per) 171.65 330.95 P +(individual mutated is approximately 1.) 171.65 316.95 T +2 F +(MutOpt\0502\051) 135.65 296.95 T +3 F +(:) 200.41 296.95 T +1.99 (scalar containing a value in the range [0, 1] for shrinking the mutation) 171.65 282.95 P +(range.) 171.65 268.95 T +(If omitted or) 171.65 254.95 T +2 F +(NaN) 235.27 254.95 T +3 F +(,) 256.86 254.95 T +2 F +(MutOpt\0502\051 = 1) 262.86 254.95 T +3 F +( is assumed \050no shrinking\051.) 356.41 254.95 T +2 F +(mutbga) 135.65 234.95 T +3 F +( is a low-level mutation function normally called by) 178.82 234.95 T +2 F +(mutate) 431 234.95 T +3 F +(.) 474.17 234.95 T +1 16 Q +(Example) 117.65 206.29 T +3 12 Q +(Consider the following population with three real-valued individuals:) 135.65 188.95 T +2 F +(OldChrom = [) 135.65 168.95 T +(40.2381 -17.1766) 153.65 154.95 T +( 28.9530) 275.98 154.95 T +(15.3883;) 347.94 154.95 T +(82.0642) 153.65 140.95 T +(13.2639) 218.41 140.95 T +(13.3596) 283.18 140.95 T +(-9.0916;) 347.94 140.95 T +(52.4396) 153.65 126.95 T +(25.6410) 218.41 126.95 T +(15.2014) 283.18 126.95 T +(-2.5435]) 347.94 126.95 T +3 F +(The bounds are de\336ned as:) 135.65 106.95 T +FMENDPAGE +%%EndPage: "17" 18 +%%Page: "18" 18 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-18) 513.33 61.29 T +2 12 Q +(FieldDR = [) 135.65 736.95 T +(-100 -50 -30 -20;) 153.65 722.95 T +( 100) 153.65 708.95 T +(50) 196.82 708.95 T +( 30) 218.41 708.95 T +(20]) 254.39 708.95 T +3 F +2.08 (T) 135.65 688.95 P +2.08 (o mutate) 142.14 688.95 P +2 F +4.99 (OldChrom) 190.93 688.95 P +3 F +2.08 ( with mutation probability) 248.5 688.95 P +2 F +4.99 (1/4) 385.41 688.95 P +3 F +2.08 ( and no shrinking of the) 407 688.95 P +(mutation range:) 135.65 674.95 T +2 F +(NewChrom = mutbga\050OldChrom, FieldDR, [1/4 1.0]\051) 135.65 654.95 T +1.38 (mutbga) 135.65 634.95 P +3 F +0.57 ( produces an internal mask table,) 178.82 634.95 P +2 F +1.38 (MutMx) 343.14 634.95 P +3 F +0.57 (, determining which variable to) 379.12 634.95 P +(mutate and the sign for adding) 135.65 620.95 T +2 F +(delta) 284.88 620.95 T +3 F +( \050see Algorithm\051, e.g.) 320.86 620.95 T +2 F +(MutMx = [) 135.65 600.95 T +(0) 153.65 586.95 T +(0) 175.24 586.95 T +( 0) 189.63 586.95 T +(1;) 218.41 586.95 T +(0) 153.65 572.95 T +(0) 175.24 572.95 T +(-1) 189.63 572.95 T +(0;) 218.41 572.95 T +(0) 153.65 558.95 T +( 0) 168.04 558.95 T +(-1) 189.63 558.95 T +(-1]) 211.22 558.95 T +3 F +(An second internal table,) 135.65 538.95 T +2 F +(delta) 258.56 538.95 T +3 F +(, speci\336es the normalized mutation step size, e.g.) 294.54 538.95 T +2 F +(delta = [) 135.65 518.95 T +(0.2500) 153.65 504.95 T +(0.2500 0.2500 0.2500;) 204.02 504.95 T +(0.0001 0.0001 0.0001 0.0001;) 153.65 490.95 T +(0.2505 0.2505 0.2505 0.2505]) 153.65 476.95 T +3 F +(Thus, after mutation) 135.65 456.95 T +2 F +(NewChrom) 236.25 456.95 T +3 F +( becomes:) 293.82 456.95 T +2 F +(NewChrom =) 135.65 436.95 T +(40.2381 -17.1766 28.9530 20.0000) 153.65 422.95 T +(82.0642) 153.65 408.95 T +(13.2638 13.3559 -9.0916) 218.41 408.95 T +(52.4396) 153.65 394.95 T +(25.6410 -7.6858 -7.5539) 218.41 394.95 T +(NewChrom - OldChrom) 135.65 374.95 T +3 F +( shows the mutation steps) 272.37 374.95 T +2 F +(NewChrom - OldChrom =) 135.65 354.95 T +(0) 196.82 340.95 T +(0) 254.39 340.95 T +(0) 311.96 340.95 T +(4.6117) 333.55 340.95 T +(0) 196.82 326.95 T +(0) 254.39 326.95 T +(-0.0037) 268.79 326.95 T +(0) 369.53 326.95 T +(0) 196.82 312.95 T +( 0) 247.2 312.95 T +(-7.5156 -5.0104) 268.79 312.95 T +1 16 Q +(Algorithm) 117.65 290.29 T +3 12 Q +(The mutation of a variable is computed as follows:) 135.65 272.95 T +(mutated variable = variable +) 135.65 252.95 T +2 F +(MutMx) 135.65 232.95 T +3 F +(=) 180.62 232.95 T +( with probability) 202.43 232.95 T +2 F +(MutOpt\0501\051) 285.39 232.95 T +3 F +(, \050+ or - with equal probability\051) 350.15 232.95 T +(else 0) 171.65 218.95 T +2 F +(range =) 135.65 198.95 T +3 F +( domain of variable \050search interval de\336ned by) 228.79 198.95 T +2 F +(FieldDR) 455.94 198.95 T +3 F +(\051.) 506.32 198.95 T +2 F +(delta =) 135.65 165.03 T +3 F +(,) 237.45 165.03 T +( with probability 1/m, else 0, m = 20.) 281.05 165.03 T +0.1 (W) 135.65 131.79 P +0.1 (ith m = 20, the mutation operator is able to locate the optimum up to a precision) 146.49 131.79 P +(of) 135.65 117.79 T +(.) 303.18 117.79 T +280.07 247.96 504.55 261.94 C +2 12 Q +0 X +0 K +(M) 281.07 252.95 T +(u) 288.98 252.95 T +(t) 296.88 252.95 T +(M) 304.78 252.95 T +(x) 312.68 252.95 T +(r) 332.46 252.95 T +(a) 340.36 252.95 T +(n) 348.27 252.95 T +(g) 356.17 252.95 T +(e) 364.07 252.95 T +(M) 383.85 252.95 T +(u) 391.75 252.95 T +(t) 399.65 252.95 T +(O) 407.55 252.95 T +(p) 415.46 252.95 T +(t) 423.36 252.95 T +(2) 438.36 252.95 T +4 F +(\050) 433.26 252.95 T +(\051) 446.16 252.95 T +2 F +(d) 464.74 252.95 T +(e) 472.64 252.95 T +(l) 480.55 252.95 T +(t) 488.45 252.95 T +(a) 496.35 252.95 T +4 F +(\264) 374.26 252.95 T +(\264) 455.16 252.95 T +(\264) 322.88 252.95 T +-8.35 24.95 603.65 816.95 C +187.39 229.43 202.43 241.99 C +3 12 Q +0 X +0 K +(1) 195.43 232.95 T +4 F +(\261) 188.39 232.95 T +-8.35 24.95 603.65 816.95 C +193.22 195.35 228.79 208.13 C +3 12 Q +0 X +0 K +(0) 194.22 198.95 T +(.) 200.21 198.95 T +(5) 203.21 198.95 T +4 F +(\264) 212.21 198.95 T +-8.35 24.95 603.65 816.95 C +189.02 147.79 237.44 186.95 C +4 12 Q +0 X +0 K +(a) 211.43 165.03 T +0 9 Q +(i) 219.46 160.38 T +3 12 Q +(2) 222.67 165.03 T +0 9 Q +(i) 233.95 171.06 T +4 F +(-) 228.67 171.06 T +0 F +(i) 191.26 150.74 T +3 F +(0) 204.7 150.74 T +4 F +(=) 196.76 150.74 T +0 F +(m) 190.02 179.81 T +3 F +(1) 205.94 179.81 T +4 F +(-) 198.76 179.81 T +4 18 Q +(\345) 193.81 161.83 T +-8.35 24.95 603.65 816.95 C +243.44 157.53 281.04 174.21 C +4 12 Q +0 X +0 K +(a) 244.69 165.03 T +0 9 Q +(i) 252.72 160.38 T +3 12 Q +(1) 273.8 165.03 T +4 F +(=) 261.22 165.03 T +-8.35 24.95 603.65 816.95 C +148.64 112.79 303.18 131.01 C +2 12 Q +0 X +0 K +(r) 149.64 117.79 T +(a) 157.54 117.79 T +(n) 165.44 117.79 T +(g) 173.34 117.79 T +(e) 181.24 117.79 T +(M) 201.02 117.79 T +4 F +(\264) 191.44 117.79 T +2 F +(u) 208.93 117.79 T +(t) 216.83 117.79 T +(O) 224.73 117.79 T +(p) 232.63 117.79 T +(t) 240.54 117.79 T +(2) 255.54 117.79 T +4 F +(\050) 250.44 117.79 T +(\051) 263.34 117.79 T +3 F +(2) 281.92 117.79 T +3 9 Q +(1) 293.2 123.88 T +(9) 297.69 123.88 T +4 F +(-) 287.92 123.88 T +4 12 Q +(\264) 272.33 117.79 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "18" 19 +%%Page: "19" 19 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-19) 513.33 61.29 T +3 12 Q +0.92 (The mutation operator) 135.65 736.95 P +2 F +2.21 (mutbga) 248.67 736.95 P +3 F +0.92 ( is able to generate most points in the hypercube) 291.84 736.95 P +0.24 (de\336ned by the variables of the individual and the range of the mutation. However) 135.65 722.95 P +0.24 (,) 528.65 722.95 P +0.93 (it tests more often near the variable, that is, the probability of small step sizes is) 135.65 708.95 P +(greater than that of lar) 135.65 694.95 T +(ger step sizes.) 242.01 694.95 T +1 16 Q +(See Also) 117.65 666.29 T +2 12 Q +(mutate) 135.65 648.95 T +3 F +(,) 178.82 648.95 T +2 F +(recdis) 184.82 648.95 T +3 F +(,) 228 648.95 T +2 F +(recint) 233.99 648.95 T +3 F +(,) 277.17 648.95 T +2 F +(reclin) 283.17 648.95 T +1 16 Q +(Refer) 117.65 626.29 T +(ence) 155.53 626.29 T +3 12 Q +3.9 ([1] H. M) 135.65 608.95 P +3.9 (\237) 185.76 608.95 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 608.95 P +3.9 (oosen, \322Predictive Models for the) 354.48 608.95 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 594.95 P +0 F +0.18 (Evolutionary) 469.02 594.95 P +(Computation) 135.65 580.95 T +3 F +(, V) 198.29 580.95 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 580.95 T +FMENDPAGE +%%EndPage: "19" 20 +%%Page: "20" 20 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-20) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(ranking) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Rank-based \336tness assignment) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(FitnV = ranking\050ObjV\051) 135.65 628.95 T +(FitnV = ranking\050ObjV, RFun\051) 135.65 608.95 T +(FitnV = ranking\050ObjV, RFun, SUBPOP\051) 135.65 588.95 T +1 16 Q +(Description) 117.65 566.29 T +2 12 Q +-0.17 (ranking) 135.65 548.95 P +3 F +-0.07 ( ranks individuals according to their objective values,) 186.02 548.95 P +2 F +-0.17 (ObjV) 444.93 548.95 P +3 F +-0.07 (, and returns) 472.17 548.95 P +1.5 (a column vector containing the corresponding individual \336tness values,) 135.65 534.95 P +2 F +3.59 (FitnV) 494.22 534.95 P +3 F +1.5 (.) 528.65 534.95 P +(This function ranks individuals for) 135.65 520.95 T +1 F +(minimisation) 305.21 520.95 T +3 F +(.) 372.52 520.95 T +2 F +(RFun) 135.65 494.95 T +3 F +( is an optional vector with 1, 2 or) 164.43 494.95 T +2 F +(length\050ObjV\051) 326.33 494.95 T +3 F +( parameters:) 412.68 494.95 T +0.28 (If) 135.65 474.95 P +2 F +0.68 (RFun) 146.92 474.95 P +3 F +0.28 ( is a scalar in) 175.7 474.95 P +2 F +0.68 ([1, 2]) 242.72 474.95 P +3 F +0.28 (, linear ranking is assumed and the scalar indicates) 286.58 474.95 P +(the selective pressure.) 135.65 460.95 T +(If) 135.65 440.95 T +2 F +(RFun) 146.63 440.95 T +3 F +( is a vector with 2 parameters:) 175.42 440.95 T +2 F +(RFun\0501\051) 135.65 420.95 T +3 F +(:) 186.02 420.95 T +(scalar indicating the selective pressure) 171.65 406.95 T +(for linear ranking) 171.65 392.95 T +2 F +(RFun\0501\051) 258.58 392.95 T +3 F +( must be in) 308.95 392.95 T +2 F +([1, 2]) 364.92 392.95 T +3 F +(for non-linear ranking) 171.65 378.95 T +2 F +(RFun\0501\051) 280.56 378.95 T +3 F +( must be in) 330.93 378.95 T +2 F +([1, length\050ObjV\051-2]) 386.91 378.95 T +3 F +(If) 171.65 364.95 T +2 F +(NaN) 182.63 364.95 T +3 F +(,) 204.22 364.95 T +2 F +(RFun\0501\051 = 2) 210.22 364.95 T +3 F +( is assumed.) 289.38 364.95 T +2 F +(RFun\0502\051) 135.65 344.95 T +3 F +(:) 186.02 344.95 T +(ranking method) 171.65 330.95 T +(0 - linear ranking) 171.65 316.95 T +(1 - non-linear ranking) 171.65 302.95 T +0.29 (If) 135.65 282.95 P +2 F +0.69 (RFun) 146.92 282.95 P +3 F +0.29 ( is a vector of) 175.71 282.95 P +2 F +0.69 (length\050ObjV\051) 245.43 282.95 P +3 F +0.29 (, it should contain the \336tness values to be) 331.78 282.95 P +(assigned to each rank.) 135.65 268.95 T +2.78 (If) 135.65 242.95 P +2 F +6.66 (RFun) 149.41 242.95 P +3 F +2.78 ( is omitted or) 178.2 242.95 P +2 F +6.66 (NaN) 255.94 242.95 P +3 F +2.78 (, linear ranking and a selective pressure of 2 are) 277.52 242.95 P +(assumed.) 135.65 228.95 T +2 F +2.19 (SUBPOP) 135.65 202.95 P +3 F +0.91 ( is an optional parameter and indicates the number of subpopulations in) 178.82 202.95 P +2 F +10.67 (ObjV) 135.65 188.95 P +3 F +4.45 (. If) 162.88 188.95 P +2 F +10.67 (SUBPOP) 188.76 188.95 P +3 F +4.45 ( is omitted or) 231.93 188.95 P +2 F +10.67 (NaN) 316.35 188.95 P +3 F +4.45 (,) 337.94 188.95 P +2 F +10.67 (SUBPOP = 1) 348.38 188.95 P +3 F +4.45 ( is assumed. All) 441.68 188.95 P +(subpopulations in) 135.65 174.95 T +2 F +(ObjV) 223.61 174.95 T +3 F +( must have the same size.) 252.39 174.95 T +2.76 (If) 135.65 148.95 P +2 F +6.63 (ranking) 149.4 148.95 P +3 F +2.76 ( is called with more than one subpopulation then the ranking is) 199.77 148.95 P +(performed separately for each subpopulation.) 135.65 134.95 T +FMENDPAGE +%%EndPage: "20" 21 +%%Page: "21" 21 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-21) 513.33 61.29 T +1 16 Q +(Example) 117.65 734.29 T +3 12 Q +(Consider a population with 10 individuals. The current objective values are:) 135.65 716.95 T +2 F +(ObjV = [1; 2; 3; 4; 5; 10; 9; 8; 7; 6]) 135.65 696.95 T +3 F +(Evaluate the \336tness with linear ranking and selective pressure 2:) 135.65 676.95 T +2 F +(FitnV = ranking\050ObjV\051) 135.65 656.95 T +(FitnV =) 135.65 636.95 T +(2.00) 153.65 622.95 T +(1.77) 153.65 608.95 T +(1.55) 153.65 594.95 T +(1.33) 153.65 580.95 T +(1.11) 153.65 566.95 T +(0) 153.65 552.95 T +(0.22) 153.65 538.95 T +(0.44) 153.65 524.95 T +(0.66) 153.65 510.95 T +(0.88) 153.65 496.95 T +3 F +(Evaluate the \336tness with non-linear ranking and selective pressure 2:) 135.65 476.95 T +2 F +(FitnV = ranking\050ObjV, [2 1]\051) 135.65 456.95 T +(FitnV =) 135.65 436.95 T +(2.00) 153.65 422.95 T +(1.66) 153.65 408.95 T +(1.38) 153.65 394.95 T +(1.15) 153.65 380.95 T +(0.95) 153.65 366.95 T +(0.38) 153.65 352.95 T +(0.45) 153.65 338.95 T +(0.55) 153.65 324.95 T +(0.66) 153.65 310.95 T +(0.79) 153.65 296.95 T +3 F +(Evaluate the \336tness with the values in RFun:) 135.65 276.95 T +2 F +(RFun = [3; 5; 7; 10; 14; 18; 25; 30; 40; 50]) 135.65 256.95 T +(FitnV = ranking\050ObjV, RFun\051) 135.65 236.95 T +FMENDPAGE +%%EndPage: "21" 22 +%%Page: "22" 22 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-22) 513.33 61.29 T +2 12 Q +(FitnV =) 135.65 736.95 T +(50) 153.65 722.95 T +(40) 153.65 708.95 T +(30) 153.65 694.95 T +(25) 153.65 680.95 T +(18) 153.65 666.95 T +( 3) 153.65 652.95 T +( 5) 153.65 638.95 T +( 7) 153.65 624.95 T +(10) 153.65 610.95 T +(14) 153.65 596.95 T +3 F +3.93 (Evaluate the \336tness with non-linear ranking and selective pressure 2 for 2) 135.65 576.95 P +(subpopulations in) 135.65 562.95 T +2 F +(ObjV) 223.61 562.95 T +3 F +(:) 251.5 562.95 T +2 F +(FitnV = ranking\050ObjV, [2 1], 2\051) 135.65 542.95 T +(FitnV =) 135.65 522.95 T +(2.00) 153.65 508.95 T +(1.28) 153.65 494.95 T +(0.83) 153.65 480.95 T +(0.53) 153.65 466.95 T +(0.34) 153.65 452.95 T +(0.34) 153.65 438.95 T +(0.53) 153.65 424.95 T +(0.83) 153.65 410.95 T +(1.28) 153.65 396.95 T +(2.00) 153.65 382.95 T +1 16 Q +(Algorithm) 117.65 360.29 T +3 12 Q +2.48 (The algorithms for both linear and non-linear ranking \336rst sorts the objective) 135.65 342.95 P +0.21 (function values into descending order) 135.65 328.95 P +0.21 (. The least \336t individual is placed in position) 316.38 328.95 P +1 (1 in the sorted list of objective values and the most \336t individual position) 135.65 314.95 P +2 F +2.41 (Nind) 502.86 314.95 P +3 F +0.08 (where) 135.65 300.95 P +2 F +0.19 (Nind) 168.02 300.95 P +3 F +0.08 ( is the number of individuals in the population. A \336tness value is then) 196.81 300.95 P +4.45 (assigned to each individual depending on its position,) 135.65 286.95 P +2 F +10.68 (Pos) 431.42 286.95 P +3 F +4.45 (, in the sorted) 453.01 286.95 P +(population.) 135.65 272.95 T +(For linear ranking individuals are assigned \336tness values according to:) 135.65 252.95 T +2 F +(FitnV\050Pos\051 =) 135.65 231.96 T +3 F +(, and) 484.28 231.96 T +(for non-linear ranking according to:) 135.65 210.97 T +2 F +(FitnV\050Pos\051 =) 135.65 178.65 T +3 F +(,) 308.28 178.65 T +(where) 135.65 121.83 T +0 F +( X) 164.95 121.83 T +3 F +( is computed as the root of the polynomial:) 175.27 121.83 T +225 226.97 484.28 240.95 C +2 12 Q +0 X +0 K +(2) 226 231.96 T +(S) 245.78 231.96 T +(P) 253.68 231.96 T +4 F +(-) 236.2 231.96 T +2 F +(2) 273.46 231.96 T +(S) 300.34 231.96 T +(P) 308.24 231.96 T +(1) 328.02 231.96 T +4 F +(-) 318.44 231.96 T +(\050) 295.24 231.96 T +(\051) 335.83 231.96 T +2 F +(P) 361.51 231.96 T +(o) 369.41 231.96 T +(s) 377.31 231.96 T +(1) 397.09 231.96 T +4 F +(-) 387.51 231.96 T +(\050) 356.41 231.96 T +(\051) 404.89 231.96 T +(\264) 344.82 231.96 T +(\264) 283.66 231.96 T +2 F +(N) 425.99 231.96 T +(i) 433.89 231.96 T +(n) 441.8 231.96 T +(d) 449.7 231.96 T +(1) 469.48 231.96 T +4 F +(-) 459.89 231.96 T +(\050) 420.89 231.96 T +(\051) 477.28 231.96 T +(\244) 413.89 231.96 T +(+) 263.88 231.96 T +-8.35 24.95 603.65 816.95 C +225 137.83 308.28 198.97 C +2 12 Q +0 X +0 K +(N) 227 185.72 T +(i) 234.9 185.72 T +(n) 242.8 185.72 T +(d) 250.71 185.72 T +0 F +(X) 270.48 185.72 T +0 9 Q +(P) 277.81 191.82 T +(o) 283.83 191.82 T +(s) 288.86 191.82 T +3 F +(1) 301.79 191.82 T +4 F +(-) 294.6 191.82 T +4 12 Q +(\264) 260.9 185.72 T +0 F +(X) 267.86 156.94 T +2 F +(i) 282.99 156.94 T +4 F +(\050) 277.89 156.94 T +(\051) 290.8 156.94 T +2 F +(i) 239.01 141.31 T +(1) 257.14 141.31 T +4 9 Q +(=) 249.21 141.31 T +2 12 Q +(N) 236.49 172.25 T +(i) 244.21 172.25 T +(n) 251.94 172.25 T +(d) 259.66 172.25 T +4 18 Q +(\345) 245.26 153.74 T +227 181.24 306.03 181.24 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "22" 23 +%%Page: "23" 23 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-23) 513.33 61.29 T +3 12 Q +(.) 473.9 730.99 T +0.08 (The vector) 135.65 709.99 P +2 F +0.19 (FitnV) 190.42 709.99 P +3 F +0.08 ( is then unsorted to re\337ect the order of the original input vector) 226.4 709.99 P +0.08 (,) 528.65 709.99 P +2 F +(ObjV) 135.65 695.99 T +3 F +(.) 162.88 695.99 T +1 16 Q +(See Also) 117.65 673.32 T +2 12 Q +(select) 135.65 655.99 T +3 F +(,) 178.82 655.99 T +2 F +(rws) 184.82 655.99 T +3 F +(,) 206.41 655.99 T +2 F +(sus) 212.41 655.99 T +1 16 Q +(Refer) 117.65 633.32 T +(ence) 155.53 633.32 T +3 12 Q +1.46 ([1] D. Whitley) 135.65 615.99 P +1.46 (, \322The GENIT) 208.07 615.99 P +1.46 (OR Algorithm and Selection Pressure: Why Rank-) 279.71 615.99 P +2.08 (Based Allocation of Reproductive T) 135.65 601.99 P +2.08 (rials is Best\323,) 317.43 601.99 P +0 F +2.08 (Pr) 390.97 601.99 P +2.08 (oc. ICGA 3) 402.52 601.99 P +3 F +2.08 (, pp. 1) 460.97 601.99 P +2.08 (16-121,) 494.67 601.99 P +(Mor) 135.65 587.99 T +(gan Kaufmann Publishers, 1989.) 156.09 587.99 T +135.65 725.99 473.9 744.95 C +2 12 Q +0 X +0 K +(0) 136.65 730.99 T +(S) 169.53 730.99 T +(P) 177.43 730.99 T +(1) 197.21 730.99 T +4 F +(-) 187.63 730.99 T +(\050) 164.43 730.99 T +(\051) 205.01 730.99 T +2 F +(X) 223.59 730.99 T +(N) 231.25 736.47 T +(i) 238.98 736.47 T +(n) 246.7 736.47 T +(d) 254.43 736.47 T +(1) 271.06 736.47 T +4 9 Q +(-) 263.87 736.47 T +4 12 Q +(\264) 214.01 730.99 T +2 F +(S) 290.84 730.99 T +(P) 298.74 730.99 T +(X) 318.52 730.99 T +(N) 326.18 736.47 T +(i) 333.9 736.47 T +(n) 341.63 736.47 T +(d) 349.35 736.47 T +(2) 365.98 736.47 T +4 9 Q +(-) 358.8 736.47 T +4 12 Q +(\264) 308.94 730.99 T +(\274) 385.76 730.99 T +2 F +(S) 410.34 730.99 T +(P) 418.24 730.99 T +(X) 438.02 730.99 T +(S) 457.8 730.99 T +(P) 465.71 730.99 T +4 F +(+) 448.22 730.99 T +(\264) 428.44 730.99 T +(+) 281.25 730.99 T +(+) 376.18 730.99 T +(+) 400.76 730.99 T +(=) 149.84 730.99 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "23" 24 +%%Page: "24" 24 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-24) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ecdis) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Discrete recombination) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = recdis\050OldChrom\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +6.77 (recdis) 135.65 588.95 P +3 F +2.82 ( performs discrete recombination between pairs of individuals in the) 178.82 588.95 P +3.85 (current population,) 135.65 574.95 P +2 F +9.24 (OldChrom) 237.62 574.95 P +3 F +3.85 (, and returns a new population after mating,) 295.18 574.95 P +2 F +(NewChrom) 135.65 560.95 T +3 F +(. Each row of) 193.22 560.95 T +2 F +(OldChrom) 260.82 560.95 T +3 F +( corresponds to one individual.) 318.39 560.95 T +1.18 (The pairs are mated in order) 135.65 534.95 P +1.18 (, odd row with the next even row) 276.62 534.95 P +1.18 (. If the number of) 442.66 534.95 P +0.5 (rows in the matrix) 135.65 520.95 P +2 F +1.2 (OldChrom) 228.25 520.95 P +3 F +0.5 ( is odd then the last row is not mated and added at) 285.82 520.95 P +4.19 (the end of) 135.65 506.95 P +2 F +10.05 (NewChrom) 199.16 506.95 P +3 F +4.19 (. The population should therefore be or) 256.73 506.95 P +4.19 (ganised into) 469.16 506.95 P +0.94 (contiguous pairs that require mating. This can be achieved by using the function) 135.65 492.95 P +2 F +0.28 (ranking) 135.65 478.95 P +3 F +0.12 ( to assign a \336tness level to each individual and a selection function \050e.g.) 186.02 478.95 P +2 F +5 (select) 135.65 464.95 P +3 F +2.09 (\051 to select individuals with a probability related to their \336tness in the) 178.82 464.95 P +(current population.) 135.65 450.95 T +2 F +(recdis) 135.65 424.95 T +3 F +( is a low-level recombination function normally called by) 178.82 424.95 T +2 F +(recombin) 457.64 424.95 T +3 F +(.) 515.2 424.95 T +1 16 Q +(Example) 117.65 396.29 T +3 12 Q +(Consider the following population with \336ve real-value individuals:) 135.65 378.95 T +2 F +(OldChrom = [) 135.65 358.95 T +( 40.23 -17.17) 153.65 344.95 T +( 28.95) 254.39 344.95 T +(15.38; % parent1) 311.96 344.95 T +( 82.06) 153.65 330.95 T +( 13.26) 204.02 330.95 T +(13.35) 261.59 330.95 T +(-9.09; % parent2) 311.96 330.95 T +( 52.43) 153.65 316.95 T +(25.64) 211.22 316.95 T +(15.20) 261.59 316.95 T +(-2.54; % parent3) 311.96 316.95 T +(-47.50) 153.65 302.95 T +(49.10) 211.22 302.95 T +(9.09) 268.79 302.95 T +( 10.65; % parent4) 304.77 302.95 T +(-90.50 -13.46 -25.63) 153.65 288.95 T +(-0.89] % parent5) 311.96 288.95 T +3 F +(T) 135.65 268.95 T +(o perform discrete recombination:) 142.14 268.95 T +2 F +(NewChrom = recdis\050OldChrom\051) 135.65 248.95 T +4.11 (recdis) 135.65 228.95 P +3 F +1.71 ( produces an internal mask table determining which parents contribute) 178.82 228.95 P +(which variables to the of) 135.65 214.95 T +(fspring, e.g.) 254.01 214.95 T +2 F +(Mask = [) 135.65 194.95 T +(1 2 1 2; % for producing offspring1) 160.84 180.95 T +( 2 2 1 1; % for producing offspring2) 153.65 166.95 T +( 2 1 2 1; % for producing offspring3) 153.65 152.95 T +( 1 1 2 2] % for producing offspring4) 153.65 138.95 T +3 F +(Thus, after recombination) 135.65 118.95 T +2 F +(NewChrom) 262.89 118.95 T +3 F +( would become:) 320.45 118.95 T +FMENDPAGE +%%EndPage: "24" 25 +%%Page: "25" 25 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-25) 513.33 61.29 T +2 12 Q +(NewChrom = [) 135.65 736.95 T +(40.23) 160.84 722.95 T +(13.26) 211.22 722.95 T +(28.95) 261.59 722.95 T +( -9.09; % Mask\0501,:\051 parent1&2) 304.77 722.95 T +(82.06) 160.84 708.95 T +(13.26) 211.22 708.95 T +(28.95) 261.59 708.95 T +( 15.38; % Mask\0502,:\051 parent1&2) 304.77 708.95 T +(-47.50) 153.65 694.95 T +(25.64) 211.22 694.95 T +( 9.09) 261.59 694.95 T +(-2.54; % Mask\0503,:\051 parent3&4) 311.96 694.95 T +(52.43) 160.84 680.95 T +( 25.64) 204.02 680.95 T +( 9.09) 261.59 680.95 T +( 10.65] % Mask\0504,:\051 parent3&4) 304.77 680.95 T +3 F +0.75 (As the number of individuals in the parent population,) 135.65 660.95 P +2 F +1.79 (OldChrom) 405.55 660.95 P +3 F +0.75 (, was odd, the) 463.12 660.95 P +-0.18 (last individual is appended without recombination to) 135.65 646.95 P +2 F +-0.43 (NewChrom) 389.9 646.95 P +3 F +-0.18 ( and the of) 447.47 646.95 P +-0.18 (fspring) 497.67 646.95 P +(returned to the users workspace, thus) 135.65 632.95 T +2 F +(NewChrom =) 135.65 612.95 T +(40.23) 160.84 598.95 T +( 13.26) 204.02 598.95 T +(28.95) 261.59 598.95 T +( -9.09) 304.77 598.95 T +(82.06) 160.84 584.95 T +(13.26) 211.22 584.95 T +(28.95) 261.59 584.95 T +( 15.38) 304.77 584.95 T +(-47.50) 153.65 570.95 T +(25.64) 211.22 570.95 T +( 9.09) 261.59 570.95 T +( -2.54) 304.77 570.95 T +(52.43) 160.84 556.95 T +( 25.64) 204.02 556.95 T +(9.09) 268.79 556.95 T +(10.65) 311.96 556.95 T +(-90.50 -13.46 -25.63) 153.65 542.95 T +( -0.89) 304.77 542.95 T +1 16 Q +(Algorithm) 117.65 520.29 T +3 12 Q +1.99 (Discrete recombination exchanges variable values between the individuals. For) 135.65 502.95 P +2.43 (each variable the parent who contributes its variable value to the of) 135.65 488.95 P +2.43 (fspring is) 484.24 488.95 P +(chosen randomly with equal probability) 135.65 474.95 T +(.) 326.08 474.95 T +0.91 (Discrete recombination can generate the corners of the hypercube de\336ned by the) 135.65 448.95 P +(parents.) 135.65 434.95 T +1 16 Q +(See Also) 117.65 406.29 T +2 12 Q +(recombin) 135.65 388.95 T +3 F +(,) 193.22 388.95 T +2 F +(recint) 199.21 388.95 T +3 F +(,) 242.39 388.95 T +2 F +(reclin) 248.39 388.95 T +3 F +(,) 291.56 388.95 T +2 F +(ranking) 297.56 388.95 T +3 F +(,) 347.93 388.95 T +2 F +(sus) 353.93 388.95 T +3 F +(,) 375.52 388.95 T +2 F +(rws) 381.51 388.95 T +1 16 Q +(Refer) 117.65 366.29 T +(ence) 155.53 366.29 T +3 12 Q +3.9 ([1] H. M) 135.65 348.95 P +3.9 (\237) 185.76 348.95 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 348.95 P +3.9 (oosen, \322Predictive Models for the) 354.48 348.95 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 334.95 P +0 F +0.18 (Evolutionary) 469.02 334.95 P +(Computation) 135.65 320.95 T +3 F +(, V) 198.29 320.95 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 320.95 T +FMENDPAGE +%%EndPage: "25" 26 +%%Page: "26" 26 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-26) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ecint) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Intermediate recombination) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = recint\050OldChrom\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.73 (recint) 135.65 588.95 P +3 F +0.3 ( performs intermediate recombination between pairs of individuals in the) 178.82 588.95 P +3.85 (current population,) 135.65 574.95 P +2 F +9.24 (OldChrom) 237.62 574.95 P +3 F +3.85 (, and returns a new population after mating,) 295.18 574.95 P +2 F +(NewChrom) 135.65 560.95 T +3 F +(. Each row of) 193.22 560.95 T +2 F +(OldChrom) 260.82 560.95 T +3 F +( corresponds to one individual.) 318.39 560.95 T +2 F +1.76 (recint) 135.65 534.95 P +3 F +0.73 ( is a function only applicable to populations of real-value variables \050and) 178.82 534.95 P +(not binary or integer\051.) 135.65 520.95 T +1.18 (The pairs are mated in order) 135.65 494.95 P +1.18 (, odd row with the next even row) 276.62 494.95 P +1.18 (. If the number of) 442.66 494.95 P +0.5 (rows in the matrix) 135.65 480.95 P +2 F +1.2 (OldChrom) 228.25 480.95 P +3 F +0.5 ( is odd then the last row is not mated and added at) 285.82 480.95 P +4.19 (the end of) 135.65 466.95 P +2 F +10.05 (NewChrom) 199.16 466.95 P +3 F +4.19 (. The population should therefore be or) 256.73 466.95 P +4.19 (ganised into) 469.16 466.95 P +0.94 (contiguous pairs that require mating. This can be achieved by using the function) 135.65 452.95 P +2 F +0.28 (ranking) 135.65 438.95 P +3 F +0.12 ( to assign a \336tness level to each individual and a selection function \050e.g.) 186.02 438.95 P +2 F +5 (select) 135.65 424.95 P +3 F +2.09 (\051 to select individuals with a probability related to their \336tness in the) 178.82 424.95 P +(current population.) 135.65 410.95 T +2 F +(recint) 135.65 384.95 T +3 F +( is a low-level recombination function normally called by) 178.82 384.95 T +2 F +(recombin) 457.64 384.95 T +3 F +(.) 515.2 384.95 T +1 16 Q +(Example) 117.65 356.29 T +3 12 Q +(Consider the following population with three real-value individuals:) 135.65 338.95 T +2 F +(OldChrom = [) 135.65 318.95 T +(40.23 -17.17) 153.65 304.95 T +( 28.95) 247.2 304.95 T +(15.38; % parent1) 304.77 304.95 T +(82.06) 153.65 290.95 T +( 13.26) 196.82 290.95 T +(13.35) 254.39 290.95 T +(-9.09; % parent2) 304.77 290.95 T +(52.43) 153.65 276.95 T +(25.64) 204.02 276.95 T +(15.20) 254.39 276.95 T +(-2.54] % parent3) 304.77 276.95 T +3 F +(T) 135.65 256.95 T +(o perform intermediate recombination:) 142.14 256.95 T +2 F +(NewChrom = recint\050OldChrom\051) 135.65 236.95 T +3 F +2.57 (New values are produced by adding the scaled dif) 135.65 216.95 P +2.57 (ference between the parent) 395.08 216.95 P +1.05 (values to the \336rst parent \050see) 135.65 202.95 P +0 F +1.05 (Algorithm) 282.51 202.95 P +3 F +1.05 ( subsection\051. An internal table of scaling) 331.15 202.95 P +(factors,) 135.65 188.95 T +2 F +(Alpha) 174.28 188.95 T +3 F +(, is produced, e.g.) 210.26 188.95 T +2 F +(Alpha = [) 135.65 168.95 T +(-0.13 0.50 0.32 0.16; % for offspring1) 153.65 154.95 T +( 1.12 0.54 0.44 1.16] % for offspring2) 153.65 140.95 T +3 F +(Thus, after recombination) 135.65 120.95 T +2 F +(NewChrom) 262.89 120.95 T +3 F +( would become:) 320.45 120.95 T +FMENDPAGE +%%EndPage: "26" 27 +%%Page: "27" 27 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-27) 513.33 61.29 T +2 12 Q +(NewChrom = [) 135.65 736.95 T +(34.40) 153.65 722.95 T +( -1.92) 196.82 722.95 T +( 23.86) 247.2 722.95 T +( 11.33; % Alpha\0501,:\051 parent1&2) 297.57 722.95 T +(87.11) 153.65 708.95 T +( -0.59) 196.82 708.95 T +(21.98 -13.04] % Alpha\0502,:\051 parent1&2) 254.39 708.95 T +3 F +0.75 (As the number of individuals in the parent population,) 135.65 688.95 P +2 F +1.79 (OldChrom) 405.55 688.95 P +3 F +0.75 (, was odd, the) 463.12 688.95 P +-0.18 (last individual is appended without recombination to) 135.65 674.95 P +2 F +-0.43 (NewChrom) 389.9 674.95 P +3 F +-0.18 ( and the of) 447.47 674.95 P +-0.18 (fspring) 497.67 674.95 P +(returned to the users workspace, thus:) 135.65 660.95 T +2 F +(NewChrom =) 135.65 640.95 T +(34.40) 153.65 626.95 T +(-1.92) 204.02 626.95 T +(23.86) 254.39 626.95 T +( 11.33) 297.57 626.95 T +(87.11) 153.65 612.95 T +(-0.59) 204.02 612.95 T +(21.98 -13.04) 254.39 612.95 T +(52.43) 153.65 598.95 T +(25.64) 204.02 598.95 T +(15.20) 254.39 598.95 T +(-2.54) 304.77 598.95 T +1 16 Q +(Algorithm) 117.65 576.29 T +3 12 Q +(Intermediate recombination combines parent values using the following rule:) 135.65 558.95 T +2 F +(offspring = parent1 +) 135.65 532.95 T +3 F +(where) 135.65 506.95 T +2 F +(Alpha) 167.95 506.95 T +3 F +( is a scaling factor chosen uniformly at random in the interval) 203.93 506.95 T +2 F +1.08 ([-0.25, 1.25]) 135.65 492.95 P +3 F +0.45 (.) 230.28 492.95 P +2 F +1.08 (recint) 236.73 492.95 P +3 F +0.45 ( produces a new Alpha for each pair of values to be) 279.9 492.95 P +(combined.) 135.65 478.95 T +1.99 (Intermediate recombination can generate any point within a hypercube slightly) 135.65 452.95 P +(lar) 135.65 438.95 T +(ger than that de\336ned by the parents.) 148.09 438.95 T +2.01 (Intermediate recombination is similar to line recombination) 135.65 412.95 P +2 F +4.82 (reclin) 438.51 412.95 P +3 F +2.01 (. Whereas) 481.69 412.95 P +2 F +5.85 (recint) 135.65 398.95 P +3 F +2.44 ( uses a new Alpha factor for each pair of values combined together) 178.82 398.95 P +2.44 (,) 528.65 398.95 P +2 F +(reclin) 135.65 384.95 T +3 F +( uses one) 178.82 384.95 T +2 F +(Alpha) 225.79 384.95 T +3 F +( factor for each pair of parents.) 261.77 384.95 T +1 16 Q +(See Also) 117.65 356.29 T +2 12 Q +(recombin) 135.65 338.95 T +3 F +(,) 193.22 338.95 T +2 F +(recdis) 199.21 338.95 T +3 F +(,) 242.39 338.95 T +2 F +(reclin) 248.39 338.95 T +3 F +(,) 291.56 338.95 T +2 F +(ranking) 297.56 338.95 T +3 F +(,) 347.93 338.95 T +2 F +(sus) 353.93 338.95 T +3 F +(,) 375.52 338.95 T +2 F +(rws) 381.51 338.95 T +1 16 Q +(Refer) 117.65 316.29 T +(ence) 155.53 316.29 T +3 12 Q +3.9 ([1] H. M) 135.65 298.95 P +3.9 (\237) 185.76 298.95 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 298.95 P +3.9 (oosen, \322Predictive Models for the) 354.48 298.95 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 284.95 P +0 F +0.18 (Evolutionary) 469.02 284.95 P +(Computation) 135.65 270.95 T +3 F +(, V) 198.29 270.95 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 270.95 T +293.96 527.96 482.85 541.94 C +2 12 Q +0 X +0 K +(A) 294.96 532.95 T +(l) 302.86 532.95 T +(p) 310.77 532.95 T +(h) 318.67 532.95 T +(a) 326.57 532.95 T +(p) 353.45 532.95 T +(a) 361.35 532.95 T +(r) 369.25 532.95 T +(e) 377.16 532.95 T +(n) 385.06 532.95 T +(t) 392.96 532.95 T +(2) 400.86 532.95 T +(p) 420.64 532.95 T +(a) 428.54 532.95 T +(r) 436.45 532.95 T +(e) 444.35 532.95 T +(n) 452.25 532.95 T +(t) 460.15 532.95 T +(1) 468.05 532.95 T +4 F +(-) 411.06 532.95 T +(\050) 348.35 532.95 T +(\051) 475.86 532.95 T +(\264) 336.77 532.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "27" 28 +%%Page: "28" 28 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-28) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(eclin) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Line recombination) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = reclin\050OldChrom\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +1.86 (reclin) 135.65 588.95 P +3 F +0.77 ( performs line recombination between pairs of individuals in the current) 178.82 588.95 P +0.89 (population,) 135.65 574.95 P +2 F +2.15 (OldChrom) 193.85 574.95 P +3 F +0.89 (, and returns a new population after mating,) 251.41 574.95 P +2 F +2.15 (NewChrom) 471.08 574.95 P +3 F +0.89 (.) 528.65 574.95 P +(Each row of) 135.65 560.95 T +2 F +(OldChrom) 197.26 560.95 T +3 F +( corresponds to one individual.) 254.83 560.95 T +2 F +1.9 (reclin) 135.65 534.95 P +3 F +0.79 ( is a function only applicable to populations of real-value variables \050) 178.82 534.95 P +1 F +0.79 (not) 514.99 534.95 P +3 F +(binary or integer\051.) 135.65 520.95 T +1.18 (The pairs are mated in order) 135.65 494.95 P +1.18 (, odd row with the next even row) 276.62 494.95 P +1.18 (. If the number of) 442.66 494.95 P +0.5 (rows in the matrix) 135.65 480.95 P +2 F +1.2 (OldChrom) 228.25 480.95 P +3 F +0.5 ( is odd then the last row is not mated and added at) 285.82 480.95 P +4.19 (the end of) 135.65 466.95 P +2 F +10.05 (NewChrom) 199.16 466.95 P +3 F +4.19 (. The population should therefore be or) 256.73 466.95 P +4.19 (ganised into) 469.16 466.95 P +0.94 (contiguous pairs that require mating. This can be achieved by using the function) 135.65 452.95 P +2 F +0.28 (ranking) 135.65 438.95 P +3 F +0.12 ( to assign a \336tness level to each individual and a selection function \050e.g.) 186.02 438.95 P +2 F +5 (select) 135.65 424.95 P +3 F +2.09 (\051 to select individuals with a probability related to their \336tness in the) 178.82 424.95 P +(current population.) 135.65 410.95 T +2 F +(reclin) 135.65 384.95 T +3 F +( is a low-level recombination function normally called by) 178.82 384.95 T +2 F +(recombin) 457.64 384.95 T +3 F +(.) 515.2 384.95 T +1 16 Q +(Example) 117.65 356.29 T +3 12 Q +(Consider the following population with three real-value individuals:) 135.65 338.95 T +2 F +(OldChrom = [) 135.65 318.95 T +( 40.23 -17.17) 153.65 304.95 T +(28.95) 261.59 304.95 T +(15.38; % parent1) 311.96 304.95 T +( 82.06) 153.65 290.95 T +( 13.26) 204.02 290.95 T +(13.35) 261.59 290.95 T +(-9.09; % parent2) 311.96 290.95 T +( 52.43) 153.65 276.95 T +(25.64) 211.22 276.95 T +(15.20) 261.59 276.95 T +(-2.54] % parent3) 311.96 276.95 T +3 F +(T) 135.65 256.95 T +(o perform line recombination:) 142.14 256.95 T +2 F +(NewChrom = reclin\050OldChrom\051) 135.65 236.95 T +3 F +2.57 (New values are produced by adding the scaled dif) 135.65 216.95 P +2.57 (ference between the parent) 395.08 216.95 P +2.19 (values to the \336rst parent \050see Algorithm\051. An internal table of scaling factors,) 135.65 202.95 P +2 F +(Alpha) 135.65 188.95 T +3 F +(, is produced, e.g.) 171.63 188.95 T +2 F +(Alpha = [) 135.65 168.95 T +(0.78; % for producing offspring1) 153.65 154.95 T +(1.05] % for producing offspring2) 153.65 140.95 T +3 F +(Thus, after recombination NewChrom would become:) 135.65 120.95 T +FMENDPAGE +%%EndPage: "28" 29 +%%Page: "29" 29 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-29) 513.33 61.29 T +2 12 Q +(NewChrom = [) 135.65 736.95 T +(72.97) 153.65 722.95 T +( 6.64 16.74) 196.82 722.95 T +(-3.77; % Alpha\0501\051 parent1&2) 290.37 722.95 T +(84.25 14.85 12.54 -10.37] % Alpha\0502\051 parent1&2) 153.65 708.95 T +3 F +0.75 (As the number of individuals in the parent population,) 135.65 688.95 P +2 F +1.79 (OldChrom) 405.55 688.95 P +3 F +0.75 (, was odd, the) 463.12 688.95 P +-0.18 (last individual is appended without recombination to) 135.65 674.95 P +2 F +-0.43 (NewChrom) 389.9 674.95 P +3 F +-0.18 ( and the of) 447.47 674.95 P +-0.18 (fspring) 497.67 674.95 P +(returned to the users workspace, thus:) 135.65 660.95 T +2 F +(NewChrom =) 135.65 640.95 T +(72.97) 153.65 626.95 T +(6.64 16.74) 204.02 626.95 T +( -3.77) 283.18 626.95 T +(84.25 14.85 12.54 -10.37) 153.65 612.95 T +(52.43 25.64 15.20) 153.65 598.95 T +( -2.54) 283.18 598.95 T +1 16 Q +(Algorithm) 117.65 576.29 T +3 12 Q +(Line recombination combines parent values using the following rule:) 135.65 558.95 T +2 F +(offspring = parent1 +) 135.65 532.95 T +3 F +(where) 135.65 506.95 T +2 F +(Alpha) 167.95 506.95 T +3 F +( is a scaling factor chosen uniformly at random in the interval) 203.93 506.95 T +2 F +0.42 ([-0.25, 1.25]) 135.65 492.95 P +3 F +0.17 (.) 229.61 492.95 P +2 F +0.42 (reclin) 235.78 492.95 P +3 F +0.17 ( produces a new Alpha for each pair of parents to be) 278.96 492.95 P +(combined.) 135.65 478.95 T +2.41 (Line recombination can generate any point on a slightly longer line than that) 135.65 452.95 P +(de\336ned by the parents.) 135.65 438.95 T +1.59 (Line recombination is similar to intermediate recombination) 135.65 412.95 P +2 F +3.82 (recint) 438.93 412.95 P +3 F +1.59 (. Whereas) 482.11 412.95 P +2 F +7.91 (reclin) 135.65 398.95 P +3 F +3.29 ( uses one Alpha factor for each pair of parents combined together) 178.82 398.95 P +3.29 (,) 528.65 398.95 P +2 F +(recint) 135.65 384.95 T +3 F +( uses a new) 178.82 384.95 T +2 F +(Alpha) 236.78 384.95 T +3 F +( factor for each pair of values.) 272.76 384.95 T +1 16 Q +(See Also) 117.65 356.29 T +2 12 Q +(recombin) 135.65 338.95 T +3 F +(,) 193.22 338.95 T +2 F +(recdis) 199.21 338.95 T +3 F +(,) 242.39 338.95 T +2 F +(recint) 248.39 338.95 T +3 F +(,) 291.56 338.95 T +2 F +(ranking) 297.56 338.95 T +3 F +(,) 347.93 338.95 T +2 F +(sus) 353.93 338.95 T +3 F +(,) 375.52 338.95 T +2 F +(rws) 381.51 338.95 T +1 16 Q +(Refer) 117.65 316.29 T +(ence) 155.53 316.29 T +3 12 Q +3.9 ([1] H. M) 135.65 298.95 P +3.9 (\237) 185.76 298.95 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 298.95 P +3.9 (oosen, \322Predictive Models for the) 354.48 298.95 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 284.95 P +0 F +0.18 (Evolutionary) 469.02 284.95 P +(Computation) 135.65 270.95 T +3 F +(, V) 198.29 270.95 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 270.95 T +293.96 527.96 482.85 541.94 C +2 12 Q +0 X +0 K +(A) 294.96 532.95 T +(l) 302.86 532.95 T +(p) 310.77 532.95 T +(h) 318.67 532.95 T +(a) 326.57 532.95 T +(p) 353.45 532.95 T +(a) 361.35 532.95 T +(r) 369.25 532.95 T +(e) 377.16 532.95 T +(n) 385.06 532.95 T +(t) 392.96 532.95 T +(2) 400.86 532.95 T +(p) 420.64 532.95 T +(a) 428.54 532.95 T +(r) 436.45 532.95 T +(e) 444.35 532.95 T +(n) 452.25 532.95 T +(t) 460.15 532.95 T +(1) 468.05 532.95 T +4 F +(-) 411.06 532.95 T +(\050) 348.35 532.95 T +(\051) 475.86 532.95 T +(\264) 336.77 532.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "29" 30 +%%Page: "30" 30 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-30) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ecmut) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Line recombination with mutation features) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = recmut\050OldChrom, FieldDR\051) 135.65 628.95 T +(NewChrom = recmut\050OldChrom, FieldDR, MutOpt\051) 135.65 608.95 T +1 16 Q +(Description) 117.65 586.29 T +2 12 Q +5.35 (recmut) 135.65 568.95 P +3 F +2.23 ( performs line recombination with mutation features between pairs of) 178.82 568.95 P +1.26 (individuals in the current population,) 135.65 554.95 P +2 F +3.03 (OldChrom) 322.53 554.95 P +3 F +1.26 (, and returns a new population) 380.1 554.95 P +(after mating,) 135.65 540.95 T +2 F +(NewChrom) 199.93 540.95 T +3 F +(. Each row of) 257.5 540.95 T +2 F +(OldChrom) 325.11 540.95 T +3 F +( corresponds to one individual.) 382.68 540.95 T +2 F +1.31 (FieldDR) 135.65 514.95 P +3 F +0.55 ( is a matrix containing the boundaries of each variable of an individual) 186.02 514.95 P +(\050see) 135.65 500.95 T +2 F +(crtrp) 157.96 500.95 T +3 F +(\051.) 193.94 500.95 T +2 F +(MutOpt) 135.65 474.95 T +3 F +( is an optional vector with a maximum of 2 parameters:) 178.82 474.95 T +2 F +(MutOpt\0501\051) 135.65 454.95 T +3 F +(:) 200.41 454.95 T +(scalar containing the recombination rate in the range) 171.65 440.95 T +2 F +([0, 1].) 426.78 440.95 T +3 F +(If omitted or) 171.65 426.95 T +2 F +(NaN) 235.27 426.95 T +3 F +(,) 256.86 426.95 T +2 F +(MutOpt\0501\051 = 1) 262.86 426.95 T +3 F +( is assumed.) 356.41 426.95 T +2 F +(MutOpt\0502\051) 135.65 406.95 T +3 F +(:) 200.41 406.95 T +-0.23 (scalar containing a value in the range [0, 1] for shrinking the recombination) 171.65 392.95 P +(range.) 171.65 378.95 T +(If omitted or) 171.65 364.95 T +2 F +(NaN) 235.27 364.95 T +3 F +(,) 256.86 364.95 T +2 F +(MutOpt\0502\051 = 1) 262.86 364.95 T +3 F +( is assumed \050no shrinking\051.) 356.41 364.95 T +2 F +1.76 (recmut) 135.65 344.95 P +3 F +0.73 ( is a function only applicable to populations of real-value variables \050and) 178.82 344.95 P +(not binary or integer\051.) 135.65 330.95 T +1.18 (The pairs are mated in order) 135.65 304.95 P +1.18 (, odd row with the next even row) 276.62 304.95 P +1.18 (. If the number of) 442.66 304.95 P +0.5 (rows in the matrix) 135.65 290.95 P +2 F +1.2 (OldChrom) 228.25 290.95 P +3 F +0.5 ( is odd then the last row is not mated and added at) 285.82 290.95 P +4.19 (the end of) 135.65 276.95 P +2 F +10.05 (NewChrom) 199.16 276.95 P +3 F +4.19 (. The population should therefore be or) 256.73 276.95 P +4.19 (ganised into) 469.16 276.95 P +0.94 (contiguous pairs that require mating. This can be achieved by using the function) 135.65 262.95 P +2 F +-0.51 (ranking) 135.65 248.95 P +3 F +-0.21 ( to assign a \336tness level to each individual and a selection function \050) 186.02 248.95 P +2 F +-0.51 (sus) 510.06 248.95 P +3 F +-0.24 (or) 135.65 234.95 P +2 F +-0.57 (rws) 148.4 234.95 P +3 F +-0.24 (\051 to select individuals with a probability related to their \336tness in the current) 169.99 234.95 P +(population.) 135.65 220.95 T +2 F +0.89 (recmut) 135.65 194.95 P +3 F +0.37 ( uses features of the mutation operator of the Breeder Genetic Algorithm) 178.82 194.95 P +2.31 (\050see) 135.65 180.95 P +2 F +5.53 (mutbga) 160.26 180.95 P +3 F +2.31 (\051. Therefore, the calling syntax of this recombination function is) 203.44 180.95 P +(identical to this of the mutation function) 135.65 166.95 T +2 F +(mutbga) 331.87 166.95 T +3 F +(.) 375.05 166.95 T +2 F +(recmut) 135.65 140.95 T +3 F +( is a low-level recombination function normally called by) 178.82 140.95 T +2 F +(mutate) 457.64 140.95 T +3 F +(.) 500.81 140.95 T +FMENDPAGE +%%EndPage: "30" 31 +%%Page: "31" 31 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-31) 513.33 61.29 T +1 16 Q +(Example) 117.65 734.29 T +3 12 Q +(Consider the following population with four real-valued individuals:) 135.65 716.95 T +2 F +(OldChrom = [) 135.65 696.95 T +(40.2381 -17.1766) 160.84 682.95 T +( 28.9530) 283.18 682.95 T +(15.3883; % parent1) 355.14 682.95 T +(82.0642) 160.84 668.95 T +(13.2639) 225.61 668.95 T +(13.3596) 290.37 668.95 T +(-9.0916; % parent2) 355.14 668.95 T +(52.4396) 160.84 654.95 T +(25.6410) 225.61 654.95 T +(15.2014) 290.37 654.95 T +(-2.5435; % parent3) 355.14 654.95 T +(-47.5381) 153.65 640.95 T +(49.1963) 225.61 640.95 T +(9.0954) 297.57 640.95 T +(10.6521] % parent4) 355.14 640.95 T +3 F +(The boundaries are de\336ned as:) 135.65 620.95 T +2 F +(FieldDR = [) 135.65 600.95 T +(-100 -50 -30 -20;) 153.65 586.95 T +( 100) 153.65 572.95 T +(50) 196.82 572.95 T +( 30) 218.41 572.95 T +(20]) 254.39 572.95 T +3 F +(T) 135.65 552.95 T +(o perform line recombination with mutation features:) 142.14 552.95 T +2 F +(NewChrom = recmut\050OldChrom, FieldDR\051) 135.65 532.95 T +4.89 (recmut) 135.65 512.95 P +3 F +2.04 ( produces an internal mask table,) 178.82 512.95 P +2 F +4.89 (RecMx) 351.94 512.95 P +3 F +2.04 (, determining which pairs of) 387.92 512.95 P +2.56 (parents to recombine \050here recombine all pairs\051 and the sign for adding) 135.65 498.95 P +2 F +6.14 (the) 510.06 498.95 P +3 F +(recombination step) 135.65 484.95 T +(\050see Algorithm\051, e.g.) 234.45 484.95 T +2 F +(RecMx = [) 135.65 464.95 T +( 1) 153.65 450.95 T +(-1) 175.24 450.95 T +(-1) 196.82 450.95 T +(-1; % for producing offspring1 & 2) 218.41 450.95 T +(-1) 153.65 436.95 T +(-1) 175.24 436.95 T +(-1) 196.82 436.95 T +(-1] % for producing offspring3 & 4) 218.41 436.95 T +3 F +6.59 (T) 135.65 416.95 P +6.59 (wo further internal tables,) 142.14 416.95 P +2 F +15.81 (delta) 295.39 416.95 P +3 F +6.59 ( and) 331.37 416.95 P +2 F +15.81 (Diff) 367.86 416.95 P +3 F +6.59 (, specify the normalized) 396.64 416.95 P +(recombination step size, e.g.) 135.65 402.95 T +2 F +(delta = [) 135.65 382.95 T +(0.1250) 153.65 368.95 T +(0.1250 0.1250 0.1250; % for offspring1 & 2) 204.02 368.95 T +(0.0005 0.0005 0.0005 0.0005] % for offspring3 & 4) 153.65 354.95 T +(Diff = [) 135.65 334.95 T +-0.68 (1.3937) 168.04 320.95 P +-0.68 (1.0143) 218.41 320.95 P +-0.68 (-0.5196) 268.79 320.95 P +-0.68 (-0.8157; % for offspring1 & 2) 326.35 320.95 P +-0.68 (-10.5712) 153.65 306.95 P +-0.68 (2.4906) 218.41 306.95 P +-0.68 (-0.6456) 268.79 306.95 P +-0.68 (1.3952] % for offspring3 & 4) 333.55 306.95 P +3 F +(Thus, after recombination NewChrom becomes:) 135.65 286.95 T +2 F +(NewChrom =) 135.65 266.95 T +(57.6637) 160.84 252.95 T +(-23.5177) 218.41 252.95 T +(30.0000) 290.37 252.95 T +(17.4281) 355.14 252.95 T +(64.6386) 160.84 238.95 T +(19.6050) 225.61 238.95 T +(11.4106) 290.37 238.95 T +(-11.1314) 347.94 238.95 T +(52.9719) 160.84 224.95 T +(25.5783) 225.61 224.95 T +(15.2112) 290.37 224.95 T +(-2.5576) 355.14 224.95 T +(-48.0704) 153.65 210.95 T +(49.2590) 225.61 210.95 T +(9.0856) 297.57 210.95 T +(10.6662) 355.14 210.95 T +1 16 Q +(Algorithm) 117.65 188.29 T +3 12 Q +(The of) 135.65 170.95 T +(fsprings of a pair of two parents are computed as follows:) 167.07 170.95 T +(of) 135.65 150.95 T +(fspring1=parent1 +) 145.42 150.95 T +(of) 135.65 130.95 T +(fspring2=parent2 +) 145.42 130.95 T +240.89 145.96 508.85 159.94 C +2 12 Q +0 X +0 K +(R) 241.89 150.95 T +(e) 249.79 150.95 T +(c) 257.69 150.95 T +(M) 265.6 150.95 T +(x) 273.5 150.95 T +(r) 293.28 150.95 T +(a) 301.18 150.95 T +(n) 309.08 150.95 T +(g) 316.98 150.95 T +(e) 324.89 150.95 T +(M) 344.67 150.95 T +(u) 352.57 150.95 T +(t) 360.47 150.95 T +(O) 368.37 150.95 T +(p) 376.27 150.95 T +(t) 384.18 150.95 T +(2) 399.18 150.95 T +4 F +(\050) 394.08 150.95 T +(\051) 406.98 150.95 T +2 F +(d) 425.56 150.95 T +(e) 433.46 150.95 T +(l) 441.36 150.95 T +(t) 449.27 150.95 T +(a) 457.17 150.95 T +4 F +(\264) 335.08 150.95 T +(\264) 415.98 150.95 T +(\264) 283.69 150.95 T +2 F +(D) 476.95 150.95 T +(i) 484.85 150.95 T +(f) 492.75 150.95 T +(f) 500.65 150.95 T +4 F +(\264) 467.36 150.95 T +-8.35 24.95 603.65 816.95 C +240.89 125.96 529.6 139.94 C +2 12 Q +0 X +0 K +(R) 241.89 130.95 T +(e) 249.79 130.95 T +(c) 257.69 130.95 T +(M) 265.6 130.95 T +(x) 273.5 130.95 T +(r) 293.28 130.95 T +(a) 301.18 130.95 T +(n) 309.08 130.95 T +(g) 316.98 130.95 T +(e) 324.89 130.95 T +(M) 344.67 130.95 T +(u) 352.57 130.95 T +(t) 360.47 130.95 T +(O) 368.37 130.95 T +(p) 376.27 130.95 T +(t) 384.18 130.95 T +(2) 399.18 130.95 T +4 F +(\050) 394.08 130.95 T +(\051) 406.98 130.95 T +2 F +(d) 425.56 130.95 T +(e) 433.46 130.95 T +(l) 441.36 130.95 T +(t) 449.27 130.95 T +(a) 457.17 130.95 T +4 F +(\264) 335.08 130.95 T +(\264) 415.98 130.95 T +(\264) 283.69 130.95 T +2 F +(D) 491.1 130.95 T +(i) 499 130.95 T +(f) 506.9 130.95 T +(f) 514.8 130.95 T +4 F +(-) 484.05 130.95 T +(\050) 478.95 130.95 T +(\051) 522.6 130.95 T +(\264) 467.36 130.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "31" 32 +%%Page: "32" 32 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-32) 513.33 61.29 T +2 12 Q +(RecMx) 135.65 736.95 T +3 F +(=) 180.62 736.95 T +( with probability) 202.43 736.95 T +2 F +(MutOpt\0501\051) 285.39 736.95 T +3 F +(, \050- with probability 0.9\051) 350.15 736.95 T +(else 0) 171.65 722.95 T +2 F +(range =) 135.65 702.95 T +3 F +( domain of variable \050search interval de\336ned by) 228.79 702.95 T +2 F +(FieldDR) 455.94 702.95 T +3 F +(\051.) 506.32 702.95 T +2 F +(delta =) 135.65 669.03 T +3 F +(,) 237.45 669.03 T +( with probability 1/m, else 0, m = 20.) 281.05 669.03 T +0.13 (The recombination operator) 135.65 600.85 P +2 F +0.31 (recmut) 272.93 600.85 P +3 F +0.13 ( generates of) 316.11 600.85 P +0.13 (fspring in a direction de\336ned by) 377.43 600.85 P +0.02 (the parents \050line recombination\051. It tests more often outside the area de\336ned by the) 135.65 586.85 P +1.11 (parents and in the direction of parent1. The point for the of) 135.65 572.85 P +1.11 (fspring is de\336ned by) 430.05 572.85 P +-0.18 (features of the mutation operator) 135.65 558.85 P +-0.18 (. The probability of small step sizes is greater than) 291.46 558.85 P +(that of bigger steps \050see) 135.65 544.85 T +2 F +(mutbga) 252.56 544.85 T +3 F +(\051.) 295.74 544.85 T +1 16 Q +(See Also) 117.65 516.18 T +2 12 Q +(mutate) 135.65 498.85 T +3 F +(,) 178.82 498.85 T +2 F +(mutbga) 184.82 498.85 T +3 F +(,) 228 498.85 T +2 F +(reclin) 233.99 498.85 T +1 16 Q +(Refer) 117.65 476.18 T +(ence) 155.53 476.18 T +3 12 Q +0.79 ([1] H. M) 135.65 458.85 P +0.79 (\237) 179.52 458.85 P +0.79 (hlenbein, \322The Breeder Genetic Algorithm - a provable optimal search) 185.52 458.85 P +6.19 (algorithm and its application\323,) 135.65 444.85 P +0 F +6.19 (IEE Colloquium, Applications of Genetic) 309.33 444.85 P +(Algorithms) 135.65 430.85 T +3 F +(, Digest No. 94/067, London, 15) 188.96 430.85 T +352.31 434.56 344.54 434.56 2 L +V +0.49 H +0 Z +N +3 10 Q +(th) 344.54 435.65 T +3 12 Q +( March 1994.) 352.31 430.85 T +3.9 ([2] H. M) 135.65 404.85 P +3.9 (\237) 185.76 404.85 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 404.85 P +3.9 (oosen, \322Predictive Models for the) 354.48 404.85 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 390.85 P +0 F +0.18 (Evolutionary) 469.02 390.85 P +(Computation) 135.65 376.85 T +3 F +(, V) 198.29 376.85 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 376.85 T +187.39 733.43 202.43 745.99 C +3 12 Q +0 X +0 K +(1) 195.43 736.95 T +4 F +(\261) 188.39 736.95 T +-8.35 24.95 603.65 816.95 C +193.22 699.35 228.79 712.13 C +3 12 Q +0 X +0 K +(0) 194.22 702.95 T +(.) 200.21 702.95 T +(5) 203.21 702.95 T +4 F +(\264) 212.21 702.95 T +-8.35 24.95 603.65 816.95 C +189.02 651.79 237.44 690.95 C +4 12 Q +0 X +0 K +(a) 211.43 669.03 T +0 9 Q +(i) 219.46 664.38 T +3 12 Q +(2) 222.67 669.03 T +0 9 Q +(i) 233.95 675.06 T +4 F +(-) 228.67 675.06 T +0 F +(i) 191.26 654.74 T +3 F +(0) 204.7 654.74 T +4 F +(=) 196.76 654.74 T +0 F +(m) 190.02 683.81 T +3 F +(1) 205.94 683.81 T +4 F +(-) 198.76 683.81 T +4 18 Q +(\345) 193.81 665.83 T +-8.35 24.95 603.65 816.95 C +243.44 661.53 281.04 678.21 C +4 12 Q +0 X +0 K +(a) 244.69 669.03 T +0 9 Q +(i) 252.72 664.38 T +3 12 Q +(1) 273.8 669.03 T +4 F +(=) 261.22 669.03 T +-8.35 24.95 603.65 816.95 C +135.65 616.85 322.93 643.79 C +2 12 Q +0 X +0 K +(D) 136.65 627.72 T +(i) 144.55 627.72 T +(f) 152.45 627.72 T +(f) 160.35 627.72 T +(p) 193.13 634.8 T +(a) 201.04 634.8 T +(r) 208.94 634.8 T +(e) 216.84 634.8 T +(n) 224.74 634.8 T +(t) 232.64 634.8 T +(2) 240.55 634.8 T +(p) 260.33 634.8 T +(a) 268.23 634.8 T +(r) 276.13 634.8 T +(e) 284.03 634.8 T +(n) 291.93 634.8 T +(t) 299.84 634.8 T +(1) 307.74 634.8 T +4 F +(-) 250.74 634.8 T +2 F +(p) 193.13 620.33 T +(a) 201.04 620.33 T +(r) 208.94 620.33 T +(e) 216.84 620.33 T +(n) 224.74 620.33 T +(t) 232.64 620.33 T +(1) 240.55 620.33 T +(p) 260.33 620.33 T +(a) 268.23 620.33 T +(r) 276.13 620.33 T +(e) 284.03 620.33 T +(n) 291.93 620.33 T +(t) 299.84 620.33 T +(2) 307.74 620.33 T +4 F +(-) 250.74 620.33 T +(=) 173.55 627.72 T +188.13 618.85 188.13 628.32 2 L +0.33 H +0 Z +N +190.13 618.85 190.13 628.32 2 L +N +318.93 618.85 318.93 628.32 2 L +N +316.93 618.85 316.93 628.32 2 L +N +187.13 630.32 320.68 630.32 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "32" 33 +%%Page: "33" 33 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-33) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ecombin) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Recombination of individuals \050high-level function\051.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = recombin\050REC_F, Chrom\051) 135.65 628.95 T +(NewChrom = recombin\050REC_F, Chrom, RecOpt\051) 135.65 608.95 T +(NewChrom = recombin\050REC_F, Chrom, RecOpt, SUBPOP\051) 135.65 588.95 T +1 16 Q +(Description) 117.65 566.29 T +2 12 Q +4.99 (recombin) 135.65 548.95 P +3 F +2.08 ( performs recombination of individuals from a population,) 193.22 548.95 P +2 F +4.99 (Chrom) 492.67 548.95 P +3 F +2.08 (,) 528.65 548.95 P +1.73 (and returns the recombined individuals in a new population,) 135.65 534.95 P +2 F +4.16 (NewChrom) 442.38 534.95 P +3 F +1.73 (. Each) 499.94 534.95 P +(row of) 135.65 520.95 T +2 F +(Chrom) 170.29 520.95 T +3 F +( and) 206.26 520.95 T +2 F +(NewChrom) 229.58 520.95 T +3 F +( corresponds to one individual.) 287.15 520.95 T +2 F +0.52 (REC_F) 135.65 494.95 P +3 F +0.22 ( is a string that contains the name of the low-level recombination function,) 171.63 494.95 P +(e.g.) 135.65 480.95 T +2 F +(recdis) 155.96 480.95 T +3 F +( or) 199.14 480.95 T +2 F +(xovsp) 215.13 480.95 T +3 F +(.) 251.11 480.95 T +2 F +4.92 (RecOpt) 135.65 454.95 P +3 F +2.05 ( is an optional parameter specifying the crossover rate. If) 178.82 454.95 P +2 F +4.92 (RecOpt) 475.42 454.95 P +3 F +2.05 ( is) 518.6 454.95 P +(omitted or) 135.65 440.95 T +2 F +(NaN,) 188.29 440.95 T +3 F +( a default value is assumed.) 217.07 440.95 T +2 F +0.01 (SUBPOP) 135.65 414.95 P +3 F +0.01 ( is an optional parameter and determines the number of subpopulations in) 178.82 414.95 P +2 F +8.57 (Chrom) 135.65 400.95 P +3 F +3.57 (. If) 171.63 400.95 P +2 F +8.57 (SUBPOP) 195.75 400.95 P +3 F +3.57 ( is omitted or) 238.93 400.95 P +2 F +8.57 (NaN,) 319.85 400.95 P +8.57 (SUBPOP = 1) 355.2 400.95 P +3 F +3.57 ( is assumed. All) 444.31 400.95 P +(subpopulations in) 135.65 386.95 T +2 F +(Chrom) 223.61 386.95 T +3 F +( must have the same size.) 259.59 386.95 T +1 16 Q +(Example) 117.65 358.29 T +3 12 Q +( For examples see) 135.65 340.95 T +2 F +(recdis) 224.91 340.95 T +3 F +(,) 268.09 340.95 T +2 F +(recint) 274.09 340.95 T +3 F +(,) 317.26 340.95 T +2 F +(reclin) 323.26 340.95 T +3 F +(,) 366.44 340.95 T +2 F +(xovsp) 372.43 340.95 T +3 F +(,) 408.41 340.95 T +2 F +(xovdp) 414.41 340.95 T +3 F +( and) 450.39 340.95 T +2 F +(xovmp) 473.71 340.95 T +3 F +(.) 509.69 340.95 T +1 16 Q +(Algorithm) 117.65 318.29 T +2 12 Q +0.22 (recombin) 135.65 300.95 P +3 F +0.09 ( checks the consistency of the input parameters and calls the low-level) 193.22 300.95 P +-0.04 (recombination function. If) 135.65 286.95 P +2 F +-0.08 (recombin) 264.79 286.95 P +3 F +-0.04 ( is called with more than one subpopulation) 322.35 286.95 P +6.44 (then the low-level recombination function is called separately for each) 135.65 272.95 P +(subpopulation.) 135.65 258.95 T +1 16 Q +(See Also) 117.65 236.29 T +2 12 Q +(recdis) 135.65 218.95 T +3 F +(,) 178.82 218.95 T +2 F +(recint) 184.82 218.95 T +3 F +(,) 228 218.95 T +2 F +(reclin) 233.99 218.95 T +3 F +(,) 277.17 218.95 T +2 F +(xovsp) 283.17 218.95 T +3 F +(,) 319.15 218.95 T +2 F +(xovdp) 325.14 218.95 T +3 F +(,) 361.12 218.95 T +2 F +(xovsh) 367.12 218.95 T +3 F +(,) 403.1 218.95 T +2 F +(mutate) 409.1 218.95 T +3 F +(,) 452.27 218.95 T +2 F +(select) 458.27 218.95 T +FMENDPAGE +%%EndPage: "33" 34 +%%Page: "34" 34 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-34) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(eins) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Reinsertion of of) 135.65 674.95 T +(fspring in the population.) 216.71 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(Chrom = reins\050Chrom, SelCh\051) 135.65 628.95 T +(Chrom = reins\050Chrom, SelCh, SUBPOP\051) 135.65 608.95 T +(Chrom = reins\050Chrom, SelCh, SUBPOP, InsOpt, ObjVCh\051) 135.65 588.95 T +([Chrom, ObjVCh]= reins\050Chrom, SelCh, SUBPOP, InsOpt,) 135.65 568.95 T +(ObjVCh, ObjVSel\051) 153.65 554.95 T +1 16 Q +(Description) 117.65 532.29 T +2 12 Q +7.41 (reins) 135.65 514.95 P +3 F +3.09 ( performs insertion of of) 171.63 514.95 P +3.09 (fspring into the current population, replacing) 301.02 514.95 P +1.7 (parents with of) 135.65 500.95 P +1.7 (fspring and returning the resulting population. The of) 210.79 500.95 P +1.7 (fspring are) 478.33 500.95 P +0.23 (contained in the matrix) 135.65 486.95 P +2 F +0.56 (SelCh) 250.51 486.95 P +3 F +0.23 ( and the parents in the matrix) 286.49 486.95 P +2 F +0.56 (Chrom) 431.02 486.95 P +3 F +0.23 (. Each row in) 467 486.95 P +2 F +(Chrom) 135.65 472.95 T +3 F +( and) 171.63 472.95 T +2 F +(Selch) 194.94 472.95 T +3 F +( corresponds to one individual.) 230.92 472.95 T +2 F +2.19 (SUBPOP) 135.65 446.95 P +3 F +0.91 ( is an optional parameter and indicates the number of subpopulations in) 178.82 446.95 P +2 F +-0.32 (Chrom) 135.65 432.95 P +3 F +-0.13 ( and) 171.63 432.95 P +2 F +-0.32 (SelCh) 194.68 432.95 P +3 F +-0.13 (. If) 230.66 432.95 P +2 F +-0.32 (SUBPOP) 247.37 432.95 P +3 F +-0.13 ( is omitted or) 290.55 432.95 P +2 F +-0.32 (NaN) 356.65 432.95 P +3 F +-0.13 (,) 378.24 432.95 P +2 F +-0.32 (SUBPOP = 1) 384.1 432.95 P +3 F +-0.13 ( is assumed. All) 455.42 432.95 P +(subpopulations in) 135.65 418.95 T +2 F +(Chrom) 223.61 418.95 T +3 F +( and) 259.59 418.95 T +2 F +(SelCh) 282.9 418.95 T +3 F +( each must have the same size.) 318.88 418.95 T +2 F +(InsOpt) 135.65 392.95 T +3 F +( is an optional vector with a maximum of 2 parameters:) 178.82 392.95 T +2 F +(InsOpt\0501\051) 135.65 372.95 T +3 F +(:) 200.41 372.95 T +(scalar indicating the selection method for replacing parents with of) 171.65 358.95 T +(fspring:) 492.2 358.95 T +(0 - uniform selection, of) 171.65 344.95 T +(fspring replace parents uniformly at random) 287.68 344.95 T +(1 - \336tness-based selection, of) 171.65 330.95 T +(fspring replace least \336t parents) 311 330.95 T +(If omitted or) 171.65 316.95 T +2 F +(NaN) 235.27 316.95 T +3 F +(,) 256.86 316.95 T +2 F +(InsOpt\0501\051 = 0) 262.86 316.95 T +3 F +( is assumed) 356.41 316.95 T +2 F +(InsOpt\0502\051) 135.65 296.95 T +3 F +(:) 200.41 296.95 T +0.2 (scalar containing the rate of reinsertion of of) 171.65 282.95 P +0.2 (fspring per subpopulation as a) 386.3 282.95 P +(fraction of subpopulation size in the range) 171.65 268.95 T +2 F +([0, 1]) 377.17 268.95 T +3 F +(.) 420.34 268.95 T +(If omitted or) 171.65 254.95 T +2 F +(NaN) 235.27 254.95 T +3 F +(,) 256.86 254.95 T +2 F +(InsOpt\0502\051 = 1.0) 262.86 254.95 T +3 F +( is assumed.) 370.8 254.95 T +(If) 171.65 240.95 T +2 F +(INSR = 0) 182.63 240.95 T +3 F +( no insertion takes place.) 240.2 240.95 T +0.41 (If) 171.65 226.95 P +2 F +0.97 (INSR) 183.04 226.95 P +3 F +0.41 ( is not 1.0) 211.82 226.95 P +2 F +0.97 (ObjVSel) 263.75 226.95 P +3 F +0.41 ( is needed for selecting the best of) 314.12 226.95 P +0.41 (fspring for) 480.28 226.95 P +(insertion \050truncation selection between of) 171.65 212.95 T +(fspring\051.) 370.62 212.95 T +(If) 135.65 192.95 T +2 F +(InsOpt) 146.63 192.95 T +3 F +( is omitted or) 189.81 192.95 T +2 F +(NaN) 256.45 192.95 T +3 F +(, then the default values are assumed.) 278.03 192.95 T +2 F +6.7 (ObjVCh) 135.65 166.95 P +3 F +2.79 ( is an optional column vector containing the objective values of the) 178.82 166.95 P +(individuals in) 135.65 152.95 T +2 F +(Chrom) 204.29 152.95 T +3 F +(.) 240.27 152.95 T +2 F +(ObjVCh) 246.26 152.95 T +3 F +( is needed for \336tness-based reinsertion.) 289.44 152.95 T +2 F +5.13 (ObjVSel) 135.65 126.95 P +3 F +2.14 ( is an optional column vector containing the objective values of the) 186.02 126.95 P +0.53 (individuals in) 135.65 112.95 P +2 F +1.28 (SelCh) 205.35 112.95 P +3 F +0.53 (.) 241.33 112.95 P +2 F +1.28 (ObjVSel) 247.87 112.95 P +3 F +0.53 ( is required if the number of of) 298.24 112.95 P +0.53 (fspring is greater) 449.31 112.95 P +FMENDPAGE +%%EndPage: "34" 35 +%%Page: "35" 35 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-35) 513.33 61.29 T +3 12 Q +1.91 (than the number of of) 135.65 736.95 P +1.91 (fspring to be reinserted into the population. In this case,) 246.99 736.95 P +(of) 135.65 722.95 T +(fspring are selected for reinsertion according to their \336tness.) 145.42 722.95 T +2.6 (If) 135.65 696.95 P +2 F +6.24 (ObjVCh) 149.23 696.95 P +3 F +2.6 ( is output parameter) 192.41 696.95 P +2.6 (,) 295.33 696.95 P +2 F +6.24 (ObjVCh) 303.93 696.95 P +3 F +2.6 ( and) 347.11 696.95 P +2 F +6.24 (ObjVSel) 375.62 696.95 P +3 F +2.6 ( are needed as input) 425.99 696.95 P +0.25 (parameters. The objective values are then copied, according to the insertion of the) 135.65 682.95 P +4.68 (of) 135.65 668.95 P +4.68 (fspring, saving the recomputation of the objective values for the whole) 145.42 668.95 P +(population.) 135.65 654.95 T +1 16 Q +(Example) 117.65 626.29 T +3 12 Q +2.57 (Consider a population of 8 parents,) 135.65 608.95 P +2 F +6.16 (Chrom) 322.6 608.95 P +3 F +2.57 (, and a population of 6 of) 358.58 608.95 P +2.57 (fspring,) 494.67 608.95 P +2 F +(SelCh) 135.65 594.95 T +3 F +(:) 171.63 594.95 T +2 F +(Chrom = [1; 2; 3; 4; 5; 6; 7; 8]) 135.65 574.95 T +(SelCh = [11; 12; 13; 14; 15; 16]) 135.65 560.95 T +3 F +(Insert all of) 135.65 540.95 T +(fspring in the population:) 190.72 540.95 T +2 F +(Chrom = reins\050Chrom, SelCh\051) 135.65 520.95 T +3 F +(Thus, a new population) 135.65 500.95 T +2 F +(Chrom) 251.24 500.95 T +3 F +( is produced, e.g.:) 287.22 500.95 T +2 F +(Chrom =) 135.65 480.95 T +(12) 153.65 466.95 T +(11) 153.65 452.95 T +(15) 153.65 438.95 T +(16) 153.65 424.95 T +( 5) 153.65 410.95 T +(13) 153.65 396.95 T +(14) 153.65 382.95 T +( 8) 153.65 368.95 T +3 F +2.5 (Consider the following) 135.65 348.95 P +2 F +6.01 (ObjVCh) 256.76 348.95 P +3 F +2.5 ( vector for the parent population) 299.94 348.95 P +2 F +6.01 (Chrom) 472.85 348.95 P +3 F +2.5 ( and) 508.83 348.95 P +2 F +(ObjVSel) 135.65 334.95 T +3 F +( for the of) 186.02 334.95 T +(fspring,) 233.43 334.95 T +2 F +(SelCh) 273.4 334.95 T +3 F +(:) 309.39 334.95 T +2 F +(ObjVCh = [21; 22; 23; 24; 25; 26; 27; 28];) 135.65 314.95 T +(ObjVSel= [31; 32; 33; 34; 35; 36]) 135.65 300.95 T +3 F +(Insert all of) 135.65 280.95 T +(fspring \336tness-based, i.e. replace least \336t parents:) 190.72 280.95 T +2 F +(Chrom = reins\050Chrom, SelCh, 1, 1, ObjVCh\051) 135.65 260.95 T +(Chrom =) 135.65 240.95 T +( 1) 153.65 226.95 T +( 2) 153.65 212.95 T +(16) 153.65 198.95 T +(15) 153.65 184.95 T +(14) 153.65 170.95 T +(13) 153.65 156.95 T +(12) 153.65 142.95 T +(11) 153.65 128.95 T +FMENDPAGE +%%EndPage: "35" 36 +%%Page: "36" 36 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-36) 513.33 61.29 T +3 12 Q +0.56 (Insert 50% of the of) 135.65 736.95 P +0.56 (fspring \336tness-based and copy the objective values according) 233.6 736.95 P +(the insertion of of) 135.65 722.95 T +(fspring:) 221.04 722.95 T +2 F +([Chrom, ObjVCh] = reins\050Chrom, SelCh, 1, [1 0.5],...) 135.65 702.95 T +(ObjVCh, ObjVSel\051) 153.65 688.95 T +(Chrom =) 135.65 668.95 T +( 1) 153.65 654.95 T +( 2) 153.65 640.95 T +( 3) 153.65 626.95 T +( 4) 153.65 612.95 T +( 5) 153.65 598.95 T +(13) 153.65 584.95 T +(12) 153.65 570.95 T +(11) 153.65 556.95 T +(ObjVCh =) 135.65 536.95 T +(21) 153.65 522.95 T +(22) 153.65 508.95 T +(23) 153.65 494.95 T +(24) 153.65 480.95 T +(25) 153.65 466.95 T +(33) 153.65 452.95 T +(32) 153.65 438.95 T +(31) 153.65 424.95 T +3 F +0.4 (Consider Chrom and SelCh consist of 2 subpopulations. Insert all of) 135.65 404.95 P +0.4 (fspring in the) 466.89 404.95 P +(appropriate subpopulations:) 135.65 390.95 T +2 F +(Chrom = reins\050Chrom, SelCh, 2\051) 135.65 370.95 T +(Chrom =) 135.65 350.95 T +(12) 153.65 336.95 T +( 2) 153.65 322.95 T +(13) 153.65 308.95 T +(11) 153.65 294.95 T +(14) 153.65 280.95 T +( 6) 153.65 266.95 T +(15) 153.65 252.95 T +(16) 153.65 238.95 T +1 16 Q +(See Also) 117.65 216.29 T +2 12 Q +(select) 135.65 198.95 T +FMENDPAGE +%%EndPage: "36" 37 +%%Page: "37" 37 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-37) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ep) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Matrix replication.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(MatOut = rep\050MatIn, REPN\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +1.03 (rep) 135.65 588.95 P +3 F +0.43 ( is a low-level replication function. Not normally used directly) 157.24 588.95 P +0.43 (,) 460.13 588.95 P +2 F +1.03 (rep) 466.56 588.95 P +3 F +0.43 ( is called) 488.15 588.95 P +(by a number of functions in the GA-T) 135.65 574.95 T +(oolbox.) 317.01 574.95 T +2 F +1.3 (rep) 135.65 548.95 P +3 F +0.54 ( performs replication of a matrix,) 157.24 548.95 P +2 F +1.3 (MatIn) 322.71 548.95 P +3 F +0.54 (, speci\336ed by the numbers in) 358.69 548.95 P +2 F +1.3 (REPN) 502.86 548.95 P +3 F +(and returns the replicated matrix,) 135.65 534.95 T +2 F +(MatOut) 297.52 534.95 T +3 F +(.) 340.7 534.95 T +2 F +1.62 (REPN) 135.65 508.95 P +3 F +0.67 ( contains the number of replications in every direction.) 164.43 508.95 P +2 F +1.62 (REPN\0501\051) 436.3 508.95 P +3 F +0.67 ( speci\336es) 486.67 508.95 P +5.83 (the number of vertical replications,) 135.65 494.95 P +2 F +14 (REPN\0502\051) 336.02 494.95 P +3 F +5.83 ( the number of horizontal) 386.4 494.95 P +(replications.) 135.65 480.95 T +1 16 Q +(Example) 117.65 452.29 T +3 12 Q +( Consider the following matrix) 135.65 434.95 T +2 F +(MatIn) 286.56 434.95 T +3 F +(:) 322.54 434.95 T +2 F +(MatIn = [) 135.65 414.95 T +(1 2 3 4;) 153.65 400.95 T +(5 6 7 8]) 153.65 386.95 T +3 F +(T) 135.65 366.95 T +(o perform matrix replication:) 142.14 366.95 T +2 F +(MatOut = rep\050MatIn, [1 2]\051) 135.65 346.95 T +(MatOut =) 135.65 326.95 T +(1 2 3 4 1 2 3 4) 153.65 312.95 T +(5 6 7 8 5 6 7 8) 153.65 298.95 T +(MatOut = rep\050MatIn, [2 1]\051) 135.65 278.95 T +(MatOut =) 135.65 258.95 T +(1 2 3 4) 153.65 244.95 T +(5 6 7 8) 153.65 230.95 T +(1 2 3 4) 153.65 216.95 T +(5 6 7 8) 153.65 202.95 T +(MatOut = rep\050MatIn, [2 3]\051) 135.65 182.95 T +(MatOut =) 135.65 162.95 T +(1 2 3 4 1 2 3 4 1 2 3 4) 153.65 148.95 T +(5 6 7 8 5 6 7 8 5 6 7 8) 153.65 134.95 T +(1 2 3 4 1 2 3 4 1 2 3 4) 153.65 120.95 T +(5 6 7 8 5 6 7 8 5 6 7 8) 153.65 106.95 T +FMENDPAGE +%%EndPage: "37" 38 +%%Page: "38" 38 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-38) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(rws) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Roulette wheel selection) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrIx = rws\050FitnV, Nsel\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.41 (rws) 135.65 588.95 P +3 F +0.17 ( probabilistically selects) 157.24 588.95 P +2 F +0.41 (Nsel) 276.67 588.95 P +3 F +0.17 ( individuals for reproduction according to their) 305.45 588.95 P +(\336tness,) 135.65 574.95 T +2 F +(FitnV) 172.3 574.95 T +3 F +(, in the current population.) 206.73 574.95 T +2 F +8.66 (NewChrIx = rws\050FitnV, Nsel\051) 135.65 548.95 P +3 F +3.61 ( selects) 355.91 548.95 P +2 F +8.66 (Nsel) 401.1 548.95 P +3 F +3.61 ( individuals from a) 429.88 548.95 P +0.33 (population using roulette wheel selection.) 135.65 534.95 P +2 F +0.78 (FitnV) 340.48 534.95 P +3 F +0.33 ( is a column vector containing a) 376.46 534.95 P +0.69 (performance measure for each individual in the population. This can be achieved) 135.65 520.95 P +1.83 (by using the function) 135.65 506.95 P +2 F +4.39 (ranking) 247.57 506.95 P +3 F +1.83 ( or) 297.94 506.95 P +2 F +4.39 (scaling) 317.58 506.95 P +3 F +1.83 ( to assign a \336tness level to each) 367.95 506.95 P +0.79 (individual. The return value,) 135.65 492.95 P +2 F +1.89 (NewChrIx) 278.7 492.95 P +3 F +0.79 (, is the index of the individuals selected) 336.26 492.95 P +0.51 (for breeding, in the order that they were selected. The selected individuals can be) 135.65 478.95 P +(recovered by evaluating) 135.65 464.95 T +2 F +(Chrom\050NewChrIx,:\051) 253.88 464.95 T +3 F +(.) 376.21 464.95 T +2 F +(rws) 135.65 438.95 T +3 F +( is a low-level selection function normally called by) 157.24 438.95 T +2 F +(select) 409.4 438.95 T +3 F +(.) 452.57 438.95 T +1 16 Q +(Example) 117.65 410.29 T +3 12 Q +(Consider a population of 8 individuals with the assigned \336tness values,) 135.65 392.95 T +2 F +(FitnV) 479.45 392.95 T +3 F +(:) 514.54 392.95 T +2 F +(FitnV = [1.50; 1.35; 1.21; 1.07; 0.92; 0.78; 0.64; 0.5]) 135.65 372.95 T +3 F +(Select the indices of 6 individuals:) 135.65 352.95 T +2 F +(NewChrIx = rws\050FitnV, 6\051) 135.65 332.95 T +3 F +(Thus,) 135.65 312.95 T +2 F +(NewChrIx) 165.63 312.95 T +3 F +( can become:) 223.2 312.95 T +2 F +(NewChrIx =) 135.65 292.95 T +(2) 153.65 278.95 T +(5) 153.65 264.95 T +(1) 153.65 250.95 T +(1) 153.65 236.95 T +(3) 153.65 222.95 T +(7) 153.65 208.95 T +1 16 Q +(Algorithm) 117.65 186.29 T +3 12 Q +0.3 (A form of roulette wheel selection is implemented by obtaining a cumulative sum) 135.65 168.95 P +5.08 (of the \336tness vector) 135.65 154.95 P +5.08 (,) 244.67 154.95 P +2 F +12.19 (FitnV) 255.75 154.95 P +3 F +5.08 (, and generating) 290.18 154.95 P +2 F +12.19 (Nsel) 385.36 154.95 P +3 F +5.08 ( uniformly at random) 414.14 154.95 P +1.07 (distributed numbers between) 135.65 140.95 P +2 F +2.57 (0) 280.43 140.95 P +3 F +1.07 ( and) 287.63 140.95 P +2 F +2.57 (sum\050FitnV\051) 313.08 140.95 P +3 F +1.07 (. The index of the individuals) 385.05 140.95 P +1.03 (selected is determined by comparing the generated numbers with the cumulative) 135.65 126.95 P +(sum vector) 135.65 112.95 T +(. The probability of an individual being selected is then given by:) 187.95 112.95 T +FMENDPAGE +%%EndPage: "38" 39 +%%Page: "39" 39 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-39) 513.33 61.29 T +3 12 Q +(,) 380.93 725.53 T +2.94 (where) 135.65 664.71 P +0 F +2.94 (f\050x) 170.89 664.71 P +0 10 Q +2.45 (i) 183.54 661.71 P +0 12 Q +2.94 (\051) 186.32 664.71 P +3 F +2.94 ( is the \336tness of individual) 190.32 664.71 P +0 F +2.94 (x) 337.92 664.71 P +0 10 Q +2.45 (i) 343.25 661.71 P +3 12 Q +2.94 ( and) 346.03 664.71 P +0 F +2.94 (F\050x) 375.23 664.71 P +0 10 Q +2.45 (i) 391.88 661.71 P +0 12 Q +2.94 (\051) 394.66 664.71 P +3 F +2.94 ( is the probability of that) 398.65 664.71 P +(individual being selected.) 135.65 650.71 T +1 16 Q +(See Also) 117.65 622.04 T +2 12 Q +(select) 135.65 604.71 T +3 F +(,) 178.82 604.71 T +2 F +(sus) 184.82 604.71 T +3 F +(,) 206.41 604.71 T +2 F +(reins) 212.41 604.71 T +3 F +(,) 248.39 604.71 T +2 F +(ranking) 254.38 604.71 T +3 F +(,) 304.76 604.71 T +2 F +(scaling) 310.75 604.71 T +1 16 Q +(Refer) 117.65 582.04 T +(ence) 155.53 582.04 T +3 12 Q +0.67 ([1] J. E. Baker) 135.65 564.71 P +0.67 (, \322Reducing bias and inef) 206.8 564.71 P +0.67 (\336ciency in the selection algorithm\323,) 330.86 564.71 P +0 F +0.67 (Pr) 508.78 564.71 P +0.67 (oc) 520.33 564.71 P +(ICGA 2) 135.65 550.71 T +3 F +(, pp. 14-21, Lawrence Erlbaum Associates, Publishers, 1987.) 172.62 550.71 T +0.59 ([2] David E. Goldber) 135.65 524.71 P +0.59 (g,) 239.13 524.71 P +0 F +0.59 (Genetic Algorithms in Sear) 251.71 524.71 P +0.59 (ch, Optimization and Machine) 383.96 524.71 P +(Learning) 135.65 510.71 T +3 F +(, Addison W) 179.63 510.71 T +(esley) 239.63 510.71 T +(, 1989.) 263.5 510.71 T +283.37 686.71 380.93 744.95 C +0 12 Q +0 X +0 K +(F) 284.37 725.53 T +(x) 299.5 725.53 T +0 9 Q +(i) 305.29 721.74 T +4 12 Q +(\050) 294.4 725.53 T +(\051) 308.4 725.53 T +0 F +(f) 343.44 735.75 T +(x) 354.58 735.75 T +0 9 Q +(i) 360.36 731.97 T +4 12 Q +(\050) 349.48 735.75 T +(\051) 363.47 735.75 T +0 F +(f) 352.9 703.95 T +(x) 364.04 703.95 T +0 9 Q +(i) 369.83 700.17 T +4 12 Q +(\050) 358.94 703.95 T +(\051) 372.93 703.95 T +0 9 Q +(i) 333.98 689.66 T +3 F +(1) 347.41 689.66 T +4 F +(=) 339.47 689.66 T +0 F +(N) 335.47 720.47 T +0 6 Q +(i) 341.82 718.02 T +(n) 343.94 718.02 T +(d) 347.4 718.02 T +4 18 Q +(\345) 336.52 700.75 T +4 12 Q +(=) 320.39 725.53 T +333.98 728.12 378.68 728.12 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "39" 40 +%%Page: "40" 40 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-40) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(scaling) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Linear \336tness scaling) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(FitnV = scaling\050ObjV, Smul\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +6.16 (scaling) 135.65 588.95 P +3 F +2.57 ( converts the objective values,) 186.02 588.95 P +2 F +6.16 (ObjV) 346.75 588.95 P +3 F +2.57 (, of a population into a \336tness) 373.99 588.95 P +(measure with a known upper bound, determined by the value of) 135.65 574.95 T +2 F +(Smul) 444.75 574.95 T +3 F +(, such that,) 473.54 574.95 T +(,) 383.11 547.75 T +0.31 (where) 135.65 519.12 P +0 F +0.31 (f\050x) 168.26 519.12 P +0 10 Q +0.26 (i) 180.91 516.12 P +0 12 Q +0.31 (\051) 183.69 519.12 P +3 F +0.31 ( is the objective value of individual) 187.68 519.12 P +0 F +0.31 (x) 362.07 519.12 P +0 10 Q +0.26 (i) 367.39 516.12 P +3 12 Q +0.31 (,) 370.17 519.12 P +0 F +0.31 (a) 376.48 519.12 P +3 F +0.31 ( is a scaling coef) 382.47 519.12 P +0.31 (\336cient,) 463.43 519.12 P +0 F +0.31 (b) 499.71 519.12 P +3 F +0.31 ( is an) 505.71 519.12 P +0.47 (of) 135.65 505.12 P +0.47 (fset and) 145.42 505.12 P +0 F +0.47 (F\050x) 187 505.12 P +0 10 Q +0.39 (i) 203.64 502.12 P +0 12 Q +0.47 (\051) 206.42 505.12 P +3 F +0.47 ( is the resulting \336tness value of individual) 210.42 505.12 P +0 F +0.47 (x) 418.07 505.12 P +0 10 Q +0.39 (i) 423.39 502.12 P +3 12 Q +0.47 (. If) 426.17 505.12 P +0 F +0.47 (f) 444.09 505.12 P +0 10 Q +0.39 (ave) 447.43 502.12 P +3 12 Q +0.47 ( is the average) 461.3 505.12 P +0.77 (objective value in the current generation, then the maximum \336tness of the scaled) 135.65 491.12 P +0.5 (population is upper bounded at) 135.65 477.12 P +0 F +0.5 (f) 289.7 477.12 P +0 10 Q +0.41 (ave) 293.03 474.12 P +4 12 Q +0.5 ( \264) 306.91 477.12 P +2 F +1.19 ( Smul) 316.98 477.12 P +3 F +0.5 (. If) 354.15 477.12 P +2 F +1.19 (Smul) 372.13 477.12 P +3 F +0.5 ( is omitted then the default) 400.91 477.12 P +0.38 (value of) 135.65 463.12 P +2 F +0.92 (Smult = 2) 178.38 463.12 P +3 F +0.38 ( is assumed. The average \336tness of the scaled population is) 244.99 463.12 P +(also set to) 135.65 449.12 T +0 F +(f) 186.62 449.12 T +0 10 Q +(ave) 189.95 446.12 T +3 12 Q +(.) 203.83 449.12 T +1.76 (In the case of some of the objective values being negative, scaling attempts to) 135.65 423.12 P +(provide an of) 135.65 409.12 T +(fset,) 199.38 409.12 T +0 F +(b) 222.7 409.12 T +3 F +(, such that the scaled \336tness values are greater than zero.) 228.69 409.12 T +1 16 Q +(Algorithm) 117.65 380.45 T +2 12 Q +(scaling) 135.65 363.12 T +3 F +( uses the linear scaling method described by Goldber) 186.02 363.12 T +(g [1].) 439.62 363.12 T +1 F +1.97 (Note:) 135.65 337.12 P +3 F +1.97 ( linear scaling is not suitable for use with objective functions that return) 163.62 337.12 P +(negative \336tness values and is included here only for completeness.) 135.65 323.12 T +1 16 Q +(See Also) 117.65 294.45 T +2 12 Q +(ranking) 135.65 277.12 T +3 F +(,) 186.02 277.12 T +2 F +(reins) 192.02 277.12 T +3 F +(,) 228 277.12 T +2 F +(rws) 233.99 277.12 T +3 F +(,) 255.58 277.12 T +2 F +(select) 261.58 277.12 T +3 F +(,) 304.76 277.12 T +2 F +(sus) 310.75 277.12 T +1 16 Q +(Refer) 117.65 254.45 T +(ence) 155.53 254.45 T +3 12 Q +2.36 ([1] D. E. Goldber) 135.65 237.12 P +2.36 (g,) 226.77 237.12 P +0 F +2.36 (Genetic Algorithms in Sear) 241.12 237.12 P +2.36 (ch, Optimization and Machine) 378.67 237.12 P +(Learning) 135.65 223.12 T +3 F +(, Addison W) 179.63 223.12 T +(esley Publishing Company) 239.63 223.12 T +(, January 1989.) 367.46 223.12 T +281.19 541.12 383.11 556.95 C +0 12 Q +0 X +0 K +(F) 282.19 547.75 T +(x) 297.33 547.75 T +0 9 Q +(i) 303.11 543.97 T +4 12 Q +(\050) 292.23 547.75 T +(\051) 306.22 547.75 T +0 F +(a) 330.8 547.75 T +(f) 337.5 547.75 T +(x) 348.64 547.75 T +0 9 Q +(i) 354.43 543.97 T +4 12 Q +(\050) 343.54 547.75 T +(\051) 357.53 547.75 T +0 F +(b) 376.11 547.75 T +4 F +(+) 366.53 547.75 T +(=) 318.21 547.75 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "40" 41 +%%Page: "41" 41 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-41) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(select) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Selection of individuals from population \050high-level function\051.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(SelCh = select\050SEL_F, Chrom, FitnV\051) 135.65 628.95 T +(SelCh = select\050SEL_F, Chrom, FitnV, GGAP\051) 135.65 608.95 T +(SelCh = select\050SEL_F, Chrom, FitnV, GGAP, SUBPOP\051) 135.65 588.95 T +1 16 Q +(Description) 117.65 566.29 T +2 12 Q +0.25 (select) 135.65 548.95 P +3 F +0.11 ( performs selection of individuals from a population,) 178.82 548.95 P +2 F +0.25 (Chrom) 435.84 548.95 P +3 F +0.11 (, and returns) 471.82 548.95 P +1.63 (the selected individuals in a new population,) 135.65 534.95 P +2 F +3.92 (SelCh) 363.6 534.95 P +3 F +1.63 (. Each row of) 399.58 534.95 P +2 F +3.92 (Chrom) 473.72 534.95 P +3 F +1.63 ( and) 509.7 534.95 P +2 F +(SelCh) 135.65 520.95 T +3 F +( corresponds to one individual.) 171.63 520.95 T +2 F +2.39 (SEL_F) 135.65 494.95 P +3 F +1 ( is a string and contains the name of the low-level selection function, for) 171.63 494.95 P +(example) 135.65 480.95 T +2 F +(rws) 179.28 480.95 T +3 F +( or) 200.87 480.95 T +2 F +(sus) 216.85 480.95 T +3 F +(.) 238.44 480.95 T +2 F +6.18 (FitnV) 135.65 454.95 P +3 F +2.57 ( is a column vector containing the \336tness values of the individuals in) 171.63 454.95 P +2 F +2.53 (Chrom) 135.65 440.95 P +3 F +1.06 (. The \336tness value indicates the expected probability of selection of each) 171.63 440.95 P +(individual.) 135.65 426.95 T +2 F +2.5 (GGAP) 135.65 400.95 P +3 F +1.04 ( is an optional parameter specifying the generation gap, the fraction of the) 164.43 400.95 P +-0.3 (population to be reproduced. If) 135.65 386.95 P +2 F +-0.72 (GGAP) 286.04 386.95 P +3 F +-0.3 ( is omitted or) 314.83 386.95 P +2 F +-0.72 (NaN,) 380.27 386.95 P +-0.72 (GGAP = 1.0) 411.75 386.95 P +3 F +-0.3 ( \050100%\051 is) 482.28 386.95 P +3.47 (assumed.) 135.65 372.95 P +2 F +8.33 (GGAP) 186.42 372.95 P +3 F +3.47 ( may also be greater than 1, allowing more of) 215.21 372.95 P +3.47 (fspring to be) 464.08 372.95 P +3.44 (produced then the number of parents. If) 135.65 358.95 P +2 F +8.25 (Chrom) 352.89 358.95 P +3 F +3.44 ( consists of more than one) 388.87 358.95 P +3.58 (subpopulation,) 135.65 344.95 P +2 F +8.58 (GGAP) 213.19 344.95 P +3 F +3.58 ( speci\336es the number of individuals to be selected per) 241.97 344.95 P +(subpopulation relative to the size of the subpopulation.) 135.65 330.95 T +2 F +0.01 (SUBPOP) 135.65 304.95 P +3 F +0.01 ( is an optional parameter and determines the number of subpopulations in) 178.82 304.95 P +2 F +8.57 (Chrom) 135.65 290.95 P +3 F +3.57 (. If) 171.63 290.95 P +2 F +8.57 (SUBPOP) 195.75 290.95 P +3 F +3.57 ( is omitted or) 238.93 290.95 P +2 F +8.57 (NaN,) 319.85 290.95 P +8.57 (SUBPOP = 1) 355.2 290.95 P +3 F +3.57 ( is assumed. All) 444.31 290.95 P +(subpopulations in) 135.65 276.95 T +2 F +(Chrom) 223.61 276.95 T +3 F +( must have the same size.) 259.59 276.95 T +1 16 Q +(Example) 117.65 248.29 T +3 12 Q +0.93 (Consider a population of 8 individuals,) 135.65 230.95 P +2 F +2.23 (Chrom) 331.45 230.95 P +3 F +0.93 (, with the assigned \336tness values,) 367.43 230.95 P +2 F +(FitnV) 135.65 216.95 T +3 F +(:) 170.74 216.95 T +FMENDPAGE +%%EndPage: "41" 42 +%%Page: "42" 42 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-42) 513.33 61.29 T +2 12 Q +(Chrom = [) 135.65 736.95 T +(1 11 21;) 153.65 722.95 T +(2 12 22;) 153.65 708.95 T +(3 13 23;) 153.65 694.95 T +(4 14 24;) 153.65 680.95 T +(5 15 25;) 153.65 666.95 T +(6 16 26;) 153.65 652.95 T +(7 17 27;) 153.65 638.95 T +(8 18 28]) 153.65 624.95 T +(FitnV = [1.50; 1.35; 1.21; 1.07; 0.92; 0.78; 0.64; 0.5]) 135.65 604.95 T +3 F +(Select 8 individuals by stochastic universal sampling,) 135.65 584.95 T +2 F +(sus) 395.5 584.95 T +3 F +(:) 417.08 584.95 T +2 F +(SelCh = select\050\324sus\325, Chrom, FitnV\051) 135.65 564.95 T +3 F +(Thus,) 135.65 544.95 T +2 F +(SelCh) 165.63 544.95 T +3 F +( can become:) 201.61 544.95 T +2 F +(SelCh =) 135.65 524.95 T +(7 17 27) 153.65 510.95 T +(1 11 21) 153.65 496.95 T +(6 16 26) 153.65 482.95 T +(1 11 21) 153.65 468.95 T +(5 15 25) 153.65 454.95 T +(2 12 22) 153.65 440.95 T +(3 13 23) 153.65 426.95 T +(4 14 24) 153.65 412.95 T +3 F +3.8 (Consider) 135.65 392.95 P +2 F +9.12 (Chrom) 185.76 392.95 P +3 F +3.8 ( consists of 2 subpopulations. Select 150% individuals per) 221.74 392.95 P +(subpopulation by roulette wheel selection,) 135.65 378.95 T +2 F +(rws) 341.52 378.95 T +3 F +(:) 363.1 378.95 T +2 F +(FitnV = [1.50; 1.16; 0.83; 0.50; 1.50; 1.16; 0.83; 0.5]) 135.65 358.95 T +(SelCh = select\050\324sus\325, Chrom, FitnV, 1.5, 2\051) 135.65 338.95 T +3 F +(Thus,) 135.65 318.95 T +2 F +(SelCh) 165.63 318.95 T +3 F +( can become:) 201.61 318.95 T +2 F +(SelCh =) 135.65 298.95 T +(3 13 23) 153.65 284.95 T +(2 12 22) 153.65 270.95 T +(1 11 21) 153.65 256.95 T +(2 12 22) 153.65 242.95 T +(2 12 22) 153.65 228.95 T +(1 11 21) 153.65 214.95 T +(6 16 26) 153.65 200.95 T +(7 17 27) 153.65 186.95 T +(7 17 27) 153.65 172.95 T +(6 16 26) 153.65 158.95 T +(7 17 27) 153.65 144.95 T +(5 15 25) 153.65 130.95 T +FMENDPAGE +%%EndPage: "42" 43 +%%Page: "43" 43 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-43) 513.33 61.29 T +1 16 Q +(Algorithm) 117.65 734.29 T +2 12 Q +4.38 (select) 135.65 716.95 P +3 F +1.83 ( checks the consistency of the input parameter and calls the low-level) 178.82 716.95 P +-0.05 (selection function. If) 135.65 702.95 P +2 F +-0.12 (select) 238.09 702.95 P +3 F +-0.05 ( is called with more than one subpopulation then the) 281.26 702.95 P +(low-level selection function is called separately for each subpopulation.) 135.65 688.95 T +1 16 Q +(See Also) 117.65 666.29 T +2 12 Q +(rws) 135.65 648.95 T +3 F +(,) 157.24 648.95 T +2 F +(sus) 163.23 648.95 T +3 F +(,) 184.82 648.95 T +2 F +(ranking) 190.82 648.95 T +3 F +(,) 241.19 648.95 T +2 F +(scaling) 247.19 648.95 T +3 F +(,) 297.56 648.95 T +2 F +(recombin) 303.56 648.95 T +3 F +(,) 361.12 648.95 T +2 F +(mutate) 367.12 648.95 T +FMENDPAGE +%%EndPage: "43" 44 +%%Page: "44" 44 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-44) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(sus) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Stochastic universal sampling) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrIx = sus\050FitnV, Nsel\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.41 (sus) 135.65 588.95 P +3 F +0.17 ( probabilistically selects) 157.24 588.95 P +2 F +0.41 (Nsel) 276.67 588.95 P +3 F +0.17 ( individuals for reproduction according to their) 305.45 588.95 P +(\336tness,) 135.65 574.95 T +2 F +(FitnV) 172.3 574.95 T +3 F +(, in the current population.) 206.73 574.95 T +2 F +8.66 (NewChrIx = rws\050FitnV, Nsel\051) 135.65 548.95 P +3 F +3.61 ( selects) 355.91 548.95 P +2 F +8.66 (Nsel) 401.1 548.95 P +3 F +3.61 ( individuals from a) 429.88 548.95 P +2.12 (population using stochastic universal sampling [1].) 135.65 534.95 P +2 F +5.09 (FitnV) 395.91 534.95 P +3 F +2.12 ( is a column vector) 431.89 534.95 P +0.51 (containing a performance measure for each individual in the population. This can) 135.65 520.95 P +0.09 (be achieved by using the function) 135.65 506.95 P +2 F +0.21 (ranking) 300.71 506.95 P +3 F +0.09 ( or) 351.08 506.95 P +2 F +0.21 (scaling) 367.24 506.95 P +3 F +0.09 ( to assign a \336tness level) 417.62 506.95 P +1.08 (to each individual. The return value,) 135.65 492.95 P +2 F +2.6 (NewChrIx) 319.34 492.95 P +3 F +1.08 (, is the index of the individuals) 376.91 492.95 P +-0.09 (selected for breeding, in the order that they were selected. The selected individuals) 135.65 478.95 P +(can be recovered by evaluating) 135.65 464.95 T +2 F +(Chrom\050NewChrIx,:\051) 287.84 464.95 T +3 F +(.) 410.18 464.95 T +2 F +(sus) 135.65 438.95 T +3 F +( is a low-level selection function normally called by) 157.24 438.95 T +2 F +(select) 409.4 438.95 T +3 F +(.) 452.57 438.95 T +1 16 Q +(Example) 117.65 410.29 T +3 12 Q +(Consider a population of 8 individuals with the assigned \336tness values,) 135.65 392.95 T +2 F +(FitnV) 479.45 392.95 T +3 F +(:) 514.54 392.95 T +2 F +(FitnV = [1.50; 1.35; 1.21; 1.07; 0.92; 0.78; 0.64; 0.5]) 135.65 372.95 T +3 F +(Select the indices of 6 individuals:) 135.65 352.95 T +2 F +(NewChrIx = sus\050FitnV, 6\051) 135.65 332.95 T +3 F +(Thus,) 135.65 312.95 T +2 F +(NewChrIx) 165.63 312.95 T +3 F +( can become:) 223.2 312.95 T +2 F +(NewChrIx =) 135.65 292.95 T +(5) 153.65 278.95 T +(6) 153.65 264.95 T +(3) 153.65 250.95 T +(1) 153.65 236.95 T +(1) 153.65 222.95 T +(2) 153.65 208.95 T +1 16 Q +(Algorithm) 117.65 186.29 T +3 12 Q +-0.07 (A form of stochastic universal sampling is implemented by obtaining a cumulative) 135.65 168.95 P +1.08 (sum of the \336tness vector) 135.65 154.95 P +1.08 (,) 256.73 154.95 P +2 F +2.58 (FitnV) 263.8 154.95 P +3 F +1.08 (, and generating) 298.23 154.95 P +2 F +2.58 (Nsel) 381.39 154.95 P +3 F +1.08 ( equally spaced numbers) 410.18 154.95 P +-0.22 (between) 135.65 140.95 P +2 F +-0.52 (0) 178.39 140.95 P +3 F +-0.22 ( and) 185.59 140.95 P +2 F +-0.52 (sum\050FitnV\051) 208.47 140.95 P +3 F +-0.22 (. Thus, only one random number is generated, all the) 280.43 140.95 P +1.83 (others used being equally spaced from that point. The index of the individuals) 135.65 126.95 P +FMENDPAGE +%%EndPage: "44" 45 +%%Page: "45" 45 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-45) 513.33 61.29 T +3 12 Q +1.03 (selected is determined by comparing the generated numbers with the cumulative) 135.65 736.95 P +(sum vector) 135.65 722.95 T +(. The probability of an individual being selected is then given by) 187.95 722.95 T +(\325) 380.43 685.53 T +2.94 (where) 135.65 624.71 P +0 F +2.94 (f\050x) 170.89 624.71 P +0 10 Q +2.45 (i) 183.54 621.71 P +0 12 Q +2.94 (\051) 186.32 624.71 P +3 F +2.94 ( is the \336tness of individual) 190.32 624.71 P +0 F +2.94 (x) 337.92 624.71 P +0 10 Q +2.45 (i) 343.25 621.71 P +3 12 Q +2.94 ( and) 346.03 624.71 P +0 F +2.94 (F\050x) 375.23 624.71 P +0 10 Q +2.45 (i) 391.88 621.71 P +0 12 Q +2.94 (\051) 394.66 624.71 P +3 F +2.94 ( is the probability of that) 398.65 624.71 P +(individual being selected.) 135.65 610.71 T +1 16 Q +(See Also) 117.65 582.04 T +2 12 Q +(select) 135.65 564.71 T +3 F +(,) 178.82 564.71 T +2 F +(rws) 184.82 564.71 T +3 F +(,) 206.41 564.71 T +2 F +(reins) 212.41 564.71 T +3 F +(,) 248.39 564.71 T +2 F +(ranking) 254.38 564.71 T +3 F +(,) 304.76 564.71 T +2 F +(scaling) 310.75 564.71 T +1 16 Q +(Refer) 117.65 542.04 T +(ence) 155.53 542.04 T +3 12 Q +0.42 ([1] J. E. Baker) 135.65 524.71 P +0.42 (, \322Reducing bias and inef) 206.05 524.71 P +0.42 (\336ciency in the selection algorithm\323,) 329.11 524.71 P +0 F +0.42 (Pr) 505.78 524.71 P +0.42 (oc.) 517.33 524.71 P +(ICGA 2) 135.65 510.71 T +3 F +(, pp. 14-21, Lawrence Erlbaum Associates, Publishers, 1987.) 172.62 510.71 T +282.87 646.71 380.43 704.95 C +0 12 Q +0 X +0 K +(F) 283.87 685.53 T +(x) 299.01 685.53 T +0 9 Q +(i) 304.79 681.74 T +4 12 Q +(\050) 293.91 685.53 T +(\051) 307.9 685.53 T +0 F +(f) 342.94 695.75 T +(x) 354.08 695.75 T +0 9 Q +(i) 359.87 691.97 T +4 12 Q +(\050) 348.98 695.75 T +(\051) 362.97 695.75 T +0 F +(f) 352.4 663.95 T +(x) 363.54 663.95 T +0 9 Q +(i) 369.33 660.17 T +4 12 Q +(\050) 358.44 663.95 T +(\051) 372.44 663.95 T +0 9 Q +(i) 333.48 649.66 T +3 F +(1) 346.91 649.66 T +4 F +(=) 338.98 649.66 T +0 F +(N) 334.98 680.47 T +0 6 Q +(i) 341.32 678.02 T +(n) 343.45 678.02 T +(d) 346.91 678.02 T +4 18 Q +(\345) 336.03 660.75 T +4 12 Q +(=) 319.89 685.53 T +333.48 688.12 378.18 688.12 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "45" 46 +%%Page: "46" 46 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-46) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovdp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Double-point crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovdp\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.62 (xov) 135.65 588.95 P +3 F +0.26 (dp performs double-point crossover between pairs of individuals contained in) 157.24 588.95 P +0.18 (the current population,) 135.65 574.95 P +2 F +0.44 (OldChrom) 248.12 574.95 P +3 F +0.18 (, according to the crossover probability) 305.69 574.95 P +0.18 (,) 493.69 574.95 P +2 F +0.44 (XOVR) 499.86 574.95 P +3 F +0.18 (,) 528.65 574.95 P +0.61 (and returns a new population after mating,) 135.65 560.95 P +2 F +1.47 (NewChrom) 346.45 560.95 P +3 F +0.61 (. Each row of) 404.02 560.95 P +2 F +1.47 (OldChrom) 474.08 560.95 P +3 F +4.74 (and) 135.65 546.95 P +2 F +11.37 (NewChrom) 160.7 546.95 P +3 F +4.74 ( corresponds to one individual. For the chromosomes any) 218.27 546.95 P +(representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xovdp) 135.65 370.95 T +3 F +( is a low-level crossover function normally called by) 171.63 370.95 T +2 F +(recombin) 427.11 370.95 T +3 F +(.) 484.68 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +(Consider the following two binary strings of the same length:) 135.65 324.95 T +2 F +(A1 = [1 1 0 1 0 1]) 135.65 304.95 T +(A2 = [1 0 1 0 1 0]) 135.65 290.95 T +3 F +3.91 (Double point crossover involves selecting uniformly at random two integer) 135.65 270.95 P +0.16 (positions,) 135.65 256.95 P +0 F +0.16 (k1) 185.13 256.95 P +3 F +0.16 (and) 199.61 256.95 P +0 F +0.16 ( k2) 216.93 256.95 P +3 F +0.16 (, between 1 and) 231.41 256.95 P +2 F +0.39 (length\050A1\051) 310.32 256.95 P +3 F +0.16 (, and swapping the variables in) 382.28 256.95 P +0.88 (positions) 135.65 242.95 P +0 F +0.88 (k1+1) 182.85 242.95 P +3 F +0.88 ( to) 208.26 242.95 P +0 F +0.88 (k2) 225.36 242.95 P +3 F +0.88 ( between) 236.68 242.95 P +2 F +2.12 (A1) 284.4 242.95 P +3 F +0.88 ( and) 298.8 242.95 P +2 F +2.12 (A2) 323.88 242.95 P +3 F +0.88 (. Thus if the crossover positions) 338.27 242.95 P +0 F +0.88 (k1) 499.8 242.95 P +3 F +0.88 ( = 3) 511.12 242.95 P +(and) 135.65 228.95 T +0 F +(k2) 155.96 228.95 T +3 F +( = 5, then) 167.29 228.95 T +2 F +(A1) 215.69 228.95 T +3 F +( and) 230.08 228.95 T +2 F +(A2) 253.4 228.95 T +3 F +( would become:) 267.79 228.95 T +2 F +(A1\325 = [1 1 0 0 1 1]) 135.65 208.95 T +(A2\325 = [1 0 1 1 0 0]) 135.65 194.95 T +(xovdp) 135.65 174.95 T +3 F +( calls) 171.63 174.95 T +2 F +(xovmp) 199.61 174.95 T +3 F +( with the appropriate parameters.) 235.59 174.95 T +1 16 Q +(See Also) 117.65 152.29 T +2 12 Q +(xovdprs) 135.65 134.95 T +3 F +(,) 186.02 134.95 T +2 F +(xovsp) 192.02 134.95 T +3 F +(,) 228 134.95 T +2 F +(xovsh) 233.99 134.95 T +3 F +(,) 269.97 134.95 T +2 F +(xovmp) 275.97 134.95 T +3 F +(,) 311.95 134.95 T +2 F +(recombin) 317.95 134.95 T +3 F +(,) 375.52 134.95 T +2 F +(select) 381.51 134.95 T +FMENDPAGE +%%EndPage: "46" 47 +%%Page: "47" 47 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-47) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovdprs) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Double-point reduced surrogate crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovdprs\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +7.01 (xov) 135.65 588.95 P +3 F +2.92 (dprs performs double-point reduced surrogate crossover between pairs of) 157.24 588.95 P +2.78 (individuals contained in the current population,) 135.65 574.95 P +2 F +6.66 (OldChrom) 382.48 574.95 P +3 F +2.78 (, according to the) 440.05 574.95 P +5.65 (crossover probability) 135.65 560.95 P +5.65 (,) 242.12 560.95 P +2 F +13.57 (XOVR) 253.77 560.95 P +3 F +5.65 (, and returns a new population after mating,) 282.55 560.95 P +2 F +10.34 (NewChrom) 135.65 546.95 P +3 F +4.31 (. Each row of) 193.22 546.95 P +2 F +10.34 (OldChrom) 278.06 546.95 P +3 F +4.31 ( and) 335.62 546.95 P +2 F +10.34 (NewChrom) 367.56 546.95 P +3 F +4.31 ( corresponds to one) 425.13 546.95 P +(individual. For the chromosomes any representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xovdp) 135.65 370.95 T +3 F +(rs is a low-level crossover function normally called by) 171.63 370.95 T +2 F +(recombin) 435.77 370.95 T +3 F +(.) 493.34 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +(For double point crossover see) 135.65 324.95 T +2 F +(xovdp) 285.88 324.95 T +3 F +(.) 321.86 324.95 T +3.35 (The) 135.65 298.95 P +0 F +3.35 (r) 160.65 298.95 P +3.35 (educed surr) 164.87 298.95 P +3.35 (ogate) 224.74 298.95 P +3 F +3.35 ( operator constrains crossover to always produce new) 251.39 298.95 P +0.99 (individuals wherever possible. This is implemented by restricting the location of) 135.65 284.95 P +1.41 (crossover points such that crossover points only occur where gene values dif) 135.65 270.95 P +1.41 (fer) 518.34 270.95 P +([1].) 135.65 256.95 T +2 F +(xovdprs) 135.65 230.95 T +3 F +( calls) 186.02 230.95 T +2 F +(xovmp) 214 230.95 T +3 F +( with the appropriate parameters.) 249.98 230.95 T +1 16 Q +(See Also) 117.65 208.29 T +2 12 Q +(xovdp) 135.65 190.95 T +3 F +(,) 171.63 190.95 T +2 F +(xovsprs) 177.62 190.95 T +3 F +(,) 228 190.95 T +2 F +(xovshrs) 233.99 190.95 T +3 F +(,) 284.37 190.95 T +2 F +(xovmp) 290.36 190.95 T +3 F +(,) 326.34 190.95 T +2 F +(recombin) 332.34 190.95 T +3 F +(,) 389.91 190.95 T +2 F +(select) 395.9 190.95 T +1 16 Q +(Refer) 117.65 168.29 T +(ence) 155.53 168.29 T +3 12 Q +1.31 ([1] L. Booker) 135.65 150.95 P +1.31 (, \322Improving search in genetic algorithms,\323 In) 203.4 150.95 P +0 F +1.31 ( Genetic Algorithms) 432.42 150.95 P +5.64 (and Simulated Annealing) 135.65 136.95 P +3 F +5.64 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 268.2 136.95 P +5.64 (gan Kaufmann) 455.06 136.95 P +(Publishers, 1987) 135.65 122.95 T +2 F +(.) 215.61 122.95 T +FMENDPAGE +%%EndPage: "47" 48 +%%Page: "48" 48 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-48) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovmp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Multi-point crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovmp\050OldChrom, XOVR, Npt, Rs\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +1.93 (xovmp) 135.65 588.95 P +3 F +0.81 ( performs multi-point crossover between pairs of individuals contained in) 171.63 588.95 P +1.7 (the current population,) 135.65 574.95 P +2 F +4.08 (OldChrom) 252.67 574.95 P +3 F +1.7 (, and returns a new population after mating,) 310.24 574.95 P +2 F +10.34 (NewChrom) 135.65 560.95 P +3 F +4.31 (. Each row of) 193.22 560.95 P +2 F +10.34 (OldChrom) 278.06 560.95 P +3 F +4.31 ( and) 335.62 560.95 P +2 F +10.34 (NewChrom) 367.56 560.95 P +3 F +4.31 ( corresponds to one) 425.13 560.95 P +(individual. For the chromosomes any representation can be used.) 135.65 546.95 T +2 F +1.74 (XOVR) 135.65 526.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 526.95 P +2 F +1.74 (XOVR) 447.77 526.95 P +3 F +0.72 ( is omitted,) 476.56 526.95 P +(empty or) 135.65 512.95 T +2 F +(NaN,) 181.62 512.95 T +(XOVR = 0.7) 213.4 512.95 T +3 F +( is assumed.) 285.36 512.95 T +2 F +(Npt) 135.65 492.95 T +3 F +( is an optional parameter specifying the number of crosspoints:) 157.24 492.95 T +(0 - shuf) 171.65 478.95 T +(\337e crossover) 208.07 478.95 T +(.) 268.36 478.95 T +(1 - single point crossover) 171.65 464.95 T +(.) 292.24 464.95 T +(2 - double point crossover) 171.65 450.95 T +(.) 296.24 450.95 T +(If) 171.65 436.95 T +2 F +(Npt) 182.63 436.95 T +3 F +( is omitted, empty or) 204.22 436.95 T +2 F +(NaN,) 306.84 436.95 T +(Npt = 0) 338.62 436.95 T +3 F +( is assumed.) 388.99 436.95 T +2 F +(Rs) 135.65 416.95 T +3 F +( is an optional parameter specifying the use of reduced surrogate:) 150.04 416.95 T +(0 - no reduced surrogate.) 171.65 402.95 T +(1 - use reduced surrogate.) 171.65 388.95 T +(If) 171.65 374.95 T +2 F +(Rs) 182.63 374.95 T +3 F +( is omitted, empty or) 197.03 374.95 T +2 F +(NaN,) 299.64 374.95 T +(Rs = 0) 331.42 374.95 T +3 F +( is assumed.) 374.6 374.95 T +1.18 (The pairs are mated in order) 135.65 354.95 P +1.18 (, odd row with the next even row) 276.62 354.95 P +1.18 (. If the number of) 442.66 354.95 P +3.35 (rows in the matrix) 135.65 340.95 P +2 F +8.05 (OldChrom) 239.67 340.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 340.95 P +-0.12 (population should therefore be or) 135.65 326.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 326.95 P +0.8 (This can be achieved by using the function) 135.65 312.95 P +2 F +1.92 (ranking) 350.55 312.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 312.95 P +2.71 (each chromosome and a selection function \050) 135.65 298.95 P +2 F +6.52 (select) 363.11 298.95 P +3 F +2.71 (,) 406.28 298.95 P +2 F +6.52 (sus) 414.99 298.95 P +3 F +2.71 ( or) 436.58 298.95 P +2 F +6.52 (rws) 458 298.95 P +3 F +2.71 (\051 to select) 479.59 298.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 284.95 T +2 F +-0.06 (xov) 135.65 264.95 P +3 F +-0.03 (mp is a low-level crossover function called by all other crossover functions. If) 157.24 264.95 P +4.29 (called by) 135.65 250.95 P +2 F +10.3 (recombine) 190.86 250.95 P +10.3 (xovmp) 262.92 250.95 P +3 F +4.29 ( performs shuf) 298.9 250.95 P +4.29 (\337e crossover without reduced) 377.21 250.95 P +(surrogate identical to) 135.65 236.95 T +2 F +(xovsh) 239.91 236.95 T +3 F +(.) 275.89 236.95 T +1 16 Q +(Algorithm) 117.65 214.29 T +3 12 Q +3.98 (The algorithms used in single-point, double-point and shuf) 135.65 196.95 P +3.98 (\337e crossover are) 445.1 196.95 P +0.69 (described in the) 135.65 182.95 P +2 F +1.66 (xovsp) 216.66 182.95 P +3 F +0.69 (,) 252.64 182.95 P +2 F +1.66 (xovdp) 259.33 182.95 P +1.66 (and xovsh) 299 182.95 P +0 F +0.69 (Refer) 374.28 182.95 P +0.69 (ence) 399.82 182.95 P +3 F +0.69 (entries) 430.65 182.95 P +0.69 (respectively) 471.48 182.95 P +0.69 (.) 528.65 182.95 P +3.23 (The algorithms used in single-point, double-point and shuf) 135.65 168.95 P +3.23 (\337e crossover with) 439.91 168.95 P +1.66 (reduced surrogates are described in the) 135.65 154.95 P +2 F +3.99 (xovsprs) 335.44 154.95 P +3 F +1.66 (,) 385.82 154.95 P +2 F +3.99 (xovdprs) 393.47 154.95 P +3.99 (and xovshrs) 448.51 154.95 P +0 F +(Refer) 135.65 140.95 T +(ence) 161.18 140.95 T +3 F +( entries respectively) 183.15 140.95 T +(.) 278.3 140.95 T +1 16 Q +(See Also) 117.65 118.29 T +2 12 Q +(xovsp) 135.65 100.95 T +3 F +(,) 171.63 100.95 T +2 F +(xovdp) 177.62 100.95 T +3 F +(,) 213.6 100.95 T +2 F +(xovsh) 219.6 100.95 T +3 F +(,) 255.58 100.95 T +2 F +(xovsprs) 261.58 100.95 T +3 F +(,) 311.95 100.95 T +2 F +(xovdprs) 317.95 100.95 T +3 F +(,) 368.32 100.95 T +2 F +(xovshrs) 374.32 100.95 T +3 F +(,) 424.69 100.95 T +2 F +(recombin) 430.69 100.95 T +FMENDPAGE +%%EndPage: "48" 49 +%%Page: "49" 49 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-49) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovsh) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Shuf) 135.65 674.95 T +(\337e crossover) 158.09 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovsh\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +2.68 (xovsh) 135.65 588.95 P +3 F +1.12 ( performs shuf) 171.63 588.95 P +1.12 (\337e crossover between pairs of individuals contained in the) 243.59 588.95 P +-0.11 (current population,) 135.65 574.95 P +2 F +-0.27 (OldChrom) 229.69 574.95 P +3 F +-0.11 (, according to the crossover probability) 287.26 574.95 P +-0.11 (,) 473.78 574.95 P +2 F +-0.27 (XOVR) 479.66 574.95 P +3 F +-0.11 (, and) 508.45 574.95 P +0.61 (returns a new population after mating,) 135.65 560.95 P +2 F +1.47 (NewChrom) 325.52 560.95 P +3 F +0.61 (. Each row of) 383.09 560.95 P +2 F +1.47 (OldChrom) 453.15 560.95 P +3 F +0.61 ( and) 510.72 560.95 P +2 F +18.88 (NewChrom) 135.65 546.95 P +3 F +7.87 ( corresponds to one individual. For the chromosomes any) 193.22 546.95 P +(representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xov) 135.65 370.95 T +3 F +(sh is a low-level crossover function normally called by) 157.24 370.95 T +2 F +(recombin) 423.38 370.95 T +3 F +(.) 480.95 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +1.5 (Shuf) 135.65 324.95 P +1.5 (\337e crossover is single-point crossover \050see) 158.09 324.95 P +2 F +3.6 (xovsp) 373.6 324.95 P +3 F +1.5 (\051, but before the bits are) 409.58 324.95 P +1.15 (exchanged, they are randomly shuf) 135.65 310.95 P +1.15 (\337ed in both parents. After recombination, the) 308.23 310.95 P +1.44 (bits in the of) 135.65 296.95 P +1.44 (fspring are unshuf) 200.04 296.95 P +1.44 (\337ed. This removes positional bias as the bits are) 289.97 296.95 P +(randomly reassigned each time crossover is performed [1].) 135.65 282.95 T +2 F +(xov) 135.65 256.95 T +3 F +(sh calls) 157.24 256.95 T +2 F +(xovmp) 195.88 256.95 T +3 F +( with the appropriate parameters.) 231.86 256.95 T +1 16 Q +(See Also) 117.65 234.29 T +2 12 Q +(xovshrs) 135.65 216.95 T +3 F +(,) 186.02 216.95 T +2 F +(xovsp) 192.02 216.95 T +3 F +(,) 228 216.95 T +2 F +(xovdp) 233.99 216.95 T +3 F +(,) 269.97 216.95 T +2 F +(xovmp) 275.97 216.95 T +3 F +(,) 311.95 216.95 T +2 F +(recombin) 317.95 216.95 T +3 F +(,) 375.52 216.95 T +2 F +(select) 381.51 216.95 T +1 16 Q +(Refer) 117.65 194.29 T +(ence) 155.53 194.29 T +3 12 Q +-0.28 ([1] R. A. Caruana, L. A. Eshelman, J. D. Schaf) 135.65 176.95 P +-0.28 (fer) 358.39 176.95 P +-0.28 (, \322Representation and hidden bias) 371.23 176.95 P +1.86 (II: Eliminating de\336ning length bias in genetic search via shuf) 135.65 162.95 P +1.86 (\337e crossover\323, In) 445.66 162.95 P +0 F +0.3 (Eleventh International Joint Confer) 135.65 148.95 P +0.3 (ence on Arti\336cial Intelligence) 307.67 148.95 P +3 F +0.3 (, N. S. Sridharan) 450.8 148.95 P +(\050Ed.\051, V) 135.65 134.95 T +(ol. 1, pp. 750-755, Mor) 173.07 134.95 T +(gan Kaufmann Publishers, 1989.) 284.79 134.95 T +FMENDPAGE +%%EndPage: "49" 50 +%%Page: "50" 50 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-50) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovshrs) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Shuf) 135.65 674.95 T +(\337e crossover with reduced surrogate) 158.09 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovshrs\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +6.55 (xov) 135.65 588.95 P +3 F +2.73 (shrs performs shuf) 157.24 588.95 P +2.73 (\337e crossover with reduced surrogates between pairs of) 251.75 588.95 P +2.78 (individuals contained in the current population,) 135.65 574.95 P +2 F +6.66 (OldChrom) 382.48 574.95 P +3 F +2.78 (, according to the) 440.05 574.95 P +5.65 (crossover probability) 135.65 560.95 P +5.65 (,) 242.12 560.95 P +2 F +13.57 (XOVR) 253.77 560.95 P +3 F +5.65 (, and returns a new population after mating,) 282.55 560.95 P +2 F +10.34 (NewChrom) 135.65 546.95 P +3 F +4.31 (. Each row of) 193.22 546.95 P +2 F +10.34 (OldChrom) 278.06 546.95 P +3 F +4.31 ( and) 335.62 546.95 P +2 F +10.34 (NewChrom) 367.56 546.95 P +3 F +4.31 ( corresponds to one) 425.13 546.95 P +(individual. For the chromosomes any representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xov) 135.65 370.95 T +3 F +(shrs is a low-level crossover function normally called by) 157.24 370.95 T +2 F +(recombin) 432.04 370.95 T +3 F +(.) 489.61 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +(For shuf) 135.65 324.95 T +(\337e crossover algorithm see) 175.74 324.95 T +2 F +(xovsh) 307.64 324.95 T +3 F +(.) 343.63 324.95 T +3.35 (The) 135.65 298.95 P +0 F +3.35 (r) 160.65 298.95 P +3.35 (educed surr) 164.87 298.95 P +3.35 (ogate) 224.74 298.95 P +3 F +3.35 ( operator constrains crossover to always produce new) 251.39 298.95 P +0.99 (individuals wherever possible. This is implemented by restricting the location of) 135.65 284.95 P +1.41 (crossover points such that crossover points only occur where gene values dif) 135.65 270.95 P +1.41 (fer) 518.34 270.95 P +([1].) 135.65 256.95 T +2 F +(xovshrs) 135.65 230.95 T +3 F +( calls) 186.02 230.95 T +2 F +(xovmp) 214 230.95 T +3 F +( with the appropriate parameters.) 249.98 230.95 T +1 16 Q +(See Also) 117.65 208.29 T +2 12 Q +(xovsh) 135.65 190.95 T +3 F +(,) 171.63 190.95 T +2 F +(xovsprs) 177.62 190.95 T +3 F +(,) 228 190.95 T +2 F +(xovdprs) 233.99 190.95 T +3 F +(,) 284.37 190.95 T +2 F +(xovmp) 290.36 190.95 T +3 F +(,) 326.34 190.95 T +2 F +(recombin) 332.34 190.95 T +3 F +(,) 389.91 190.95 T +2 F +(select) 395.9 190.95 T +1 16 Q +(Refer) 117.65 168.29 T +(ence) 155.53 168.29 T +3 12 Q +1.31 ([1] L. Booker) 135.65 150.95 P +1.31 (, \322Improving search in genetic algorithms,\323 In) 203.4 150.95 P +0 F +1.31 ( Genetic Algorithms) 432.42 150.95 P +5.64 (and Simulated Annealing) 135.65 136.95 P +3 F +5.64 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 268.2 136.95 P +5.64 (gan Kaufmann) 455.06 136.95 P +(Publishers, 1987.) 135.65 122.95 T +FMENDPAGE +%%EndPage: "50" 51 +%%Page: "51" 51 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-51) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovsp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Single-point crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovsp\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +2.04 (xov) 135.65 588.95 P +3 F +0.85 (sp performs single-point crossover between pairs of individuals contained in) 157.24 588.95 P +0.18 (the current population,) 135.65 574.95 P +2 F +0.44 (OldChrom) 248.12 574.95 P +3 F +0.18 (, according to the crossover probability) 305.69 574.95 P +0.18 (,) 493.69 574.95 P +2 F +0.44 (XOVR) 499.86 574.95 P +3 F +0.18 (,) 528.65 574.95 P +0.77 (and returns a new population after mating,) 135.65 560.95 P +2 F +1.85 (NewChrom) 347.57 560.95 P +3 F +0.77 (.) 405.14 560.95 P +2 F +1.85 (OldChrom) 411.91 560.95 P +3 F +0.77 ( contains the) 469.48 560.95 P +0.96 (chromosomes of the current population, each row corresponds to one individual.) 135.65 546.95 P +(For the chromosomes any representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xovsp) 135.65 370.95 T +3 F +( is a low-level crossover function normally called by) 171.63 370.95 T +2 F +(recombin) 427.11 370.95 T +3 F +(.) 484.68 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +(Consider the following two binary strings of the same length:) 135.65 324.95 T +2 F +(A1 = [1 1 0 1 0 1]) 135.65 304.95 T +(A2 = [1 0 1 0 1 0]) 135.65 290.95 T +3 F +0.1 (Single-point crossover involves selecting uniformly at random an integer position,) 135.65 270.95 P +0 F +1.68 (k) 135.65 256.95 P +3 F +1.68 (, between 1 and) 140.97 256.95 P +2 F +4.03 (\050length\050A1\051-1\051) 225.95 256.95 P +3 F +1.68 (, and swapping the variables in positions) 326.7 256.95 P +0 F +0.9 (k+1) 135.65 242.95 P +3 F +0.9 ( to) 155.07 242.95 P +2 F +2.16 (length\050A1\051) 172.19 242.95 P +3 F +0.9 ( between) 244.15 242.95 P +2 F +2.16 (A1) 291.91 242.95 P +3 F +0.9 ( and) 306.3 242.95 P +2 F +2.16 (A2) 331.41 242.95 P +3 F +0.9 (. Thus if the crossover position) 345.8 242.95 P +0 F +0.9 (k) 502.77 242.95 P +3 F +0.9 ( = 3,) 508.09 242.95 P +(then) 135.65 228.95 T +2 F +(A1) 159.3 228.95 T +3 F +( and) 173.69 228.95 T +2 F +(A2) 197.01 228.95 T +3 F +( would become:) 211.4 228.95 T +2 F +(A1\325 = [1 1 0 0 1 0]) 135.65 208.95 T +(A2\325 = [1 0 1 1 0 1]) 135.65 194.95 T +(xovsp) 135.65 174.95 T +3 F +( calls) 171.63 174.95 T +2 F +(xovmp) 199.61 174.95 T +3 F +( with the appropriate parameters.) 235.59 174.95 T +1 16 Q +(See Also) 117.65 152.29 T +2 12 Q +(xovsprs) 135.65 134.95 T +3 F +(,) 186.02 134.95 T +2 F +(xovdp) 192.02 134.95 T +3 F +(,) 228 134.95 T +2 F +(xovsh) 233.99 134.95 T +3 F +(,) 269.97 134.95 T +2 F +(xovmp) 275.97 134.95 T +3 F +(,) 311.95 134.95 T +2 F +(recombin) 317.95 134.95 T +3 F +(,) 375.52 134.95 T +2 F +(select) 381.51 134.95 T +FMENDPAGE +%%EndPage: "51" 52 +%%Page: "52" 52 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-52) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovsprs) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Single-point reduced surrogate crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovsprs\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +8.61 (xov) 135.65 588.95 P +3 F +3.59 (sprs performs single-point reduced surrogate crossover between pairs of) 157.24 588.95 P +2.78 (individuals contained in the current population,) 135.65 574.95 P +2 F +6.66 (OldChrom) 382.48 574.95 P +3 F +2.78 (, according to the) 440.05 574.95 P +5.65 (crossover probability) 135.65 560.95 P +5.65 (,) 242.12 560.95 P +2 F +13.57 (XOVR) 253.77 560.95 P +3 F +5.65 (, and returns a new population after mating,) 282.55 560.95 P +2 F +5.91 (NewChrom) 135.65 546.95 P +3 F +2.46 (.) 193.22 546.95 P +2 F +5.91 (OldChrom) 201.68 546.95 P +3 F +2.46 ( contains the chromosomes of the current population,) 259.24 546.95 P +0.6 (each row corresponds to one individual. For the chromosomes any representation) 135.65 532.95 P +(can be used.) 135.65 518.95 T +2 F +1.74 (XOVR) 135.65 492.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 492.95 P +2 F +1.74 (XOVR) 447.77 492.95 P +3 F +0.72 ( is omitted,) 476.56 492.95 P +(empty or) 135.65 478.95 T +2 F +(NaN,) 181.62 478.95 T +(XOVR = 0.7) 213.4 478.95 T +3 F +( is assumed.) 285.36 478.95 T +1.18 (The pairs are mated in order) 135.65 452.95 P +1.18 (, odd row with the next even row) 276.62 452.95 P +1.18 (. If the number of) 442.66 452.95 P +3.35 (rows in the matrix) 135.65 438.95 P +2 F +8.05 (OldChrom) 239.67 438.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 438.95 P +-0.12 (population should therefore be or) 135.65 424.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 424.95 P +0.8 (This can be achieved by using the function) 135.65 410.95 P +2 F +1.92 (ranking) 350.55 410.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 410.95 P +2.71 (each chromosome and a selection function \050) 135.65 396.95 P +2 F +6.52 (select) 363.11 396.95 P +3 F +2.71 (,) 406.28 396.95 P +2 F +6.52 (sus) 414.99 396.95 P +3 F +2.71 ( or) 436.58 396.95 P +2 F +6.52 (rws) 458 396.95 P +3 F +2.71 (\051 to select) 479.59 396.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 382.95 T +2 F +(xovsp) 135.65 356.95 T +3 F +(rs is a low-level crossover function normally called by) 171.63 356.95 T +2 F +(recombin) 435.77 356.95 T +3 F +(.) 493.34 356.95 T +1 16 Q +(Algorithm) 117.65 328.29 T +3 12 Q +(For single-point crossover see) 135.65 310.95 T +2 F +(xovsp) 282.88 310.95 T +3 F +(.) 318.86 310.95 T +3.35 (The) 135.65 290.95 P +0 F +3.35 (r) 160.65 290.95 P +3.35 (educed surr) 164.87 290.95 P +3.35 (ogate) 224.74 290.95 P +3 F +3.35 ( operator constrains crossover to always produce new) 251.39 290.95 P +0.99 (individuals wherever possible. This is implemented by restricting the location of) 135.65 276.95 P +1.41 (crossover points such that crossover points only occur where gene values dif) 135.65 262.95 P +1.41 (fer) 518.34 262.95 P +([1].) 135.65 248.95 T +2 F +(xovsprs) 135.65 228.95 T +3 F +( calls) 186.02 228.95 T +2 F +(xovmp) 214 228.95 T +3 F +( with the appropriate parameters.) 249.98 228.95 T +1 16 Q +(See Also) 117.65 206.29 T +2 12 Q +(xovsp) 135.65 188.95 T +3 F +(,) 171.63 188.95 T +2 F +(xovdp) 177.62 188.95 T +3 F +(,) 213.6 188.95 T +2 F +(xovdprs) 219.6 188.95 T +3 F +(,) 269.97 188.95 T +2 F +(xovsh) 275.97 188.95 T +3 F +(,) 311.95 188.95 T +2 F +(xovshrs) 317.95 188.95 T +3 F +(,) 368.32 188.95 T +2 F +(xovmp) 374.32 188.95 T +3 F +(,) 410.3 188.95 T +2 F +(recombin) 416.29 188.95 T +3 F +(,) 473.86 188.95 T +2 F +(select) 479.86 188.95 T +1 16 Q +(Refer) 117.65 166.29 T +(ence) 155.53 166.29 T +3 12 Q +1.31 ([1] L. Booker) 135.65 148.95 P +1.31 (, \322Improving search in genetic algorithms,\323 In) 203.4 148.95 P +0 F +1.31 (Genetic Algorithms) 436.73 148.95 P +5.64 (and Simulated Annealing) 135.65 134.95 P +3 F +5.64 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 268.2 134.95 P +5.64 (gan Kaufmann) 455.06 134.95 P +(Publishers, 198) 135.65 120.95 T +2 F +(7.) 209.61 120.95 T +FMENDPAGE +%%EndPage: "52" 53 +%%Trailer +%%BoundingBox: 0 0 595.3 841.9 +%%Pages: 52 1 +%%DocumentFonts: Times-Italic +%%+ Times-Bold +%%+ Courier +%%+ Times-Roman +%%+ Symbol diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/BS2RV.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/BS2RV.M" index 0d407f06e071c2c32d8d1dea132afcad3768ffe2..b2e812e89ba6bf888a225eab01d5e545942f6b8c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/BS2RV.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/BS2RV.M" @@ -1,3 +1,115 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2a42fa20681fe57381f8c961409149366d60da9ffbfcf3efb169d6dcbbc66a28 -size 3217 +% BS2RV.m - Binary string to real vector +% +% This function decodes binary chromosomes into vectors of reals. The +% chromosomes are seen as the concatenation of binary strings of given +% length, and decoded into real numbers in a specified interval using +% either standard binary or Gray decoding. +% +% Syntax: Phen = bs2rv(Chrom,FieldD) +% +% Input parameters: +% +% Chrom - Matrix containing the chromosomes of the current +% population. Each line corresponds to one +% individual's concatenated binary string +% representation. Leftmost bits are MSb and +% rightmost are LSb. +% +% FieldD - Matrix describing the length and how to decode +% each substring in the chromosome. It has the +% following structure: +% +% [len; (num) +% lb; (num) +% ub; (num) +% code; (0=binary | 1=gray) +% scale; (0=arithmetic | 1=logarithmic) +% lbin; (0=excluded | 1=included) +% ubin]; (0=excluded | 1=included) +% +% where +% len - row vector containing the length of +% each substring in Chrom. sum(len) +% should equal the individual length. +% lb, +% ub - Lower and upper bounds for each +% variable. +% code - binary row vector indicating how each +% substring is to be decoded. +% scale - binary row vector indicating where to +% use arithmetic and/or logarithmic +% scaling. +% lbin, +% ubin - binary row vectors indicating whether +% or not to include each bound in the +% representation range +% +% Output parameter: +% +% Phen - Real matrix containing the population phenotypes. + +% +% Author: Carlos Fonseca, Updated: Andrew Chipperfield +% Date: 08/06/93, Date: 26-Jan-94 + +function Phen = bs2rv(Chrom,FieldD) + +% Identify the population size (Nind) +% and the chromosome length (Lind) +[Nind,Lind] = size(Chrom); + +% Identify the number of decision variables (Nvar) +[seven,Nvar] = size(FieldD); + +if seven ~= 7 + error('FieldD must have 7 rows.'); +end + +% Get substring properties +len = FieldD(1,:); +lb = FieldD(2,:); +ub = FieldD(3,:); +code = ~(~FieldD(4,:)); +scale = ~(~FieldD(5,:)); +lin = ~(~FieldD(6,:)); +uin = ~(~FieldD(7,:)); + +% Check substring properties for consistency +if sum(len) ~= Lind, + error('Data in FieldD must agree with chromosome length'); +end + +if ~all(lb(scale).*ub(scale)>0) + error('Log-scaled variables must not include 0 in their range'); +end + +% Decode chromosomes +Phen = zeros(Nind,Nvar); + +lf = cumsum(len); +li = cumsum([1 len]); +Prec = .5 .^ len; + +logsgn = sign(lb(scale)); +lb(scale) = log( abs(lb(scale)) ); +ub(scale) = log( abs(ub(scale)) ); +delta = ub - lb; + +Prec = .5 .^ len; +num = (~lin) .* Prec; +den = (lin + uin - 1) .* Prec; + +for i = 1:Nvar, + idx = li(i):lf(i); + if code(i) % Gray decoding + Chrom(:,idx)=rem(cumsum(Chrom(:,idx)')',2); + end + Phen(:,i) = Chrom(:,idx) * [ (.5).^(1:len(i))' ]; + Phen(:,i) = lb(i) + delta(i) * (Phen(:,i) + num(i)) ./ (1 - den(i)); +end + +expand = ones(Nind,1); +if any(scale) + Phen(:,scale) = logsgn(expand,:) .* exp(Phen(:,scale)); +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CONTENTS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CONTENTS.M" index 780354bbcbd28d9e302eeaeb32bdc9414009edad..675708b6266fd34653d1afec5bbae223820ae80f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CONTENTS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CONTENTS.M" @@ -1,3 +1,54 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:cd8ddbf0dc11c2eac9a9c1b0dd1dda6ef6ce04f08aca45a11652054507cc54f5 -size 1835 +% Genetic Algorithm Toolbox. +% Version 1.2 15-Apr-94 +% Department of Automatic Control and Systems Engineering +% University of Sheffield, England +% +% Creating populations +% crtbase - create a base vector +% crtbp - create a binary population +% crtrp - create a real-valued population +% +% Fitness assignment +% ranking - rank-based fitness assignment +% scaling - proportional fitness-scaling +% +% Selection and reinsertion +% reins - uniform random and fitness-based reinsertion +% rws - roulette wheel selection +% select - high-level selection routine +% sues - stochastic universal sampling +% +% Mutation operators +% mut - discrete mutation +% mutate - high-level mutation function +% mutbga - real-value mutation +% +% Crossover operators +% recdis - discrete recombination +% recint - intermediate recombination +% reclin - line recombination +% recmut - line recombination with mutation features +% recombin - high-level recombination function +% xovdp - double-point crossover +% xovdprs - double-point reduced surrogate crossover +% xovmp - general multi-point crossover +% xovsh - shuffle crossover +% xovshrs - shuffle reduced surrogate crossover +% xovsp - single-point crossover +% xovsprs - single-point reduced surrogate crossover +% +% Subpopulation support +% migrate - exchange individuals between subpopulations +% +% +% Utility functions +% bs2rv - binary string to real-value conversion +% rep - matrix replication +% +% Demonstration and other functions +% mpga - multi-population genetic algorithm demonstration +% objfun1 - De Jongs first test function (used by sga) +% objharv - harvest function (used in mpga) +% resplot - result plotting (used in mpga) +% sga - simple genetic algorithm demonstration + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTBASE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTBASE.M" index 5e3f0420223cb4a9e553552bf383f1c3dbe72540..c2ef387b81778c368247ce1f1d5c0dc6b7357066 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTBASE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTBASE.M" @@ -1,3 +1,47 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:e0a5dec9709b6d5c6ebafa3f4a452d455710626114c4add503b1968c4c62a22a -size 1168 +% CRTBASE.m - Create base vector +% +% This function creates a vector containing the base of the loci +% in a chromosome. +% +% Syntax: BaseVec = crtbase(Lind, Base) +% +% Input Parameters: +% +% Lind - A scalar or vector containing the lengths +% of the alleles. Sum(Lind) is the length of +% the corresponding chromosome. +% +% Base - A scalar or vector containing the base of +% the loci contained in the Alleles. +% +% Output Parameters: +% +% BaseVec - A vector whose elements correspond to the base +% of the loci of the associated chromosome structure. + +% Author: Andrew Chipperfield +% Date: 19-Jan-94 + +function BaseVec = crtbase(Lind, Base) + +[ml LenL] = size(Lind) ; +if nargin < 2 + Base = 2 * ones(LenL,1) ; % default to base 2 +end +[mb LenB] = size(Base) ; + +% check parameter consistency +if ml > 1 | mb > 1 + error( 'Lind or Base is not a vector') ; +elseif (LenL > 1 & LenB > 1 & LenL ~= LenB) | (LenL == 1 & LenB > 1 ) + error( 'Vector dimensions must agree' ) ; +elseif LenB == 1 & LenL > 1 + Base = Base * ones(LenL,1) ; + +end + +BaseVec = [] ; +for i = 1:LenL + BaseVec = [BaseVec, Base(i)*ones(Lind(i),1)']; +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTBP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTBP.M" index 1df58c568d8e56b8058936ef7eca1bdb08e4766c..ed9188cb90f28358ad8a0a86660709e61cb63fa9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTBP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTBP.M" @@ -1,3 +1,72 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:894b8535d97486a598d8143bcf8fef1d72907caff3870db4955f7a996518a5d2 -size 2187 +% CRTP.m - Create an initial population +% +% This function creates a binary population of given size and structure. +% +% Syntax: [Chrom Lind BaseV] = crtbp(Nind, Lind, Base) +% +% Input Parameters: +% +% Nind - Either a scalar containing the number of individuals +% in the new population or a row vector of length two +% containing the number of individuals and their length. +% +% Lind - A scalar containing the length of the individual +% chromosomes. +% +% Base - A scalar containing the base of the chromosome +% elements or a row vector containing the base(s) +% of the loci of the chromosomes. +% +% Output Parameters: +% +% Chrom - A matrix containing the random valued chromosomes +% row wise. +% +% Lind - A scalar containing the length of the chromosome. +% +% BaseV - A row vector containing the base of the +% chromosome loci. + +% Author: Andrew Chipperfield +% Date: 19-Jan-94 + +function [Chrom, Lind, BaseV] = crtbp(Nind, Lind, Base) +nargs = nargin ; + +% Check parameter consistency + +if nargs >= 1, [mN, nN] = size(Nind) ; end +if nargs >= 2, [mL, nL] = size(Lind) ; end +if nargs == 3, [mB, nB] = size(Base) ; end + +if nN == 2 + if (nargs == 1) + Lind = Nind(2) ; Nind = Nind(1) ; BaseV = crtbase(Lind) ; + elseif (nargs == 2 & nL == 1) + BaseV = crtbase(Nind(2),Lind) ; Lind = Nind(2) ; Nind = Nind(1) ; + elseif (nargs == 2 & nL > 1) + if Lind ~= length(Lind), error('Lind and Base disagree'); end + BaseV = Lind ; Lind = Nind(2) ; Nind = Nind(1) ; + end +elseif nN == 1 + if nargs == 2 + if nL == 1, BaseV = crtbase(Lind) ; + else, BaseV = Lind ; Lind = nL ; end + elseif nargs == 3 + if nB == 1, BaseV = crtbase(Lind,Base) ; + elseif nB ~= Lind, error('Lind and Base disagree') ; + else BaseV = Base ; end + end +else + error('Input parameters inconsistent') ; +end + +% Create a structure of random chromosomes in row wise order, dimensions +% Nind by Lind. The base of each chromosomes loci is given by the value +% of the corresponding element of the row vector base. + +Chrom = floor(rand(Nind,Lind).*BaseV(ones(Nind,1),:)) ; + + +% End of file + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTRP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTRP.M" index 806adf2a21f3d6f8762cf198c70ad4e0936638f4..8ddb36b34404a9c7cff7c8682f08bbc60fa9ce91 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTRP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/CRTRP.M" @@ -1,3 +1,53 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:900cb8e84a5ad67fa6798ce0ae0b4a45b9bef93b5cad9a8119c108ecadfd1b36 -size 2091 +% CRTRP.M (CReaTe an initial (Real-value) Population) +% +% This function creates a population of given size of random real-values. +% +% Syntax: Chrom = crtrp(Nind,FieldDR); +% +% Input parameters: +% Nind - A scalar containing the number of individuals in the new +% population. +% +% FieldDR - A matrix of size 2 by number of variables describing the +% boundaries of each variable. It has the following structure: +% [lower_bound; (vector with lower bound for each veriable) +% upper_bound] (vector with upper bound for each veriable) +% [lower_bound_var_1 lower_bound_var_2 ... lower_bound_var_Nvar; +% upper_bound_var_1 upper_bound_var_2 ... upper_bound_var_Nvar] +% example - each individuals consists of 4 variables: +% FieldDR = [-100 -50 -30 -20; % lower bound +% 100 50 30 20] % upper bound +% +% Output parameter: +% Chrom - A matrix containing the random valued individuals of the +% new population of size Nind by number of variables. + +% Author: Hartmut Pohlheim +% History: 23.11.93 file created +% 25.02.94 clean up, check parameter consistency + + +function Chrom = crtrp(Nind,FieldDR); + +% Check parameter consistency + if nargin < 2, error('parameter FieldDR missing'); end + if nargin > 2, nargin = 2; end + + [mN, nN] = size(Nind); + [mF, Nvar] = size(FieldDR); + + if (mN ~= 1 & nN ~= 1), error('Nind has to be a scalar'); end + if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end + +% Compute Matrix with Range of variables and Matrix with Lower value + Range = rep((FieldDR(2,:)-FieldDR(1,:)),[Nind 1]); + Lower = rep(FieldDR(1,:), [Nind 1]); + +% Create initial population +% Each row contains one individual, the values of each variable uniformly +% distributed between lower and upper bound (given by FieldDR) + Chrom = rand(Nind,Nvar) .* Range + Lower; + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MIGRATE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MIGRATE.M" index 3aba7a1a0b52f47c0362456fbab46ce78ae5af9f..d5d122be6acc1030714d00d400456363c00a060d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MIGRATE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MIGRATE.M" @@ -1,3 +1,149 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8294ef22c9e4017f0b8f14ca16d39e04ff6a922b813b78f5bb7c3034d2efeeb3 -size 7205 +% MIGRATE.M (MIGRATion of individuals between subpopulations) +% +% This function performs migration of individuals. +% +% Syntax: [Chrom, ObjV] = migrate(Chrom, SUBPOP, MigOpt, ObjV) +% +% Input parameters: +% Chrom - Matrix containing the individuals of the current +% population. Each row corresponds to one individual. +% SUBPOP - Number of subpopulations +% MigOpt - (optional) Vector containing migration parameters +% MigOpt(1): MIGR - Rate of individuals to be migrated per +% subpopulation (% of subpopulation) +% if omitted or NaN, 0.2 (20%) is assumed +% MigOpt(2): Select - number indicating the selection method +% of replacing individuals +% 0 - uniform selection +% 1 - fitness-based selection (replace worst +% individuals) +% if omitted or NaN, 0 is assumed +% MigOpt(3): Structure - number indicating the structure +% of the subpopulations for migration +% 0 - net structure (unconstrained migration) +% 1 - neighbourhood structure +% 2 - ring structure +% if omitted or NaN, 0 is assumed +% ObjV - (optional) Column vector containing the objective values +% of the individuals in the current population, needed for +% fitness-based migration, this saves the +% recalculation of objective values for population. +% +% Output parameters: +% Chrom - Matrix containing the individuals of the current +% population after migration. +% ObjV - if ObjV is input parameter, than column vector containing +% the objective values of the individuals of the current +% generation after migration. + +% Author: Hartmut Pohlheim +% History: 16.02.94 file created +% 18.02.94 comments at the beginning added +% exchange of ObjV too +% 25.02.94 clean up +% 26.02.94 ObjV optional input parameter +% Select and Structure added, parameter reordered +% 17.03.94 renamed to migrate.m, more parameter checks + +function [Chrom, ObjV] = migrate(Chrom, SUBPOP, MigOpt, ObjV); + + +% Check parameter consistency + if nargin < 2, error('Input parameter SUBPOP missing'); end + if (nargout == 2 & nargin < 4), error('Input parameter ObjV missing'); end + + [Nind, Nvar] = size(Chrom); + if length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + if SUBPOP == 1, return; end + if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('Chrom and SUBPOP disagree'); end + NIND = Nind/SUBPOP; % Compute number of individuals per subpopulation + + if nargin > 3, + [mO, nO] = size(ObjV); + if nO ~= 1, error('ObjV must be a column vector'); end + if Nind ~= mO, error('Chrom and ObjV disagree'); end + IsObjV = 1; + else IsObjV = 0; ObjV = []; + end + + if nargin < 3, MIGR = 0.2; Select = 0; Structure = 0; end + if nargin > 2, + if isempty(MigOpt), MIGR = 0.2; Select = 0; Structure = 0; + elseif isnan(MigOpt), MIGR = 0.2; Select = 0; Structure = 0; + else + MIGR = NaN; Select = NaN; Structure = NaN; + if length(MigOpt) > 3, error('Parameter MigOpt is too long'); end + if length(MigOpt) >= 1, MIGR = MigOpt(1); end + if length(MigOpt) >= 2, Select = MigOpt(2); end + if length(MigOpt) >= 3, Structure = MigOpt(3); end + if isnan(MIGR), MIGR =0.2; end + if isnan(Select), Select = 0; end + if isnan(Structure), Structure = 0; end + end + end + + if (MIGR < 0 | MIGR > 1), error('Parameter for migration rate must be a scalar in [0 1]'); end + if (Select ~= 0 & Select ~= 1), error('Parameter for selection method must be 0 or 1'); end + if (Structure < 0 | Structure > 2), error ('Parameter for structure must be 0, 1 or 2'); end + if (Select == 1 & IsObjV == 0), error('ObjV for fitness-based migration needed');end + + if MIGR == 0, return; end + MigTeil = max(floor(NIND * MIGR), 1); % Number of individuals to migrate + +% Perform migration between subpopulations --> create a matrix for migration +% in every subpopulation from best individuals of the other subpopulations + + % Clear storing matrices + ChromMigAll = []; + if IsObjV == 1, ObjVAll = []; end + + % Create matrix with best/uniform individuals of all subpopulations + for irun = 1:SUBPOP + % sort ObjV of actual subpopulation + if Select == 1, % fitness-based selection + [Dummy, IndMigSo]=sort(ObjV((irun-1)*NIND+1:irun*NIND)); + else % if Select == 0 % uniform selection + [Dummy, IndMigSo]=sort(rand(NIND, 1)); + end + % take MigTeil (best) individuals, copy individuals and objective values + IndMigTeil=IndMigSo(1:MigTeil)+(irun-1)*NIND; + ChromMigAll = [ChromMigAll; Chrom(IndMigTeil,:)]; + if IsObjV == 1, ObjVAll = [ObjVAll; ObjV(IndMigTeil,:)]; end + end + + % perform migration + for irun = 1:SUBPOP + ChromMig = ChromMigAll; + if IsObjV == 1, ObjVMig = ObjVAll; end + if Structure == 1, % neighbourhood + % select individuals of neighbourhood subpopulations for ChromMig and ObjVMig + popnum = [SUBPOP 1:SUBPOP 1]; + ins1 = popnum(irun); ins2 = popnum(irun + 2); + InsRows = [(ins1-1)*MigTeil+1:ins1*MigTeil (ins2-1)*MigTeil+1:ins2*MigTeil]; + ChromMig = ChromMig(InsRows,:); + if IsObjV == 1, ObjVMig = ObjVMig(InsRows,:); end + elseif Structure == 2, % ring + % select individuals of actual-1 subpopulation for ChromMig and ObjVMig + popnum = [SUBPOP 1:SUBPOP 1]; + ins1 = popnum(irun); + InsRows = (ins1-1)*MigTeil+1:ins1*MigTeil; + ChromMig = ChromMig(InsRows,:); + if IsObjV == 1, ObjVMig = ObjVMig(InsRows,:); end + else % if Structure == 0, % complete net + % delete individuals of actual subpopulation from ChromMig and ObjVMig + DelRows = (irun-1)*MigTeil+1:irun*MigTeil; + ChromMig(DelRows,:) = []; + if IsObjV == 1, ObjVMig(DelRows,:) = []; end + end + % Create an index from a sorted vector with random numbers + [Dummy,IndMigRa]=sort(rand(size(ChromMig,1),1)); + % Take MigTeil numbers from the random vector + IndMigN=IndMigRa((1:MigTeil)'); + % copy MigTeil individuals into Chrom and ObjV + Chrom((1:MigTeil)+(irun-1)*NIND,:) = ChromMig(IndMigN,:); + if IsObjV == 1, ObjV((1:MigTeil)+(irun-1)*NIND,:) = ObjVMig(IndMigN,:); end + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MPGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MPGA.M" index 153850ca22ef86f5213b076f928a242deebe4615..47dc198b9e94f9974b5571ba40f963522f8fd54b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MPGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MPGA.M" @@ -1,3 +1,119 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3be3ef407462f6d47ada9326340791bb891df5a4e5cecd7e783b01e9b693b195 -size 4019 +% mpga multi population genetic algorithm +% +% This script implements the Multi Population Genetic Algorithm. +% A real-valued representation of the individuals is used. +% + +% Author: Andrew Chipperfield +% History: 30-Mar-94 file created + +NVAR = 20; % No. of decision variables (control steps) +RANGE = [0;200]; % Bounds on decision variables + +% Set field descriptor + FieldD = rep(RANGE,[1,NVAR]); + +% Define GA Parameters + GGAP = .8; % Generation gap, how many new individuals are created + XOVR = 1; % Crossover rate + MUTR = 1/NVAR; % Mutation rate depending on NVAR + MAXGEN = 1200; % Maximum number of generations + TERMEXACT = 1e-4; % Value for termination if minimum reached + INSR = .9; % Insertion rate, how many of the offspring are inserted + SUBPOP = 8; % Number of subpopulations + MIGR = 0.2; % Migration rate between subpopulations + MIGGEN = 20; % Number of generations between migration + NIND = 20; % Number of individuals per subpopulation + +% Specify other routines as strings + SEL_F = 'sus'; % Name of selection function + XOV_F = 'recdis'; % Name of recombination function for individuals + MUT_F = 'mutbga'; % Name of mutation function + OBJ_F = 'objharv'; % Name of function for objective values + + +% Get value of minimum, defined in objective function + GlobalMin = feval(OBJ_F,[],3); + +% Get title of objective function, defined in objective function + FigTitle = [feval(OBJ_F,[],2) ' (' int2str(SUBPOP) ':' int2str(MAXGEN) ') ']; + +% Clear Best and storing matrix + % Initialise Matrix for storing best results + Best = NaN * ones(MAXGEN,3); + Best(:,3) = zeros(size(Best,1),1); + % Matrix for storing best individuals + IndAll = []; + +% Create real population + Chrom = crtrp(SUBPOP*NIND,FieldD); + +% reset count variables + gen = 0; + +% Calculate objective function for population + ObjV = feval(OBJ_F,Chrom); + % count number of objective function evaluations + Best(gen+1,3) = Best(gen+1,3) + NIND; + +% Generational loop + while gen < MAXGEN, + + % Save the best and average objective values and the best individual + [Best(gen+1,1),ix] = min(ObjV); + Best(gen+1,2) = mean(ObjV); + IndAll = [IndAll; Chrom(ix,:)]; + + % Fitness assignment to whole population + FitnV = ranking(ObjV,2 ,SUBPOP); + + % Select individuals from population + SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); + + % Recombine selected individuals + SelCh=recombin(XOV_F, SelCh, XOVR, SUBPOP); + + % Mutate offspring + SelCh=mutate(MUT_F, SelCh, FieldD, [MUTR], SUBPOP); + + % Calculate objective function for offsprings + ObjVOff = feval(OBJ_F,SelCh); + Best(gen+1,3) = Best(gen+1,3) + size(SelCh,1); + + % Insert best offspring in population replacing worst parents + [Chrom, ObjV] = reins(Chrom, SelCh, SUBPOP, [1 INSR], ObjV, ObjVOff); + + gen=gen+1; + + % Plot some results, rename title of figure for graphic output + if ((rem(gen,20) == 1) | (rem(gen,MAXGEN) == 0)), + set(gcf,'Name',[FigTitle ' in ' int2str(gen)]); + resplot(Chrom(1:2:size(Chrom,1),:),... + IndAll(max(1,gen-39):size(IndAll,1),:),... + [ObjV; GlobalMin], Best(max(1,gen-19):gen,[1 2]), gen); + end + + + % migrate individuals between subpopulations + if (rem(gen,MIGGEN) == 0) + [Chrom, ObjV] = migrate(Chrom, SUBPOP, [MIGR, 1, 0], ObjV); + end + + end + + +% Results + % add number of objective function evaluations + Results = cumsum(Best(1:gen,3)); + % number of function evaluation, mean and best results + Results = [Results Best(1:gen,2) Best(1:gen,1)]; + +% Plot Results and show best individuals => optimum + figure('Name',['Results of ' FigTitle]); + subplot(2,1,1), plot(Results(:,1),Results(:,2),'-',Results(:,1),Results(:,3),':'); + subplot(2,1,2), plot(IndAll(gen-4:gen,:)'); + + +% End of script + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MUT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MUT.M" index 97670ab6d17e49a1cfc8ba383a6a22e2feebff1b..07e58149d6e75735021811ebf20a833c50bc081e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MUT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MUT.M" @@ -1,3 +1,54 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f5deb82096f3db334fb30159caacc236ae351eeb99cac69a4b214ed2f88d4d80 -size 1609 +% MUT.m +% +% This function takes the representation of the current population, +% mutates each element with given probability and returns the resulting +% population. +% +% Syntax: NewChrom = mut(OldChrom,Pm,BaseV) +% +% Input parameters: +% +% OldChrom - A matrix containing the chromosomes of the +% current population. Each row corresponds to +% an individuals string representation. +% +% Pm - Mutation probability (scalar). Default value +% of Pm = 0.7/Lind, where Lind is the chromosome +% length is assumed if omitted. +% +% BaseV - Optional row vector of the same length as the +% chromosome structure defining the base of the +% individual elements of the chromosome. Binary +% representation is assumed if omitted. +% +% Output parameter: +% +% NewChrom - A Matrix containing a mutated version of +% OldChrom. +% + +% Author: Andrew Chipperfield +% Date: 25-Jan-94 + +function NewChrom = mut(OldChrom,Pm,BaseV) + +% get population size (Nind) and chromosome length (Lind) +[Nind, Lind] = size(OldChrom) ; + +% check input parameters +if nargin < 2, Pm = 0.7/Lind ; end +if isnan(Pm), Pm = 0.7/Lind; end + +if (nargin < 3), BaseV = crtbase(Lind); end +if (isnan(BaseV)), BaseV = crtbase(Lind); end +if (isempty(BaseV)), BaseV = crtbase(Lind); end + +if (nargin == 3) & (Lind ~= length(BaseV)) + error('OldChrom and BaseV are incompatible'), end + +% create mutation mask matrix +BaseM = BaseV(ones(Nind,1),:) ; + +% perform mutation on chromosome structure +NewChrom = rem(OldChrom+(rand(Nind,Lind) 4, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('OldChrom and SUBPOP disagree'); end + Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation + +% Select individuals of one subpopulation and call low level function + NewChrom = []; + for irun = 1:SUBPOP, + ChromSub = OldChrom((irun-1)*Nind+1:irun*Nind,:); + if IsDiscret == 1, NewChromSub = feval(MUT_F, ChromSub, MutOpt, FieldDR); + elseif IsDiscret == 0, NewChromSub = feval(MUT_F, ChromSub, FieldDR, MutOpt); end + NewChrom=[NewChrom; NewChromSub]; + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MUTBGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MUTBGA.M" index e3bf6ec246c1647f5beb2c6df4510a94d17c8062..bf50a83f63d79bbcc154faf9d29b30d0e5e425c9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MUTBGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/MUTBGA.M" @@ -1,3 +1,113 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b9fe17257bc5a3c5ee901553861c8a13ca51711984d5e24a9dc8d76b391ddf53 -size 4943 +% MUTBGA.M (real-value MUTation like Breeder Genetic Algorithm) +% +% This function takes a matrix OldChrom containing the real +% representation of the individuals in the current population, +% mutates the individuals with probability MutR and returns +% the resulting population. +% +% This function implements the mutation operator of the Breeder Genetic +% Algorithm. (Muehlenbein et. al.) +% +% Syntax: NewChrom = mutbga(OldChrom, FieldDR, MutOpt) +% +% Input parameter: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual. +% FieldDR - Matrix describing the boundaries of each variable. +% MutOpt - (optional) Vector containing mutation rate and shrink value +% MutOpt(1): MutR - number containing the mutation rate - +% probability for mutation of a variable +% if omitted or NaN, MutR = 1/variables per individual +% is assumed +% MutOpt(2): MutShrink - (optional) number for shrinking the +% mutation range in the range [0 1], possibility to +% shrink the range of the mutation depending on, +% for instance actual generation. +% if omitted or NaN, MutShrink = 1 is assumed +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mutation in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 23.11.93 file created +% 24.11.93 function optimised (for,for-loop to for-loop) +% mutation rate included +% style improved +% 06.12.93 change of function name +% check of boundaries after mutation out of loop +% 16.12.93 NewMutMat and OldMutMat included for compability +% 16.02.94 preparation for multi-subpopulations at once +% 25.02.94 NewMutMat and OldMutMat removed (now in mutran10.m) +% clean up +% change of function name in mutbga.m +% 03.03.94 Lower and Upper directly used (less memory) +% 19.03.94 multipopulation support removed +% more parameter checks +% 27.03.94 Delta exact calculated, for loop saved + + +function NewChrom = mutbga(OldChrom, FieldDR, MutOpt); + +% Check parameter consistency + if nargin < 2, error('Not enough input parameter'); end + + % Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + + [mF, nF] = size(FieldDR); + if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end + if Nvar ~= nF, error('FieldDR and OldChrom disagree'); end + + if nargin < 3, MutR = 1/Nvar; MutShrink = 1; + elseif isempty(MutOpt), MutR = 1/Nvar; MutShrink = 1; + elseif isnan(MutOpt), MutR = 1/Nvar; MutShrink = 1; + else + if length(MutOpt) == 1, MutR = MutOpt; MutShrink = 1; + elseif length(MutOpt) == 2, MutR = MutOpt(1); MutShrink = MutOpt(2); + else, error(' Too many parameter in MutOpt'); end + end + + if isempty(MutR), MutR = 1/Nvar; + elseif isnan(MutR), MutR = 1/Nvar; + elseif length(MutR) ~= 1, error('Parameter for mutation rate must be a scalar'); + elseif (MutR < 0 | MutR > 1), error('Parameter for mutation rate must be a scalar in [0, 1]'); end + + if isempty(MutShrink), MutShrink = 1; + elseif isnan(MutShrink), MutShrink = 1; + elseif length(MutShrink) ~= 1, error('Parameter for shrinking mutation range must be a scalar'); + elseif (MutShrink < 0 | MutShrink > 1), + error('Parameter for shrinking mutation range must be a scalar in [0, 1]'); + end + +% the variables are mutated with probability MutR +% NewChrom = OldChrom (+ or -) * Range * MutShrink * Delta +% Range = 0.5 * (upperbound - lowerbound) +% Delta = Sum(Alpha_i * 2^-i) from 0 to ACCUR; Alpha_i = rand(ACCUR,1) < 1/ACCUR + +% Matrix with range values for every variable + Range = rep(0.5 * MutShrink *(FieldDR(2,:)-FieldDR(1,:)),[Nind 1]); + +% zeros and ones for mutate or not this variable, together with Range + Range = Range .* (rand(Nind,Nvar) < MutR); + +% compute, if + or - sign + Range = Range .* (1 - 2 * (rand(Nind,Nvar) < 0.5)); + +% used for later computing, here only ones computed + ACCUR = 20; + Vect = 2 .^ (-(0:(ACCUR-1))'); + Delta = (rand(Nind,ACCUR) < 1/ACCUR) * Vect; + Delta = rep(Delta, [1 Nvar]); + +% perform mutation + NewChrom = OldChrom + Range .* Delta; + +% Ensure variables boundaries, compare with lower and upper boundaries + NewChrom = max(rep(FieldDR(1,:),[Nind 1]), NewChrom); + NewChrom = min(rep(FieldDR(2,:),[Nind 1]), NewChrom); + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/OBJFUN1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/OBJFUN1.M" index da49989d1cd5d7f0468836d7b6aea9481f11973d..73dc9b465d7290d94ef8252f96fd1694bda1cc0f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/OBJFUN1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/OBJFUN1.M" @@ -1,3 +1,71 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:95863e65c0113af3f1400e6d4fbb0c3d376e840e9330202a38bf19551bb6ea9e -size 2629 +% OBJFUN1.M (OBJective function for De Jong's FUNction 1) +% +% This function implements the De Jong function 1. +% +% Syntax: ObjVal = objfun1(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 26.11.93 file created +% 27.11.93 text of title and switch added +% 30.11.93 show Dim in figure title +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objfun1(Chrom,switch); + +% Dimension of objective function + Dim = 20; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['DE JONG function 1-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = 100*[-5.12; 5.12]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 1, sum of xi^2 for i = 1:Dim (Dim=30) + % n = Dim, -5.12 <= xi <= 5.12 + % global minimum at (xi)=(0) ; fmin=0 + ObjVal = sum((Chrom .* Chrom)')'; + % ObjVal = diag(Chrom * Chrom'); % both lines produce the same + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/OBJHARV.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/OBJHARV.M" index 0a06fbddb9b0e6fca015f108a6138388f066a0c5..d056d7b3f9e7aa0e74085dfa58d2070ec0d9ccbd 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/OBJHARV.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/OBJHARV.M" @@ -1,3 +1,78 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a6208b888f3af5f91cd4717815f2702f3eba5edc0e9ef1fd36a98ae33d1ea36f -size 2559 +% OBJHARV.M (OBJective function for HARVest problem) +% +% This function implements the HARVEST PROBLEM. +% +% Syntax: ObjVal = objharv(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 18.02.94 file created (copy of vallinq.m) +% 01.03.94 name changed in obj* + +function ObjVal = objharv(Chrom,switch); + +% global gen; + +% Dimension of objective function + Dim = 20; + +% values from MICHALEWICZ + a = 1.1; + x0 = 100; + xend = x0; + XENDWEIGHT = 0.4/(Dim^0.6); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['HARVEST PROBLEM-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = -sqrt(x0*(a^Dim-1)^2/(a^(Dim-1)*(a-1))); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal1 = [0; 10*Dim]; + ObjVal = rep(ObjVal1,[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + ObjVal = zeros(Nind,1); + X = rep(x0,[Nind 1]); + for irun = 1:Nvar, + X = a*X - Chrom(:,irun); + end + X; + ObjVal = -(sum(sqrt(Chrom)')' - XENDWEIGHT * abs(X-x0)); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RANKING.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RANKING.M" index f816ea7d86d2051fb07ab800e0903630ded9bb70..af9127e20152816091ae4a8e88188e14a42bef1b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RANKING.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RANKING.M" @@ -1,3 +1,125 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:90523e59f9863d00812e95c0952b04e2064d7e08ca14dfa3830770cf580bb0bb -size 4709 +% RANKING.M (RANK-based fitness assignment) +% +% This function performs ranking of individuals. +% +% Syntax: FitnV = ranking(ObjV, RFun, SUBPOP) +% +% This function ranks individuals represented by their associated +% cost, to be *minimized*, and returns a column vector FitnV +% containing the corresponding individual fitnesses. For multiple +% subpopulations the ranking is performed separately for each +% subpopulation. +% +% Input parameters: +% ObjV - Column vector containing the objective values of the +% individuals in the current population (cost values). +% RFun - (optional) If RFun is a scalar in [1, 2] linear ranking is +% assumed and the scalar indicates the selective pressure. +% If RFun is a 2 element vector: +% RFun(1): SP - scalar indicating the selective pressure +% RFun(2): RM - ranking method +% RM = 0: linear ranking +% RM = 1: non-linear ranking +% If RFun is a vector with length(Rfun) > 2 it contains +% the fitness to be assigned to each rank. It should have +% the same length as ObjV. Usually RFun is monotonously +% increasing. +% If RFun is omitted or NaN, linear ranking +% and a selective pressure of 2 are assumed. +% SUBPOP - (optional) Number of subpopulations +% if omitted or NaN, 1 subpopulation is assumed +% +% Output parameters: +% FitnV - Column vector containing the fitness values of the +% individuals in the current population. +% + +% Author: Hartmut Pohlheim (Carlos Fonseca) +% History: 01.03.94 non-linear ranking +% 10.03.94 multiple populations + +function FitnV = ranking(ObjV, RFun, SUBPOP); + +% Identify the vector size (Nind) + [Nind,ans] = size(ObjV); + + if nargin < 2, RFun = []; end + if nargin > 1, if isnan(RFun), RFun = []; end, end + if prod(size(RFun)) == 2, + if RFun(2) == 1, NonLin = 1; + elseif RFun(2) == 0, NonLin = 0; + else error('Parameter for ranking method must be 0 or 1'); end + RFun = RFun(1); + if isnan(RFun), RFun = 2; end + elseif prod(size(RFun)) > 2, + if prod(size(RFun)) ~= Nind, error('ObjV and RFun disagree'); end + end + + if nargin < 3, SUBPOP = 1; end + if nargin > 2, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('ObjV and SUBPOP disagree'); end + Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation + +% Check ranking function and use default values if necessary + if isempty(RFun), + % linear ranking with selective pressure 2 + RFun = 2*[0:Nind-1]'/(Nind-1); + elseif prod(size(RFun)) == 1 + if NonLin == 1, + % non-linear ranking + if RFun(1) < 1, error('Selective pressure must be greater than 1'); + elseif RFun(1) > Nind-2, error('Selective pressure too big'); end + Root1 = roots([RFun(1)-Nind [RFun(1)*ones(1,Nind-1)]]); + RFun = (abs(Root1(1)) * ones(Nind,1)) .^ [(0:Nind-1)']; + RFun = RFun / sum(RFun) * Nind; + else + % linear ranking with SP between 1 and 2 + if (RFun(1) < 1 | RFun(1) > 2), + error('Selective pressure for linear ranking must be between 1 and 2'); + end + RFun = 2-RFun + 2*(RFun-1)*[0:Nind-1]'/(Nind-1); + end + end; + + FitnV = []; + +% loop over all subpopulations +for irun = 1:SUBPOP, + % Copy objective values of actual subpopulation + ObjVSub = ObjV((irun-1)*Nind+1:irun*Nind); + % Sort does not handle NaN values as required. So, find those... + NaNix = isnan(ObjVSub); + Validix = find(~NaNix); + % ... and sort only numeric values (smaller is better). + [ans,ix] = sort(-ObjVSub(Validix)); + + % Now build indexing vector assuming NaN are worse than numbers, + % (including Inf!)... + ix = [find(NaNix) ; Validix(ix)]; + % ... and obtain a sorted version of ObjV + Sorted = ObjVSub(ix); + + % Assign fitness according to RFun. + i = 1; + FitnVSub = zeros(Nind,1); + for j = [find(Sorted(1:Nind-1) ~= Sorted(2:Nind)); Nind]', + FitnVSub(i:j) = sum(RFun(i:j)) * ones(j-i+1,1) / (j-i+1); + i =j+1; + end + + % Finally, return unsorted vector. + [ans,uix] = sort(ix); + FitnVSub = FitnVSub(uix); + + % Add FitnVSub to FitnV + FitnV = [FitnV; FitnVSub]; +end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECDIS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECDIS.M" index 06de83a8ed1662c5b1bbdb70d2676354f073e28b..0c6ed8a67af00986661aa95b81d94f9a04ead856 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECDIS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECDIS.M" @@ -1,3 +1,52 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3509a126379548e879abb7f9eec4abb67786958f23516a46bc0ea71a44354d0d -size 1825 +% RECDIS.M (RECombination DIScrete) +% +% This function performs discret recombination between pairs of individuals +% and returns the new individuals after mating. +% +% Syntax: NewChrom = recdis(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real-values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. (not used, only for compatibility) +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 23.11.93 file created +% 24.11.93 style improved +% 06.12.93 change of name of function +% 25.02.94 clean up +% 19.03.94 multipopulation support removed + +function NewChrom = recdis(OldChrom, XOVR); + +% Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + +% Identify the number of matings + Xops = floor(Nind/2); + +% which parent gives the value + Mask1 = (rand(Xops,Nvar)<0.5); + Mask2 = (rand(Xops,Nvar)<0.5); + +% Performs crossover + odd = 1:2:Nind-1; + even= 2:2:Nind; + NewChrom(odd,:) = (OldChrom(odd,:).* Mask1) + (OldChrom(even,:).*(~Mask1)); + NewChrom(even,:) = (OldChrom(odd,:).* Mask2) + (OldChrom(even,:).*(~Mask2)); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population + if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECINT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECINT.M" index 7d9aafbbf73a550417eb34b56486dbe19edacb92..cac6d76a3d5f4a48ca82601e2b13d4d1e2bf3e0e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECINT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECINT.M" @@ -1,3 +1,55 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f28039ff4addb00e9527bb5c81eb6c73fdf542b9ebe15a9b929cca771cf5cd0b -size 1895 +% RECINT.M (RECombination extended INTermediate) +% +% This function performs extended intermediate recombination between +% pairs of individuals and returns the new individuals after mating. +% +% Syntax: NewChrom = recint(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one +% individual +% XOVR - Probability of crossover occurring between pairs +% of individuals. (not used, only for compatibility) +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 06.12.93 change of name of function +% 25.02.94 clean up +% 19.03.94 multipopulation support removed + +function NewChrom = recint(OldChrom, XOVR); + +% Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + +% Identify the number of matings + Xops = floor(Nind/2); + +% Performs recombination + odd = 1:2:Nind-1; + even= 2:2:Nind; + + % position of value of offspring compared to parents + Alpha = -0.25 + 1.5 * rand(Xops,Nvar); + + % recombination + NewChrom(odd,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); + + % the same ones more for second half of offspring + Alpha = -0.25 + 1.5 * rand(Xops,Nvar); + NewChrom(even,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population + if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECLIN.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECLIN.M" index 721f62b4d5ded537ccf9c9369e09975bc92db245..d76084444d778b795004e0f8042442dd8a5e8654 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECLIN.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECLIN.M" @@ -1,3 +1,57 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:34f0a46f19e514e77b173b8841a91e686cef0a5f864c3dff6725cb4ab59ff861 -size 1953 +% RECLIN.M (RECombination extended LINe) +% +% This function performs extended line recombination between +% pairs of individuals and returns the new individuals after mating. +% +% Syntax: NewChrom = reclin(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one +% individual +% XOVR - Probability of crossover occurring between pairs +% of individuals. (not used, only for compatibility) +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 26.11.93 file created +% 06.12.93 change of name of function +% 25.02.94 clean up +% 19.03.94 multipopulation support removed + +function NewChrom = reclin(OldChrom, XOVR); + +% Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + +% Identify the number of matings + Xops = floor(Nind/2); + +% Performs recombination + odd = 1:2:Nind-1; + even= 2:2:Nind; + + % position of value of offspring compared to parents + Alpha = -0.25 + 1.5 * rand(Xops,1); + Alpha = Alpha(1:Xops,ones(Nvar,1)); + + % recombination + NewChrom(odd,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); + + % the same ones more for second half of offspring + Alpha = -0.25 + 1.5 * rand(Xops,1); + Alpha = Alpha(1:Xops,ones(Nvar,1)); + NewChrom(even,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population + if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECMUT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECMUT.M" index a2447ff5122359772a59db31f3b7cce1c1f6d574..12642cb9125aafaa9729e24def4504d0ace42335 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECMUT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECMUT.M" @@ -1,3 +1,118 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1dba80855d9d825d038f939d30b7cddb249dc460ae0b449d0cf6cb9f6a4bc738 -size 4852 +% RECLIN.M (line RECombination with MUTation features) +% +% This function performs line recombination with mutation features between +% pairs of individuals and returns the new individuals after mating. +% +% Syntax: NewChrom = recmut(OldChrom, FieldDR, MutOpt) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% FieldDR - Matrix describing the boundaries of each variable. +% MutOpt - (optional) Vector containing recombination rate and shrink value +% MutOpt(1): MutR - number containing the recombination rate - +% probability for recombine a pair of parents +% if omitted or NaN, MutOpt(1) = 1 is assumed +% MutOpt(2): MutShrink - (optional) number for shrinking the +% recombination range in the range [0 1], possibility to +% shrink the range of the recombination depending on, +% for instance actual generation. +% if omitted or NaN, MutOpt(2) = 1 is assumed +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 27.03.94 file created + +function NewChrom = recmut(OldChrom, FieldDR, MutOpt); + +% Check parameter consistency + if nargin < 2, error('Not enough input parameter'); end + + % Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + + [mF, nF] = size(FieldDR); + if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end + if Nvar ~= nF, error('FieldDR and OldChrom disagree'); end + + if nargin < 3, MutR = 1; MutShrink = 1; + elseif isempty(MutOpt), MutR = 1; MutShrink = 1; + elseif isnan(MutOpt), MutR = 1; MutShrink = 1; + else + if length(MutOpt) == 1, MutR = MutOpt; MutShrink = 1; + elseif length(MutOpt) == 2, MutR = MutOpt(1); MutShrink = MutOpt(2); + else, error(' Too many parameter in MutOpt'); end + end + + if isempty(MutR), MutR = 1; + elseif isnan(MutR), MutR = 1; + elseif length(MutR) ~= 1, error('Parameter for recombination rate must be a scalar'); + elseif (MutR < 0 | MutR > 1), error('Parameter for recombination rate must be a scalar in [0, 1]'); end + + if isempty(MutShrink), MutShrink = 1; + elseif isnan(MutShrink), MutShrink = 1; + elseif length(MutShrink) ~= 1, error('Parameter for shrinking recombination range must be a scalar'); + elseif (MutShrink < 0 | MutShrink > 1), + error('Parameter for shrinking recombination range must be a scalar in [0, 1]'); + end + +% Identify the number of matings + Xops = floor(Nind/2); + +% NewChrom = OldChrom (+ or -) * Range * MutShrink * Delta * ChromDiff +% - with probability 0.9, + with probability 0.1 +% Range = 0.5 * (upperbound - lowerbound), given by FieldDR +% Delta = Sum(Alpha_i * 2^-i) from 0 to ACCUR; Alpha_i = rand(ACCUR,1) < 1/ACCUR +% ChromDiff = (individual1 - individual2) / Distance between individuals + +% Matrix with range values for every variable + Range = rep(0.5 * MutShrink *(FieldDR(2,:)-FieldDR(1,:)),[Xops 1]); + +% zeros and ones for recombine or not this variable, together with Range + if MutR < 1, Range = Range .* rep((rand(Xops,1) < MutR), [1 Nvar]); end + +% compute, if + or - sign + Range = Range .* (1 - 2 * (rand(Xops,Nvar) < 0.9)); + +% compute distance between mating pairs + NormO = zeros(Xops,1); + for irun = 1:Xops, + NormO(irun) = max(realmin,abs(norm(OldChrom(2*irun,:)) - norm(OldChrom(2*irun-1,:)))); + end + +% compute difference between variables divided by distance + ChromDiff = zeros(Xops,Nvar); + for irun = 1:Xops + ChromDiff(irun,:) = diff([OldChrom(2*irun-1,:); OldChrom(2*irun,:)]) / NormO(irun); + end + +% compute delta value for all individuals + ACCUR = 20; + Vect = 2 .^ (-(0:(ACCUR-1))'); + Delta = (rand(Xops,ACCUR) < 1/ACCUR) * Vect; + Delta = rep(Delta, [1 Nvar]); + +% Performs recombination + odd = 1:2:Nind-1; + even= 2:2:Nind; + + % recombination + NewChrom(odd,:) = OldChrom(odd,:) + Range .* Delta .* (ChromDiff); + NewChrom(even,:) = OldChrom(even,:) + Range .* Delta .* (-ChromDiff); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population + if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end + +% Ensure variables boundaries, compare with lower and upper boundaries + NewChrom = max(rep(FieldDR(1,:),[Nind 1]), NewChrom); + NewChrom = min(rep(FieldDR(2,:),[Nind 1]), NewChrom); + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECOMBIN.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECOMBIN.M" index 760a482ee729bee15d30775766209361a64cdb54..9c47af9e83f9ddb26eb58828fef7ac404ac25760 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECOMBIN.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RECOMBIN.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1beb08befa03089753f61e6daa8117587823cc59d2e0949e5f78fc4cfa2db767 -size 2438 +% RECOMBIN.M (RECOMBINation high-level function) +% +% This function performs recombination between pairs of individuals +% and returns the new individuals after mating. The function handles +% multiple populations and calls the low-level recombination function +% for the actual recombination process. +% +% Syntax: NewChrom = recombin(REC_F, OldChrom, RecOpt, SUBPOP) +% +% Input parameters: +% REC_F - String containing the name of the recombination or +% crossover function +% Chrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% RecOpt - (optional) Scalar containing the probability of +% recombination/crossover occurring between pairs +% of individuals. +% if omitted or NaN, 1 is assumed +% SUBPOP - (optional) Number of subpopulations +% if omitted or NaN, 1 subpopulation is assumed +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after recombination in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 18.03.94 file created + + +function NewChrom = recombin(REC_F, Chrom, RecOpt, SUBPOP); + + +% Check parameter consistency + if nargin < 2, error('Not enough input parameter'); end + + % Identify the population size (Nind) + [Nind,Nvar] = size(Chrom); + + if nargin < 4, SUBPOP = 1; end + if nargin > 3, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('Chrom and SUBPOP disagree'); end + Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation + + if nargin < 3, RecOpt = 0.7; end + if nargin > 2, + if isempty(RecOpt), RecOpt = 0.7; + elseif isnan(RecOpt), RecOpt = 0.7; + elseif length(RecOpt) ~= 1, error('RecOpt must be a scalar'); + elseif (RecOpt < 0 | RecOpt > 1), error('RecOpt must be a scalar in [0, 1]'); end + end + + +% Select individuals of one subpopulation and call low level function + NewChrom = []; + for irun = 1:SUBPOP, + ChromSub = Chrom((irun-1)*Nind+1:irun*Nind,:); + NewChromSub = feval(REC_F, ChromSub, RecOpt); + NewChrom=[NewChrom; NewChromSub]; + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/REINS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/REINS.M" index fc150a058d9411f715e8b425ec400e966f0836c8..87074fbe810db520bc05b7978065adcac19f7af9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/REINS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/REINS.M" @@ -1,3 +1,123 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3f260e5b26029fd5b658901251e50c7c6c66ec858682f07c14ad986a44fda98d -size 5574 +% REINS.M (RE-INSertion of offspring in population replacing parents) +% +% This function reinserts offspring in the population. +% +% Syntax: [Chrom, ObjVCh] = reins(Chrom, SelCh, SUBPOP, InsOpt, ObjVCh, ObjVSel) +% +% Input parameters: +% Chrom - Matrix containing the individuals (parents) of the current +% population. Each row corresponds to one individual. +% SelCh - Matrix containing the offspring of the current +% population. Each row corresponds to one individual. +% SUBPOP - (optional) Number of subpopulations +% if omitted or NaN, 1 subpopulation is assumed +% InsOpt - (optional) Vector containing the insertion method parameters +% ExOpt(1): Select - number indicating kind of insertion +% 0 - uniform insertion +% 1 - fitness-based insertion +% if omitted or NaN, 0 is assumed +% ExOpt(2): INSR - Rate of offspring to be inserted per +% subpopulation (% of subpopulation) +% if omitted or NaN, 1.0 (100%) is assumed +% ObjVCh - (optional) Column vector containing the objective values +% of the individuals (parents - Chrom) in the current +% population, needed for fitness-based insertion +% saves recalculation of objective values for population +% ObjVSel - (optional) Column vector containing the objective values +% of the offspring (SelCh) in the current population, needed for +% partial insertion of offspring, +% saves recalculation of objective values for population +% +% Output parameters: +% Chrom - Matrix containing the individuals of the current +% population after reinsertion. +% ObjVCh - if ObjVCh and ObjVSel are input parameter, than column +% vector containing the objective values of the individuals +% of the current generation after reinsertion. + +% Author: Hartmut Pohlheim +% History: 10.03.94 file created +% 19.03.94 parameter checking improved + +function [Chrom, ObjVCh] = reins(Chrom, SelCh, SUBPOP, InsOpt, ObjVCh, ObjVSel); + + +% Check parameter consistency + if nargin < 2, error('Not enough input parameter'); end + if (nargout == 2 & nargin < 6), error('Input parameter missing: ObjVCh and/or ObjVSel'); end + + [NindP, NvarP] = size(Chrom); + [NindO, NvarO] = size(SelCh); + + if nargin == 2, SUBPOP = 1; end + if nargin > 2, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (NindP/SUBPOP) ~= fix(NindP/SUBPOP), error('Chrom and SUBPOP disagree'); end + if (NindO/SUBPOP) ~= fix(NindO/SUBPOP), error('SelCh and SUBPOP disagree'); end + NIND = NindP/SUBPOP; % Compute number of individuals per subpopulation + NSEL = NindO/SUBPOP; % Compute number of offspring per subpopulation + + IsObjVCh = 0; IsObjVSel = 0; + if nargin > 4, + [mO, nO] = size(ObjVCh); + if nO ~= 1, error('ObjVCh must be a column vector'); end + if NindP ~= mO, error('Chrom and ObjVCh disagree'); end + IsObjVCh = 1; + end + if nargin > 5, + [mO, nO] = size(ObjVSel); + if nO ~= 1, error('ObjVSel must be a column vector'); end + if NindO ~= mO, error('SelCh and ObjVSel disagree'); end + IsObjVSel = 1; + end + + if nargin < 4, INSR = 1.0; Select = 0; end + if nargin >= 4, + if isempty(InsOpt), INSR = 1.0; Select = 0; + elseif isnan(InsOpt), INSR = 1.0; Select = 0; + else + INSR = NaN; Select = NaN; + if (length(InsOpt) > 2), error('Parameter InsOpt too long'); end + if (length(InsOpt) >= 1), Select = InsOpt(1); end + if (length(InsOpt) >= 2), INSR = InsOpt(2); end + if isnan(Select), Select = 0; end + if isnan(INSR), INSR =1.0; end + end + end + + if (INSR < 0 | INSR > 1), error('Parameter for insertion rate must be a scalar in [0, 1]'); end + if (INSR < 1 & IsObjVSel ~= 1), error('For selection of offspring ObjVSel is needed'); end + if (Select ~= 0 & Select ~= 1), error('Parameter for selection method must be 0 or 1'); end + if (Select == 1 & IsObjVCh == 0), error('ObjVCh for fitness-based exchange needed'); end + + if INSR == 0, return; end + NIns = min(max(floor(INSR*NSEL+.5),1),NIND); % Number of offspring to insert + +% perform insertion for each subpopulation + for irun = 1:SUBPOP, + % Calculate positions in old subpopulation, where offspring are inserted + if Select == 1, % fitness-based reinsertion + [Dummy, ChIx] = sort(-ObjVCh((irun-1)*NIND+1:irun*NIND)); + else % uniform reinsertion + [Dummy, ChIx] = sort(rand(NIND,1)); + end + PopIx = ChIx((1:NIns)')+ (irun-1)*NIND; + % Calculate position of Nins-% best offspring + if (NIns < NSEL), % select best offspring + [Dummy,OffIx] = sort(ObjVSel((irun-1)*NSEL+1:irun*NSEL)); + else + OffIx = (1:NIns)'; + end + SelIx = OffIx((1:NIns)')+(irun-1)*NSEL; + % Insert offspring in subpopulation -> new subpopulation + Chrom(PopIx,:) = SelCh(SelIx,:); + if (IsObjVCh == 1 & IsObjVSel == 1), ObjVCh(PopIx) = ObjVSel(SelIx); end + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/REP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/REP.M" index ba187d520acfadd5aa12492f6861b2f74094cff6..9255c007f35ec19293b0a3abbeed12f5e6829db1 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/REP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/REP.M" @@ -1,3 +1,46 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:78ec47d1d557452415eae600d8b8bfb01621fc1a319e1f8c8e62d45b887ef7c7 -size 1208 +% REP.m Replicate a matrix +% +% This function replicates a matrix in both dimensions. +% +% Syntax: MatOut = rep(MatIn,REPN); +% +% Input parameters: +% MatIn - Input Matrix (before replicating) +% +% REPN - Vector of 2 numbers, how many replications in each dimension +% REPN(1): replicate vertically +% REPN(2): replicate horizontally +% +% Example: +% +% MatIn = [1 2 3] +% REPN = [1 2]: MatOut = [1 2 3 1 2 3] +% REPN = [2 1]: MatOut = [1 2 3; +% 1 2 3] +% REPN = [3 2]: MatOut = [1 2 3 1 2 3; +% 1 2 3 1 2 3; +% 1 2 3 1 2 3] +% +% Output parameter: +% MatOut - Output Matrix (after replicating) +% + +% Author: Carlos Fonseca & Hartmut Pohlheim +% History: 14.02.94 file created + + +function MatOut = rep(MatIn,REPN) + +% Get size of input matrix + [N_D,N_L] = size(MatIn); + +% Calculate + Ind_D = rem(0:REPN(1)*N_D-1,N_D) + 1; + Ind_L = rem(0:REPN(2)*N_L-1,N_L) + 1; + +% Create output matrix + MatOut = MatIn(Ind_D,Ind_L); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RESPLOT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RESPLOT.M" index dd669edea0aa1ce64db0c9e5e2ad3c1feb6fc9a1..f7ee499f07fed7997d04dc353d0e5662081c9a3b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RESPLOT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RESPLOT.M" @@ -1,3 +1,56 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f1c65ba1bd79521d9bd0ce65a2a5381bed89e3e767071ca11c95dd781c637622 -size 2080 +% RESPLOT.M (RESult PLOTing) +% +% This function plots some results during computation. +% +% Syntax: resplot(Chrom,IndAll,ObjV,Best,gen) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each line corresponds to one individual. +% IndAll - Matrix containing the best individual (variables) of each +% generation. Each line corresponds to one individual. +% ObjV - Vector containing objective values of the current +% generation +% Best - Matrix containing the best and average Objective values of +% each generation, [best value per generation,average value +% per generation] +% gen - Scalar containing the number of the current generation +% +% Output parameter: +% no output parameter + +% Author: Hartmut Pohlheim +% History: 27.11.93 file created +% 29.11.93 decision, if plot or not deleted +% yscale not log +% 15.12.93 MutMatrix as parameter and plot added +% 16.03.94 function cleaned, MutMatrix removed, IndAll added + +function resplot(Chrom,IndAll,ObjV,Best,gen); + + % plot of best and mean value per generation + subplot(2,2,1), plot(Best); + title('Best and mean objective value'); + xlabel('generation'), ylabel('objective value'); + + % plot of best individuals in all generations + subplot(2,2,2), plot(IndAll); + title(['Best individuals']); + xlabel('generation'), ylabel('value of variable'); + + % plot of variables of all individuals in current generation + subplot(2,2,3), plot(Chrom'); + title(['All individuals in gen ',num2str(gen)]); + xlabel('number of variable'), ylabel('value of variable'); + + % plot of all objective values in current generation + subplot(2,2,4), plot(ObjV,'y.'); + title(['All objective values']); + xlabel('number of individual'), ylabel('objective value'); + + drawnow; + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RWS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RWS.M" index cf4492cf5a6688a9b9ec9c0c9480172a101cdd56..f6d5c146d5cea92cee0d560fac2cfadb4397d9c4 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RWS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/RWS.M" @@ -1,3 +1,31 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1b6fe643ae24bb2a32e135ec0f2d88a2b0b62fa7261b19b427315020161ce7e2 -size 1090 +% RWS.m - Roulette Wheel Selection +% +% Syntax: +% NewChrIx = rws(FitnV, Nsel) +% +% This function selects a given number of individuals Nsel from a +% population. FitnV is a column vector containing the fitness +% values of the individuals in the population. +% +% The function returns another column vector containing the +% indexes of the new generation of chromosomes relative to the +% original population matrix, shuffled. The new population, ready +% for mating, can be obtained by calculating +% OldChrom(NewChrIx, :). + +% Author: Carlos Fonseca, Updated: Andrew Chipperfield +% Date: 04/10/93, Date: 27-Jan-94 + +function NewChrIx = rws(FitnV,Nsel); + +% Identify the population size (Nind) +[Nind,ans] = size(FitnV); + +% Perform Stochastic Sampling with Replacement +cumfit = cumsum(FitnV); +trials = cumfit(Nind) .* rand(Nsel, 1); +Mf = cumfit(:, ones(1, Nsel)); +Mt = trials(:, ones(1, Nind))'; +[NewChrIx, ans] = find(Mt < Mf & ... + [ zeros(1, Nsel); Mf(1:Nind-1, :) ] <= Mt); + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SCALING.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SCALING.M" index 63238cf32b4aa039a9d27dbcc84843a125aea408..fe854dacc550cd57add8e1c9d7ce5d752c347a69 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SCALING.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SCALING.M" @@ -1,3 +1,52 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9f95050c5b2cedddd9606d27edcf0515f83f9b2fec85a1090d30180e24b0a09b -size 1270 +% SCALING.m - linear fitness scaling +% +% This function implements a linear fitness scaling algorithm as described +% by Goldberg in "Genetic Algorithms in Search, Optimization and Machine +% Learning", Addison Wesley, 1989. It use is not recommended when fitness +% functions produce negative results as the scaling will become unreliable. +% It is included in this version of the GA Toolbox only for the sake of +% completeness. +% +% Syntax: FitnV = scaling(ObjV, Smul) +% +% Input parameters: +% +% Objv - A vector containing the values of individuals +% fitness. +% +% Smul - Optional scaling parameter (default 2). +% +% Output parameters: +% +% FitnV - A vector containing the individual fitnesses +% for the current population. +% +% + +% Author: Andrew Chipperfield +% Date: 24-Feb-94 + + +function FitnV = scaling( ObjV, Smul ) + +if nargin == 1 + Smul = 2 ; +end + +[Nind, Nobj] = size( ObjV ) ; +Oave = sum( ObjV ) / Nind ; +Omin = min( ObjV ) ; +Omax = max( ObjV ) ; + +if (Omin > ( Smul * Oave - Omax ) / ( Smul - 1.0 )) + delta = Omax - Oave + a = ( Smul - 1.0 ) * Oave / delta + b = Oave * ( Omax - Smul * Oave ) / delta +else + delta = Oave - Omin ; + a = Oave / delta ; + b = -Omin * Oave / delta ; +end + +FitnV = ObjV.*a + b ; + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SELECT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SELECT.M" index 0c07bdf5a26a41687e8ba64a5b74b82505c28917..627fb50670a6f88d991badf5802655b60849f39a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SELECT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SELECT.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:93e9c1b839da6ecb637ea9004d21115ecb1084036ee1372172393ad8da6588be -size 2401 +% SELECT.M (universal SELECTion) +% +% This function performs universal selection. The function handles +% multiple populations and calls the low level selection function +% for the actual selection process. + +% +% Syntax: SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP) +% +% Input parameters: +% SEL_F - Name of the selection function +% Chrom - Matrix containing the individuals (parents) of the current +% population. Each row corresponds to one individual. +% FitnV - Column vector containing the fitness values of the +% individuals in the population. +% GGAP - (optional) Rate of individuals to be selected +% if omitted 1.0 is assumed +% SUBPOP - (optional) Number of subpopulations +% if omitted 1 subpopulation is assumed +% +% Output parameters: +% SelCh - Matrix containing the selected individuals. + +% Author: Hartmut Pohlheim +% History: 10.03.94 file created + +function SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); + +% Check parameter consistency + if nargin < 3, error('Not enough input parameter'); end + + % Identify the population size (Nind) + [NindCh,Nvar] = size(Chrom); + [NindF,VarF] = size(FitnV); + if NindCh ~= NindF, error('Chrom and FitnV disagree'); end + if VarF ~= 1, error('FitnV must be a column vector'); end + + if nargin < 5, SUBPOP = 1; end + if nargin > 4, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (NindCh/SUBPOP) ~= fix(NindCh/SUBPOP), error('Chrom and SUBPOP disagree'); end + Nind = NindCh/SUBPOP; % Compute number of individuals per subpopulation + + if nargin < 4, GGAP = 1; end + if nargin > 3, + if isempty(GGAP), GGAP = 1; + elseif isnan(GGAP), GGAP = 1; + elseif length(GGAP) ~= 1, error('GGAP must be a scalar'); + elseif (GGAP < 0), error('GGAP must be a scalar bigger than 0'); end + end + +% Compute number of new individuals (to select) + NSel=max(floor(Nind*GGAP+.5),2); + +% Select individuals from population + SelCh = []; + for irun = 1:SUBPOP, + FitnVSub = FitnV((irun-1)*Nind+1:irun*Nind); + ChrIx=feval(SEL_F, FitnVSub, NSel)+(irun-1)*Nind; + SelCh=[SelCh; Chrom(ChrIx,:)]; + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SGA.M" index a4af7ee703999c688081450150f035bb8c700c88..f01cd948dda399b04bca0504e66130f036e4f77a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SGA.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ed469760636b72242f946ec8e3a852688c48ba5f6059ae2835a4fff3bda61b56 -size 2143 +% sga +% +% This script implements the Simple Genetic Algorithm described +% in the examples section of the GA Toolbox manual. +% + +% Author: Andrew Chipperfield +% History: 23-Mar-94 file created + + +NIND = 40; % Number of individuals per subpopulations +MAXGEN = 300; % maximum Number of generations +GGAP = .9; % Generation gap, how many new individuals are created +NVAR = 20; % Generation gap, how many new individuals are created +PRECI = 20; % Precision of binary representation + +% Build field descriptor + FieldD = [rep([PRECI],[1, NVAR]); rep([-512;512],[1, NVAR]);... + rep([1; 0; 1 ;1], [1, NVAR])]; + +% Initialise population + Chrom = crtbp(NIND, NVAR*PRECI); + +% Reset counters + Best = NaN*ones(MAXGEN,1); % best in current population + gen = 0; % generational counter + +% Evaluate initial population + ObjV = objfun1(bs2rv(Chrom,FieldD)); + +% Track best individual and display convergence + Best(gen+1) = min(ObjV); + plot(log10(Best),'ro');xlabel('generation'); ylabel('log10(f(x))'); + text(0.5,0.95,['Best = ', num2str(Best(gen+1))],'Units','normalized'); + drawnow; + + +% Generational loop + while gen < MAXGEN, + + % Assign fitness-value to entire population + FitnV = ranking(ObjV); + + % Select individuals for breeding + SelCh = select('sus', Chrom, FitnV, GGAP); + + % Recombine selected individuals (crossover) + SelCh = recombin('xovsp',SelCh,0.7); + + % Perform mutation on offspring + SelCh = mut(SelCh); + + % Evaluate offspring, call objective function + ObjVSel = objfun1(bs2rv(SelCh,FieldD)); + + % Reinsert offspring into current population + [Chrom ObjV]=reins(Chrom,SelCh,1,1,ObjV,ObjVSel); + + % Increment generational counter + gen = gen+1; + + % Update display and record current best individual + Best(gen+1) = min(ObjV); + plot(log10(Best),'ro'); xlabel('generation'); ylabel('log10(f(x))'); + text(0.5,0.95,['Best = ', num2str(Best(gen+1))],'Units','normalized'); + drawnow; + end +% End of GA + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SUS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SUS.M" index c2c69374c32708ede202103d0a783a53d3c7d5f2..89f38577421926d597bc7ed205077935033220ad 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SUS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/SUS.M" @@ -1,3 +1,41 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2b10ad5906524d4e218787b0fb5d1f3c52c24cc66dc847d05fd714d0f0b01d9a -size 1319 +% SUS.M (Stochastic Universal Sampling) +% +% This function performs selection with STOCHASTIC UNIVERSAL SAMPLING. +% +% Syntax: NewChrIx = sus(FitnV, Nsel) +% +% Input parameters: +% FitnV - Column vector containing the fitness values of the +% individuals in the population. +% Nsel - number of individuals to be selected +% +% Output parameters: +% NewChrIx - column vector containing the indexes of the selected +% individuals relative to the original population, shuffled. +% The new population, ready for mating, can be obtained +% by calculating OldChrom(NewChrIx,:). + +% Author: Hartmut Pohlheim (Carlos Fonseca) +% History: 12.12.93 file created +% 22.02.94 clean up, comments + + +function NewChrIx = sus(FitnV,Nsel); + +% Identify the population size (Nind) + [Nind,ans] = size(FitnV); + +% Perform stochastic universal sampling + cumfit = cumsum(FitnV); + trials = cumfit(Nind) / Nsel * (rand + (0:Nsel-1)'); + Mf = cumfit(:, ones(1, Nsel)); + Mt = trials(:, ones(1, Nind))'; + [NewChrIx, ans] = find(Mt < Mf & [ zeros(1, Nsel); Mf(1:Nind-1, :) ] <= Mt); + +% Shuffle new population + [ans, shuf] = sort(rand(Nsel, 1)); + NewChrIx = NewChrIx(shuf); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/DEMOGA1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/DEMOGA1.M" index 24fe9f60580009447a287314da5bcb113ae8820f..84cdcafa128f15fc5ddadf499aa5e8f7165e0168 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/DEMOGA1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/DEMOGA1.M" @@ -1,3 +1,118 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8c93f0a6c891265b64430b43ee597e54872267bde5189c2200cec9397548cb01 -size 5035 +% DEMOGA1.M (DEMO of Genetic Algorithms 1) +% +% This function displays a number of figures. Select a number of these +% figures with the mouse by click in the area of the shape. These +% figure are the parents for the next generation. The offspring are +% created by recombination and mutation. The user is the selector. +% +% The shape of the figures is defined by Points X- and Y-values each. +% These points are ploted by patch(), each figure in a rectangle. +% The X- and Y-values are the variables of a individual. +% +% Aim of this demo is, to "construct" a special figure, e.g. a square +% or a star or ..., imagine, what you want and select appropriate. +% +% Parameters inside function for changing: +% Num - Number of figures (4, 9, 16, 25, ...) +% Points - Number of Points per figure (3, 4, 5...), 5 recommended +% MAXGEN - Number of generations (more than 30 recommended) +% +% Syntax: demoga1(); +% +% Input parameters: +% no input parameter +% Output parameter: +% no output parameter + +% Author: Hartmut Pohlheim +% History: 24.03.94 file created + + +function demoga1(); + +Num = 16; % Number of figures +Points = 6; % Number of points per figure +MAXGEN = 30; % Number of generations +FieldDR = rep([0; 1], [1 Points]); % Fielddescription for mutation + +% Function needs as many rows as columns, every place has to be filled +if sqrt(Num) ~= ceil(sqrt(Num)), + error('sqrt(Num) must be an integer'); +end + +ColRowNum = ceil(sqrt(Num)); % Number of columns and rows +Shrink=Num/ColRowNum; % Value for shrinking of area +SelectNumber = ColRowNum; % Number of parents by selection + +Cols = 1:1:ColRowNum; % Index of individuals in first columns +Rows = 1:ColRowNum:Num; % Index of individuals in first row + +h = figure; % Open a new figure for output +axes('Position',[0 0 1 1]); % Set axes to whole figure +set(gca, 'xcolor',[0 0 0]); % Make X-Axis invisible +set(gca, 'ycolor',[0 0 0]); % Make Y-Axis invisible +axis('ij'); % Position start in left-upper corner +axis(axis); % Freeze axes + +XStart = (Cols(1:ColRowNum-1)/Shrink); % Calculate X-start- and Y-endvalues of lines +XLine1 = [XStart; XStart]; % between figures +YLine1 = [zeros(1,ColRowNum-1); ones(1,ColRowNum-1)]; % X-end- and Y-startvalues +XLine = [XLine1 YLine1]; YLine = [YLine1 XLine1]; % Assemble line vectors + +MatX=rand(Points,Num); % Create X-values of figures at random +MatY=rand(Points,Num); % Create Y-values of figures at random + +for igen = 1:MAXGEN, % Loop over all generations + + % Recombine individuals + MatXYOff = recombin('recint', [MatX MatY]',NaN, 2); + + % Mutate individuals + MatXYOff = mutbga(MatXYOff, FieldDR, 1/Points); + + MatXYOff = MatXYOff'; % Invert matrix of individuals + MatX = MatXYOff(:,1:Num); % Select X- and Y-values + MatY = MatXYOff(:,size(MatXYOff,2)/2+1:size(MatXYOff,2)/2+Num); + + PolyMatX = MatX / Shrink; % Shrink X-values for fitting in small area + PolyMatY = MatY / Shrink; % Shrink Y-values for fitting in small area + + % Add a value to the X-value for placing individual in the appropriate column + for irun = 1:ColRowNum-1, + PolyMatX(:,Rows+irun)=PolyMatX(:,Rows+irun)+(irun)/Shrink; + end + + % Add a value to the Y-value for placing individual in the appropriate row + for irun = 1:ColRowNum-1, + PolyMatY(:,Cols+(irun*ColRowNum))= ... + PolyMatY(:,Cols+(irun*ColRowNum))+(irun)/Shrink; + end + + cla; % Clear axes, removes all earlier figures + patch(PolyMatX,PolyMatY,'b'); % Plot shape of figures + lh = line(XLine, YLine); % Plot lines between figures + set(lh,'Color',[.6 .6 .6]); % Set linecolor to grey + + xclick = []; yclick = []; % Reset vectors for storing click points + for isel = 1:SelectNumber, % Loop for as many points as individuals to select + set(gcf,'Name',[ ' Select ' int2str(isel) '. figure (of ' ... + int2str(SelectNumber) ') with mouseclick (Generation ' ... + int2str(igen) ' of ' int2str(MAXGEN) ')']); + [xclick1 yclick1] = ginput(1); % get position of mouse click + xclick = [xclick; xclick1]; yclick = [yclick; yclick1]; % add position to vectors + end + + xpos = ceil(xclick * Shrink); % Calculate column of mouse click + ypos = ceil(yclick * Shrink); % Calculate row of mouse click + + SelNumber = xpos + ColRowNum * (ypos-1); % Calculate numbers of selected figures + + % select X- and Y-values of individuals and repeat them + MatX = rep(MatX(:,SelNumber),[1 ceil(Num/SelectNumber)]); + MatY = rep(MatY(:,SelNumber),[1 ceil(Num/SelectNumber)]); + +end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/MPGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/MPGA.M" index 2a177f22c771a9962e156f4b3330f936527005ea..b3ebdaeaa4d52bea2d5cec4b7857437189ceee6e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/MPGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/MPGA.M" @@ -1,3 +1,127 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c2f727ca711d45d9d3092595193ceb9f562b7dac9a509abb74694ecb1b8a31aa -size 4726 +% MPGA.M (Multi Population Genetic Algorithm) +% +% This script implements the Multi Population Genetic Algorithm. +% Real valued representation for the individuals is used. +% +% Author: Hartmut Pohlheim +% History: 23.03.94 file created + +GGAP = .8; % Generation gap, how many new individuals are created +INSR = .9; % Insertion rate, how many of the offspring are inserted +XOVR = 1; % Crossover rate +SP = 2; % Selective Pressure +MUTR = 1; % Mutation rate; only a factor; +MIGR = 0.2; % Migration rate between subpopulations +MIGGEN = 20; % Number of generations between migration (isolation time) + +TERMEXACT = 1e-4; % Value for termination if minimum reached + +SEL_F = 'sus'; % Name of selection function +XOV_F = 'recdis'; % Name of recombination function for individuals +MUT_F = 'mutbga'; % Name of mutation function + +OBJ_F = 'objharv'; % Name of function for objective values + +% Get boundaries of objective function + FieldDR = feval(OBJ_F,[],1); + +% compute SUBPOP, NIND depending on number of variables (defined in objective function) + NVAR = size(FieldDR,2); % Get number of variables from objective function + SUBPOP = 2 * floor(sqrt(NVAR)); % Number of subpopulations + NIND = 20 + 5 * floor(NVAR/50); % Number of individuals per subpopulations + MAXGEN = 300 * floor(sqrt(NVAR)); % Maximal number of generations + MUTR = MUTR / NVAR; % Mutation rate depending on NVAR + +% Get value of minimum, defined in objective function + GlobalMin = feval(OBJ_F,[],3); + +% Get title of objective function, defined in objective function + FigTitle = [feval(OBJ_F,[],2) ' (' int2str(SUBPOP) ':' int2str(MAXGEN) ') ']; + +% Clear Best and storing matrix + % Initialise Matrix for storing best results + Best = NaN * ones(MAXGEN,3); + Best(:,3) = zeros(size(Best,1),1); + % Matrix for storing best individuals + IndAll = []; + +% Create real population + Chrom = crtrp(SUBPOP*NIND,FieldDR); + +% reset count variables + gen = 0; + termopt = 0; + +% Calculate objective function for population + ObjV = feval(OBJ_F,Chrom); + % count number of objective function evaluations + Best(gen+1,3) = Best(gen+1,3) + NIND; + +% Iterate subpopulation till termination or MAXGEN + while ((gen < MAXGEN) & (termopt == 0)), + + % Save the best and average objective values and the best individual + [Best(gen+1,1),ix] = min(ObjV); + Best(gen+1,2) = mean(ObjV); + IndAll = [IndAll; Chrom(ix,:)]; + + % Fitness assignement to whole population + FitnV = ranking(ObjV,[2 0],SUBPOP); + + % Select individuals from population + SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); + + % Recombine selected individuals + SelCh=recombin(XOV_F, SelCh, XOVR, SUBPOP); + + % Mutate offspring + SelCh=mutate(MUT_F, SelCh, FieldDR, [MUTR], SUBPOP); + + % Calculate objective function for offsprings + ObjVOff = feval(OBJ_F,SelCh); + Best(gen+1,3) = Best(gen+1,3) + size(SelCh,1); + + % Insert best offspring in population replacing worst parents + [Chrom, ObjV] = reins(Chrom, SelCh, SUBPOP, [1 INSR], ObjV, ObjVOff); + + gen=gen+1; + + % Plot some results, rename title of figure for graphic output + if ((rem(gen,20) == 1) | (rem(gen,MAXGEN) == 0) | (termopt == 1)), + set(gcf,'Name',[FigTitle ' in ' int2str(gen)]); + resplot(Chrom(1:2:size(Chrom,1),:),... + IndAll(max(1,gen-39):size(IndAll,1),:),... + [ObjV; GlobalMin], Best(max(1,gen-19):gen,[1 2]), gen); + end + + % Check, if best objective value near GlobalMin -> termination criterion + % compute differenz between GlobalMin and best objective value + ActualMin = abs(min(ObjV) - GlobalMin); + % if ActualMin smaller than TERMEXACT --> termination + if ((ActualMin < (TERMEXACT * abs(GlobalMin))) | (ActualMin < TERMEXACT)) + termopt = 1; + end + + % migrate individuals between subpopulations + if ((termopt ~= 1) & (rem(gen,MIGGEN) == 0)) + [Chrom, ObjV] = migrate(Chrom, SUBPOP, [MIGR, 1, 0], ObjV); + end + + end + + +% Results + % add number of objective function evaluations + Results = cumsum(Best(1:gen,3)); + % number of function evaluation, mean and best results + Results = [Results Best(1:gen,2) Best(1:gen,1)]; + +% Plot Results and show best individuals => optimum + figure('Name',['Results of ' FigTitle]); + subplot(2,1,1), plot(Results(:,1),Results(:,2),'-',Results(:,1),Results(:,3),':'); + subplot(2,1,2), plot(IndAll(gen-4:gen,:)'); + + +% End of script + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJBRAN.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJBRAN.M" index e1584434e51a3abe3c95cedcd4daab0651090282..6a5ddff67b3363e96657402d9689ef40729d44ee 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJBRAN.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJBRAN.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8cff116c0c77ce82edb0fe38de3c3b5d53b1862a196c4cec016126fba51dd19d -size 2529 +% OBJBRAN.M (OBJective function for BRANin RCOS function) +% +% This function implements the BRANIN RCOS function. +% +% Syntax: ObjVal = objbran(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 27.11.93 text of title and switch added +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objbran(Chrom,switch); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [] + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = 'BRANINs RCOS function'; + % return value of global minimum + elseif switch == 3 + ObjVal = 0.397887; + % define size of boundary-matrix and values + else + % x1 x2 + ObjVal = [-5 0; % lower bounds + 10 15]; % upper bounds + end + % if two variables, compute values of function + elseif Nvar == 2 + % BRANIN's RCOS function + % -5 <= x1 <= 10 ; 0 <= x2 <= 15 + % global minimum at (x1,x2)=(-pi,12.275), (pi,2.275), and + % (9.42478,2.475) ; fmin=0.397887 + x1 = Chrom(:,1); + x2 = Chrom(:,2); + ObjVal = 1*(x2-(5.1/(4*pi^2))*x1.^2+(5/pi)*x1-6).^2+10*(1-(1/(8*pi))).*cos(x1)+10; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJDOPI.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJDOPI.M" index b0c1a488bc7f527ea1595c9c36aefc4096855f24..e96bcfe5e94fc9f64212d6e505c9c0e5b5cbfc11 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJDOPI.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJDOPI.M" @@ -1,3 +1,107 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:686287fbe6f7298dec81cc21f54f0325462f6c61fe7ec41dcb7ae9ec01f6c66f -size 4051 +% OBJDOPI.M (OBJective function for DOuble Integrator) +% +% This function implements the Double Integrator. +% +% Syntax: ObjVal = objdopi(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 17.12.93 file created (copy of valfun7.m) +% 19.12.93 Dim reintroduced +% Dim and STEPSIMU independend from each other, rk23 +% can compute control between times +% 01.03.94 name changed in obj* +% 05.04.94 trapz used + +function [ObjVal,t,x] = objdopi(Chrom,switch); + +% Define used method + method = 1; % 1 - sim: simulink model + % 2 - ode: ordinary differential equations + % 3 - con: transfer function to state space + +% Dimension of objective function + Dim = 20; + TSTART = 0; + TEND = 1; + STEPSIMU = min(0.1,abs((TEND-TSTART)/(Dim-1))); + TIMEVEC = linspace(TSTART,TEND,Dim)'; + +% initial conditions + XINIT = [ 0; -1]; + +% end conditions + XEND = [ 0; 0]; + +% weights for control and end + XENDWEIGHT = 12 * [1; 1]; % XEND(1); XEND(2) + UWEIGHT = [0.5]; % Control vector + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then + if Nind == 0 + % return text of title for graphic output + if switch == 2 + if method == 2, ObjVal = ['Double Integrator (ode)-' int2str(Dim)]; + elseif method == 3, ObjVal = ['Double Integrator (con)-' int2str(Dim)]; + else ObjVal = ['Double Integrator (sim)-' int2str(Dim)]; + end + % return value of global minimum + elseif switch == 3 + ObjVal = 2; % UWEIGHT * 3 * (TEND - TSTART); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal1 = [-15; 15]; + ObjVal = rep(ObjVal1,[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + if method == 3, % Convert transfer function to state space system + [Ai2 Bi2 Ci2 Di2] = tf2ss(1, [1 0 0]); + t = TIMEVEC; + end + ObjVal = zeros(Nind,1); + for indrun = 1:Nind + steuerung = [TIMEVEC [Chrom(indrun,:)]']; + if method == 2, + [t x] = rk23('simdopi2',[TSTART TEND],XINIT,[1e-3;STEPSIMU;STEPSIMU],steuerung); + elseif method == 3, + [y x] = lsim(Ai2, Bi2, Ci2, Di2, Chrom(indrun,:),TIMEVEC, XINIT); + else + [t x] = rk23('simdopi1',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); + end + % Calculate objective function, endvalues, trapez-integration for control vector + ObjVal(indrun) = sum(XENDWEIGHT .* abs( x(size(x,1),:)' - XEND )) + ... + (UWEIGHT / (Dim-1) * trapz(Chrom(indrun,:).^2)); + end + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJEASO.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJEASO.M" index d5cf20f38293d617f40e57f10c40ea9132f52d13..ca51b7f221a7003afee3c76865509141792df7dd 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJEASO.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJEASO.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:038c5bb2a6c7567435818ba7da42a9f0f4a39c648cd1e7f061a84f952582938e -size 2427 +% OBJEASO.M (OBJective function for EASom function) +% +% This function implements the EASOM function. +% +% Syntax: ObjVal = objeaso(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 27.11.93 text of title and switch added +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + + +function ObjVal = objeaso(Chrom,switch); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [] + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = 'EASOMs function'; + % return value of global minimum + elseif switch == 3 + ObjVal = -1; + % define size of boundary-matrix and values + else + % x1 x2 + ObjVal = [-100 -100; % lower bounds + 100 100]; % upper bounds + end + % if two variables, compute values of function + elseif Nvar == 2 + % EASOM's function + % -100(-5) <= x1 <= 100(5) ; -100(-5) <= x2 <= 100(5) + % global minimum at (x1,x2)=(pi,pi) ; fmin=-1 + x1 = Chrom(:,1); + x2 = Chrom(:,2); + ObjVal = -cos(x1).*cos(x2).*exp(-((x1-pi).^2+(x2-pi).^2)); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1.M" index a69ab884966a7706841bafb96315a12c14728204..3bd95876aca4503259f107936f4abcf1e08f72e7 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1.M" @@ -1,3 +1,71 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:24eea201ce7f79221e27da8a5ae9d5b1719f0c54eedc0dac275bc2c750e2ddbe -size 2629 +% OBJFUN1.M (OBJective function for de jong's FUNction 1) +% +% This function implements the DE JONG function 1. +% +% Syntax: ObjVal = objfun1(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 26.11.93 file created +% 27.11.93 text of title and switch added +% 30.11.93 show Dim in figure titel +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objfun1(Chrom,switch); + +% Dimension of objective function + Dim = 20; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['DE JONG function 1-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = 100*[-5.12; 5.12]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 1, sum of xi^2 for i = 1:Dim (Dim=30) + % n = Dim, -5.12 <= xi <= 5.12 + % global minimum at (xi)=(0) ; fmin=0 + ObjVal = sum((Chrom .* Chrom)')'; + % ObjVal = diag(Chrom * Chrom'); % both lines produce the same + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1A.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1A.M" index 92911f849cc4a3ae8cf1515e2c15e42a9de4f7f9..7ecf1528deceac63936915fc669afad80baa0b57 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1A.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1A.M" @@ -1,3 +1,68 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:335e74ac50e7b5fa5eeb6732ab08d3c7258a88ba8615e4b9b75655fed29b20eb -size 2501 +% OBJFUN1A.M (OBJective function for axis parallel hyper-ellipsoid) +% +% This function implements the axis parallel hyper-ellipsoid. +% +% Syntax: ObjVal = objfun1a(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 07.04.94 file created + +function ObjVal = objfun1a(Chrom,switch); + +% Dimension of objective function + Dim = 10; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['Axis Parallel Hyper-Ellipsoid 1a-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = 100*[-5.12; 5.12]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 1a, sum of i * xi^2 for i = 1:Dim (Dim=30) + % n = Dim, -5.12 <= xi <= 5.12 + % global minimum at (xi)=(0) ; fmin=0 + nummer = rep(1:Dim,[Nind 1]); + ObjVal = sum((nummer .* (Chrom .* Chrom))')'; + % ObjVal = diag((nummer .* (Chrom * Chrom))'); % both lines produce the same + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1B.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1B.M" index c02207ca72b8faa14ed2e348db5ff32f3d2f6f5e..eba7140333b8d5d9a6f1349bb1ab678af4b17329 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1B.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN1B.M" @@ -1,3 +1,66 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9ec112b6d95a471539bfeaa4614e10c249dd5e200240eb1d8fd094e572d5a0c6 -size 2360 +% OBJFUN1B.M (OBJective function for rotated hyper-ellipsoid) +% +% This function implements the rotated hyper-ellipsoid. +% +% Syntax: ObjVal = objfun1b(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 07.04.94 file created + +function ObjVal = objfun1b(Chrom,switch); + +% Dimension of objective function + Dim = 10; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['Rotated Hyper-Ellipsoid 1b-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-65; 65]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 1b, sum over i of ( sum of xj )^2 for i = 1:Dim, j = 1:i (Dim=30) + % n = Dim, -65 <= xj <= 65 + % global minimum at (xi)=(0) ; fmin=0 + ObjVal = sum(cumsum(Chrom').^2)'; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN2.M" index b2462f4af9a069e3720c222426ae483fd27010c1..fab9da9cd44282815f8debaf8637fd24a3a4a225 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN2.M" @@ -1,3 +1,72 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9c23916aaee358f3bff7e371882a0278ee1b6e002d613b9436b65f0e9fc4946d -size 2522 +% OBJFUN2.M (OBJective function for rosenbrock's FUNction) +% +% This function implements the ROSENBROCK valley (DE JONG's Function 2). +% +% Syntax: ObjVal = objfun2(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one +% individual's string representation. +% if called with Chrom == [], then boundaries of +% the function or title for figure will be returned +% switch - if Chrom == [] and switch == 1 (or []) then return +% boundaries, if switch == 2 return title +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% the matrix with the boundaries of the function or +% the Text for the title of the graphic output +% + +% Author: Hartmut Pohlheim +% History: 26.01.94 file created +% 01.03.94 name changed in obj* + + +function ObjVal = objfun2(Chrom,switch); + +% Dimension of objective function + Dim = 2; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['ROSENBROCKs function 2-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-2; 2]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 11, sum of 100* (x(i+1) -xi^2)^2+(1-xi)^2 for i = 1:Dim (Dim=10) + % n = Dim, -10 <= xi <= 10 + % global minimum at (xi)=(1) ; fmin=0 + Mat1 = Chrom(:,1:Nvar-1); + Mat2 = Chrom(:,2:Nvar); + if Dim == 2 + ObjVal = 100*(Mat2-Mat1.^2).^2+(1-Mat1).^2; + else + ObjVal = sum((100*(Mat2-Mat1.^2).^2+(1-Mat1).^2)')'; + end + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN6.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN6.M" index ed9f13b8b8cbdca7d3bf43c1dcda0306ecece6ba..f03c49ceba5258fbe72ddde19001721144f50600 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN6.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN6.M" @@ -1,3 +1,73 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9e9b9d03f1ad19c8e5b5492ff7a1e6289d6e8564d07235fa7beafc1b51c5ca5a -size 2735 +% OBJFUN6.M (OBJective function for rastrigins FUNction 6) +% +% This function implements the RASTRIGIN function 6. +% +% Syntax: ObjVal = objfun6(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 26.11.93 file created +% 27.11.93 text of title and switch added +% 30.11.93 show Dim in figure titel +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objfun6(Chrom,switch); + +% Dimension of objective function + Dim = 20; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['RASTRIGINs function 6-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-5.12; 5.12]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 6, Dim*A + sum of (xi^2 - A*cos(Omega*xi)) for i = 1:Dim (Dim=20) + % n = Dim, -5.12 <= xi <= 5.12 + % global minimum at (xi)=(0) ; fmin=0 + A = 10; + Omega = 2 * pi; + ObjVal = Dim * A + sum(((Chrom .* Chrom) - A * cos(Omega * Chrom))')'; + % ObjVal = diag(Chrom * Chrom'); % both lines produce the same + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN7.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN7.M" index cc34ec0fb8b59a72bbb07e84781e946b355833c6..c1651dfd78c5c99810a4acd6a1b66cc8aebd1979 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN7.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN7.M" @@ -1,3 +1,68 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c2d8e97be04a95910b9ef6ee144e39d018a0a8e902ffc6bc0d8dae7f9d50a3bc -size 2449 +% OBJFUN7.M (OBJective function for schwefel's FUNction) +% +% This function implements the SCHWEFEL function 7. +% +% Syntax: ObjVal = objfun7(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one +% individual's string representation. +% if called with Chrom == [], then boundaries of +% the function or title for figure will be returned +% switch - if Chrom == [] and switch == 1 (or []) then return +% boundaries, if switch == 2 return title +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% the matrix with the boundaries of the function or +% the Text for the title of the graphic output +% + +% Author: Hartmut Pohlheim +% History: 27.11.93 file created +% 30.11.93 show Dim in figure titel +% 01.03.94 name changed in obj* + + +function ObjVal = objfun7(Chrom,switch); + +% Dimension of objective function + Dim = 20; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['SCHWEFELs function 7-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + xmin = 420.9687; + ObjVal = Dim * (-xmin * sin(sqrt(abs(xmin)))); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-500; 500]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 7, sum of -xi*sin(sqrt(abs(xi))) for i = 1:Dim (Dim=10) + % n = Dim, -500 <= xi <= 500 + % global minimum at (xi)=(420.9687) ; fmin=? + ObjVal = sum((-Chrom .* sin(sqrt(abs(Chrom))))')'; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN8.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN8.M" index bba085560b0eba3b404448883add6a502f2a9939..388454c280eb7bae4b17db561a46ebcdefa42f11 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN8.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN8.M" @@ -1,3 +1,72 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:48d08e996e74eee124e3e7cd224bdf1ef1fe12dd78410276efaab2af1245f7b5 -size 2664 +% OBJFUN8.M (OBJective function for griewangk's FUNction) +% +% This function implements the GRIEWANGK function 8. +% +% Syntax: ObjVal = objfun8(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 12.12.93 file created (copy of valfun7.m) +% 16.12.93 switch == 3, return value of global minimum +% 27.01.94 20* in formula, correction ?? +% 01.03.94 name changed in obj* + + +function ObjVal = objfun8(Chrom,switch); + +% Dimension of objective function + Dim = 10; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['GRIEWANGKs function 8-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-600; 600]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 8, sum(xi^2/4000) - 20*prod(cos(xi/sqrt(i))) + 1 for i = 1:Dim (Dim=10) + % n = Dim, -600 <= xi <= 600 + % global minimum at (xi)=(0) ; fmin=0 + % nummer = 1:Dim; + nummer = rep(1:Dim,[Nind 1]); + ObjVal = sum(((Chrom.^2) / 4000)')' - prod(cos(Chrom ./ sqrt(nummer))')' + 1; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN9.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN9.M" index 4c6849502eecabec838cf9dd6387f336ba55755a..13864aeeb9d215e83f25598a2415e30d66272df1 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN9.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJFUN9.M" @@ -1,3 +1,67 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:bf0e7e8d9a68317c34ca930b133d0d156e6655425f6397d6ebad000dc4927574 -size 2386 +% OBJFUN9.M (OBJective function for sum of different power FUNction 9) +% +% This function implements the sum of different power. +% +% Syntax: ObjVal = objfun9(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 07.04.94 file created + +function ObjVal = objfun9(Chrom,switch); + +% Dimension of objective function + Dim = 10; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['Sum of different Power 9-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-1; 1]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 9, sum of abs(xi)^(i+1) for i = 1:Dim (Dim=30) + % n = Dim, -1 <= xi <= 1 + % global minimum at (xi)=(0) ; fmin=0 + nummer = rep(1:Dim,[Nind 1]); + ObjVal = sum((abs(Chrom).^(nummer+1))')'; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJGOLD.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJGOLD.M" index 4388b3c5b4b8ec21bedc1bc0b24a96f3ac965707..1be67cc00cb1becaee2be41c4ee2db07fcffb433 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJGOLD.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJGOLD.M" @@ -1,3 +1,71 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:683ff891777d96ffa9aa34b86b508f6a819deaf524e463c0f0b3e00a6d5745f7 -size 2615 +% OBJGOLD.M (OBJective function for GOLDstein-price function) +% +% This function implements the GOLDSTEIN-PRICE function. +% +% Syntax: ObjVal = objgold(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 27.11.93 text of title and switch added +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + + +function ObjVal = objgold(Chrom,switch); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = 'GOLDSTEIN-PRICE function'; + % return value of global minimum + elseif switch == 3 + ObjVal = 3; + % define size of boundary-matrix and values + else + brd = 3; + % x1 x2 + ObjVal = [-brd -brd; % lower bounds + brd brd]; % upper bounds + end + % if two variables, compute values of function + elseif Nvar == 2 + % GOLDSTEIN-PRICE function + % -2 <= x1 <= 2 ; -2 <= x2 <= 2 (or -10 <= xi <= 10) + % global minimum at (x1,x2)=(0,-1) ; fmin=3 + x1 = Chrom(:,1); + x2 = Chrom(:,2); + ObjVal = ((1+(x1+x2+1).^2.*(19-14*x1+3*x1.^2-14*x2+6*x1.*x2+3*x2.^2))... + .*(30+(2*x1-3*x2).^2.*(18-32*x1+12*x1.^2+48*x2-36*x1.*x2+27*x2.^2))); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJHARV.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJHARV.M" index 8fb5b4f3dcf5a2232cc715532968c55e0b0f4d6e..432489a155efe37e1d7993c801613a4bd237b298 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJHARV.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJHARV.M" @@ -1,3 +1,78 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:771ae25c9b3f8818c984b601db80fcd04e73cdeb37b7d629a8c5d3bfe953c806 -size 2560 +% OBJHARV.M (OBJective function for HARVest problem) +% +% This function implements the HARVEST PROBLEM. +% +% Syntax: ObjVal = objharv(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 18.02.94 file created (copy of vallinq.m) +% 01.03.94 name changed in obj* + +function ObjVal = objharv(Chrom,switch); + +% global gen; + +% Dimension of objective function + Dim = 20; + +% values from MICHALEWICZ + a = 1.1; + x0 = 100; + xend = x0; + XENDWEIGHT = 0.4/(Dim^0.6); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['HARVEST PROBLEM-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = -sqrt(x0*(a^Dim-1)^2/(a^(Dim-1)*(a-1))); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal1 = [0; 10*Dim]; + ObjVal = rep(ObjVal1,[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + ObjVal = zeros(Nind,1); + X = rep(x0,[Nind 1]); + for irun = 1:Nvar, + X = a*X - Chrom(:,irun); + end + X; + ObjVal = -(sum(sqrt(Chrom)')' - XENDWEIGHT * abs(X-x0)); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJLINQ.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJLINQ.M" index e37975533bf8f6de2d68110436a9462b69a454fe..230c143c5f9be5df379d12738186591892271140 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJLINQ.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJLINQ.M" @@ -1,3 +1,86 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2a429b54f46b0bd5a7d4b02a8966c9194485c3be57e32ef747ae7220fef2a7da -size 3297 +% OBJLINQ.M (OBJective function for LINear Quadratic problem) +% +% This function implements the discret LINEAR-QUADRATIC PROBLEM. +% +% Syntax: ObjVal = objlinq(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 18.02.94 file created (copy of valfun7.m) +% 01.03.94 name changed in obj* + +function ObjVal = objlinq(Chrom,switch); + +% Dimension of objective function + Dim = 45; + +% values from MICHALEWICZ + x0 = 100; % start of X + var = 1; % 1 - 10 possible + Para = [ 1 1 1 1 1 16180.3399; + 10 1 1 1 1 109160.7978; + 1000 1 1 1 1 10009990.0200; + 1 10 1 1 1 37015.6212; + 1 1000 1 1 1 287569.3725; + 1 1 0 1 1 16180.3399; + 1 1 1000 1 1 16180.3399; + 1 1 1 0.01 1 10000.5000; + 1 1 1 1 0.01 431004.0987; + 1 1 1 1 100 10000.9999]; + s = Para(var,1); r = Para(var,2); q = Para(var,3); + a = Para(var,4); b = Para(var,5); GlobalMinimum = Para(var,6); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['Linear-quadratic problem (dis)-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = GlobalMinimum; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal1 = [-100 -70 -50; 20 20 20]; + ObjVal = [ObjVal1 rep([-30;20],[1 Dim-3])]; + end + % if Dim variables, compute values of function + elseif Nvar == Dim + ObjVal = zeros(Nind,1); + X = zeros(Nind,Nvar+1); + X(:,1) = rep(x0,[Nind 1]); + for irun = 1:Nvar, + X(:,irun+1) = a*X(:,irun) + b*Chrom(:,irun); + end + ObjVal = q * X(:,Nvar+1).^2 + sum((s * X(:,1:Nvar).^2 + r * Chrom.^2)')'; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJLINQ2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJLINQ2.M" index 87f94a842656df799ba059c46308f5d49b45faec..50f7f218f6b89b87f3758e816110825be1a20b8e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJLINQ2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJLINQ2.M" @@ -1,3 +1,105 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:73e21e33e6f035caad2f6e5ece899eae4fdcfd478e906fe407259566f77e5562 -size 3952 +% OBJLINQ2.M (OBJective function for LINear Quadratic problem) +% +% This function implements the continuous LINear Quadratic problem. +% +% Syntax: ObjVal = objlinq2(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 03.03.94 file created +% 06.04.94 all linq (sim, ode, con) in 1 file + +function [ObjVal,t,x] = objlinq2(Chrom,switch); + +% Define used method + method = 1; % 1 - sim: simulink model + % 2 - ode: ordinary differential equations + % 3 - con: transfer function to state space + +% Dimension of objective function + Dim = 50; + TSTART = 0; + TEND = 1; + STEPSIMU = min(0.1,abs((TEND-TSTART)/(Dim-1))); + TIMEVEC = linspace(TSTART,TEND,Dim)'; + +% initial conditions + XINIT = [100]; + +% end conditions + XEND = [0]; + +% weights for control and end + XENDWEIGHT = [20]; % XEND + XWEIGHT = [2]; % State vector + UWEIGHT = [1]; % Control vector + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then + if Nind == 0 + % return text of title for graphic output + if switch == 2 + if method == 2, ObjVal = ['Linear-quadratic problem (ode)-' int2str(Dim)]; + elseif method == 3, ObjVal = ['Linear-quadratic problem (con)-' int2str(Dim)]; + else ObjVal = ['Linear-quadratic problem (sim)-' int2str(Dim)]; + end + % return value of global minimum + elseif switch == 3 + ObjVal = 16180.3399; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = rep([-600; 0],[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + if method == 3, % Convert transfer function to state space system + [NC DC]=cloop(1, [1 0], +1); + [Ai2 Bi2 Ci2 Di2] = tf2ss(NC, DC); + t = TIMEVEC; + end + ObjVal = zeros(Nind,1); + for indrun = 1:Nind + steuerung = [TIMEVEC Chrom(indrun,:)']; + if method == 2, + [t x] = linsim('simlinq2',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); + elseif method == 3, + [y x] = lsim(Ai2, Bi2, Ci2, Di2, Chrom(indrun,:),TIMEVEC, XINIT); + else + [t x] = linsim('simlinq1',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); + end + % Calculate objective function, endvalues, trapez-integration for control vector + ObjVal(indrun) = (XENDWEIGHT * ( x(size(x,1),:)^2 )) + ... + (UWEIGHT / (Dim-1) * trapz(Chrom(indrun,:).^2)) + ... + (XWEIGHT / size(x,1) * sum(x.^2)); + end + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJPUSH.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJPUSH.M" index 883dc59c8512248efcc5af1ff1390f2b3916e2de..192cc3cc874b71848f18e0fc9ad236983e859c73 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJPUSH.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJPUSH.M" @@ -1,3 +1,75 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d1be6b1755abd35d4b7c98b1bcc52f996c17d89230edd10856279f5a1016df3c -size 2595 +% OBJPUSH.M (OBJective function for PUSH-cart problem) +% +% This function implements the PUSH-CART PROBLEM. +% +% Syntax: ObjVal = objpush(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 19.02.94 file created (copy of valharv.m) +% 01.03.94 name changed in obj* + +function ObjVal = objpush(Chrom,switch); + +% Dimension of objective function + Dim = 20; + +% values from MICHALEWICZ + x0 = [0 0]; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['PUSH-CART PROBLEM-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = -(1/3 - ((3*Dim-1)/(6*Dim^2)) - (1/(2*Dim^3))*sum((1:Dim-1).^2)); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [0; 5]; + ObjVal = rep(ObjVal,[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + ObjVal = zeros(Nind,1); + X = rep(x0,[Nind 1]); + for irun = 1:Nvar, + Xsave = X; + X(:,1) = Xsave(:,2); + X(:,2) = 2 * X(:,2) - Xsave(:,1) + (1/Dim^2) * Chrom(:,irun); + end + X; + ObjVal = -(X(:,1) - (1/(2*Dim)) * sum((Chrom.^2)')'); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJSIXH.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJSIXH.M" index c96ff94530b49a5a92f6a1efc6c43bad9818c264..5824ce29d4cefb34f64bdf625513ff255c3f40f9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJSIXH.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/OBJSIXH.M" @@ -1,3 +1,68 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:61da893b40bb39e526de184ec3e52e610b1b8af6bfae65d782fe38550d399394 -size 2525 +% OBJSIXH.M (OBJective function for SIX Hump camelback function) +% +% This function implements the six hump camelback function. +% +% Syntax: ObjVal = objsixh(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 27.11.93 text of title and switch added +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objsixh(Chrom,switch); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = 'six-hump camelback function'; + % return value of global minimum + elseif switch == 3 + ObjVal = -1.0316; + % define size of boundary-matrix and values + else + % x1 x2 + ObjVal = [-3 -2; % lower bounds + 3 2]; % upper bounds + end + % if two variables, compute values of function + elseif Nvar == 2 + % six-hump camelback function + % -3 <= x1 <= 3 ; -2 <= x2 <= 2 + % global minimum at (x1,x2)=(-0.0898,0.7126),(0.0898,-0.7126) ; fmin=-1.0316 + x1 = Chrom(:,1); + x2 = Chrom(:,2); + ObjVal = (4-2.1*x1.^2+1/3*x1.^4).*x1.^2+x1.*x2+(-4+4*x2.^2).*x2.^2; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/RESPLOT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/RESPLOT.M" index b1632ce6f6c27142c7189ddc8fbe61d547733ddc..be2c3eba8bfdded9d64fb89addadbc451aa522f2 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/RESPLOT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/RESPLOT.M" @@ -1,3 +1,55 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:15424c52c7db18fd673d1d7d2004f7177a6ef38a34607db94dd1d37b3856bd37 -size 2067 +% RESPLOT.M (RESult PLOTing) +% +% This function plots some of the results during computation. +% +% Syntax: resplot(Chrom,IndAll,ObjV,Best,gen) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each line corresponds to one individual. +% IndAll - Matrix containing the best individual (variables) of each +% generation. Each line corresponds to one individual. +% ObjV - Vector containing objective values of the current +% generation +% Best - Matrix containing the best and average Objective values of each +% generation, [best value per generation,average value per generation] +% gen - Scalar containing the number of the current generation +% +% Output parameter: +% no output parameter + +% Author: Hartmut Pohlheim +% History: 27.11.93 file created +% 29.11.93 decision, if plot or not deleted +% yscale not log +% 15.12.93 MutMatrix as parameter and plot added +% 16.03.94 function cleaned, MutMatrix removed, IndAll added + +function resplot(Chrom,IndAll,ObjV,Best,gen); + + % plot of best and mean value per generation + subplot(2,2,1), plot(Best); + title('Best and mean objective value'); + xlabel('generation'), ylabel('objective value'); + + % plot of best individuals in all generations + subplot(2,2,2), plot(IndAll); + title(['Best individuals']); + xlabel('generation'), ylabel('value of variable'); + + % plot of variables of all individuals in current generation + subplot(2,2,3), plot(Chrom'); + title(['All individuals in gen ',num2str(gen)]); + xlabel('number of variable'), ylabel('value of variable'); + + % plot of all objective values in current generation + subplot(2,2,4), plot(ObjV,'y.'); + title(['All objective values']); + xlabel('number of individual'), ylabel('objective value'); + + drawnow; + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SGA.M" index 2136fd475839e3d8c51ffff26b4a12dd35bff651..e7abb4f4ebc44e217f6c6aecde82a421936f34aa 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SGA.M" @@ -1,3 +1,67 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:e65330edf6404154493ef42c844dbcc005548383ac20ea3e5b5436237289736c -size 1911 +% SGA.M (Simple Genetic Algorithm) +% +% This script implements the Simple Genetic Algorithm. +% Binary representation for the individuals is used. +% +% Author: Hartmut Pohlheim +% History: 23.03.94 file created + +NIND = 20; % Number of individuals per subpopulations +MAXGEN = 300; % maximal Number of generations +GGAP = .8; % Generation gap, how many new individuals are created + +SEL_F = 'sus'; % Name of selection function +XOV_F = 'xovsp'; % Name of recombination function for individuals +MUT_F = 'mut'; % Name of mutation function for individuals +OBJ_F = 'objfun1'; % Name of function for objective values + +% Get boundaries of objective function + FieldDR = feval(OBJ_F,[],1); + +% Number of variables of objective function, in OBJ_F defined + NVAR = size(FieldDR,2); + +% Build fielddescription matrix + PRECI = 20; % Precisicion of binary representation + FieldDD = [rep([PRECI],[1, NVAR]);... + FieldDR;... + rep([1; 0; 1 ;1], [1, NVAR])]; + +% Create population + Chrom = crtbp(NIND, NVAR*PRECI); + +% reset count variables + gen = 0; + Best = NaN*ones(MAXGEN,1); + +% Iterate population + while gen < MAXGEN, + + % Calculate objective function for population + ObjV = feval(OBJ_F,bs2rv(Chrom, FieldDD)); + Best(gen+1) = min(ObjV); + plot(log10(Best),'ro'); + drawnow; + + % Fitness assignement to whole population + FitnV = ranking(ObjV); + + % Select individuals from population + SelCh = select(SEL_F, Chrom, FitnV, GGAP); + + % Recombine selected individuals (crossover) + SelCh=recombin(XOV_F, SelCh); + + % Mutate offspring + SelCh=mutate(MUT_F, SelCh); + + % Insert offspring in population replacing parents + Chrom = reins(Chrom, SelCh); + + gen=gen+1; + + end + +% End of script + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMDOPI1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMDOPI1.M" index c10d64b65c8f4b675a287bdaf5048e766310a504..ae4f9981a671506d108f7e26c279a18a06459ab0 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMDOPI1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMDOPI1.M" @@ -1,3 +1,80 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:72e18d256066390606b71890a08513834396f3adf51dadd1b53013a60b79b6dd -size 2690 +function [ret,x0,str]=simdopi1(t,x,u,flag); +%SIMDOPI1 is the M-file description of the SIMULINK system named SIMDOPI1. +% The block-diagram can be displayed by typing: SIMDOPI1. +% +% SYS=SIMDOPI1(T,X,U,FLAG) returns depending on FLAG certain +% system values given time point, T, current state vector, X, +% and input vector, U. +% FLAG is used to indicate the type of output to be returned in SYS. +% +% Setting FLAG=1 causes SIMDOPI1 to return state derivatives, FLAG=2 +% discrete states, FLAG=3 system outputs and FLAG=4 next sample +% time. For more information and other options see SFUNC. +% +% Calling SIMDOPI1 with a FLAG of zero: +% [SIZES]=SIMDOPI1([],[],[],0), returns a vector, SIZES, which +% contains the sizes of the state vector and other parameters. +% SIZES(1) number of states +% SIZES(2) number of discrete states +% SIZES(3) number of outputs +% SIZES(4) number of inputs. +% For the definition of other parameters in SIZES, see SFUNC. +% See also, TRIM, LINMOD, LINSIM, EULER, RK23, RK45, ADAMS, GEAR. + +% Note: This M-file is only used for saving graphical information; +% after the model is loaded into memory an internal model +% representation is used. + +% the system will take on the name of this mfile: +sys = mfilename; +new_system(sys) +simver(1.2) +if(0 == (nargin + nargout)) + set_param(sys,'Location',[100,100,600,400]) + open_system(sys) +end; +set_param(sys,'algorithm', 'RK-45') +set_param(sys,'Start time', '0.0') +set_param(sys,'Stop time', '1') +set_param(sys,'Min step size', '0.001') +set_param(sys,'Max step size', '0.01') +set_param(sys,'Relative error','1e-3') +set_param(sys,'Return vars', '') + +add_block('built-in/Inport',[sys,'/','Inport']) +set_param([sys,'/','Inport'],... + 'position',[65,95,85,115]) + +add_block('built-in/Note',[sys,'/','Doppelintegrator']) +set_param([sys,'/','Doppelintegrator'],... + 'position',[225,10,230,15]) + +add_block('built-in/Note',[sys,'/','Steuerung']) +set_param([sys,'/','Steuerung'],... + 'position',[75,65,80,70]) + +add_block('built-in/Integrator',[sys,'/','Integrator1']) +set_param([sys,'/','Integrator1'],... + 'position',[175,95,195,115]) + +add_block('built-in/Integrator',[sys,'/','Integrator2']) +set_param([sys,'/','Integrator2'],... + 'Initial','-1',... + 'position',[280,95,300,115]) +add_line(sys,[90,105;165,105]) +add_line(sys,[200,105;270,105]) + +% Return any arguments. +if (nargin | nargout) + % Must use feval here to access system in memory + if (nargin > 3) + if (flag == 0) + eval(['[ret,x0,str]=',sys,'(t,x,u,flag);']) + else + eval(['ret =', sys,'(t,x,u,flag);']) + end + else + [ret,x0,str] = feval(sys); + end +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMDOPI2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMDOPI2.M" index 5a7bb989ad6ab8b90bafd59c08fe70361cefe552..5b9b359ae753d7c5ca6bc3fbbf2aca187b4846ef 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMDOPI2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMDOPI2.M" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:255cafd990073ce958dc1325fd285885e3c58af02c8cfedfed68658f9a27cc9c -size 873 +% SIMDOPI2.M (Modell of DOPpelINTegrator, s-function) +% +% This function implements the modell of the DOPPELINTEGRATOR. +% +% Syntax: [sys, x0] = simdopi2(t, x, u, flag) +% +% Input parameters: +% t - given time point +% x - current state vector +% u - input vector +% flag - flags +% +% Output parameters: +% sys - Vector containing the new state derivatives +% x0 - initial value + +% Author: Hartmut Pohlheim +% History: 17.12.93 file created + +function [sys, x0] = simdopi2(t, x, u, flag); + +% Linear Systems Description + + if abs(flag) == 1 + sys(1) = u(1); % Derivatives + sys(2) = x(1); % Derivatives + elseif abs(flag) == 0 + sys=[2,0,0,1,0,0]; x0 = [0; -1]; + else + sys = []; % Real time update (ignored). + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMLINQ1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMLINQ1.M" index 9c2fa4244f94aa096a39308a26a00775fce6b44a..43d905fd47f68409dc52cffbdca46f14f0f897b2 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMLINQ1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMLINQ1.M" @@ -1,3 +1,73 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2afe43a7503bbfb0053683720878eb62368da4a7462acf99cf8dbf196ad5cabb -size 2445 +function [ret,x0,str]=simlinq1(t,x,u,flag); +%SIMLINQ1 is the M-file description of the SIMULINK system named SIMLINQ1. +% The block-diagram can be displayed by typing: SIMLINQ1. +% +% SYS=SIMLINQ1(T,X,U,FLAG) returns depending on FLAG certain +% system values given time point, T, current state vector, X, +% and input vector, U. +% FLAG is used to indicate the type of output to be returned in SYS. +% +% Setting FLAG=1 causes SIMLINQ1 to return state derivatives, FLAG=2 +% discrete states, FLAG=3 system outputs and FLAG=4 next sample +% time. For more information and other options see SFUNC. +% +% Calling SIMLINQ1 with a FLAG of zero: +% [SIZES]=SIMLINQ1([],[],[],0), returns a vector, SIZES, which +% contains the sizes of the state vector and other parameters. +% SIZES(1) number of states +% SIZES(2) number of discrete states +% SIZES(3) number of outputs +% SIZES(4) number of inputs. +% For the definition of other parameters in SIZES, see SFUNC. +% See also, TRIM, LINMOD, LINSIM, EULER, RK23, RK45, ADAMS, GEAR. + +% Note: This M-file is only used for saving graphical information; +% after the model is loaded into memory an internal model +% representation is used. + +% the system will take on the name of this mfile: +sys = mfilename; +new_system(sys) +simver(1.2) +if(0 == (nargin + nargout)) + set_param(sys,'Location',[208,245,596,426]) + open_system(sys) +end; +set_param(sys,'algorithm', 'RK-45') +set_param(sys,'Start time', '0.0') +set_param(sys,'Stop time', '1') +set_param(sys,'Min step size', '0.05') +set_param(sys,'Max step size', '0.05') +set_param(sys,'Relative error','1e-3') +set_param(sys,'Return vars', '') + +add_block('built-in/Sum',[sys,'/','Sum']) +set_param([sys,'/','Sum'],... + 'position',[110,65,130,85]) + +add_block('built-in/Integrator',[sys,'/','Integrator']) +set_param([sys,'/','Integrator'],... + 'Initial','100',... + 'position',[180,65,200,85]) + +add_block('built-in/Inport',[sys,'/','Inport']) +set_param([sys,'/','Inport'],... + 'position',[25,70,45,90]) +add_line(sys,[135,75;170,75]) +add_line(sys,[205,75;205,40;90,40;90,70;100,70]) +add_line(sys,[50,80;100,80]) + +% Return any arguments. +if (nargin | nargout) + % Must use feval here to access system in memory + if (nargin > 3) + if (flag == 0) + eval(['[ret,x0,str]=',sys,'(t,x,u,flag);']) + else + eval(['ret =', sys,'(t,x,u,flag);']) + end + else + [ret,x0,str] = feval(sys); + end +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMLINQ2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMLINQ2.M" index ef70654c63fda68e2f4dd25ae3eeda8aef5d00a8..80dab36b37f5282486a703e7332405092c526d84 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMLINQ2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMLINQ2.M" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a4740cd7ba9cba0f82b2830778204d2f3c1d08f588fd7a3df4d08066150fea35 -size 854 +% SIMLINQ2.M (Modell of Linear Quadratic Problem, s-function) +% +% This function implements the modell of the Linear Quadratic Problem. +% +% Syntax: [sys, x0] = simlinq2(t, x, u, flag) +% +% Input parameters: +% t - given time point +% x - current state vector +% u - input vector +% flag - flags +% +% Output parameters: +% sys - Vector containing the new state derivatives +% x0 - initial value + +% Author: Hartmut Pohlheim +% History: 23.03.94 file created + +function [sys, x0] = simlinq2(t, x, u, flag); + +% Linear Systems Description + + if abs(flag) == 1 + sys(1) = u(1) + x(1); % Derivatives + elseif abs(flag) == 0 + sys=[1,0,0,1,0,0]; x0 = [100]; + else + sys = []; % Real time update (ignored). + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMOBJP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMOBJP.M" index 0e7c78dc1a22c19413e8510ad3a074b7557f1f05..772ec2096b440e33a55c79a947c0ab50f0d37332 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMOBJP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/SIMOBJP.M" @@ -1,3 +1,22 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:4ae538fcd5128e0492210f325e63d2f7b5ebf41d4f02ff1bb0e3ad71d1c9448f -size 535 +% SIMOBJP.M (Plot SIMulation results of OBJective function) +% +% This function takes the name of a simulation objective +% function and the matrix of the best individuals and +% plots the states of the system over time for the +% last best individual. + +% Author: Hartmut Pohlheim +% History: 25.03.94 file created + +function [val, t, x] = simobjp(OBJ_F, IndAll); + +BestInd1=IndAll(size(IndAll,1),:); + +[val t x] = feval(OBJ_F, BestInd1); + +set(gcf,'Name',feval(OBJ_F,[],2)); +plot(t, x); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/TEST_FNS.PS" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/TEST_FNS.PS" index cbfa1ca1b5f7a7e1491c57d625d33e21443ed9fb..5bc62a5fa61cb23f3e21f82d1b9e1c8ccc51d93b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/TEST_FNS.PS" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/TEST_FNS/TEST_FNS.PS" @@ -1,3 +1,6239 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d31867c6f030b7a43c5154fed1ceed2a59756a9742678e00cfd41d33cb177d84 -size 140988 +%!PS-Adobe-3.0 +%%Creator: Windows PSCRIPT +%%Title: Microsoft Word - TEST_FCN.DOC +%%BoundingBox: 18 23 577 819 +%%DocumentNeededResources: (atend) +%%DocumentSuppliedResources: (atend) +%%Pages: (atend) +%%BeginResource: procset Win35Dict 3 1 +/Win35Dict 290 dict def Win35Dict begin/bd{bind def}bind def/in{72 +mul}bd/ed{exch def}bd/ld{load def}bd/tr/translate ld/gs/gsave ld/gr +/grestore ld/M/moveto ld/L/lineto ld/rmt/rmoveto ld/rlt/rlineto ld +/rct/rcurveto ld/st/stroke ld/n/newpath ld/sm/setmatrix ld/cm/currentmatrix +ld/cp/closepath ld/ARC/arcn ld/TR{65536 div}bd/lj/setlinejoin ld/lc +/setlinecap ld/ml/setmiterlimit ld/sl/setlinewidth ld/scignore false +def/sc{scignore{pop pop pop}{0 index 2 index eq 2 index 4 index eq +and{pop pop 255 div setgray}{3{255 div 3 1 roll}repeat setrgbcolor}ifelse}ifelse}bd +/FC{bR bG bB sc}bd/fC{/bB ed/bG ed/bR ed}bd/HC{hR hG hB sc}bd/hC{ +/hB ed/hG ed/hR ed}bd/PC{pR pG pB sc}bd/pC{/pB ed/pG ed/pR ed}bd/sM +matrix def/PenW 1 def/iPen 5 def/mxF matrix def/mxE matrix def/mxUE +matrix def/mxUF matrix def/fBE false def/iDevRes 72 0 matrix defaultmatrix +dtransform dup mul exch dup mul add sqrt def/fPP false def/SS{fPP{ +/SV save def}{gs}ifelse}bd/RS{fPP{SV restore}{gr}ifelse}bd/EJ{gsave +showpage grestore}bd/#C{userdict begin/#copies ed end}bd/FEbuf 2 string +def/FEglyph(G )def/FE{1 exch{dup 16 FEbuf cvrs FEglyph exch 1 exch +putinterval 1 index exch FEglyph cvn put}for}bd/SM{/iRes ed/cyP ed +/cxPg ed/cyM ed/cxM ed 72 100 div dup scale dup 0 ne{90 eq{cyM exch +0 eq{cxM exch tr -90 rotate -1 1 scale}{cxM cxPg add exch tr +90 rotate}ifelse}{cyP +cyM sub exch 0 ne{cxM exch tr -90 rotate}{cxM cxPg add exch tr -90 +rotate 1 -1 scale}ifelse}ifelse}{pop cyP cyM sub exch 0 ne{cxM cxPg +add exch tr 180 rotate}{cxM exch tr 1 -1 scale}ifelse}ifelse 100 iRes +div dup scale 0 0 transform .25 add round .25 sub exch .25 add round +.25 sub exch itransform translate}bd/SJ{1 index 0 eq{pop pop/fBE false +def}{1 index/Break ed div/dxBreak ed/fBE true def}ifelse}bd/ANSIVec[ +16#0/grave 16#1/acute 16#2/circumflex 16#3/tilde 16#4/macron 16#5/breve +16#6/dotaccent 16#7/dieresis 16#8/ring 16#9/cedilla 16#A/hungarumlaut +16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave +16#7C/bar 16#82/quotesinglbase 16#83/florin 16#84/quotedblbase 16#85 +/ellipsis 16#86/dagger 16#87/daggerdbl 16#88/circumflex 16#89/perthousand +16#8A/Scaron 16#8B/guilsinglleft 16#8C/OE 16#91/quoteleft 16#92/quoteright +16#93/quotedblleft 16#94/quotedblright 16#95/bullet 16#96/endash 16#97 +/emdash 16#98/tilde 16#99/trademark 16#9A/scaron 16#9B/guilsinglright +16#9C/oe 16#9F/Ydieresis 16#A0/space 16#A1/exclamdown 16#A4/currency +16#A5/yen 16#A6/brokenbar 16#A7/section 16#A8/dieresis 16#A9/copyright +16#AA/ordfeminine 16#AB/guillemotleft 16#AC/logicalnot 16#AD/hyphen +16#AE/registered 16#AF/macron 16#B0/degree 16#B1/plusminus 16#B2/twosuperior +16#B3/threesuperior 16#B4/acute 16#B5/mu 16#B6/paragraph 16#B7/periodcentered +16#B8/cedilla 16#B9/onesuperior 16#BA/ordmasculine 16#BB/guillemotright +16#BC/onequarter 16#BD/onehalf 16#BE/threequarters 16#BF/questiondown +16#C0/Agrave 16#C1/Aacute 16#C2/Acircumflex 16#C3/Atilde 16#C4/Adieresis +16#C5/Aring 16#C6/AE 16#C7/Ccedilla 16#C8/Egrave 16#C9/Eacute 16#CA +/Ecircumflex 16#CB/Edieresis 16#CC/Igrave 16#CD/Iacute 16#CE/Icircumflex +16#CF/Idieresis 16#D0/Eth 16#D1/Ntilde 16#D2/Ograve 16#D3/Oacute 16#D4 +/Ocircumflex 16#D5/Otilde 16#D6/Odieresis 16#D7/multiply 16#D8/Oslash +16#D9/Ugrave 16#DA/Uacute 16#DB/Ucircumflex 16#DC/Udieresis 16#DD/Yacute +16#DE/Thorn 16#DF/germandbls 16#E0/agrave 16#E1/aacute 16#E2/acircumflex +16#E3/atilde 16#E4/adieresis 16#E5/aring 16#E6/ae 16#E7/ccedilla 16#E8 +/egrave 16#E9/eacute 16#EA/ecircumflex 16#EB/edieresis 16#EC/igrave +16#ED/iacute 16#EE/icircumflex 16#EF/idieresis 16#F0/eth 16#F1/ntilde +16#F2/ograve 16#F3/oacute 16#F4/ocircumflex 16#F5/otilde 16#F6/odieresis +16#F7/divide 16#F8/oslash 16#F9/ugrave 16#FA/uacute 16#FB/ucircumflex +16#FC/udieresis 16#FD/yacute 16#FE/thorn 16#FF/ydieresis ] def/reencdict +12 dict def/IsChar{basefontdict/CharStrings get exch known}bd/MapCh{dup +IsChar not{pop/bullet}if newfont/Encoding get 3 1 roll put}bd/MapDegree{16#b0 +/degree IsChar{/degree}{/ring}ifelse MapCh}bd/MapBB{16#a6/brokenbar +IsChar{/brokenbar}{/bar}ifelse MapCh}bd/ANSIFont{reencdict begin/newfontname +ed/basefontname ed FontDirectory newfontname known not{/basefontdict +basefontname findfont def/newfont basefontdict maxlength dict def basefontdict{exch +dup/FID ne{dup/Encoding eq{exch dup length array copy newfont 3 1 roll +put}{exch newfont 3 1 roll put}ifelse}{pop pop}ifelse}forall newfont +/FontName newfontname put 127 1 159{newfont/Encoding get exch/bullet +put}for ANSIVec aload pop ANSIVec length 2 idiv{MapCh}repeat MapDegree +MapBB newfontname newfont definefont pop}if newfontname end}bd/SB{FC +/ULlen ed/str ed str length fBE not{dup 1 gt{1 sub}if}if/cbStr ed +/dxGdi ed/y0 ed/x0 ed str stringwidth dup 0 ne{/y1 ed/x1 ed y1 y1 +mul x1 x1 mul add sqrt dxGdi exch div 1 sub dup x1 mul cbStr div exch +y1 mul cbStr div}{exch abs neg dxGdi add cbStr div exch}ifelse/dyExtra +ed/dxExtra ed x0 y0 M fBE{dxBreak 0 BCh dxExtra dyExtra str awidthshow}{dxExtra +dyExtra str ashow}ifelse fUL{x0 y0 M dxUL dyUL rmt ULlen fBE{Break +add}if 0 mxUE transform gs rlt cyUL sl [] 0 setdash st gr}if fSO{x0 +y0 M dxSO dySO rmt ULlen fBE{Break add}if 0 mxUE transform gs rlt cyUL +sl [] 0 setdash st gr}if n/fBE false def}bd/font{/name ed/Ascent ed +0 ne/fT3 ed 0 ne/fSO ed 0 ne/fUL ed/Sy ed/Sx ed 10.0 div/ori ed -10.0 +div/esc ed/BCh ed name findfont/xAscent 0 def/yAscent Ascent def/ULesc +esc def ULesc mxUE rotate pop fT3{/esc 0 def xAscent yAscent mxUE transform +/yAscent ed/xAscent ed}if [Sx 0 0 Sy neg xAscent yAscent] esc mxE +rotate mxF concatmatrix makefont setfont [Sx 0 0 Sy neg 0 Ascent] mxUE +mxUF concatmatrix pop fUL{currentfont dup/FontInfo get/UnderlinePosition +known not{pop/Courier findfont}if/FontInfo get/UnderlinePosition get +1000 div 0 exch mxUF transform/dyUL ed/dxUL ed}if fSO{0 .3 mxUF transform +/dySO ed/dxSO ed}if fUL fSO or{currentfont dup/FontInfo get/UnderlineThickness +known not{pop/Courier findfont}if/FontInfo get/UnderlineThickness get +1000 div Sy mul/cyUL ed}if}bd/min{2 copy gt{exch}if pop}bd/max{2 copy +lt{exch}if pop}bd/CP{/ft ed{{ft 0 eq{clip}{eoclip}ifelse}stopped{currentflat +1 add setflat}{exit}ifelse}loop}bd/patfont 10 dict def patfont begin +/FontType 3 def/FontMatrix [1 0 0 -1 0 0] def/FontBBox [0 0 16 16] +def/Encoding StandardEncoding def/BuildChar{pop pop 16 0 0 0 16 16 +setcachedevice 16 16 false [1 0 0 1 .25 .25]{pat}imagemask}bd end/p{ +/pat 32 string def{}forall 0 1 7{dup 2 mul pat exch 3 index put dup +2 mul 1 add pat exch 3 index put dup 2 mul 16 add pat exch 3 index +put 2 mul 17 add pat exch 2 index put pop}for}bd/pfill{/PatFont patfont +definefont setfont/ch(AAAA)def X0 64 X1{Y1 -16 Y0{1 index exch M ch +show}for pop}for}bd/vert{X0 w X1{dup Y0 M Y1 L st}for}bd/horz{Y0 w +Y1{dup X0 exch M X1 exch L st}for}bd/fdiag{X0 w X1{Y0 M X1 X0 sub dup +rlt st}for Y0 w Y1{X0 exch M Y1 Y0 sub dup rlt st}for}bd/bdiag{X0 w +X1{Y1 M X1 X0 sub dup neg rlt st}for Y0 w Y1{X0 exch M Y1 Y0 sub dup +neg rlt st}for}bd/AU{1 add cvi 15 or}bd/AD{1 sub cvi -16 and}bd/SHR{pathbbox +AU/Y1 ed AU/X1 ed AD/Y0 ed AD/X0 ed}bd/hfill{/w iRes 37.5 div round +def 0.1 sl [] 0 setdash n dup 0 eq{horz}if dup 1 eq{vert}if dup 2 eq{fdiag}if +dup 3 eq{bdiag}if dup 4 eq{horz vert}if 5 eq{fdiag bdiag}if}bd/F{/ft +ed fm 256 and 0 ne{gs FC ft 0 eq{fill}{eofill}ifelse gr}if fm 1536 +and 0 ne{SHR gs HC ft CP fm 1024 and 0 ne{/Tmp save def pfill Tmp restore}{fm +15 and hfill}ifelse gr}if}bd/S{PenW sl PC st}bd/m matrix def/GW{iRes +12 div PenW add cvi}bd/DoW{iRes 50 div PenW add cvi}bd/DW{iRes 8 div +PenW add cvi}bd/SP{/PenW ed/iPen ed iPen 0 eq iPen 6 eq or{[] 0 setdash}if +iPen 1 eq{[DW GW] 0 setdash}if iPen 2 eq{[DoW GW] 0 setdash}if iPen +3 eq{[DW GW DoW GW] 0 setdash}if iPen 4 eq{[DW GW DoW GW DoW GW] 0 +setdash}if}bd/E{m cm pop tr scale 1 0 moveto 0 0 1 0 360 arc cp m sm}bd +/AG{/sy ed/sx ed sx div 4 1 roll sy div 4 1 roll sx div 4 1 roll sy +div 4 1 roll atan/a2 ed atan/a1 ed sx sy scale a1 a2 ARC}def/A{m cm +pop tr AG m sm}def/P{m cm pop tr 0 0 M AG cp m sm}def/RRect{n 4 copy +M 3 1 roll exch L 4 2 roll L L cp}bd/RRCC{/r ed/y1 ed/x1 ed/y0 ed/x0 +ed x0 x1 add 2 div y0 M x1 y0 x1 y1 r arcto 4{pop}repeat x1 y1 x0 y1 +r arcto 4{pop}repeat x0 y1 x0 y0 r arcto 4{pop}repeat x0 y0 x1 y0 r +arcto 4{pop}repeat cp}bd/RR{2 copy 0 eq exch 0 eq or{pop pop RRect}{2 +copy eq{pop RRCC}{m cm pop/y2 ed/x2 ed/ys y2 x2 div 1 max def/xs x2 +y2 div 1 max def/y1 exch ys div def/x1 exch xs div def/y0 exch ys div +def/x0 exch xs div def/r2 x2 y2 min def xs ys scale x0 x1 add 2 div +y0 M x1 y0 x1 y1 r2 arcto 4{pop}repeat x1 y1 x0 y1 r2 arcto 4{pop}repeat +x0 y1 x0 y0 r2 arcto 4{pop}repeat x0 y0 x1 y0 r2 arcto 4{pop}repeat +m sm cp}ifelse}ifelse}bd/PP{{rlt}repeat}bd/OB{gs 0 ne{7 3 roll/y ed +/x ed x y translate ULesc rotate x neg y neg translate x y 7 -3 roll}if +sc B fill gr}bd/B{M/dy ed/dx ed dx 0 rlt 0 dy rlt dx neg 0 rlt cp}bd +/CB{B clip n}bd/ErrHandler{errordict dup maxlength exch length gt +dup{errordict begin}if/errhelpdict 12 dict def errhelpdict begin/stackunderflow(operand stack underflow)def +/undefined(this name is not defined in a dictionary)def/VMerror(you have used up all the printer's memory)def +/typecheck(operator was expecting a different type of operand)def +/ioerror(input/output error occured)def end{end}if errordict begin +/handleerror{$error begin newerror{/newerror false def showpage 72 +72 scale/x .25 def/y 9.6 def/Helvetica findfont .2 scalefont setfont +x y moveto(Offending Command = )show/command load{dup type/stringtype +ne{(max err string)cvs}if show}exec/y y .2 sub def x y moveto(Error = )show +errorname{dup type dup( max err string )cvs show( : )show/stringtype +ne{( max err string )cvs}if show}exec errordict begin errhelpdict errorname +known{x 1 add y .2 sub moveto errhelpdict errorname get show}if end +/y y .4 sub def x y moveto(Stack =)show ostack{/y y .2 sub def x 1 +add y moveto dup type/stringtype ne{( max err string )cvs}if show}forall +showpage}if end}def end}bd end +%%EndResource +/SVDoc save def +%%EndProlog +%%BeginSetup +Win35Dict begin +ErrHandler +statusdict begin 0 setjobtimeout end +statusdict begin statusdict /jobname (Microsoft Word - TEST_FCN.DOC) put end +/oldDictCnt countdictstack def {}stopped +{ countdictstack oldDictCnt lt { Win35Dict begin } +{1 1 countdictstack oldDictCnt sub {pop end } for } ifelse } if +/oldDictCnt countdictstack def {a4 +}stopped +{ countdictstack oldDictCnt lt { Win35Dict begin } +{1 1 countdictstack oldDictCnt sub {pop end } for } ifelse } if +[ +{mark 1.0 1.0 .98 .9 .82 .68 .56 .48 .28 .1 .06 .0 counttomark dup 3 add -1 roll exch 2 sub mul dup floor cvi dup 3 1 roll sub exch dup 3 add index exch 2 add index dup 4 1 roll sub mul add counttomark 1 add 1 roll cleartomark } bind +/exec load currenttransfer /exec load] cvx settransfer +%%EndSetup +%%Page: 1 1 +%%PageResources: (atend) +SS +0 0 25 31 776 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Rotated hyper-ellipsoid) 553 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +962 1849 416 (................................) 416 SB +1378 1849 416 (................................) 416 SB +1794 1849 221 (.................) 221 SB +2026 1849 25 (4) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +397 1924 935 (2.4. Rosenbrock's valley \(De Jong's function 2\)) 935 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1339 1924 416 (................................) 416 SB +1755 1924 260 (....................) 260 SB +2026 1924 25 (4) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +397 1999 509 (2.5. 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74 454 1171 B +1 F +n +2 74 927 1171 B +1 F +n +5 74 2048 1171 B +1 F +n +gs 196 78 258 1246 CB +372 1267 25 (3) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1246 CB +480 1271 240 (objfun1b) 240 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1246 CB +952 1267 448 (rotated hyper-ellipsoid) 448 SB +gr +5 2 252 1246 B +1 F +n +195 2 258 1246 B +1 F +n +2 2 454 1246 B +1 F +n +469 2 457 1246 B +1 F +n +2 2 927 1246 B +1 F +n +1117 2 930 1246 B +1 F +n +5 2 2048 1246 B +1 F +n +5 74 252 1249 B +1 F +n +2 74 454 1249 B +1 F +n +2 74 927 1249 B +1 F +n +5 74 2048 1249 B +1 F +n +gs 196 78 258 1324 CB +372 1345 25 (4) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1324 CB +480 1349 210 (objfun2) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1324 CB +952 1345 754 (Rosenbrock's valley \(banana function\)) 754 SB +gr +5 2 252 1324 B +1 F +n +195 2 258 1324 B +1 F +n +2 2 454 1324 B +1 F +n +469 2 457 1324 B +1 F +n +2 2 927 1324 B +1 F +n +1117 2 930 1324 B +1 F +n +5 2 2048 1324 B +1 F +n +5 74 252 1327 B +1 F +n +2 74 454 1327 B +1 F +n +2 74 927 1327 B +1 F +n +5 74 2048 1327 B +1 F +n +gs 196 78 258 1402 CB +372 1423 25 (5) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1402 CB +480 1427 210 (objfun6) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1402 CB +952 1423 401 (Rastrigins's function) 401 SB +gr +5 2 252 1402 B +1 F +n +195 2 258 1402 B +1 F +n +2 2 454 1402 B +1 F +n +469 2 457 1402 B +1 F +n +2 2 927 1402 B +1 F +n +1117 2 930 1402 B +1 F +n +5 2 2048 1402 B +1 F +n +5 74 252 1405 B +1 F +n +2 74 454 1405 B +1 F +n +2 74 927 1405 B +1 F +n +5 74 2048 1405 B +1 F +n +gs 196 78 258 1480 CB +372 1501 25 (6) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1480 CB +480 1505 210 (objfun7) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman 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50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1636 CB +480 1661 210 (objfun9) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1636 CB +952 1657 454 (sum of different power) 454 SB +gr +5 2 252 1636 B +1 F +n +195 2 258 1636 B +1 F +n +2 2 454 1636 B +1 F +n +469 2 457 1636 B +1 F +n +2 2 927 1636 B +1 F +n +1117 2 930 1636 B +1 F +n +5 2 2048 1636 B +1 F +n +5 74 252 1639 B +1 F +n +2 74 454 1639 B +1 F +n +2 74 927 1639 B +1 F +n +5 74 2048 1639 B +1 F +n +gs 196 81 258 1714 CB +372 1738 25 (9) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 81 457 1714 CB +480 1742 210 (objdopi) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 81 930 1714 CB +952 1738 342 (double integrator) 342 SB +gr +5 5 252 1714 B +1 F +n +195 5 258 1714 B +1 F +n +5 5 454 1714 B +1 F +n +466 5 460 1714 B +1 F +n +5 5 927 1714 B +1 F +n +1114 5 933 1714 B +1 F +n +5 5 2048 1714 B +1 F +n +5 74 252 1720 B +1 F +n +2 74 454 1720 B +1 F +n +2 74 927 1720 B +1 F +n +5 74 2048 1720 B +1 F +n +gs 196 78 258 1795 CB +347 1816 50 (10) 50 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1795 CB +480 1820 210 (objharv) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1795 CB +952 1816 319 (harvest problem) 319 SB +gr +5 2 252 1795 B +1 F +n +195 2 258 1795 B +1 F +n +2 2 454 1795 B +1 F +n +469 2 457 1795 B +1 F +n +2 2 927 1795 B +1 F +n +1117 2 930 1795 B +1 F +n +5 2 2048 1795 B +1 F +n +5 74 252 1798 B +1 F +n +2 74 454 1798 B +1 F +n +2 74 927 1798 B +1 F +n +5 74 2048 1798 B +1 F +n +gs 196 78 258 1873 CB +347 1894 50 (11) 50 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1873 CB +480 1898 210 (objlinq) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1873 CB +952 1894 842 (linear-quadratic problem \(discret function\)) 842 SB +gr +5 2 252 1873 B +1 F +n +195 2 258 1873 B +1 F 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(100) 75 SB +991 736 25 (1) 25 SB +1320 736 25 (2) 25 SB +1364 736 75 (048) 75 SB +1577 736 25 (2) 25 SB +1620 736 75 (048) 75 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +443 696 17 (a) 17 SB +490 696 17 (f) 17 SB + +%%BeginResource: font MSTT31c2af +/G63 [17.0 0.0 2.0 -15.0 14.0 50.0] +/G63 { + 12 65 true [1 0 0 -1 -2.0 50.0] {<00100030006000c001c0018003800300070006000e000e001c001c001c003c003800380078007800 +780078007000f000f000f000f000f000f000f000f000f000f000f000f000f000f000f000f000f000 +f000f00070007800780078007800380038003c001c001c001c000e000e0006000600030003000180 +01c000c0006000300010>} imagemask + } + 99 /G63 MSTT31c2af AddChar +%%EndResource + +711 696 17 (c) 17 SB + +%%BeginResource: font MSTT31c2af +/G68 [17.0 0.0 0.0 -15.0 13.0 50.0] +/G68 { + 13 65 true [1 0 0 -1 0.0 50.0] {<400060007000300018000c000c000600070003000380038001c001c001c001e000e000e000f000f0 +00f000f0007000700078007800780078007800780078007800780078007800780078007800780078 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MSTT31c2af AddChar +%%EndResource + +1098 696 17 (g) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +517 730 27 (=) 27 SB +694 730 13 (\327) 13 SB +808 730 27 (-) 27 SB +941 730 27 (+) 27 SB +1021 730 27 (-) 27 SB +1284 730 27 (-) 27 SB +1448 730 27 (\243) 27 SB +1538 730 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +765 764 16 (+) 16 SB +575 800 16 (=) 16 SB +578 700 16 (-) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +557 716 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1346 736 13 (,) 13 SB +1602 736 13 (,) 13 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 869 333 (global minimum) 333 SB +732 869 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 867 22 (x) 22 SB +1004 867 14 (f) 14 SB +1048 867 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 900 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +842 863 27 (=) 27 SB +1101 863 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +877 869 25 (1) 25 SB +1141 869 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1027 828 17 (a) 17 SB +1074 828 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1001 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 1007 270 (objfun2.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 1001 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 1168 634 (2.5. Rastrigin's function 6) 634 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1353 99 (This ) 103 SB +382 1353 176 (function ) 180 SB +562 1353 44 (is ) 48 SB +610 1353 125 (based ) 129 SB +739 1353 63 (on ) 67 SB +806 1353 176 (function ) 180 SB +986 1353 38 (1 ) 42 SB +1028 1353 100 (with ) 104 SB +1132 1353 74 (the ) 78 SB +1210 1353 174 (addition ) 178 SB +1388 1353 54 (of ) 58 SB +1446 1353 138 (cosine ) 142 SB +1588 1353 237 (modulation ) 242 SB +1830 1353 54 (to ) 59 SB +1889 1353 162 (produce) 162 SB +279 1428 119 (many ) 123 SB +402 1428 107 (local ) 111 SB +513 1428 170 (minima. ) 174 SB +687 1428 125 (Thus, ) 129 SB +816 1428 74 (the ) 78 SB +894 1428 84 (test ) 88 SB +982 1428 176 (function ) 180 SB +1162 1428 44 (is ) 48 SB +1210 1428 133 (highly ) 137 SB +1347 1428 249 (multimodal. ) 253 SB +1600 1428 209 (However, ) 213 SB +1813 1428 74 (the ) 79 SB +1892 1428 159 (location) 159 SB +279 1503 771 (of the minima are regularly distributed.) 771 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 1617 14 (f) 14 SB +464 1617 22 (x) 22 SB +627 1617 25 (n) 25 SB +777 1617 22 (x) 22 SB +1128 1617 22 (x) 22 SB +1523 1617 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +800 1649 8 (i) 8 SB +1151 1649 8 (i) 8 SB +705 1685 8 (i) 8 SB +717 1585 15 (n) 15 SB +1546 1649 8 (i) 8 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +422 1650 15 (6) 15 SB +803 1616 15 (2) 15 SB +731 1686 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +552 1619 50 (10) 50 SB +865 1619 50 (10) 50 SB +1023 1619 25 (2) 25 SB +1383 1619 25 (5) 25 SB +1420 1619 50 (12) 50 SB +1610 1619 25 (5) 25 SB +1647 1619 50 (12) 50 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +443 1579 17 (a) 17 SB +489 1579 17 (f) 17 SB +1005 1579 17 (b) 17 SB +1167 1579 17 (g) 17 SB +756 1579 17 (c) 17 SB +1184 1579 17 (h) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +517 1613 27 (=) 27 SB +608 1613 13 (\327) 13 SB +661 1613 27 (+) 27 SB +832 1613 27 (-) 27 SB +921 1613 13 (\327) 13 SB +1055 1613 13 (\327) 13 SB +1107 1613 13 (\327) 13 SB +1347 1613 27 (-) 27 SB +1482 1613 27 (\243) 27 SB +1571 1613 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +715 1683 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +697 1599 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +939 1619 66 (cos) 66 SB +1407 1619 13 (,) 13 SB +1633 1619 13 (,) 13 SB +32 0 0 50 50 0 0 0 51 /Symbol font +1073 1613 27 (p) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 1752 333 (global minimum) 333 SB +731 1752 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 1750 22 (x) 22 SB +1012 1750 14 (f) 14 SB +1056 1750 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 1783 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +841 1746 27 (=) 27 SB +1109 1746 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +881 1752 25 (0) 25 SB +1149 1752 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1035 1711 17 (a) 17 SB +1082 1711 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1884 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 1890 270 (objfun6.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 1884 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 2051 621 (2.6. Schwefel's function 7) 621 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2236 221 (Schwefel's ) 223 SB +502 2236 176 (function ) 178 SB +680 2236 44 (is ) 46 SB +726 2236 202 (deceptive ) 204 SB +930 2236 49 (in ) 51 SB +981 2236 89 (that ) 91 SB +1072 2236 74 (the ) 76 SB +1148 2236 134 (global ) 136 SB +1284 2236 197 (minimum ) 199 SB +1483 2236 44 (is ) 47 SB +1530 2236 268 (geometricaly ) 271 SB +1801 2236 158 (distant, ) 161 SB +1962 2236 89 (over) 89 SB +279 2311 74 (the ) 78 SB +357 2311 212 (parameter ) 216 SB +573 2311 136 (space, ) 140 SB +713 2311 108 (from ) 112 SB +825 2311 74 (the ) 79 SB +904 2311 98 (next ) 103 SB +1007 2311 93 (best ) 98 SB +1105 2311 107 (local ) 112 SB +1217 2311 170 (minima. ) 175 SB +1392 2311 222 (Therefore, ) 227 SB +1619 2311 74 (the ) 79 SB +1698 2311 139 (search ) 144 SB +1842 2311 209 (algorithms) 209 SB +279 2386 1191 (are potentially prone to convergence in the wrong direction.) 1191 SB +1 lc +1 lj +0 0 0 pC +0 2 SP +831 2504 M 0 60 1 PP +S +n +880 2504 M 0 60 1 PP +S +n +797 2543 M 6 -3 1 PP +S +n +0 4 SP +803 2541 M 10 25 1 PP +S +n +0 2 SP +814 2566 M 12 -71 1 PP +S +n +826 2495 M 61 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 2500 14 (f) 14 SB +464 2500 22 (x) 22 SB +650 2500 22 (x) 22 SB +839 2500 22 (x) 22 SB +1217 2500 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +673 2532 8 (i) 8 SB +862 2532 8 (i) 8 SB +564 2568 8 (i) 8 SB +576 2468 15 (n) 15 SB +1240 2532 8 (i) 8 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +423 2533 15 (7) 15 SB +590 2569 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1089 2502 75 (500) 75 SB +1304 2502 75 (500) 75 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +442 2462 17 (a) 17 SB +489 2462 17 (f) 17 SB + +%%BeginResource: font MSTT31c2af +/G65 [17.0 0.0 2.0 -18.0 14.0 61.0] +/G65 { + 12 79 true [1 0 0 -1 -2.0 61.0] {<001000300060006000c000c00180038003000300060006000e000e000c001c001c001c003c003800 +38003800780078007800780070007000f000f000f000f000f000f000f000f000f000f000f000f000 +f000f000f000f000f000f000f000f000f000f000f000700078007800780078007800380038003800 +3c001c001c001c000c000e000e0006000600030003000300018001c000c00060006000300010>} imagemask + } + 101 /G65 MSTT31c2af AddChar +%%EndResource + +776 2462 17 (e) 17 SB + +%%BeginResource: font MSTT31c2af +/G6a [17.0 0.0 0.0 -18.0 13.0 61.0] +/G6a { + 13 79 true [1 0 0 -1 0.0 61.0] {<4000600060003000380018000c000c00060006000700030003800380038001c001c001c001e000e0 +00e000e000f000f000f000f000700070007000780078007800780078007800780078007800780078 +007800780078007800780078007800780078007800700070007000f000f000f000f000e000e000e0 +01e001c001c001c003800380038003000700060006000c000c00180038003000600060004000>} imagemask + } + 106 /G6a MSTT31c2af AddChar +%%EndResource + +890 2462 17 (j) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +517 2496 27 (=) 27 SB +617 2496 27 (-) 27 SB +699 2496 13 (\327) 13 SB +1053 2496 27 (-) 27 SB +1176 2496 27 (\243) 27 SB +1265 2496 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +574 2566 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +556 2482 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +716 2502 58 (sin) 58 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 2635 333 (global minimum) 333 SB +732 2635 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 2633 22 (x) 22 SB +1180 2633 14 (f) 14 SB +1224 2633 22 (x) 22 SB +1317 2633 25 (n) 25 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 2666 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +842 2629 27 (=) 27 SB +1277 2629 27 (=) 27 SB +1348 2629 13 (\327) 13 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +882 2635 75 (420) 75 SB +975 2635 100 (9687) 100 SB +1367 2635 75 (418) 75 SB +1458 2635 100 (9829) 100 SB +957 2635 13 (,) 13 SB +1440 2635 13 (,) 13 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1203 2594 17 (a) 17 SB +1250 2594 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2767 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 2773 270 (objfun7.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 2767 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 5 5 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 414 (2. Parametric Optimization) 414 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (5) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 210 677 (2.7. Griewangk's function 8) 677 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 395 259 (Griewangk's ) 269 SB +548 395 176 (function ) 186 SB +734 395 44 (is ) 54 SB +788 395 144 (similar ) 154 SB +942 395 54 (to ) 64 SB +1006 395 219 (Rastrigin's ) 229 SB +1235 395 189 (function. ) 199 SB +1434 395 45 (It ) 55 SB +1489 395 78 (has ) 89 SB +1578 395 119 (many ) 130 SB +1708 395 238 (widespread ) 249 SB +1957 395 94 (local) 94 SB +279 470 1396 (minima. However, the location of the minima are regularly distributed.) 1396 SB +1 lc +1 lj +0 0 0 pC +0 2 SP +617 618 M 106 0 1 PP +S +n +937 660 M 6 -4 1 PP +S +n +0 4 SP +943 657 M 9 15 1 PP +S +n +0 2 SP +953 672 M 13 -46 1 PP +S +n +966 626 M 19 0 1 PP +S +n +932 618 M 57 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 584 14 (f) 14 SB +463 584 22 (x) 22 SB +649 552 22 (x) 22 SB +943 552 22 (x) 22 SB +968 623 14 (i) 14 SB +1390 584 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +672 585 8 (i) 8 SB +563 652 8 (i) 8 SB +575 552 15 (n) 15 SB +966 585 8 (i) 8 SB +781 652 8 (i) 8 SB +794 552 15 (n) 15 SB +1413 616 8 (i) 8 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +422 617 15 (8) 15 SB +675 551 15 (2) 15 SB +589 653 15 (1) 15 SB +808 653 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +621 625 100 (4000) 100 SB +1056 586 25 (1) 25 SB +1262 586 75 (600) 75 SB +1476 586 75 (600) 75 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +441 546 17 (a) 17 SB +488 546 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +516 580 27 (=) 27 SB +734 580 27 (-) 27 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +905 520 19 (F) 19 SB +905 580 19 (H) 19 SB +905 551 19 (G) 19 SB +991 520 19 (I) 19 SB +991 580 19 (K) 19 SB +991 551 19 (J) 19 SB +32 0 0 50 50 0 0 0 51 /Symbol font +1024 580 27 (+) 27 SB +1226 580 27 (-) 27 SB +1348 580 27 (\243) 27 SB +1438 580 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +573 650 16 (=) 16 SB +792 650 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +555 566 53 (\345) 53 SB +770 566 62 (\325) 62 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +838 586 66 (cos) 66 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 719 333 (global minimum) 333 SB +731 719 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 717 22 (x) 22 SB +1012 717 14 (f) 14 SB +1056 717 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 750 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +841 713 27 (=) 27 SB +1109 713 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +881 719 25 (0) 25 SB +1149 719 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1035 678 17 (a) 17 SB +1082 678 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 851 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 857 270 (objfun8.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 851 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 1018 1002 (2.8. Sum of different Powers \(function 9\)) 1002 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1203 1435 (The sum of different powers is a commonly used unimodal test function.) 1435 SB +619 1321 M 0 60 1 PP +S +n +668 1321 M 0 60 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 1317 14 (f) 14 SB +464 1317 22 (x) 22 SB +627 1317 22 (x) 22 SB +992 1317 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +650 1349 8 (i) 8 SB +684 1307 8 (i) 8 SB +564 1385 8 (i) 8 SB +576 1285 15 (n) 15 SB +1015 1349 8 (i) 8 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +422 1350 15 (9) 15 SB +710 1308 15 (1) 15 SB +590 1386 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +918 1319 25 (1) 25 SB +1075 1319 25 (1) 25 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +443 1279 17 (a) 17 SB +489 1279 17 (f) 17 SB + +%%BeginResource: font MSTT31c2d2 +/MSTT31c2d2 [58.0 0 0 0 0 0] 17 -136 [-58.0 -58.0 58.0 58.0] [1 58 div 0 0 1 58 div 0 0] /MSTT31c2d2 GreNewFont +%%EndResource + +32 0 0 58 58 0 0 1 49 /MSTT31c2d2 font + +%%BeginResource: font MSTT31c2d2 +/G61 [10.0 0.0 1.0 -6.0 8.0 23.0] +/G61 { + 7 29 true [1 0 0 -1 -1.0 23.0] {<020408103020606060c0c0c0c0c0c0c0c0c0c0c0606060203010080402>} imagemask + } + 97 /G61 MSTT31c2d2 AddChar +%%EndResource + +673 1284 10 (a) 10 SB + +%%BeginResource: font MSTT31c2d2 +/G66 [10.0 0.0 1.0 -6.0 8.0 23.0] +/G66 { + 7 29 true [1 0 0 -1 -1.0 23.0] {<804020101008080c0c04060606060606060606040c0c08081010204080>} imagemask + } + 102 /G66 MSTT31c2d2 AddChar +%%EndResource + +724 1284 10 (f) 10 SB +32 0 0 50 50 0 0 0 51 /Symbol font +517 1313 27 (=) 27 SB +886 1313 27 (-) 27 SB +951 1313 27 (\243) 27 SB +1040 1313 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +695 1305 16 (+) 16 SB +574 1383 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +556 1299 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 1452 333 (global minimum) 333 SB +731 1452 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 1450 22 (x) 22 SB +1012 1450 14 (f) 14 SB +1056 1450 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 1483 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +841 1446 27 (=) 27 SB +1109 1446 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +881 1452 25 (0) 25 SB +1149 1452 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1035 1411 17 (a) 17 SB +1082 1411 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1584 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 1590 270 (objfun9.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 1584 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font MSTT31c2d2 +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 6 6 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 376 (3. Dynamic optimization) 376 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (6) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 67 67 0 0 0 61 /Times-Bold /font29 ANSIFont font +279 305 702 (3. Dynamic optimization) 702 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 499 189 (Dynamic ) 200 SB +479 499 155 (control ) 166 SB +645 499 195 (problems ) 206 SB +851 499 74 (are ) 85 SB +936 499 181 (complex ) 193 SB +1129 499 84 (and ) 96 SB +1225 499 166 (difficult ) 178 SB +1403 499 54 (to ) 66 SB +1469 499 129 (solve. ) 141 SB +1610 499 90 (The ) 102 SB +1712 499 79 (use ) 91 SB +1803 499 54 (of ) 66 SB +1869 499 182 (dynamic-) 182 SB +279 574 261 (optimization ) 262 SB +541 574 162 (specific ) 163 SB +704 574 194 (methods, ) 195 SB +899 574 103 (such ) 104 SB +1003 574 54 (as ) 55 SB +1058 574 268 (Hamiltonian, ) 269 SB +1327 574 44 (is ) 45 SB +1372 574 253 (complicated ) 254 SB +1626 574 84 (and ) 86 SB +1712 574 260 (problematic. ) 262 SB +1974 574 77 (The) 77 SB +279 649 799 (application of specific methods requires ) 800 SB +1079 649 35 (a ) 36 SB +1115 649 111 (large ) 112 SB +1227 649 162 (amount ) 163 SB +1390 649 54 (of ) 55 SB +1445 649 275 (mathematical ) 276 SB +1721 649 165 (support ) 166 SB +1887 649 105 (even ) 106 SB +1993 649 58 (for) 58 SB +279 724 1696 (systems of moderate size, and only the most trivial systems can be solved analytically.) 1696 SB +279 849 54 (In ) 71 SB +350 849 74 (the ) 91 SB +441 849 201 (following ) 218 SB +659 849 177 (example ) 194 SB +853 849 208 (problems, ) 225 SB +1078 849 103 (each ) 121 SB +1199 849 206 (individual ) 224 SB +1423 849 49 (in ) 67 SB +1490 849 74 (the ) 92 SB +1582 849 261 (evolutionary ) 279 SB +1861 849 190 (algorithm) 190 SB +279 924 255 (corresponds ) 261 SB +540 924 54 (to ) 60 SB +600 924 35 (a ) 41 SB +641 924 201 (\(discrete\) ) 207 SB +848 924 155 (control ) 161 SB +1009 924 152 (vector. ) 158 SB +1167 924 112 (Each ) 119 SB +1286 924 168 (variable ) 175 SB +1461 924 49 (in ) 56 SB +1517 924 59 (an ) 66 SB +1583 924 206 (individual ) 213 SB +1796 924 44 (is ) 51 SB +1847 924 204 (associated) 204 SB +279 999 1027 (with the control input at a time step of the dynamic ) 1028 SB +1307 999 261 (optimization ) 262 SB +1569 999 189 (problem. ) 190 SB +1759 999 54 (In ) 55 SB +1814 999 83 (this ) 84 SB +1898 999 153 (section,) 153 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +279 1074 22 (x) 22 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +301 1074 460 ( is the state vector and ) 460 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +761 1074 25 (u) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +786 1074 618 ( the control vector of a system.) 618 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 1239 542 (3.1. Double integrator) 542 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1424 1510 (The double integrator problem is described by the following state equations.) 1510 SB + +%%BeginResource: font MSTT31c2ea +/MSTT31c2ea [50.0 0 0 0 0 0] 20 -140 [-50.0 -50.0 50.0 50.0] [1 50 div 0 0 1 50 div 0 0] /MSTT31c2ea GreNewFont +%%EndResource + +32 0 0 50 50 0 0 1 40 /MSTT31c2ea font + +%%BeginResource: font MSTT31c2ea +/G26 [17.0 0.0 6.0 27.0 12.0 32.0] +/G26 { + 6 5 true [1 0 0 -1 -6.0 32.0] {<78fcfcfc78>} imagemask + } + 38 /G26 MSTT31c2ea AddChar +%%EndResource + +412 1504 17 (&) 17 SB +408 1580 17 (&) 17 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +407 1499 22 (x) 22 SB +497 1499 25 (u) 25 SB +403 1576 22 (x) 22 SB +501 1576 22 (x) 22 SB +424 1653 22 (y) 22 SB +501 1653 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +428 1533 15 (1) 15 SB +426 1609 15 (2) 15 SB +522 1609 15 (1) 15 SB +524 1686 15 (2) 15 SB +32 0 0 50 50 0 0 0 51 /Symbol font +458 1495 27 (=) 27 SB +458 1572 27 (=) 27 SB +458 1649 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1782 90 (The ) 95 SB +374 1782 118 (value ) 123 SB +497 1782 54 (of ) 59 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +562 1780 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +585 1814 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +606 1782 13 ( ) 18 SB +624 1782 78 (has ) 83 SB +707 1782 54 (to ) 59 SB +766 1782 59 (be ) 64 SB +830 1782 177 (changed ) 182 SB +1012 1782 141 (during ) 146 SB +1158 1782 35 (a ) 40 SB +1198 1782 99 (time ) 104 SB +1302 1782 140 (period ) 145 SB +1447 1782 100 (with ) 106 SB +1553 1782 54 (as ) 60 SB +1613 1782 101 (little ) 107 SB +1720 1782 155 (control ) 161 SB +1881 1782 123 (effort ) 129 SB +2010 1782 41 (as) 41 SB +279 1862 172 (possible ) 185 SB +464 1862 84 (and ) 97 SB +561 1862 74 (the ) 87 SB +648 1862 98 (final ) 111 SB +759 1862 218 (conditions ) 232 SB +991 1862 109 (must ) 123 SB +1114 1862 59 (be ) 73 SB +1187 1862 100 (met, ) 114 SB +1301 1862 103 (such ) 117 SB +1418 1862 89 (that ) 103 SB +1521 1862 74 (the ) 88 SB +1609 1862 201 (following ) 215 SB +1824 1862 152 (criteria ) 166 SB +1990 1862 61 (are) 61 SB +279 1937 174 (satisfied.) 174 SB +321 2037 17 (-) 17 SB +397 2037 100 (time:) 100 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +578 2037 25 (0) 25 SB +715 2037 25 (1) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +614 2031 27 (\243) 27 SB +680 2031 27 (\243) 27 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +653 2035 14 (t) 14 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +321 2132 17 (-) 17 SB +397 2132 341 (initial conditions:) 341 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +877 2130 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +898 2164 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +935 2132 25 (0) 25 SB +1029 2132 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +916 2091 17 (a) 17 SB +962 2091 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +989 2126 27 (=) 27 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +1321 2130 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +1344 2164 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1383 2132 25 (0) 25 SB +1506 2132 25 (1) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1365 2091 17 (a) 17 SB +1410 2091 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +1438 2126 27 (=) 27 SB +1478 2126 27 (-) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +321 2232 17 (-) 17 SB +397 2232 317 (final conditions:) 317 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +877 2230 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +898 2264 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +930 2232 25 (1) 25 SB +1020 2232 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +916 2191 17 (a) 17 SB +953 2191 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +980 2226 27 (=) 27 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +1321 2230 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +1344 2264 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1468 2232 25 (0) 25 SB +1379 2232 25 (1) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1365 2191 17 (a) 17 SB +1402 2191 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +1429 2226 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2362 832 (The objective function to be minimized is:) 832 SB +321 2482 17 (-) 17 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 2481 14 (f) 14 SB +449 2481 25 (u) 25 SB +581 2481 25 (u) 25 SB +625 2481 14 (t) 14 SB +683 2481 39 (dt) 39 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +542 2555 8 (t) 8 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +431 2443 17 (a) 17 SB +476 2443 17 (f) 17 SB +607 2443 17 (a) 17 SB +642 2443 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +502 2482 28 (=) 28 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +552 2556 16 (=) 16 SB +660 2476 15 (2) 15 SB +570 2556 15 (0) 15 SB +556 2443 15 (1) 15 SB +32 0 0 150 150 0 0 0 126 /MSTT31c2c7 font +%%BeginResource: font MSTT31c2c7 +currentfile eexec +9e67edc6b858a3e762244b628c0ab7daa0b706cbfc30718cf7399d83b4740f145229fb5ebdf788594b78bd5bf887825721eed2187e122621fabcc001faf87e69 +55872dd11bc9d0c6e3ec101e88b39d47077e52e02d7beecfd26e5d831e87d0280b97317bd99f4c0fcba055becc1f50cdc54bcd98e175c7aae256ab25b2c1f3f7 +780254f44e71c247e618c37736f3bc442d257fc46894d8bf47dc3306e73d59d1fd0bb04a6d2131749f481f3c9cf0496abd9bf2305eaa45f704f1da62443b86ac +87f1afa4dc4b1c11ff429d5e9109b5e1ad76301fcf7dd3c688b11bc52d9fb47ac50b5503e0ebe4054414cb2ec04a1dd50e6c625aa0164854e7db634a16393dff +45764f66ebea31f889dc747ef85310dd41e5dbbc8beff08726609f26871a7a177fc24d4fb038f1b5fd1d127deb25874e05c3871265ae26967e5c6d53852da61f +0ad3c982c70edbb404e8caf1616c6776810160a11655 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 + +cleartomark +%%EndResource +552 2419 21 (z) 21 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +730 2482 13 (.) 13 SB +279 2658 1132 (For these conditions an analytical solution is found to be:) 1132 SB +321 2753 17 (-) 17 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +399 2751 25 (u) 25 SB +635 2751 14 (t) 14 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +435 2754 28 (=) 28 SB +502 2754 13 ( ) 13 SB +524 2754 17 (-) 17 SB +549 2754 13 ( ) 13 SB +810 2754 200 (Minimum) 200 SB +1022 2754 28 (=) 28 SB +1057 2754 50 (12) 50 SB +474 2754 25 (6) 25 SB +561 2754 50 (12) 50 SB +32 0 0 50 50 0 0 0 51 /Symbol font +617 2748 13 (\327) 13 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +650 2754 13 (,) 13 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1110 2753 13 (.) 13 SB +279 2883 141 (Figure ) 141 SB +420 2883 25 (1) 25 SB +445 2883 1414 ( shows the optimal control vector and states for the continuous system:) 1414 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font MSTT31c2ea +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 7 7 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 376 (3. Dynamic optimization) 376 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (7) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +1 lc +1 lj +0 0 0 pC +0 4 SP +361 841 M 0 -568 1 PP +S +n +353 841 M 8 0 1 PP +S +n +353 747 M 8 0 1 PP +S +n +353 652 M 8 0 1 PP +S +n +353 557 M 8 0 1 PP +S +n +353 462 M 8 0 1 PP +S +n +353 368 M 8 0 1 PP +S +n +353 273 M 8 0 1 PP +S +n +361 841 M 1136 0 1 PP +S +n +361 849 M 0 -16 1 PP +S +n +475 849 M 0 -16 1 PP +S +n +588 849 M 0 -16 1 PP +S +n +702 849 M 0 -16 1 PP +S +n +815 849 M 0 -16 1 PP +S +n +929 849 M 0 -16 1 PP +S +n +1043 849 M 0 -16 1 PP +S +n +1156 849 M 0 -16 1 PP +S +n +1270 849 M 0 -16 1 PP +S +n +1384 849 M 0 -16 1 PP +S +n +1497 849 M 0 -16 1 PP +S +n +1 1 SP +gs 115 58 361 273 CB +361 273 M 114 57 1 PP +S +n +gr +gs 114 58 475 330 CB +475 330 M 113 57 1 PP +S +n +gr +gs 115 57 588 387 CB +588 387 M 114 56 1 PP +S +n +gr +gs 114 58 702 443 CB +702 443 M 113 57 1 PP +S +n +gr +gs 115 58 815 500 CB +815 500 M 114 57 1 PP +S +n +gr +gs 115 58 929 557 CB +929 557 M 114 57 1 PP +S +n +gr +gs 114 58 1043 614 CB +1043 614 M 113 57 1 PP +S +n +gr +gs 115 58 1156 671 CB +1156 671 M 114 57 1 PP +S +n +gr +gs 115 58 1270 728 CB +1270 728 M 114 57 1 PP +S +n +gr +gs 114 57 1384 785 CB +1384 785 M 113 56 1 PP +S +n +gr +2 1 SP +gs 115 2 361 603 CB +361 604 M 114 -1 1 PP +S +n +gr +gs 114 4 475 600 CB +475 603 M 113 -3 1 PP +S +n +gr +gs 115 7 588 594 CB +588 600 M 114 -6 1 PP +S +n +gr +gs 114 7 702 588 CB +702 594 M 113 -6 1 PP +S +n +gr +gs 115 8 815 581 CB +815 588 M 114 -7 1 PP +S +n +gr +gs 115 8 929 574 CB +929 581 M 114 -7 1 PP +S +n +gr +gs 114 8 1043 567 CB +1043 574 M 113 -7 1 PP +S +n +gr +gs 115 6 1156 562 CB +1156 567 M 114 -5 1 PP +S +n +gr +gs 115 5 1270 558 CB +1270 562 M 114 -4 1 PP +S +n +gr +gs 114 2 1384 557 CB +1384 558 M 113 -1 1 PP +S +n +gr +0 1 SP +gs 115 26 361 532 CB +361 557 M 114 -25 1 PP +S +n +gr +gs 114 21 475 512 CB +475 532 M 113 -20 1 PP +S +n +gr +gs 115 16 588 497 CB +588 512 M 114 -15 1 PP +S +n +gr +gs 114 9 702 489 CB +702 497 M 113 -8 1 PP +S +n +gr +gs 115 4 815 486 CB +815 489 M 114 -3 1 PP +S +n +gr +gs 115 4 929 486 CB +929 486 M 114 3 1 PP +S +n +gr +gs 114 9 1043 489 CB +1043 489 M 113 8 1 PP +S +n +gr +gs 115 16 1156 497 CB +1156 497 M 114 15 1 PP +S +n +gr +gs 115 21 1270 512 CB +1270 512 M 114 20 1 PP +S +n +gr +gs 114 26 1384 532 CB +1384 532 M 113 25 1 PP +S +n +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 1287 749 278 201 CB +299 817 35 (-6) 35 SB +gr +gs 1287 749 278 201 CB +299 722 35 (-4) 35 SB +gr +gs 1287 749 278 201 CB +299 627 35 (-2) 35 SB +gr +gs 1287 749 278 201 CB +313 533 21 (0) 21 SB +gr +gs 1287 749 278 201 CB +313 438 21 (2) 21 SB +gr +gs 1287 749 278 201 CB +313 343 21 (4) 21 SB +gr +gs 1287 749 278 201 CB +313 248 21 (6) 21 SB +gr +gs 1287 749 278 201 CB +351 874 21 (0) 21 SB +gr +gs 1287 749 278 201 CB +562 874 53 (0.2) 53 SB +gr +gs 1287 749 278 201 CB +789 874 53 (0.4) 53 SB +gr +gs 1287 749 278 201 CB +1016 874 53 (0.6) 53 SB +gr +gs 1287 749 278 201 CB +1244 874 53 (0.8) 53 SB +gr +gs 1287 749 278 201 CB +1487 874 21 (1) 21 SB +gr +gs 57 75 1019 418 CB +1026 431 42 (x1) 42 SB +gr +gs 57 75 529 589 CB +537 602 42 (x2) 42 SB +gr +gs 36 75 549 305 CB +557 318 21 (u) 21 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 976 78 (Fig. ) 78 SB +357 976 21 (1) 21 SB +378 976 12 (:) 12 SB +456 976 956 (Input and states of double integrator for optimal solution) 956 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1090 90 (The ) 101 SB +380 1090 147 (double ) 159 SB +539 1090 208 (integrator ) 220 SB +759 1090 44 (is ) 56 SB +815 1090 266 (implemented ) 278 SB +1093 1090 49 (in ) 61 SB +1154 1090 74 (the ) 86 SB +1240 1090 128 (m-file ) 140 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1380 1096 270 (objdopi.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1650 1090 13 ( ) 25 SB +1675 1090 118 (using ) 130 SB +1805 1090 35 (a ) 47 SB +1852 1090 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +1880 1099 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1167 148 (model, ) 150 SB +429 1167 59 (an ) 61 SB +490 1167 212 (s-function ) 214 SB +704 1167 84 (and ) 86 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +790 1167 168 (Control ) 170 SB +960 1167 151 (System ) 154 SB +1114 1167 164 (Toolbox) 164 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1278 1167 13 ( ) 16 SB +1294 1167 186 (routines. ) 189 SB +1483 1167 90 (The ) 93 SB +1576 1167 318 (implementation ) 321 SB +1897 1167 104 (used ) 107 SB +2004 1167 47 (by) 47 SB +279 1242 74 (the ) 79 SB +358 1242 192 (objective ) 197 SB +555 1242 176 (function ) 182 SB +737 1242 44 (is ) 50 SB +787 1242 150 (chosen ) 156 SB +943 1242 169 (through ) 175 SB +1118 1242 59 (an ) 65 SB +1183 1242 175 (optional ) 181 SB +1364 1242 212 (parameter ) 218 SB +1582 1242 127 (inside ) 133 SB +1715 1242 74 (the ) 80 SB +1795 1242 189 (function, ) 195 SB +1990 1242 61 (the) 61 SB +279 1317 267 (default is the ) 267 SB +546 1317 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +574 1326 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +745 1317 148 ( model.) 148 SB +0 lc +0 lj +6 4 SP +255 255 255 fC +149 124 633 1403 B +1 F +S +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +0 0 0 fC +683 1433 58 (1/s) 58 SB +255 255 255 fC +149 124 983 1403 B +1 F +S +n +0 0 0 fC +1033 1433 58 (1/s) 58 SB +255 255 255 fC +149 124 283 1403 B +1 F +S +n +0 0 0 fC +333 1433 25 (1) 25 SB +1 lc +1 lj +433 1478 M 200 0 1 PP +S +n +633 1478 M -25 -25 1 PP +S +n +608 1503 M 25 -25 1 PP +S +n +783 1478 M 200 0 1 PP +S +n +983 1478 M -25 -25 1 PP +S +n +958 1503 M 25 -25 1 PP +S +n +1133 1478 M 200 0 1 PP +S +n +1333 1478 M -25 -25 1 PP +S +n +1308 1503 M 25 -25 1 PP +S +n +808 1408 131 (state 1) 131 SB +1158 1408 131 (state 2) 131 SB +308 1534 119 (inport) 119 SB +608 1534 233 (integrator 1) 233 SB +958 1534 233 (integrator 2) 233 SB +0 lc +0 lj +255 255 255 fC +149 124 1333 1403 B +1 F +S +n +0 0 0 fC +1383 1433 25 (1) 25 SB +1333 1534 149 (outport) 149 SB +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 1618 78 (Fig. ) 78 SB +357 1618 21 (2) 21 SB +378 1618 12 (:) 12 SB +456 1618 593 (Block diagram of double integrator) 593 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1732 90 (The ) 90 SB +369 1732 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +397 1741 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +568 1732 660 ( method uses the model in figure ) 660 SB +1228 1732 25 (2) 25 SB +1253 1732 30 ( \() 30 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1283 1738 300 (simdopi1.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1583 1732 345 (\). The s-function ) 346 SB +1929 1732 122 (solves) 122 SB +279 1807 74 (the ) 76 SB +355 1807 122 (linear ) 124 SB +479 1807 203 (equations ) 205 SB +684 1807 17 (\() 17 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +701 1813 300 (simdopi2.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1001 1807 30 (\) ) 32 SB +1033 1807 120 (given ) 122 SB +1155 1807 131 (above ) 133 SB +1288 1807 84 (and ) 86 SB +1374 1807 74 (the ) 77 SB +1451 1807 106 (third ) 109 SB +1560 1807 162 (method ) 165 SB +1725 1807 17 (\() 17 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +1742 1807 168 (Control ) 171 SB +1913 1807 138 (System) 138 SB +279 1884 164 (Toolbox) 164 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +443 1884 543 (\) uses the transfer function:) 543 SB +1 lc +1 lj +0 2 SP +545 2024 M 48 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +400 1990 36 (G) 36 SB +456 1990 19 (s) 19 SB +549 2029 19 (s) 19 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +437 1952 17 (a) 17 SB +477 1952 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +504 1986 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +557 1960 25 (1) 25 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +571 2028 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +601 1992 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 2191 712 (3.2. Linear-quadratic system) 712 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2376 944 (The linear-quadratic system is one-dimensional:) 944 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 2465 22 (x) 22 SB +446 2465 22 (k) 22 SB +602 2465 25 (a) 25 SB +654 2465 22 (x) 22 SB +697 2465 22 (k) 22 SB +785 2465 25 (b) 25 SB +833 2465 25 (u) 25 SB +878 2465 22 (k) 22 SB +1017 2465 22 (k) 22 SB +32 0 0 50 50 0 0 0 51 /Symbol font +479 2461 27 (+) 27 SB +562 2461 27 (=) 27 SB +633 2461 13 (\327) 13 SB +748 2461 27 (+) 27 SB +816 2461 13 (\327) 13 SB +1053 2461 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +512 2467 25 (1) 25 SB +1089 2467 25 (1) 25 SB +1128 2467 25 (2) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +427 2426 17 (a) 17 SB +535 2426 17 (f) 17 SB +679 2426 17 (a) 17 SB +724 2426 17 (f) 17 SB +859 2426 17 (a) 17 SB +904 2426 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1110 2467 13 (,) 13 SB +1153 2467 13 (,) 13 SB +1169 2467 13 (.) 13 SB +1184 2467 13 (.) 13 SB +1199 2467 13 (.) 13 SB +1215 2467 13 (,) 13 SB +1233 2467 36 (N) 36 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1276 2467 13 (.) 13 SB +279 2601 1054 (The objective function for minimization is defined as:) 1054 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 2715 14 (f) 14 SB +452 2715 22 (x) 22 SB +494 2715 25 (u) 25 SB +587 2715 25 (q) 25 SB +639 2715 22 (x) 22 SB +685 2715 33 (N) 33 SB +947 2715 19 (s) 19 SB +993 2715 22 (x) 22 SB +1037 2715 22 (k) 22 SB +1146 2715 19 (r) 19 SB +1190 2715 25 (u) 25 SB +1235 2715 22 (k) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +874 2783 13 (k) 13 SB +886 2683 19 (N) 19 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +476 2717 13 (,) 13 SB +547 2717 28 (=) 28 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +431 2677 17 (a) 17 SB +520 2677 17 (f) 17 SB +664 2677 17 (a) 17 SB +786 2677 17 (f) 17 SB +1018 2677 17 (a) 17 SB +1063 2677 17 (f) 17 SB +1216 2677 17 (a) 17 SB +1261 2677 17 (f) 17 SB + +%%BeginResource: font MSTT31c2af +/G64 [17.0 0.0 2.0 -16.0 14.0 56.0] +/G64 { + 12 72 true [1 0 0 -1 -2.0 56.0] {<00100030006000e000c00180018003000300060006000e000e001c001c001c003c003c0038003800 +780078007800780070007000f000f000f000f000f000f000f000f000f000f000f000f000f000f000 +f000f000f000f000f000f0007000780078007800780078003800380038003c001c001c001c000e00 +0e0006000600030003000180018000c000e0006000300010>} imagemask + } + 100 /G64 MSTT31c2af AddChar +%%EndResource + +928 2677 17 (d) 17 SB + +%%BeginResource: font MSTT31c2af +/G69 [17.0 0.0 0.0 -16.0 13.0 56.0] +/G69 { + 13 72 true [1 0 0 -1 0.0 56.0] {<400060007000300018001c000c000e0006000700030003800380018001c001c001c001e000e000e0 +00f000f000f000f00070007000780078007800780078007800780078007800780078007800780078 +007800780078007800780078007000f000f000f000f000f000e000e001e001c001c001c001800380 +03800300070006000e000c001c00180030007000e0004000>} imagemask + } + 105 /G69 MSTT31c2af AddChar +%%EndResource + +1301 2677 17 (i) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +618 2711 13 (\327) 13 SB +730 2711 27 (+) 27 SB +832 2711 27 (+) 27 SB +973 2711 13 (\327) 13 SB +1110 2711 27 (+) 27 SB +1173 2711 13 (\327) 13 SB +32 0 0 29 29 0 0 0 29 /Symbol font +890 2781 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +869 2697 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +763 2717 25 (1) 25 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +803 2710 15 (2) 15 SB +1080 2710 15 (2) 15 SB +1279 2710 15 (2) 15 SB +906 2784 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1322 2717 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 8 8 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 376 (3. Dynamic optimization) 376 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (8) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 231 81 270 202 CB +357 226 56 (set) 56 SB +gr +gs 162 81 504 202 CB +567 226 36 (N) 36 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 162 81 669 202 CB +706 221 25 (x) 25 SB +gr +gs 162 81 669 202 CB +751 221 25 (0) 25 SB +gr +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +gs 162 81 669 202 CB +732 180 17 (a) 17 SB +gr +gs 162 81 669 202 CB +778 180 17 (f) 17 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 163 81 834 202 CB +906 226 19 (s) 19 SB +gr +gs 162 81 1000 202 CB +1073 226 17 (r) 17 SB +gr +gs 163 81 1165 202 CB +1234 226 25 (q) 25 SB +gr +gs 162 81 1331 202 CB +1401 226 22 (a) 22 SB +gr +gs 162 81 1496 202 CB +1566 226 24 (b) 24 SB +gr +gs 375 81 1661 202 CB +1711 226 277 (exact solution) 277 SB +gr +5 5 264 202 B +1 F +n +5 5 264 202 B +1 F +n +230 5 270 202 B +1 F +n +5 5 501 202 B +1 F +n +158 5 507 202 B +1 F +n +5 5 666 202 B +1 F +n +158 5 672 202 B +1 F +n +5 5 831 202 B +1 F +n +159 5 837 202 B +1 F +n +5 5 997 202 B +1 F +n +158 5 1003 202 B +1 F +n +5 5 1162 202 B +1 F +n +159 5 1168 202 B +1 F +n +5 5 1328 202 B +1 F +n +158 5 1334 202 B +1 F +n +5 5 1493 202 B +1 F +n +158 5 1499 202 B +1 F +n +5 5 1658 202 B +1 F +n +371 5 1664 202 B +1 F +n +5 5 2036 202 B +1 F +n +5 5 2036 202 B +1 F +n +5 74 264 208 B +1 F +n +2 74 501 208 B +1 F +n +2 74 666 208 B +1 F +n +2 74 831 208 B +1 F +n +2 74 997 208 B +1 F +n +2 74 1162 208 B +1 F +n +2 74 1328 208 B +1 F +n +2 74 1493 208 B +1 F +n +2 74 1658 208 B +1 F +n +5 74 2036 208 B +1 F +n +gs 231 81 270 283 CB +419 307 25 (1) 25 SB +gr +gs 162 81 504 283 CB +571 307 50 (45) 50 SB +gr +gs 162 81 669 283 CB +712 307 75 (100) 75 SB +gr +gs 163 81 834 283 CB +927 307 25 (1) 25 SB +gr +gs 162 81 1000 283 CB +1093 307 25 (1) 25 SB +gr +gs 163 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SB +1592 2328 212 (s-function ) 216 SB +1808 2328 84 (and ) 88 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +1896 2328 155 (Control) 155 SB +279 2401 151 (System ) 185 SB +464 2401 164 (Toolbox) 164 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +628 2401 13 ( ) 47 SB +675 2401 173 (routines ) 207 SB +882 2401 44 (is ) 78 SB +960 2401 266 (implemented ) 300 SB +1260 2401 49 (in ) 83 SB +1343 2401 74 (the ) 108 SB +1451 2401 128 (m-file ) 162 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1613 2407 300 (objlinq2.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1913 2401 26 (. ) 61 SB +1974 2401 77 (The) 77 SB +279 2478 318 (implementation ) 322 SB +601 2478 104 (used ) 108 SB +709 2478 60 (by ) 64 SB +773 2478 74 (the ) 79 SB +852 2478 192 (objective ) 197 SB +1049 2478 176 (function ) 181 SB +1230 2478 44 (is ) 49 SB +1279 2478 150 (chosen ) 155 SB +1434 2478 169 (through ) 174 SB +1608 2478 59 (an ) 64 SB +1672 2478 175 (optional ) 180 SB +1852 2478 199 (parameter) 199 SB +279 2553 731 (inside the function, the default is the ) 731 SB +1010 2553 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +1038 2562 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1209 2553 148 ( model.) 148 SB +0 lc +0 lj +6 4 SP +255 255 255 fC +149 124 983 2714 B +1 F +S +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +0 0 0 fC +1033 2744 58 (1/s) 58 SB +255 255 255 fC +149 124 283 2714 B +1 F +S +n +0 0 0 fC +333 2744 25 (1) 25 SB +1 lc +1 lj +433 2789 M 200 0 1 PP +S +n +633 2789 M -25 -25 1 PP +S +n +608 2814 M 25 -25 1 PP +S +n +1133 2789 M 225 0 1 PP +S +n +1358 2789 M -25 -25 1 PP +S +n +1333 2814 M 25 -25 1 PP +S +n +1158 2719 131 (state 1) 131 SB +308 2844 119 (inport) 119 SB +958 2844 233 (integrator 1) 233 SB +0 lc +0 lj +255 255 255 fC +149 124 1358 2714 B +1 F +S +n +0 0 0 fC +1408 2744 25 (1) 25 SB +1358 2844 149 (outport) 149 SB +1 lc +1 lj +1308 2639 M 0 150 1 PP +S +n +533 2639 M 775 0 1 PP +S +n +0 lc +0 lj +255 255 255 fC +149 124 633 2714 B +1 F +S +n +0 0 0 fC +658 2844 90 (Sum) 90 SB +1 lc +1 lj +533 2639 M 0 100 1 PP +S +n +533 2739 M 100 0 1 PP +S +n +633 2739 M -25 -25 1 PP +S +n +633 2739 M -25 25 1 PP +S +n +644 2713 28 (+) 28 SB +644 2763 28 (+) 28 SB +783 2789 M 200 0 1 PP +S +n +983 2789 M -25 -25 1 PP +S +n +958 2814 M 25 -25 1 PP +S +n +6 6 1308 2788 E +1 F +n +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 2928 78 (Fig. ) 78 SB +357 2928 21 (4) 21 SB +378 2928 12 (:) 12 SB +456 2928 699 (Block diagram of linear-quadratic system) 699 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2c7 +%%+ font 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Dynamic optimization) 376 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (9) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 218 90 (The ) 90 SB +369 218 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +397 227 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +568 218 660 ( method uses the model in figure ) 660 SB +1228 218 25 (4) 25 SB +1253 218 30 ( \() 30 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1283 224 300 (simlinq1.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1583 218 345 (\). The s-function ) 346 SB +1929 218 122 (solves) 122 SB +279 293 416 (the linear equations \() 416 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +695 299 300 (simlinq2.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +995 293 31 (\):) 31 SB +32 0 0 50 50 0 0 1 40 /MSTT31c2ea font +408 373 17 (&) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +535 447 13 (.) 13 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 369 22 (x) 22 SB +496 369 22 (x) 22 SB +580 369 25 (u) 25 SB +419 445 22 (y) 22 SB +496 445 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +424 402 15 (1) 15 SB +517 402 15 (1) 15 SB +517 478 15 (1) 15 SB +32 0 0 50 50 0 0 0 51 /Symbol font +454 365 27 (=) 27 SB +544 365 27 (+) 27 SB +454 441 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 578 443 (and the third method \() 443 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +722 578 483 (Control System Toolbox) 483 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1205 578 543 (\) uses the transfer function:) 543 SB +1 lc +1 lj +0 0 0 pC +0 2 SP +546 718 M 88 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +400 684 36 (G) 36 SB +456 684 19 (s) 19 SB +549 723 19 (s) 19 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +437 646 17 (a) 17 SB +477 646 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +505 680 27 (=) 27 SB +578 719 27 (-) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +577 654 25 (1) 25 SB +610 725 25 (1) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +639 686 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 885 483 (3.3. Harvest system) 483 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1070 1599 (The harvest system is a one-dimensional equation of growth with one constraint:) 1599 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 1159 22 (x) 22 SB +446 1159 22 (k) 22 SB +602 1159 25 (a) 25 SB +654 1159 22 (x) 22 SB +697 1159 22 (k) 22 SB +783 1159 25 (u) 25 SB +828 1159 22 (k) 22 SB +967 1159 22 (k) 22 SB +32 0 0 50 50 0 0 0 51 /Symbol font +479 1155 27 (+) 27 SB +562 1155 27 (=) 27 SB +633 1155 13 (\327) 13 SB +748 1155 27 (-) 27 SB +1004 1155 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +512 1161 25 (1) 25 SB +1039 1161 25 (1) 25 SB +1078 1161 25 (2) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +427 1120 17 (a) 17 SB +535 1120 17 (f) 17 SB +679 1120 17 (a) 17 SB +724 1120 17 (f) 17 SB +809 1120 17 (a) 17 SB +854 1120 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1060 1161 13 (,) 13 SB +1103 1161 13 (,) 13 SB +1119 1161 13 (.) 13 SB +1134 1161 13 (.) 13 SB +1150 1161 13 (.) 13 SB +1165 1161 13 (,) 13 SB +1184 1161 36 (N) 36 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1226 1161 13 (,) 13 SB +397 1265 192 (such that ) 192 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +595 1263 22 (x) 22 SB +734 1263 22 (x) 22 SB +780 1263 33 (N) 33 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +638 1265 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +619 1224 17 (a) 17 SB +665 1224 17 (f) 17 SB +759 1224 17 (a) 17 SB +818 1224 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +692 1259 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +839 1265 13 (.) 13 SB +279 1395 1247 (The objective function for minimization is therefore defined as:) 1247 SB +621 1552 M 7 -4 1 PP +S +n +0 4 SP +628 1549 M 9 22 1 PP +S +n +0 2 SP +638 1571 M 12 -63 1 PP +S +n +650 1508 M 91 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 1509 14 (f) 14 SB +449 1509 25 (u) 25 SB +652 1509 25 (u) 25 SB +697 1509 22 (k) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +563 1577 13 (k) 13 SB +576 1477 19 (N) 19 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +431 1471 17 (a) 17 SB +476 1471 17 (f) 17 SB +678 1471 17 (a) 17 SB +723 1471 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +502 1511 28 (=) 28 SB +541 1511 17 (-) 17 SB +32 0 0 29 29 0 0 0 29 /Symbol font +580 1575 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +559 1491 53 (\345) 53 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +595 1578 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +747 1511 13 (.) 13 SB +279 1678 943 (The exact solution can be analytically found by:) 943 SB +704 1856 M 293 0 1 PP +S +n +671 1866 M 6 -4 1 PP +S +n +0 4 SP +677 1863 M 9 59 1 PP +S +n +0 2 SP +687 1922 M 13 -156 1 PP +S +n +700 1766 M 301 0 1 PP +S +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 1823 200 (Minimum) 200 SB +612 1823 28 (=) 28 SB +651 1823 17 (-) 17 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +709 1782 22 (x) 22 SB +836 1782 25 (a) 25 SB +735 1860 25 (a) 25 SB +862 1860 25 (a) 25 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +866 1779 19 (N) 19 SB +764 1858 19 (N) 19 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +752 1784 25 (0) 25 SB +933 1784 25 (1) 25 SB +928 1862 25 (1) 25 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +974 1769 15 (2) 15 SB +803 1859 15 (1) 15 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +734 1744 17 (a) 17 SB +779 1744 17 (f) 17 SB +817 1744 17 (c) 17 SB +956 1744 17 (h) 17 SB +843 1822 17 (a) 17 SB +951 1822 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +801 1778 13 (\327) 13 SB +901 1778 27 (-) 27 SB +826 1856 13 (\327) 13 SB +896 1856 27 (-) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +787 1856 16 (-) 16 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1005 1823 13 (.) 13 SB +279 1999 141 (Figure ) 141 SB +420 1999 25 (5) 25 SB +445 1999 1194 ( shows the control vector for the harvest system with N=20.) 1194 SB +0 4 SP +440 2573 M 0 -423 1 PP +S +n +434 2573 M 6 0 1 PP +S +n +434 2503 M 6 0 1 PP +S +n +434 2432 M 6 0 1 PP +S +n +434 2362 M 6 0 1 PP +S +n +434 2291 M 6 0 1 PP +S +n +434 2220 M 6 0 1 PP +S +n +434 2150 M 6 0 1 PP +S +n +440 2573 M 1061 0 1 PP +S +n +440 2579 M 0 -12 1 PP +S +n +496 2579 M 0 -12 1 PP +S +n +552 2579 M 0 -12 1 PP +S +n +608 2579 M 0 -12 1 PP +S +n +663 2579 M 0 -12 1 PP +S +n +719 2579 M 0 -12 1 PP +S +n +775 2579 M 0 -12 1 PP +S +n +831 2579 M 0 -12 1 PP +S +n +887 2579 M 0 -12 1 PP +S +n +943 2579 M 0 -12 1 PP +S +n +998 2579 M 0 -12 1 PP +S +n +1054 2579 M 0 -12 1 PP +S +n +1110 2579 M 0 -12 1 PP +S +n +1166 2579 M 0 -12 1 PP +S +n +1221 2579 M 0 -12 1 PP +S +n +1277 2579 M 0 -12 1 PP +S +n +1333 2579 M 0 -12 1 PP +S +n +1389 2579 M 0 -12 1 PP +S +n +1445 2579 M 0 -12 1 PP +S +n +1501 2579 M 0 -12 1 PP +S +n +0 1 SP +gs 57 3 440 2560 CB +440 2562 M 56 -2 1 PP +S +n +gr +gs 57 4 496 2557 CB +496 2560 M 56 -3 1 PP +S +n +gr +gs 57 5 552 2553 CB +552 2557 M 56 -4 1 PP +S +n +gr +gs 56 6 608 2548 CB +608 2553 M 55 -5 1 PP +S +n +gr +gs 57 5 663 2544 CB +663 2548 M 56 -4 1 PP +S +n +gr +gs 57 6 719 2539 CB +719 2544 M 56 -5 1 PP +S +n +gr +gs 57 11 775 2529 CB +775 2539 M 56 -10 1 PP +S +n +gr +gs 57 9 831 2521 CB +831 2529 M 56 -8 1 PP +S +n +gr +gs 57 10 887 2512 CB +887 2521 M 56 -9 1 PP +S +n +gr +gs 56 17 943 2496 CB +943 2512 M 55 -16 1 PP +S +n +gr +gs 57 22 998 2475 CB +998 2496 M 56 -21 1 PP +S +n +gr +gs 57 17 1054 2459 CB +1054 2475 M 56 -16 1 PP +S +n +gr +gs 57 23 1110 2437 CB +1110 2459 M 56 -22 1 PP +S +n +gr +gs 56 39 1166 2399 CB +1166 2437 M 55 -38 1 PP +S +n +gr +gs 57 29 1221 2371 CB +1221 2399 M 56 -28 1 PP +S +n +gr +gs 57 42 1277 2330 CB +1277 2371 M 56 -41 1 PP +S +n +gr +gs 57 55 1333 2276 CB +1333 2330 M 56 -54 1 PP +S +n +gr +gs 57 70 1389 2207 CB +1389 2276 M 56 -69 1 PP +S +n +gr +gs 57 51 1445 2157 CB +1445 2207 M 56 -50 1 PP +S +n +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 85 75 928 2664 CB +935 2677 70 (u\(k\)) 70 SB +gr +32 -2700 -2700 42 42 0 0 0 37 /Times-Roman /font32 ANSIFont font +gs 75 77 293 2323 CB +304 2393 62 (f\(u\)) 62 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 1283 674 278 2080 CB +394 2549 21 (0) 21 SB +gr +gs 1283 674 278 2080 CB +373 2478 42 (10) 42 SB +gr +gs 1283 674 278 2080 CB +373 2408 42 (20) 42 SB +gr +gs 1283 674 278 2080 CB +373 2337 42 (30) 42 SB +gr +gs 1283 674 278 2080 CB +373 2266 42 (40) 42 SB +gr +gs 1283 674 278 2080 CB +373 2196 42 (50) 42 SB +gr +gs 1283 674 278 2080 CB +373 2125 42 (60) 42 SB +gr +gs 1283 674 278 2080 CB +430 2604 21 (1) 21 SB +gr +gs 1283 674 278 2080 CB +541 2604 21 (3) 21 SB +gr +gs 1283 674 278 2080 CB +653 2604 21 (5) 21 SB +gr +gs 1283 674 278 2080 CB +765 2604 21 (7) 21 SB +gr +gs 1283 674 278 2080 CB +876 2604 21 (9) 21 SB +gr +gs 1283 674 278 2080 CB +977 2604 42 (11) 42 SB +gr +gs 1283 674 278 2080 CB +1089 2604 42 (13) 42 SB +gr +gs 1283 674 278 2080 CB +1200 2604 42 (15) 42 SB +gr +gs 1283 674 278 2080 CB +1312 2604 42 (17) 42 SB +gr +gs 1283 674 278 2080 CB +1424 2604 42 (19) 42 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 2780 78 (Fig. ) 78 SB +357 2780 21 (5) 21 SB +378 2780 12 (:) 12 SB +456 2780 956 (Optimal control vector for the harvest system with N=20) 956 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2894 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 2900 270 (objharv.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 2894 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font MSTT31c2ea +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 10 10 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 376 (3. Dynamic optimization) 376 SB +1930 116 83 (Page ) 83 SB +2013 116 38 (10) 38 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 210 526 (3.4. Push-cart system) 526 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 395 1746 (The push-cart system is a two-dimensional system described by the following equations:) 1746 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 484 22 (x) 22 SB +461 484 22 (k) 22 SB +619 484 22 (x) 22 SB +682 484 22 (k) 22 SB +921 484 22 (k) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +424 518 15 (1) 15 SB +642 518 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +527 486 25 (1) 25 SB +993 486 25 (1) 25 SB +1032 486 25 (2) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +494 480 27 (+) 27 SB +577 480 27 (=) 27 SB +957 480 27 (=) 27 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +442 445 17 (a) 17 SB +549 445 17 (f) 17 SB +663 445 17 (a) 17 SB +708 445 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1014 486 13 (,) 13 SB +1057 486 13 (,) 13 SB +1073 486 13 (.) 13 SB +1088 486 13 (.) 13 SB +1103 486 13 (.) 13 SB +1119 486 13 (,) 13 SB +1138 486 36 (N) 36 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1180 486 13 (,) 13 SB +1 lc +1 lj +0 0 0 pC +0 2 SP +972 635 M 67 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 601 22 (x) 22 SB +466 601 22 (k) 22 SB +673 601 22 (x) 22 SB +736 601 22 (k) 22 SB +825 601 22 (x) 22 SB +884 601 22 (k) 22 SB +978 640 33 (N) 33 SB +1047 601 25 (u) 25 SB +1091 601 22 (k) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +426 635 15 (2) 15 SB +696 635 15 (2) 15 SB +847 635 15 (1) 15 SB +1017 639 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +531 603 25 (1) 25 SB +621 603 25 (2) 25 SB +993 571 25 (1) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +499 597 27 (+) 27 SB +582 597 27 (=) 27 SB +652 597 13 (\327) 13 SB +786 597 27 (-) 27 SB +934 597 27 (+) 27 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +447 563 17 (a) 17 SB +554 563 17 (f) 17 SB +717 563 17 (a) 17 SB +762 563 17 (f) 17 SB +865 563 17 (a) 17 SB +910 563 17 (f) 17 SB +1072 563 17 (a) 17 SB +1117 563 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1139 603 13 (.) 13 SB +279 762 1247 (The objective function for minimization is therefore defined as:) 1247 SB +829 910 M 94 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 876 14 (f) 14 SB +452 876 22 (x) 22 SB +494 876 25 (u) 25 SB +606 876 22 (x) 22 SB +667 876 33 (N) 33 SB +884 915 33 (N) 33 SB +991 876 25 (u) 25 SB +1058 876 22 (k) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +936 944 13 (k) 13 SB +948 844 19 (N) 19 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +476 878 13 (,) 13 SB +547 878 28 (=) 28 SB +585 878 17 (-) 17 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +431 838 17 (a) 17 SB +520 838 17 (f) 17 SB +645 838 17 (a) 17 SB +767 838 17 (f) 17 SB +1039 838 17 (a) 17 SB +1084 838 17 (f) 17 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +627 909 15 (1) 15 SB +1018 875 15 (2) 15 SB +968 945 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +744 878 25 (1) 25 SB +864 846 25 (1) 25 SB +832 917 25 (2) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +712 872 27 (+) 27 SB +791 872 27 (+) 27 SB +863 911 13 (\327) 13 SB +32 0 0 29 29 0 0 0 29 /Symbol font +952 942 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +932 858 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1105 878 13 (.) 13 SB +279 1045 943 (The exact solution can be analytically found by:) 943 SB +688 1193 M 28 0 1 PP +S +n +765 1193 M 153 0 1 PP +S +n +966 1193 M 115 0 1 PP +S +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 1161 200 (Minimum) 200 SB +612 1161 28 (=) 28 SB +690 1129 25 (1) 25 SB +691 1200 25 (3) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +652 1155 27 (-) 27 SB +727 1155 27 (+) 27 SB +796 1123 13 (\327) 13 SB +862 1123 27 (-) 27 SB +817 1194 13 (\327) 13 SB +928 1155 27 (+) 27 SB +1000 1194 13 (\327) 13 SB +32 0 0 29 29 0 0 0 29 /Symbol font +1110 1225 16 (=) 16 SB +1114 1125 16 (-) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +1089 1141 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +767 1129 25 (3) 25 SB +894 1129 25 (1) 25 SB +786 1200 25 (6) 25 SB +1011 1129 25 (1) 25 SB +969 1200 25 (2) 25 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +876 1196 15 (2) 15 SB +1059 1196 15 (3) 15 SB +1177 1158 15 (2) 15 SB +1126 1228 15 (1) 15 SB +1130 1128 15 (1) 15 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +817 1127 33 (N) 33 SB +838 1198 33 (N) 33 SB +1021 1198 33 (N) 33 SB +1150 1159 22 (k) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +1094 1227 13 (k) 13 SB +1091 1127 19 (N) 19 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1201 1161 13 (.) 13 SB +279 1328 141 (Figure ) 141 SB +420 1328 25 (6) 25 SB +445 1328 1237 ( shows the control vector for the push-cart system with N=20.) 1237 SB +0 4 SP +451 1905 M 0 -426 1 PP +S +n +445 1905 M 6 0 1 PP +S +n +445 1820 M 6 0 1 PP +S +n +445 1735 M 6 0 1 PP +S +n +445 1650 M 6 0 1 PP +S +n +445 1564 M 6 0 1 PP +S +n +445 1479 M 6 0 1 PP +S +n +451 1905 M 1047 0 1 PP +S +n +451 1911 M 0 -12 1 PP +S +n +506 1911 M 0 -12 1 PP +S +n +561 1911 M 0 -12 1 PP +S +n +616 1911 M 0 -12 1 PP +S +n +671 1911 M 0 -12 1 PP +S +n +726 1911 M 0 -12 1 PP +S +n +782 1911 M 0 -12 1 PP +S +n +837 1911 M 0 -12 1 PP +S +n +892 1911 M 0 -12 1 PP +S +n +947 1911 M 0 -12 1 PP +S +n +1002 1911 M 0 -12 1 PP +S +n +1057 1911 M 0 -12 1 PP +S +n +1112 1911 M 0 -12 1 PP +S +n +1167 1911 M 0 -12 1 PP +S +n +1222 1911 M 0 -12 1 PP +S +n +1277 1911 M 0 -12 1 PP +S +n +1332 1911 M 0 -12 1 PP +S +n +1387 1911 M 0 -12 1 PP +S +n +1443 1911 M 0 -12 1 PP +S +n +1498 1911 M 0 -12 1 PP +S +n +0 1 SP +gs 56 22 451 1500 CB +451 1500 M 55 21 1 PP +S +n +gr +gs 56 23 506 1521 CB +506 1521 M 55 22 1 PP +S +n +gr +gs 56 22 561 1543 CB +561 1543 M 55 21 1 PP +S +n +gr +gs 56 23 616 1564 CB +616 1564 M 55 22 1 PP +S +n +gr +gs 56 22 671 1586 CB +671 1586 M 55 21 1 PP +S +n +gr +gs 57 22 726 1607 CB +726 1607 M 56 21 1 PP +S +n +gr +gs 56 22 782 1628 CB +782 1628 M 55 21 1 PP +S +n +gr +gs 56 23 837 1649 CB +837 1649 M 55 22 1 PP +S +n +gr +gs 56 22 892 1671 CB +892 1671 M 55 21 1 PP +S +n +gr +gs 56 23 947 1692 CB +947 1692 M 55 22 1 PP +S +n +gr +gs 56 22 1002 1714 CB +1002 1714 M 55 21 1 PP +S +n +gr +gs 56 22 1057 1735 CB +1057 1735 M 55 21 1 PP +S +n +gr +gs 56 23 1112 1756 CB +1112 1756 M 55 22 1 PP +S +n +gr +gs 56 22 1167 1778 CB +1167 1778 M 55 21 1 PP +S +n +gr +gs 56 22 1222 1799 CB +1222 1799 M 55 21 1 PP +S +n +gr +gs 56 22 1277 1820 CB +1277 1820 M 55 21 1 PP +S +n +gr +gs 56 23 1332 1841 CB +1332 1841 M 55 22 1 PP +S +n +gr +gs 57 22 1387 1863 CB +1387 1863 M 56 21 1 PP +S +n +gr +gs 56 22 1443 1884 CB +1443 1884 M 55 21 1 PP +S +n +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 85 75 932 1996 CB +939 2009 70 (u\(k\)) 70 SB +gr +32 -2700 -2700 42 42 0 0 0 37 /Times-Roman /font32 ANSIFont font +gs 75 108 293 1638 CB +304 1739 94 (f\(x,u\)) 94 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 1280 677 278 1409 CB +405 1881 21 (0) 21 SB +gr +gs 1280 677 278 1409 CB +373 1796 53 (0.2) 53 SB +gr +gs 1280 677 278 1409 CB +373 1710 53 (0.4) 53 SB +gr +gs 1280 677 278 1409 CB +373 1625 53 (0.6) 53 SB +gr +gs 1280 677 278 1409 CB +373 1540 53 (0.8) 53 SB +gr +gs 1280 677 278 1409 CB +405 1454 21 (1) 21 SB +gr +gs 1280 677 278 1409 CB +440 1936 21 (1) 21 SB +gr +gs 1280 677 278 1409 CB +551 1936 21 (3) 21 SB +gr +gs 1280 677 278 1409 CB +661 1936 21 (5) 21 SB +gr +gs 1280 677 278 1409 CB +771 1936 21 (7) 21 SB +gr +gs 1280 677 278 1409 CB +881 1936 21 (9) 21 SB +gr +gs 1280 677 278 1409 CB +981 1936 42 (11) 42 SB +gr +gs 1280 677 278 1409 CB +1091 1936 42 (13) 42 SB +gr +gs 1280 677 278 1409 CB +1201 1936 42 (15) 42 SB +gr +gs 1280 677 278 1409 CB +1311 1936 42 (17) 42 SB +gr +gs 1280 677 278 1409 CB +1422 1936 42 (19) 42 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 2112 78 (Fig. ) 78 SB +357 2112 21 (6) 21 SB +378 2112 12 (:) 12 SB +456 2112 992 (Optimal control vector for the push-cart system with N=20) 992 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2226 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 2232 270 (objpush.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 2226 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 11 11 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References) 207 SB +1930 116 83 (Page ) 83 SB +2013 116 38 (11) 38 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 67 67 0 0 0 61 /Times-Bold /font29 ANSIFont font +279 305 382 (4. References) 382 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 499 162 ([Mic92]) 162 SB +515 499 1370 (Michalewicz, Z.: "Genetic Algorithms + Data Structures = Evolution) 1370 SB +515 574 1160 (Programs"; Berlin, Heidelberg, New York: Springer, 1992) 1160 SB +279 699 189 ([MSB91]) 189 SB +515 699 44 (M) 44 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +559 699 25 (\374) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +584 699 1456 (hlenbein, H., Schomisch, M. and Born, J.: "The parallel genetic algorithm) 1456 SB +515 774 1304 (as function optimizer"; Parallel Computing, 17, pp.619-632, 1991) 1304 SB +279 899 192 ([OGH93]) 192 SB +515 899 1526 (Ostermeier, A., Gawelczyk, A. and Hansen, N.: "A Derandomized Approach) 1526 SB +515 974 1474 (to Self Adaptation of Evolution Strategies"; Technical Report TR-93-003,) 1474 SB +515 1049 326 (TU Berlin, 1993) 326 SB +279 1174 161 ([Rec73]) 161 SB +515 1174 1534 (Rechenberg, I.: "Evolutionsstrategie - Optimierung technischer Systeme nach) 1534 SB +515 1249 1435 (Prinzipien der biologischen Evolution"; Stuttgart: Frommann-Holzboog,) 1435 SB +515 1324 100 (1973) 100 SB +279 1449 161 ([Rec94]) 161 SB +515 1449 1475 (Rechenberg, I.: "Evolutionsstrategie 94"; Stuttgart: Frommann-Holzboog,) 1475 SB +515 1524 100 (1994) 100 SB +279 1649 158 ([Sch81]) 158 SB +515 1649 1507 (Schwefel, H.-P.: "Numerical optimization of computer models"; Chichester:) 1507 SB +515 1724 402 (Wiley & Sons, 1981) 402 SB +279 1849 143 ([SE92]) 143 SB +515 1849 1418 (Stuckmann, B. E.; Easom, E. E.: "A Comparison of Bayesian/Sampling) 1418 SB +515 1924 1516 (Global Optimization Techniques"; IEEE Transactions on Systems, Man, and) 1516 SB +515 1999 980 (Cybernetics, Vol. 22, No. 5, pp.1024-1032, 1992) 980 SB +279 2124 175 ([SHF94]) 175 SB +515 2124 74 (Sch) 74 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +589 2124 25 (\366) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +614 2124 1416 (neburg, E., Heinzmann, F. and Feddersen, S.: "Genetische Algorithmen) 1416 SB +515 2199 1470 (und Evolutionsstrategien"; Bonn, Paris, Reading, Mass.: Addison-Wesley,) 1470 SB +515 2274 100 (1994) 100 SB +279 2399 145 ([TZ89]) 145 SB +515 2399 1468 (T\366rn, A. and Zilinskas, A.: "Global Optimization"; volume 350 of Lecture) 1468 SB +515 2474 1494 (Notes in Computer Science, Berlin, Heidelberg, New York: Springer, 1989) 1494 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Times-Bold +%%+ font Times-Roman +%%Trailer +SVDoc restore +end +%%Pages: 11 +% TrueType font name key: +% MSTT310000 = +% MSTT310000 = +% MSTT310000 = +% MSTT310000 = +% MSTT310000 = +% MSTT31c1c0 = 2aa7DTimes New RomanF00000000000001900000 +% MSTT31c1cd = 2aa7DTimes New RomanF00000032000001900000 +% MSTT31c26e = 2aa7DTimes New RomanF00000043000002bc0000 +% MSTT31c27b = 2aa7DTimes New RomanF00000028000001900000 +% MSTT31c288 = 2aa7DTimes New RomanF0000002a000001900000 +% MSTT31c295 = 2aa7DTimes New RomanF00000026000001900000 +% MSTT31c20e = 2aa7DCourier NewF00000032000001900000 +% MSTT31c2a2 = 2aa7DTimes New RomanF0000003a000002bc0000 +% MSTT31c2af = 2aa7DFencesF00000064000001900000 +% MSTT31c2ba = 2aa7DTimes New RomanF00000010000001900000 +% MSTT31c2c7 = 2aa7DFencesF00000000000001900000 +% MSTT31c2d2 = 2aa7DFencesF0000003a000001900000 +% MSTT31c2dd = 2aa7DTimes New RomanF00000032000001900001 +% MSTT31c2ea = 2aa7DMT ExtraF00000032000001900000 +% MSTT31c2f5 = 2aa7DArialF00000021000002bc0000 +% MSTT31c300 = 2aa7DTimes New RomanF0000000a000001900000 +% MSTT31c30d = 2aa7DTimes New RomanF0000001a000001900000 +% MSTT31c31a = 2aa7DTimes New RomanF0000002af57401900000 +%%DocumentSuppliedResources: procset Win35Dict 3 1 +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font MSTT31c2d2 +%%+ font MSTT31c2ea + +%%DocumentNeededResources: font Courier +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman + +%%EOF + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVDP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVDP.M" index edcbd786d18e2b455ea6fc29c9bd0e01c76e6848..76aab634fbcad1e9a5e57fc67037e00552782be3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVDP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVDP.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:36e7e1f37a0707c6785ec214489d551b56d157f8c2c1227e27f93a880df6c70b -size 1042 +% XOVDP.M (CROSSOVer Double Point) +% +% This function performs double point crossover between pairs of +% individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovdp(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovdp(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 2, 0); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVDPRS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVDPRS.M" index 902f4f6c09a3473197b746d4714c397960859a6b..e65331226383389f327e7b596f6db1aca13058dd 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVDPRS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVDPRS.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9e38f004605377c6c745681434ae98682be231ea910b71894507753f334c8e54 -size 1090 +% XOVDPRS.M (CROSSOVer Double-Point with Reduced Surrogate) +% +% This function performs double-point 'reduced surrogate' crossover between +% pairs of individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovdprs(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovdprs(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low-level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 2, 1); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVMP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVMP.M" index 0125c287895f7b43b938db33b4691ad377c536d9..1b49416566cdb5b2088b055891d1a34ac22609d3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVMP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVMP.M" @@ -1,3 +1,84 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:492c5255f6c08d5cd3a89d284b09cbbe072271fcb15b44833df2758df7dc7425 -size 2795 +% XOVMP.m Multi-point crossover +% +% Syntax: NewChrom = xovmp(OldChrom, Px, Npt, Rs) +% +% This function takes a matrix OldChrom containing the binary +% representation of the individuals in the current population, +% applies crossover to consecutive pairs of individuals with +% probability Px and returns the resulting population. +% +% Npt indicates how many crossover points to use (1 or 2, zero +% indicates shuffle crossover). +% Rs indicates whether or not to force the production of +% offspring different from their parents. +% + +% Author: Carlos Fonseca, Updated: Andrew Chipperfield +% Date: 28/09/93, Date: 27-Jan-94 + +function NewChrom = xovmp(OldChrom, Px, Npt, Rs); + +% Identify the population size (Nind) and the chromosome length (Lind) +[Nind,Lind] = size(OldChrom); + +if Lind < 2, NewChrom = OldChrom; return; end + +if nargin < 4, Rs = 0; end +if nargin < 3, Npt = 0; Rs = 0; end +if nargin < 2, Px = 0.7; Npt = 0; Rs = 0; end +if isnan(Px), Px = 0.7; end +if isnan(Npt), Npt = 0; end +if isnan(Rs), Rs = 0; end +if isempty(Px), Px = 0.7; end +if isempty(Npt), Npt = 0; end +if isempty(Rs), Rs = 0; end + +Xops = floor(Nind/2); +DoCross = rand(Xops,1) < Px; +odd = 1:2:Nind-1; +even = 2:2:Nind; + +% Compute the effective length of each chromosome pair +Mask = ~Rs | (OldChrom(odd, :) ~= OldChrom(even, :)); +Mask = cumsum(Mask')'; + +% Compute cross sites for each pair of individuals, according to their +% effective length and Px (two equal cross sites mean no crossover) +xsites(:, 1) = Mask(:, Lind); +if Npt >= 2, + xsites(:, 1) = ceil(xsites(:, 1) .* rand(Xops, 1)); +end +xsites(:,2) = rem(xsites + ceil((Mask(:, Lind)-1) .* rand(Xops, 1)) ... + .* DoCross - 1 , Mask(:, Lind) )+1; + +% Express cross sites in terms of a 0-1 mask +Mask = (xsites(:,ones(1,Lind)) < Mask) == ... + (xsites(:,2*ones(1,Lind)) < Mask); + +if ~Npt, + shuff = rand(Lind,Xops); + [ans,shuff] = sort(shuff); + for i=1:Xops + OldChrom(odd(i),:)=OldChrom(odd(i),shuff(:,i)); + OldChrom(even(i),:)=OldChrom(even(i),shuff(:,i)); + end +end + +% Perform crossover +NewChrom(odd,:) = (OldChrom(odd,:).* Mask) + (OldChrom(even,:).*(~Mask)); +NewChrom(even,:) = (OldChrom(odd,:).*(~Mask)) + (OldChrom(even,:).*Mask); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population +if rem(Nind,2), + NewChrom(Nind,:)=OldChrom(Nind,:); +end + +if ~Npt, + [ans,unshuff] = sort(shuff); + for i=1:Xops + NewChrom(odd(i),:)=NewChrom(odd(i),unshuff(:,i)); + NewChrom(even(i),:)=NewChrom(even(i),unshuff(:,i)); + end +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSH.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSH.M" index 738452b855b533b9c25c985217770a2aa05e8c2a..f44f5b6d039c6b0363c290e5db4d5c1936416ce8 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSH.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSH.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:fba081244535a69f8765c25d7dc572af5fdc23be033333c847981673ec02a2a4 -size 1032 +% XOVSH.M (CROSSOVer SHuffle) +% +% This function performs shuffle crossover between pairs of +% individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovsh(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovsh(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 0, 0); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSHRS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSHRS.M" index a9c8be0baeda8668ede638f71df18ef5db466e73..4ceea7550e2f8ccb2cd1c560cc31fcc130bd40ae 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSHRS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSHRS.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:05e39153994c1cd4415d9c9412e1f5a2d7298171fdf2501fbd053f3bd3749894 -size 1080 +% XOVSHRS.M (CROSSOVer SHuffle with Reduced Surrogate) +% +% This function performs shuffle 'reduced surrogate' crossover between +% pairs of individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovshrs(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovshrs(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 0, 1); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSP.M" index c4ae37ba22b78fec3557b99d4b8080ba05904a9f..b5f029eccfc239ae1d6a578552568dca6dc1687a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSP.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:83492d75f6a1da8f4624cff6a540a7844f89ccdd99d046251a2cf80cae2e2245 -size 1043 +% XOVSP.M (CROSSOVer Single-Point) +% +% This function performs single-point crossover between pairs of +% individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovsp(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovsp(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 1, 0); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSPRS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSPRS.M" index 7305f1eb57cfc9186cc2151720fe0e20251af26d..0809b4dc4cd913f9cd7b516869a85e74ee4d17a7 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSPRS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-origin/SRC/XOVSPRS.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1fd4438f59f1e79d28ca7949a48dd466fc29300d0a969728af9657bea8809c26 -size 1090 +% XOVSPRS.M (CROSSOVer Single-Point with Reduced Surrogate) +% +% This function performs single-point 'reduced surrogate' crossover between +% pairs of individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovsprs(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real-values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovsprs(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low-level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 1, 1); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/BS2RV.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/BS2RV.M" index 0d407f06e071c2c32d8d1dea132afcad3768ffe2..b2e812e89ba6bf888a225eab01d5e545942f6b8c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/BS2RV.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/BS2RV.M" @@ -1,3 +1,115 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2a42fa20681fe57381f8c961409149366d60da9ffbfcf3efb169d6dcbbc66a28 -size 3217 +% BS2RV.m - Binary string to real vector +% +% This function decodes binary chromosomes into vectors of reals. The +% chromosomes are seen as the concatenation of binary strings of given +% length, and decoded into real numbers in a specified interval using +% either standard binary or Gray decoding. +% +% Syntax: Phen = bs2rv(Chrom,FieldD) +% +% Input parameters: +% +% Chrom - Matrix containing the chromosomes of the current +% population. Each line corresponds to one +% individual's concatenated binary string +% representation. Leftmost bits are MSb and +% rightmost are LSb. +% +% FieldD - Matrix describing the length and how to decode +% each substring in the chromosome. It has the +% following structure: +% +% [len; (num) +% lb; (num) +% ub; (num) +% code; (0=binary | 1=gray) +% scale; (0=arithmetic | 1=logarithmic) +% lbin; (0=excluded | 1=included) +% ubin]; (0=excluded | 1=included) +% +% where +% len - row vector containing the length of +% each substring in Chrom. sum(len) +% should equal the individual length. +% lb, +% ub - Lower and upper bounds for each +% variable. +% code - binary row vector indicating how each +% substring is to be decoded. +% scale - binary row vector indicating where to +% use arithmetic and/or logarithmic +% scaling. +% lbin, +% ubin - binary row vectors indicating whether +% or not to include each bound in the +% representation range +% +% Output parameter: +% +% Phen - Real matrix containing the population phenotypes. + +% +% Author: Carlos Fonseca, Updated: Andrew Chipperfield +% Date: 08/06/93, Date: 26-Jan-94 + +function Phen = bs2rv(Chrom,FieldD) + +% Identify the population size (Nind) +% and the chromosome length (Lind) +[Nind,Lind] = size(Chrom); + +% Identify the number of decision variables (Nvar) +[seven,Nvar] = size(FieldD); + +if seven ~= 7 + error('FieldD must have 7 rows.'); +end + +% Get substring properties +len = FieldD(1,:); +lb = FieldD(2,:); +ub = FieldD(3,:); +code = ~(~FieldD(4,:)); +scale = ~(~FieldD(5,:)); +lin = ~(~FieldD(6,:)); +uin = ~(~FieldD(7,:)); + +% Check substring properties for consistency +if sum(len) ~= Lind, + error('Data in FieldD must agree with chromosome length'); +end + +if ~all(lb(scale).*ub(scale)>0) + error('Log-scaled variables must not include 0 in their range'); +end + +% Decode chromosomes +Phen = zeros(Nind,Nvar); + +lf = cumsum(len); +li = cumsum([1 len]); +Prec = .5 .^ len; + +logsgn = sign(lb(scale)); +lb(scale) = log( abs(lb(scale)) ); +ub(scale) = log( abs(ub(scale)) ); +delta = ub - lb; + +Prec = .5 .^ len; +num = (~lin) .* Prec; +den = (lin + uin - 1) .* Prec; + +for i = 1:Nvar, + idx = li(i):lf(i); + if code(i) % Gray decoding + Chrom(:,idx)=rem(cumsum(Chrom(:,idx)')',2); + end + Phen(:,i) = Chrom(:,idx) * [ (.5).^(1:len(i))' ]; + Phen(:,i) = lb(i) + delta(i) * (Phen(:,i) + num(i)) ./ (1 - den(i)); +end + +expand = ones(Nind,1); +if any(scale) + Phen(:,scale) = logsgn(expand,:) .* exp(Phen(:,scale)); +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CONTENTS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CONTENTS.M" index 780354bbcbd28d9e302eeaeb32bdc9414009edad..675708b6266fd34653d1afec5bbae223820ae80f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CONTENTS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CONTENTS.M" @@ -1,3 +1,54 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:cd8ddbf0dc11c2eac9a9c1b0dd1dda6ef6ce04f08aca45a11652054507cc54f5 -size 1835 +% Genetic Algorithm Toolbox. +% Version 1.2 15-Apr-94 +% Department of Automatic Control and Systems Engineering +% University of Sheffield, England +% +% Creating populations +% crtbase - create a base vector +% crtbp - create a binary population +% crtrp - create a real-valued population +% +% Fitness assignment +% ranking - rank-based fitness assignment +% scaling - proportional fitness-scaling +% +% Selection and reinsertion +% reins - uniform random and fitness-based reinsertion +% rws - roulette wheel selection +% select - high-level selection routine +% sues - stochastic universal sampling +% +% Mutation operators +% mut - discrete mutation +% mutate - high-level mutation function +% mutbga - real-value mutation +% +% Crossover operators +% recdis - discrete recombination +% recint - intermediate recombination +% reclin - line recombination +% recmut - line recombination with mutation features +% recombin - high-level recombination function +% xovdp - double-point crossover +% xovdprs - double-point reduced surrogate crossover +% xovmp - general multi-point crossover +% xovsh - shuffle crossover +% xovshrs - shuffle reduced surrogate crossover +% xovsp - single-point crossover +% xovsprs - single-point reduced surrogate crossover +% +% Subpopulation support +% migrate - exchange individuals between subpopulations +% +% +% Utility functions +% bs2rv - binary string to real-value conversion +% rep - matrix replication +% +% Demonstration and other functions +% mpga - multi-population genetic algorithm demonstration +% objfun1 - De Jongs first test function (used by sga) +% objharv - harvest function (used in mpga) +% resplot - result plotting (used in mpga) +% sga - simple genetic algorithm demonstration + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTBASE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTBASE.M" index 5e3f0420223cb4a9e553552bf383f1c3dbe72540..c2ef387b81778c368247ce1f1d5c0dc6b7357066 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTBASE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTBASE.M" @@ -1,3 +1,47 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:e0a5dec9709b6d5c6ebafa3f4a452d455710626114c4add503b1968c4c62a22a -size 1168 +% CRTBASE.m - Create base vector +% +% This function creates a vector containing the base of the loci +% in a chromosome. +% +% Syntax: BaseVec = crtbase(Lind, Base) +% +% Input Parameters: +% +% Lind - A scalar or vector containing the lengths +% of the alleles. Sum(Lind) is the length of +% the corresponding chromosome. +% +% Base - A scalar or vector containing the base of +% the loci contained in the Alleles. +% +% Output Parameters: +% +% BaseVec - A vector whose elements correspond to the base +% of the loci of the associated chromosome structure. + +% Author: Andrew Chipperfield +% Date: 19-Jan-94 + +function BaseVec = crtbase(Lind, Base) + +[ml LenL] = size(Lind) ; +if nargin < 2 + Base = 2 * ones(LenL,1) ; % default to base 2 +end +[mb LenB] = size(Base) ; + +% check parameter consistency +if ml > 1 | mb > 1 + error( 'Lind or Base is not a vector') ; +elseif (LenL > 1 & LenB > 1 & LenL ~= LenB) | (LenL == 1 & LenB > 1 ) + error( 'Vector dimensions must agree' ) ; +elseif LenB == 1 & LenL > 1 + Base = Base * ones(LenL,1) ; + +end + +BaseVec = [] ; +for i = 1:LenL + BaseVec = [BaseVec, Base(i)*ones(Lind(i),1)']; +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTBP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTBP.M" index 1df58c568d8e56b8058936ef7eca1bdb08e4766c..ed9188cb90f28358ad8a0a86660709e61cb63fa9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTBP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTBP.M" @@ -1,3 +1,72 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:894b8535d97486a598d8143bcf8fef1d72907caff3870db4955f7a996518a5d2 -size 2187 +% CRTP.m - Create an initial population +% +% This function creates a binary population of given size and structure. +% +% Syntax: [Chrom Lind BaseV] = crtbp(Nind, Lind, Base) +% +% Input Parameters: +% +% Nind - Either a scalar containing the number of individuals +% in the new population or a row vector of length two +% containing the number of individuals and their length. +% +% Lind - A scalar containing the length of the individual +% chromosomes. +% +% Base - A scalar containing the base of the chromosome +% elements or a row vector containing the base(s) +% of the loci of the chromosomes. +% +% Output Parameters: +% +% Chrom - A matrix containing the random valued chromosomes +% row wise. +% +% Lind - A scalar containing the length of the chromosome. +% +% BaseV - A row vector containing the base of the +% chromosome loci. + +% Author: Andrew Chipperfield +% Date: 19-Jan-94 + +function [Chrom, Lind, BaseV] = crtbp(Nind, Lind, Base) +nargs = nargin ; + +% Check parameter consistency + +if nargs >= 1, [mN, nN] = size(Nind) ; end +if nargs >= 2, [mL, nL] = size(Lind) ; end +if nargs == 3, [mB, nB] = size(Base) ; end + +if nN == 2 + if (nargs == 1) + Lind = Nind(2) ; Nind = Nind(1) ; BaseV = crtbase(Lind) ; + elseif (nargs == 2 & nL == 1) + BaseV = crtbase(Nind(2),Lind) ; Lind = Nind(2) ; Nind = Nind(1) ; + elseif (nargs == 2 & nL > 1) + if Lind ~= length(Lind), error('Lind and Base disagree'); end + BaseV = Lind ; Lind = Nind(2) ; Nind = Nind(1) ; + end +elseif nN == 1 + if nargs == 2 + if nL == 1, BaseV = crtbase(Lind) ; + else, BaseV = Lind ; Lind = nL ; end + elseif nargs == 3 + if nB == 1, BaseV = crtbase(Lind,Base) ; + elseif nB ~= Lind, error('Lind and Base disagree') ; + else BaseV = Base ; end + end +else + error('Input parameters inconsistent') ; +end + +% Create a structure of random chromosomes in row wise order, dimensions +% Nind by Lind. The base of each chromosomes loci is given by the value +% of the corresponding element of the row vector base. + +Chrom = floor(rand(Nind,Lind).*BaseV(ones(Nind,1),:)) ; + + +% End of file + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTRP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTRP.M" index 806adf2a21f3d6f8762cf198c70ad4e0936638f4..8ddb36b34404a9c7cff7c8682f08bbc60fa9ce91 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTRP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/CRTRP.M" @@ -1,3 +1,53 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:900cb8e84a5ad67fa6798ce0ae0b4a45b9bef93b5cad9a8119c108ecadfd1b36 -size 2091 +% CRTRP.M (CReaTe an initial (Real-value) Population) +% +% This function creates a population of given size of random real-values. +% +% Syntax: Chrom = crtrp(Nind,FieldDR); +% +% Input parameters: +% Nind - A scalar containing the number of individuals in the new +% population. +% +% FieldDR - A matrix of size 2 by number of variables describing the +% boundaries of each variable. It has the following structure: +% [lower_bound; (vector with lower bound for each veriable) +% upper_bound] (vector with upper bound for each veriable) +% [lower_bound_var_1 lower_bound_var_2 ... lower_bound_var_Nvar; +% upper_bound_var_1 upper_bound_var_2 ... upper_bound_var_Nvar] +% example - each individuals consists of 4 variables: +% FieldDR = [-100 -50 -30 -20; % lower bound +% 100 50 30 20] % upper bound +% +% Output parameter: +% Chrom - A matrix containing the random valued individuals of the +% new population of size Nind by number of variables. + +% Author: Hartmut Pohlheim +% History: 23.11.93 file created +% 25.02.94 clean up, check parameter consistency + + +function Chrom = crtrp(Nind,FieldDR); + +% Check parameter consistency + if nargin < 2, error('parameter FieldDR missing'); end + if nargin > 2, nargin = 2; end + + [mN, nN] = size(Nind); + [mF, Nvar] = size(FieldDR); + + if (mN ~= 1 & nN ~= 1), error('Nind has to be a scalar'); end + if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end + +% Compute Matrix with Range of variables and Matrix with Lower value + Range = rep((FieldDR(2,:)-FieldDR(1,:)),[Nind 1]); + Lower = rep(FieldDR(1,:), [Nind 1]); + +% Create initial population +% Each row contains one individual, the values of each variable uniformly +% distributed between lower and upper bound (given by FieldDR) + Chrom = rand(Nind,Nvar) .* Range + Lower; + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GA TOOLBOX FREQUENTLY ASKED QUESTIONS.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GA TOOLBOX FREQUENTLY ASKED QUESTIONS.txt" index 93daa862e2ca053d741161250025ecae0cec2bc4..8d88f695fde058e2dbe29f159ccfe5c35ccc374c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GA TOOLBOX FREQUENTLY ASKED QUESTIONS.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GA TOOLBOX FREQUENTLY ASKED QUESTIONS.txt" @@ -1,3 +1,346 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:e5494399b2862195fa10e2b74cdab3877d8e513655c439ac3a59a2f2c635d29d -size 12501 +GA TOOLBOX FREQUENTLY ASKED QUESTIONS +===================================== + +1. GENERAL QUESTIONS + + 1.1 'Where can I find information about the GA Toolbox?' + + 1.2 'What version(s) of MATLAB does the GA Toolbox work with?' + + 1.3 'Do you have a version of the GA Toolbox suitable for + MATLAB 5/6/7/... available?' + + 1.4 'Do you have a MOGA version of the GA Toolbox available?' + + 1.5 'How do I use the GA Toolbox to solve my particular problem?' + + 1.6 'How can I contact the authors of the GA Toolbox?' + +2. DOWNLOAD QUESTIONS + + 2.1 'I filled out the download form correctly, and pushed the + "Download" button - but I never received the GA Toolbox by + email. Why?' + + 2.2 'Why does your download form ask for my email address when + I just want a copy of the GA Toolbox?' + +3. INSTALLATION QUESTIONS + + 3.1 'How do I install the GA Toolbox?' + +4. RUN-TIME QUESTIONS + + 4.1 'Why do I get the error message(s): + + "identifier" expected, "switch" found, or + + Illegal use of reserved keyword "switch" + + 4.2 'Why do I get the error message(s): + + ??? Undefined function or variable "NonLin", or + + Warning: Reference to uninitialized variable "NonLin" + + 4.3 'Why is the function-specific help not working for the + GA Toolbox functions?' + + +===================================================================== + +ANSWERS TO GA TOOLBOX FREQUENTLY ASKED QUESTIONS +================================================ + +1. GENERAL QUESTIONS +==================== + +------------------------------------------------ + +1.1 The GA Toolbox homepage is at: + + http://www.shef.ac.uk/acse/research/ecrg/gat.html + +------------------------------------------------ + +1.2 'What version(s) of MATLAB does the GA Toolbox work with?' + +The GA Toolbox was written for MATLAB v4.2. It is usable with all +subsequent releases of MATLAB, but there are some minor syntax +issues that have to be fixed by hand when using the Toolbox with +MATLAB v5.3 and above. + +See Section 4 of this FAQ. + +------------------------------------------------ + +1.3 'Do you have a version of the GA Toolbox suitable for + MATLAB 5/6/7/... available?' + +The GA Toolbox was originally written for MATLAB v4.2, and it +is this version of the Toolbox which we make available for download. + +This version of the Toolbox can be (and has been) successfully +used with any later release of MATLAB, but, depending on the actual +release of MATLAB being used, some minor syntax fixes may need to be +applied to the Toolbox M files by hand. + +See Question 1.2 and Section 4 of this FAQ. + +In the future, we *may* make available versions of the GA Toolbox +which have the relevant corrections applied for the various +releases of MATLAB, but these are not yet available. + +------------------------------------------------ + +1.4 'Do you have a MOGA version of the GA Toolbox available?' + +No. + +But, in the future, we *may* make such a version of the +GA Toolbox available. + +------------------------------------------------ + +1.5 'How do I use the GA Toolbox to solve my particular problem?' + +Whilst we happily make the GA Toolbox available for free download +and are always interested to hear of your experiences in using it, +we do *not* have the resources to offer a general GA consulting service. + +So we will not reply to email sent to us asking for advice in using +the toolbox to solve particular problems. + +We encourage all users of the GA Toolbox to read carefully the +accompanying documentation and tutorial examples. For general +'how do I ... ?' questions, we suggest you post a question +to the relevant Usenet group comp.ai.genetic. + +------------------------------------------------ + +1.6 'How can I contact the authors of the GA Toolbox?' + +The authors of the GA Toolbox can be contacted by sending email +to ga-toolbox@acse.sheffield.ac.uk. + +We encourage you to send us email about errors you encounter when +using the GA Toolbox, as well as requests for enhancement to the +toolbox, and general comments about your experiences with it. + +Please read this FAQ carefully before sending any such email, and +please in particular note Question 1.5 of this FAQ. + +================================================ + +2. DOWNLOAD QUESTIONS +===================== + +------------------------------------------------ + +2.1 'I filled out the download form correctly, and pushed the + "Download" button - but I never received the GA Toolbox by + email. Why?' + +The GA Toolbox download mechanism works by programatically emailing +a copy of the toolbox to the email address supplied in the +download form. The Toolbox is sent as a MIME attachment in ZIP'ed +format. + +If, having filled in the download form using your correct email +address, you do not receive a copy of the Toolbox by email, then it +is almost certainly the case that *your* email system is +explicitly blocking incoming email which contains ZIP file attachments. +(Some mail administrators like to do this in an attempt to stop +certain types of email viruses and worms.) + +If this is the case, you should ask your mail administrator for advice +on your local email policy. + +A workaround is to setup a 'hotmail'-style address and use that +for the GA Toolbox download. + +------------------------------------------------ + +2.2 'Why does your download form ask for my email address when + I just want a copy of the GA Toolbox?' + +The GA Toolbox download mechanism works by programatically emailing +a copy of the toolbox to the email address supplied in the +download form. + +We guarantee that we will not use your email address (or any of the +other information you supply on the download form) for any other +purpose other than to create statistics - purely for internal use - +about download and usage patterns for the GA Toolbox. None of +the information you supply will be divulged to any third party. + +================================================ + +3. INSTALLATION QUESTIONS +========================= + +------------------------------------------------ + +3.1 'How do I install the GA Toolbox?' + +We advise you to ignore any purported high-level installation +help from MATLAB itself and, instead, to install the toolbox by hand. +If you have a completely local copy of MATLAB on a PC, then this +shouldn't be a problem; if you're using a networked version of MATLAB, +then you may have to get the system administrator to do this process on +the server - alternatively, you can use the toolbox files locally from +your own filestore. + +The details go something like this: + +3.1.1 If you have a completely local copy of MATLAB on your PC: + + a. Unzip the GA Toolbox somewhere in your own filestore: it will + unzip to two folders 'src' and 'doc'. + + b. Rename the 'src' folder to 'genetic' and move it into your + C:\Matlab_nn\toolbox folder + + (The 'nn' here is whatever your MATLAB version number is.) + + c. Go to your C:\Matlab_nn\toolbox\local directory and locate the + file 'pathdef.m'. Take a copy of the file for a backup, then + open the file with a text editor. You will see that it + specifies the paths to all the toolboxes you have. To add the + GA toolbox to the path, add the two lines: + + matlabroot,'\toolbox\genetic;',... + matlabroot,'\toolbox\genetic\test_fns;',... + + in a suitable place. + + d. That's it: if you restart MATLAB should have access to the + GA toolbox.; + +3.1.2 If you are using a networked copy of MATLAB, then either: + + A. The system administrator should do the same as the above + for the system installation of MATLAB, + + - or - + + B. You use the toolbox locally, in this way: + + a. Unzip the GA Toolbox somewhere in your own filestore: it will + unzip to two folders 'src' and 'doc'. + + b. Rename the 'src' folder to 'genetic'. You might also want to + move it somewhere else. Let's say it ends up in + d:\work\matlab\toolboxes\genetic. + + c. Add the two lines + + path(path, 'd:\work\matlab\toolboxes\genetic'); + path(path, 'd:\work\matlab\toolboxes\genetic\test_fns'); + + to the file 'startup.m' in your working directory. Your working + dir is going to be something like 'c:\matlab-nn\work' for a + modern PC installation of MATLAB; you might have to create the + file 'startup.m' there if it doesn't already exist. + + d. Again, that's it. When you restart MATLAB you should then + see the GA toolbox. + +Note that the process described in 3.1.2.B above is the same thing +you'd do to use your own M scripts: at this level, there is nothing +significant about the fact that the GA scripts are a 'toolbox' - +they are just a collection of M scripts, and the only issue is getting +their location mapped into the MATLAB path search path. To find out +more about the MATLAB search path and related matters then, for a +start, type 'help path' at the MATLAB prompt. + +================================================ + +4. RUN-TIME QUESTIONS +===================== + +------------------------------------------------ + +4.1 'Why do I get the error message(s): + + "identifier" expected, "switch" found, or + + Illegal use of reserved keyword "switch" + +This error message may be encountered when using the 'objfun1' +function, for example, and reflects one of the syntactical +differences between MATLAB 6 and previous releases of MATLAB. The +actual error message you see may depend on the actual release +of MATLAB you are using. + +The GA toolbox was developed for MATLAB v4.2, and should also +work unchanged for MATLAB releases up to including v5.2. +For later releases of MATLAB, some minor syntax fixes may +have to be applied to the M files of the toolbox by hand. These +fixes should generally be obvious to an experienced +user of MATLAB. + +In this case, the problem is that, in MATLAB v6, 'switch' is a +reserved word: in previous versions of MATLAB it was not. +To fix the problem, edit the relevant M file to change all +reference to 'switch' to something else like (eg 'myswitch') +instead. + +------------------------------------------------ + +4.2 'Why do I get the error message(s): + + ??? Undefined function or variable "NonLin", or + + Warning: Reference to uninitialized variable "NonLin" + +The actual error message you see may depend on the actual +release of MATLAB you are using. + +The GA toolbox was developed for MATLAB v4.2, and should also +work unchanged for MATLAB releases up to including v5.2. +For later releases of MATLAB, some minor syntax fixes may +have to be applied to the M files of the toolbox by hand. These +fixes should generally be obvious to an experienced +user of MATLAB. + +In this case, the problem is that the behaviour of MATLAB +with respect to uninitialized variables differs between MATLAB +releases. + +Please see The Mathworks Technical Solution note on this issue, +namely: + + http://www.mathworks.com/support/solutions/data/1-18GTU.html + +and then apply a suitable correction to the relevant M file(s) +of the GA Toolbox. + +------------------------------------------------ + +4.3 'Why is the function-specific help not working for the + GA Toolbox functions?' + +We have had unconfirmed reports that, when used with certain +releases of MATLAB, function-specific help for the GA Toolbox +(eg 'help mutate') does not work as expected. + +For MATLAB M files, function-specific help information is +encoded in comments within the M files themselves. It may +be that the detail of the allowable layouts of these comments +differs between some of the releases of MATLAB. If you find +that function-specific help is *not* working for you, please +check the documentation for your release of MATLAB, and compare +the detailed requirements for the 'help' comments with the format +used in the M files of the GA Toolbox. + +In addition, if you *do* have this problem, please email +ga-toolbox@acse.sheffield.ac.uk with the details of your version +of MATLAB so that we can update this FAQ. + +The workaround for function-specific help for GA Toolbox +functions not working from the MATLAB command line is simply +to read the help information contained within the relevant +M files using any text editor. + +================================================ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GATBXA0.LOG" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GATBXA0.LOG" index f2ee9352f9346526c64ebaea0185d8c9ba3853d1..1cfd3dfe40dda13c53e84cd6dca7dca45ad1517e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GATBXA0.LOG" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GATBXA0.LOG" @@ -1,3 +1,3 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:7f1dab054127c4dc96e13edb4a915f79107daf0ea4d1f8cafea7872f24e550e8 -size 273 +%%[ Warning: Times-Roman not found, using Font Substitution. 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/gstring exch def + /gfile exch def + /gindex 0 def + { + gfile read pop + dup 10 eq {exit} if + dup 13 eq {exit} if + gstring exch gindex exch put + /gindex gindex 1 add def + } loop + pop + gstring 0 gindex getinterval true + } def + } if +/FMVERSION { + FMversion ne { + /Times-Roman findfont 18 scalefont setfont + 100 100 moveto + (FrameMaker version does not match postscript_prolog!) + dup = + show showpage + } if + } def +/FMLOCAL { + FrameDict begin + 0 def + end + } def + /gstring FMLOCAL + /gfile FMLOCAL + /gindex FMLOCAL + /orgxfer FMLOCAL + /orgproc FMLOCAL + /organgle FMLOCAL + /orgfreq FMLOCAL + /yscale FMLOCAL + /xscale FMLOCAL + /manualfeed FMLOCAL + /paperheight FMLOCAL + /paperwidth FMLOCAL +/FMDOCUMENT { + array /FMfonts exch def + /#copies exch def + FrameDict begin + 0 ne dup {setmanualfeed} if + /manualfeed exch def + /paperheight exch def + /paperwidth exch def + /yscale exch def + /xscale exch def + currenttransfer cvlit /orgxfer exch def + currentscreen cvlit /orgproc exch def + /organgle exch def /orgfreq exch def + setpapername + manualfeed {true} {papersize} ifelse + {manualpapersize} {false} ifelse + {desperatepapersize} if + end + } def + /pagesave FMLOCAL + /orgmatrix FMLOCAL + /landscape FMLOCAL +/FMBEGINPAGE { + FrameDict begin + /pagesave save def + 3.86 setmiterlimit + /landscape exch 0 ne def + landscape { + 90 rotate 0 exch neg translate pop + } + {pop pop} + ifelse + xscale yscale scale + /orgmatrix matrix def + gsave + } def +/FMENDPAGE { + grestore + pagesave restore + end + showpage + } def +/FMFONTDEFINE { + FrameDict begin + findfont + ReEncode + 1 index exch + definefont + FMfonts 3 1 roll + put + end + } def +/FMFILLS { + FrameDict begin + array /fillvals exch def + end + } def +/FMFILL { + FrameDict begin + fillvals 3 1 roll put + end + } def +/FMNORMALIZEGRAPHICS { + newpath + 0.0 0.0 moveto + 1 setlinewidth + 0 setlinecap + 0 0 0 sethsbcolor + 0 setgray + } bind def + /fx FMLOCAL + /fy FMLOCAL + /fh FMLOCAL + /fw FMLOCAL + /llx FMLOCAL + /lly FMLOCAL + /urx FMLOCAL + /ury FMLOCAL +/FMBEGINEPSF { + end + /FMEPSF save def + /showpage {} def + FMNORMALIZEGRAPHICS + [/fy /fx /fh /fw /ury /urx /lly /llx] {exch def} forall + fx fy translate + rotate + fw urx llx sub div fh ury lly sub div scale + llx neg lly neg translate + } bind def +/FMENDEPSF { + FMEPSF restore + FrameDict begin + } bind def +FrameDict begin +/setmanualfeed { +%%BeginFeature *ManualFeed True + statusdict /manualfeed true put +%%EndFeature + } def +/max {2 copy lt {exch} if pop} bind def +/min {2 copy gt {exch} if pop} bind def +/inch {72 mul} def +/pagedimen { + paperheight sub abs 16 lt exch + paperwidth sub abs 16 lt and + {/papername exch def} {pop} ifelse + } def + /papersizedict FMLOCAL +/setpapername { + /papersizedict 14 dict def + papersizedict begin + /papername /unknown def + /Letter 8.5 inch 11.0 inch pagedimen + /LetterSmall 7.68 inch 10.16 inch pagedimen + /Tabloid 11.0 inch 17.0 inch pagedimen + /Ledger 17.0 inch 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+/manualpapersize { + papersizedict begin + /Letter {letter} def + /LetterSmall {lettersmall} def + /Tabloid {11x17} def + /Ledger {ledger} def + /Legal {legal} def + /Statement {statement} def + /Executive {executive} def + /A3 {a3} def + /A4 {a4} def + /A4Small {a4small} def + /B4 {b4} def + /B5 {b5} def + /unknown {unknown} def + papersizedict dup papername known {papername} {/unknown} ifelse get + end + stopped + } def +/desperatepapersize { + statusdict /setpageparams known + { + paperwidth paperheight 0 1 + statusdict begin + {setpageparams} stopped pop + end + } if + } def +/savematrix { + orgmatrix currentmatrix pop + } bind def +/restorematrix { + orgmatrix setmatrix + } bind def +/dmatrix matrix def +/dpi 72 0 dmatrix defaultmatrix dtransform + dup mul exch dup mul add sqrt def +/freq dpi 18.75 div 8 div round dup 0 eq {pop 1} if 8 mul dpi exch div def +/sangle 1 0 dmatrix defaultmatrix dtransform exch atan def +/DiacriticEncoding [ +/.notdef /.notdef /.notdef /.notdef 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/icircumflex /idieresis /ntilde /oacute /ograve +/ocircumflex /odieresis /otilde /uacute /ugrave /ucircumflex +/udieresis /dagger /.notdef /cent /sterling /section /bullet +/paragraph /germandbls /registered /copyright /trademark /acute +/dieresis /.notdef /AE /Oslash /.notdef /.notdef /.notdef /.notdef +/yen /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/ordfeminine /ordmasculine /.notdef /ae /oslash /questiondown +/exclamdown /logicalnot /.notdef /florin /.notdef /.notdef +/guillemotleft /guillemotright /ellipsis /.notdef /Agrave /Atilde +/Otilde /OE /oe /endash /emdash /quotedblleft /quotedblright +/quoteleft /quoteright /.notdef /.notdef /ydieresis /Ydieresis +/fraction /currency /guilsinglleft /guilsinglright /fi /fl /daggerdbl +/periodcentered /quotesinglbase /quotedblbase /perthousand +/Acircumflex /Ecircumflex /Aacute /Edieresis /Egrave /Iacute +/Icircumflex /Idieresis /Igrave /Oacute /Ocircumflex /.notdef /Ograve +/Uacute /Ucircumflex /Ugrave /dotlessi /circumflex /tilde /macron +/breve /dotaccent /ring /cedilla /hungarumlaut /ogonek /caron +] def +/ReEncode { + dup + length + dict begin + { + 1 index /FID ne + {def} + {pop pop} ifelse + } forall + 0 eq {/Encoding DiacriticEncoding def} if + currentdict + end + } bind def +/graymode true def + /bwidth FMLOCAL + /bpside FMLOCAL + /bstring FMLOCAL + /onbits FMLOCAL + /offbits FMLOCAL + /xindex FMLOCAL + /yindex FMLOCAL + /x FMLOCAL + /y FMLOCAL +/setpattern { + /bwidth exch def + /bpside exch def + /bstring exch def + /onbits 0 def /offbits 0 def + freq sangle landscape {90 add} if + {/y exch def + /x exch def + /xindex x 1 add 2 div bpside mul cvi def + /yindex y 1 add 2 div bpside mul cvi def + bstring yindex bwidth mul xindex 8 idiv add get + 1 7 xindex 8 mod sub bitshift and 0 ne + {/onbits onbits 1 add def 1} + {/offbits offbits 1 add def 0} + ifelse + } + setscreen + {} settransfer + offbits offbits onbits add div FMsetgray + /graymode false def + } bind def +/grayness { + FMsetgray + graymode not { + /graymode true def + orgxfer cvx settransfer + orgfreq organgle orgproc cvx setscreen + } if + } bind def + /HUE FMLOCAL + /SAT FMLOCAL + /BRIGHT FMLOCAL + /Colors FMLOCAL +FMPrintInColor + + { + /HUE 0 def + /SAT 0 def + /BRIGHT 0 def + % array of arrays Hue and Sat values for the separations [HUE BRIGHT] + /Colors + [[0 0 ] % black + [0 0 ] % white + [0.00 1.0] % red + [0.37 1.0] % green + [0.60 1.0] % blue + [0.50 1.0] % cyan + [0.83 1.0] % magenta + [0.16 1.0] % comment / yellow + ] def + + /BEGINBITMAPCOLOR { + BITMAPCOLOR} def + /BEGINBITMAPCOLORc { + BITMAPCOLORc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUECOLOR } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUECOLORc } def + /K { + Colors exch get dup + 0 get /HUE exch store + 1 get /BRIGHT exch store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } def + /FMsetgray { + /SAT exch 1.0 exch sub store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } bind def + } + + { + /BEGINBITMAPCOLOR { + BITMAPGRAY} def + /BEGINBITMAPCOLORc { + BITMAPGRAYc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUEGRAY } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUEGRAYc } def + /FMsetgray {setgray} bind def + /K { + pop + } def + } +ifelse +/normalize { + transform round exch round exch itransform + } bind def +/dnormalize { + dtransform round exch round exch idtransform + } bind def +/lnormalize { + 0 dtransform exch cvi 2 idiv 2 mul 1 add exch idtransform pop + } bind def +/H { + lnormalize setlinewidth + } bind def +/Z { + setlinecap + } bind def + /fillvals FMLOCAL +/X { + fillvals exch get + dup type /stringtype eq + {8 1 setpattern} + {grayness} + ifelse + } bind def +/V { + gsave eofill grestore + } bind def +/N { + stroke + } bind def +/M {newpath moveto} bind def +/E {lineto} bind def +/D {curveto} bind def +/O {closepath} bind def + /n FMLOCAL +/L { + /n exch def + newpath + normalize + moveto + 2 1 n {pop normalize lineto} for + } bind def +/Y { + L + closepath + } bind def + /x1 FMLOCAL + /x2 FMLOCAL + /y1 FMLOCAL + /y2 FMLOCAL + /rad FMLOCAL +/R { + /y2 exch def + /x2 exch def + /y1 exch def + /x1 exch def + x1 y1 + x2 y1 + x2 y2 + x1 y2 + 4 Y + } bind def +/RR { + /rad exch def + normalize + /y2 exch def + /x2 exch def + normalize + /y1 exch def + /x1 exch def + newpath + x1 y1 rad add moveto + x1 y2 x2 y2 rad arcto + x2 y2 x2 y1 rad arcto + x2 y1 x1 y1 rad arcto + x1 y1 x1 y2 rad arcto + closepath + 16 {pop} repeat + } bind def +/C { + grestore + gsave + R + clip + } bind def + /FMpointsize FMLOCAL +/F { + FMfonts exch get + FMpointsize scalefont + setfont + } bind def +/Q { + /FMpointsize exch def + F + } bind def +/T { + moveto show + } bind def +/RF { + rotate + 0 ne {-1 1 scale} if + } bind def +/TF { + gsave + moveto + RF + show + grestore + } bind def +/P { + moveto + 0 32 3 2 roll widthshow + } bind def +/PF { + gsave + moveto + RF + 0 32 3 2 roll widthshow + grestore + } bind def +/S { + moveto + 0 exch ashow + } bind def +/SF { + gsave + moveto + RF + 0 exch ashow + grestore + } bind def +/B { + moveto + 0 32 4 2 roll 0 exch awidthshow + } bind def +/BF { + gsave + moveto + RF + 0 32 4 2 roll 0 exch awidthshow + grestore + } bind def +/G { + gsave + newpath + normalize translate 0.0 0.0 moveto + dnormalize scale + 0.0 0.0 1.0 5 3 roll arc + closepath fill + grestore + } bind def +/A { + gsave + savematrix + newpath + 2 index 2 div add exch 3 index 2 div sub exch + normalize 2 index 2 div sub exch 3 index 2 div add exch + translate + scale + 0.0 0.0 1.0 5 3 roll arc + restorematrix + stroke + grestore + } bind def + /x FMLOCAL + /y FMLOCAL + /w FMLOCAL + /h FMLOCAL + /xx FMLOCAL + /yy FMLOCAL + /ww FMLOCAL + /hh FMLOCAL + /FMsaveobject FMLOCAL + /FMoptop FMLOCAL + /FMdicttop FMLOCAL +/BEGINPRINTCODE { + /FMdicttop countdictstack 1 add def + /FMoptop count 4 sub def + /FMsaveobject save def + userdict begin + /showpage {} def + FMNORMALIZEGRAPHICS + 3 index neg 3 index neg translate + } bind def +/ENDPRINTCODE { + count -1 FMoptop {pop pop} for + countdictstack -1 FMdicttop {pop end} for + FMsaveobject restore + } bind def +/gn { + 0 + { 46 mul + cf read pop + 32 sub + dup 46 lt {exit} if + 46 sub add + } loop + add + } bind def + /str FMLOCAL +/cfs { + /str sl string def + 0 1 sl 1 sub {str exch val put} for + str def + } bind def +/ic [ + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 + {0 hx} {1 hx} {2 hx} {3 hx} {4 hx} {5 hx} {6 hx} {7 hx} {8 hx} {9 hx} + {10 hx} {11 hx} {12 hx} {13 hx} {14 hx} {15 hx} {16 hx} {17 hx} {18 hx} + {19 hx} {gn hx} {0} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12} + {13} {14} {15} {16} {17} {18} {19} {gn} {0 wh} {1 wh} {2 wh} {3 wh} + {4 wh} {5 wh} {6 wh} {7 wh} {8 wh} {9 wh} {10 wh} {11 wh} {12 wh} + {13 wh} {14 wh} {gn wh} {0 bl} {1 bl} {2 bl} {3 bl} {4 bl} {5 bl} {6 bl} + {7 bl} {8 bl} {9 bl} {10 bl} {11 bl} {12 bl} {13 bl} {14 bl} {gn bl} + {0 fl} {1 fl} {2 fl} {3 fl} {4 fl} {5 fl} {6 fl} {7 fl} {8 fl} {9 fl} + {10 fl} {11 fl} {12 fl} {13 fl} {14 fl} {gn fl} + ] def + /sl FMLOCAL + /val FMLOCAL + /ws FMLOCAL + /im FMLOCAL + /bs FMLOCAL + /cs FMLOCAL + /len FMLOCAL + /pos FMLOCAL +/ms { + /sl exch def + /val 255 def + /ws cfs + /im cfs + /val 0 def + /bs cfs + /cs cfs + } bind def +400 ms +/ip { + is + 0 + cf cs readline pop + { ic exch get exec + add + } forall + pop + + } bind def +/wh { + /len exch def + /pos exch def + ws 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/bl { + /len exch def + /pos exch def + bs 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/s1 1 string def +/fl { + /len exch def + /pos exch def + /val cf s1 readhexstring pop 0 get def + pos 1 pos len add 1 sub {im exch val put} for + pos len + } bind def +/hx { + 3 copy getinterval + cf exch readhexstring pop pop + } bind def + /h FMLOCAL + /w FMLOCAL + /d FMLOCAL + /lb FMLOCAL + /bitmapsave FMLOCAL + /is FMLOCAL + /cf FMLOCAL +/wbytes { + dup + 8 eq {pop} {1 eq {7 add 8 idiv} {3 add 4 idiv} ifelse} ifelse + } bind def +/BEGINBITMAPBWc { + 1 {} COMMONBITMAPc + } bind def +/BEGINBITMAPGRAYc { + 8 {} COMMONBITMAPc + } bind def +/BEGINBITMAP2BITc { + 2 {} COMMONBITMAPc + } bind def +/COMMONBITMAPc { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + r + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} image + bitmapsave restore + grestore + } bind def +/BEGINBITMAPBW { + 1 {} COMMONBITMAP + } bind def +/BEGINBITMAPGRAY { + 8 {} COMMONBITMAP + } bind def +/BEGINBITMAP2BIT { + 2 {} COMMONBITMAP + } bind def +/COMMONBITMAP { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + r + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} image + bitmapsave restore + grestore + } bind def + /proc1 FMLOCAL + /proc2 FMLOCAL + /newproc FMLOCAL +/Fmcc { + /proc2 exch cvlit def + /proc1 exch cvlit def + /newproc proc1 length proc2 length add array def + newproc 0 proc1 putinterval + newproc proc1 length proc2 putinterval + newproc cvx +} bind def +/ngrayt 256 array def +/nredt 256 array def +/nbluet 256 array def +/ngreent 256 array def + /gryt FMLOCAL + /blut FMLOCAL + /grnt FMLOCAL + /redt FMLOCAL + /indx FMLOCAL + /cynu FMLOCAL + /magu FMLOCAL + /yelu FMLOCAL + /k FMLOCAL + /u FMLOCAL +/colorsetup { + currentcolortransfer + /gryt exch def + /blut exch def + /grnt exch def + /redt exch def + 0 1 255 { + /indx exch def + /cynu 1 red indx get 255 div sub def + /magu 1 green indx get 255 div sub def + /yelu 1 blue indx get 255 div sub def + /k cynu magu min yelu min def + /u k currentundercolorremoval exec def + nredt indx 1 0 cynu u sub max sub redt exec put + ngreent indx 1 0 magu u sub max sub grnt exec put + nbluet indx 1 0 yelu u sub max sub blut exec put + ngrayt indx 1 k currentblackgeneration exec sub gryt exec put + } for + {255 mul cvi nredt exch get} + {255 mul cvi ngreent exch get} + {255 mul cvi nbluet exch get} + {255 mul cvi ngrayt exch get} + setcolortransfer + {pop 0} setundercolorremoval + {} setblackgeneration + } bind def + /tran FMLOCAL +/fakecolorsetup { + /tran 256 string def + 0 1 255 {/indx exch def + tran indx + red indx get 77 mul + green indx get 151 mul + blue indx get 28 mul + add add 256 idiv put} for + currenttransfer + {255 mul cvi tran exch get 255.0 div} + exch Fmcc settransfer +} bind def +/BITMAPCOLOR { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + colorsetup + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPCOLORc { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + colorsetup + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLORc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip} {gip} {bip} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLOR { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop } + { cf gis readhexstring pop } + { cf bis readhexstring pop } + true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUEGRAYc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip gip bip w gray} image + bitmapsave restore + grestore + } bind def +/ww FMLOCAL +/r FMLOCAL +/g FMLOCAL +/b FMLOCAL +/i FMLOCAL +/gray { + /ww exch def + /b exch def + /g exch def + /r exch def + 0 1 ww 1 sub { /i exch def r i get .299 mul g i get .587 mul + b i get .114 mul add add r i 3 -1 roll floor cvi put } for + r + } bind def +/BITMAPTRUEGRAY { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop + cf gis readhexstring pop + cf bis readhexstring pop w gray} image + bitmapsave restore + grestore + } bind def +/BITMAPGRAY { + 8 {fakecolorsetup} COMMONBITMAP + } bind def +/BITMAPGRAYc { + 8 {fakecolorsetup} COMMONBITMAPc + } bind def +/ENDBITMAP { + } bind def +end + /ALDsave FMLOCAL + /ALDmatrix matrix def ALDmatrix 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+(..........................................) 360.45 504.95 T +(1-12) 486.65 504.95 T +(Crossover) 171.65 488.95 T +(........................................................................................) 222.52 488.95 T +(1-12) 486.65 488.95 T +(Multi-point Crossover) 207.65 472.95 T +(.........................................................) 315.47 472.95 T +(1-12) 486.65 472.95 T +(Uniform Crossover) 207.65 456.95 T +(............................................................) 306.48 456.95 T +(1-13) 486.65 456.95 T +(Other Crossover Operators) 207.65 440.95 T +(.................................................) 339.46 440.95 T +(1-14) 486.65 440.95 T +(Intermediate Recombination) 207.65 424.95 T +(...............................................) 345.45 424.95 T +(1-14) 486.65 424.95 T +(Line Recombination) 207.65 408.95 T +(...........................................................) 309.47 408.95 T +(1-15) 486.65 408.95 T +(Discussion) 207.65 392.95 T +(..........................................................................) 264.5 392.95 T +(1-15) 486.65 392.95 T +(Mutation) 171.65 376.95 T +(.........................................................................................) 219.52 376.95 T +(1-16) 486.65 376.95 T +(Reinsertion) 171.65 360.95 T +(......................................................................................) 228.52 360.95 T +(1-18) 486.65 360.95 T +(T) 171.65 344.95 T +(ermination of the GA) 178.14 344.95 T +(...................................................................) 285.49 344.95 T +(1-18) 486.65 344.95 T +(Data Structures) 135.65 324.95 T +(...........................................................................................) 213.53 324.95 T +(1-20) 486.65 324.95 T +(Chromosomes) 171.65 308.95 T +(.................................................................................) 243.51 308.95 T +(1-20) 486.65 308.95 T +(Phenotypes) 171.65 292.95 T +(.....................................................................................) 231.52 292.95 T +(1-20) 486.65 292.95 T +(Objective Function V) 171.65 276.95 T +(alues) 274.25 276.95 T +(.............................................................) 303.48 276.95 T +(1-21) 486.65 276.95 T +(Fitness V) 171.65 260.95 T +(alues) 215.96 260.95 T +(.................................................................................) 243.51 260.95 T +(1-22) 486.65 260.95 T +(Support for Multiple Populations) 135.65 240.95 T +(..............................................................) 300.48 240.95 T +(1-23) 486.65 240.95 T +(Examples) 135.65 220.95 T +(....................................................................................................) 186.54 220.95 T +(1-26) 486.65 220.95 T +(The Simple GA) 171.65 204.95 T +(..............................................................................) 252.51 204.95 T +(1-26) 486.65 204.95 T +(A Multi-population GA) 171.65 188.95 T +(..................................................................) 288.48 188.95 T +(1-30) 486.65 188.95 T +(Demonstration Scripts) 171.65 172.95 T +(.....................................................................) 279.49 172.95 T +(1-36) 486.65 172.95 T +(References) 135.65 152.95 T +(...................................................................................................) 189.54 152.95 T +(1-37) 486.65 152.95 T +3 28 Q +(2 Refer) 63.65 122.29 T +(ence) 150.98 122.29 T +0 12 Q +(..............................................................................................) 204.53 122.29 T +(2-1) 486.65 122.29 T +FMENDPAGE +%%EndPage: "3" 4 +%%Trailer +%%BoundingBox: 0 0 595.3 841.9 +%%Pages: 3 1 +%%DocumentFonts: Times-Roman +%%+ Symbol +%%+ Times-Italic +%%+ Times-Bold diff --git 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"b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/GATBXA1.LOG" @@ -1,3 +1,5 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9cc9c87d999bb7a53ba3816caba407cf5dac35081bdba75acef3789150547377 -size 458 +%%[ Warning: Times-Italic not found, using Font Substitution. 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/gstring exch def + /gfile exch def + /gindex 0 def + { + gfile read pop + dup 10 eq {exit} if + dup 13 eq {exit} if + gstring exch gindex exch put + /gindex gindex 1 add def + } loop + pop + gstring 0 gindex getinterval true + } def + } if +/FMVERSION { + FMversion ne { + /Times-Roman findfont 18 scalefont setfont + 100 100 moveto + (FrameMaker version does not match postscript_prolog!) + dup = + show showpage + } if + } def +/FMLOCAL { + FrameDict begin + 0 def + end + } def + /gstring FMLOCAL + /gfile FMLOCAL + /gindex FMLOCAL + /orgxfer FMLOCAL + /orgproc FMLOCAL + /organgle FMLOCAL + /orgfreq FMLOCAL + /yscale FMLOCAL + /xscale FMLOCAL + /manualfeed FMLOCAL + /paperheight FMLOCAL + /paperwidth FMLOCAL +/FMDOCUMENT { + array /FMfonts exch def + /#copies exch def + FrameDict begin + 0 ne dup {setmanualfeed} if + /manualfeed exch def + /paperheight exch def + /paperwidth exch def + /yscale exch def + /xscale exch def + currenttransfer cvlit /orgxfer exch def + currentscreen cvlit /orgproc exch def + /organgle exch def /orgfreq exch def + setpapername + manualfeed {true} {papersize} ifelse + {manualpapersize} {false} ifelse + {desperatepapersize} if + end + } def + /pagesave FMLOCAL + /orgmatrix FMLOCAL + /landscape FMLOCAL +/FMBEGINPAGE { + FrameDict begin + /pagesave save def + 3.86 setmiterlimit + /landscape exch 0 ne def + landscape { + 90 rotate 0 exch neg translate pop + } + {pop pop} + ifelse + xscale yscale scale + /orgmatrix matrix def + gsave + } def +/FMENDPAGE { + grestore + pagesave restore + end + showpage + } def +/FMFONTDEFINE { + FrameDict begin + findfont + ReEncode + 1 index exch + definefont + FMfonts 3 1 roll + put + end + } def +/FMFILLS { + FrameDict begin + array /fillvals exch def + end + } def +/FMFILL { + FrameDict begin + fillvals 3 1 roll put + end + } def +/FMNORMALIZEGRAPHICS { + newpath + 0.0 0.0 moveto + 1 setlinewidth + 0 setlinecap + 0 0 0 sethsbcolor + 0 setgray + } bind def + /fx FMLOCAL + /fy FMLOCAL + /fh FMLOCAL + /fw FMLOCAL + /llx FMLOCAL + /lly FMLOCAL + /urx FMLOCAL + /ury FMLOCAL +/FMBEGINEPSF { + end + /FMEPSF save def + /showpage {} def + FMNORMALIZEGRAPHICS + [/fy /fx /fh /fw /ury /urx /lly /llx] {exch def} forall + fx fy translate + rotate + fw urx llx sub div fh ury lly sub div scale + llx neg lly neg translate + } bind def +/FMENDEPSF { + FMEPSF restore + FrameDict begin + } bind def +FrameDict begin +/setmanualfeed { +%%BeginFeature *ManualFeed True + statusdict /manualfeed true put +%%EndFeature + } def +/max {2 copy lt {exch} if pop} bind def +/min {2 copy gt {exch} if pop} bind def +/inch {72 mul} def +/pagedimen { + paperheight sub abs 16 lt exch + paperwidth sub abs 16 lt and + {/papername exch def} {pop} ifelse + } def + /papersizedict FMLOCAL +/setpapername { + /papersizedict 14 dict def + papersizedict begin + /papername /unknown def + /Letter 8.5 inch 11.0 inch pagedimen + /LetterSmall 7.68 inch 10.16 inch pagedimen + /Tabloid 11.0 inch 17.0 inch pagedimen + /Ledger 17.0 inch 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+/manualpapersize { + papersizedict begin + /Letter {letter} def + /LetterSmall {lettersmall} def + /Tabloid {11x17} def + /Ledger {ledger} def + /Legal {legal} def + /Statement {statement} def + /Executive {executive} def + /A3 {a3} def + /A4 {a4} def + /A4Small {a4small} def + /B4 {b4} def + /B5 {b5} def + /unknown {unknown} def + papersizedict dup papername known {papername} {/unknown} ifelse get + end + stopped + } def +/desperatepapersize { + statusdict /setpageparams known + { + paperwidth paperheight 0 1 + statusdict begin + {setpageparams} stopped pop + end + } if + } def +/savematrix { + orgmatrix currentmatrix pop + } bind def +/restorematrix { + orgmatrix setmatrix + } bind def +/dmatrix matrix def +/dpi 72 0 dmatrix defaultmatrix dtransform + dup mul exch dup mul add sqrt def +/freq dpi 18.75 div 8 div round dup 0 eq {pop 1} if 8 mul dpi exch div def +/sangle 1 0 dmatrix defaultmatrix dtransform exch atan def +/DiacriticEncoding [ +/.notdef /.notdef /.notdef /.notdef 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/tilde /macron +/breve /dotaccent /ring /cedilla /hungarumlaut /ogonek /caron +] def +/ReEncode { + dup + length + dict begin + { + 1 index /FID ne + {def} + {pop pop} ifelse + } forall + 0 eq {/Encoding DiacriticEncoding def} if + currentdict + end + } bind def +/graymode true def + /bwidth FMLOCAL + /bpside FMLOCAL + /bstring FMLOCAL + /onbits FMLOCAL + /offbits FMLOCAL + /xindex FMLOCAL + /yindex FMLOCAL + /x FMLOCAL + /y FMLOCAL +/setpattern { + /bwidth exch def + /bpside exch def + /bstring exch def + /onbits 0 def /offbits 0 def + freq sangle landscape {90 add} if + {/y exch def + /x exch def + /xindex x 1 add 2 div bpside mul cvi def + /yindex y 1 add 2 div bpside mul cvi def + bstring yindex bwidth mul xindex 8 idiv add get + 1 7 xindex 8 mod sub bitshift and 0 ne + {/onbits onbits 1 add def 1} + {/offbits offbits 1 add def 0} + ifelse + } + setscreen + {} settransfer + offbits offbits onbits add div FMsetgray + /graymode false def + } bind def +/grayness { + FMsetgray + graymode not { + /graymode true def + orgxfer cvx settransfer + orgfreq organgle orgproc cvx setscreen + } if + } bind def + /HUE FMLOCAL + /SAT FMLOCAL + /BRIGHT FMLOCAL + /Colors FMLOCAL +FMPrintInColor + + { + /HUE 0 def + /SAT 0 def + /BRIGHT 0 def + % array of arrays Hue and Sat values for the separations [HUE BRIGHT] + /Colors + [[0 0 ] % black + [0 0 ] % white + [0.00 1.0] % red + [0.37 1.0] % green + [0.60 1.0] % blue + [0.50 1.0] % cyan + [0.83 1.0] % magenta + [0.16 1.0] % comment / yellow + ] def + + /BEGINBITMAPCOLOR { + BITMAPCOLOR} def + /BEGINBITMAPCOLORc { + BITMAPCOLORc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUECOLOR } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUECOLORc } def + /K { + Colors exch get dup + 0 get /HUE exch store + 1 get /BRIGHT exch store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } def + /FMsetgray { + /SAT exch 1.0 exch sub store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } bind def + } + + { + /BEGINBITMAPCOLOR { + BITMAPGRAY} def + /BEGINBITMAPCOLORc { + BITMAPGRAYc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUEGRAY } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUEGRAYc } def + /FMsetgray {setgray} bind def + /K { + pop + } def + } +ifelse +/normalize { + transform round exch round exch itransform + } bind def +/dnormalize { + dtransform round exch round exch idtransform + } bind def +/lnormalize { + 0 dtransform exch cvi 2 idiv 2 mul 1 add exch idtransform pop + } bind def +/H { + lnormalize setlinewidth + } bind def +/Z { + setlinecap + } bind def + /fillvals FMLOCAL +/X { + fillvals exch get + dup type /stringtype eq + {8 1 setpattern} + {grayness} + ifelse + } bind def +/V { + gsave eofill grestore + } bind def +/N { + stroke + } bind def +/M {newpath moveto} bind def +/E {lineto} bind def +/D {curveto} bind def +/O {closepath} bind def + /n FMLOCAL +/L { + /n exch def + newpath + normalize + moveto + 2 1 n {pop normalize lineto} for + } bind def +/Y { + L + closepath + } bind def + /x1 FMLOCAL + /x2 FMLOCAL + /y1 FMLOCAL + /y2 FMLOCAL + /rad FMLOCAL +/R { + /y2 exch def + /x2 exch def + /y1 exch def + /x1 exch def + x1 y1 + x2 y1 + x2 y2 + x1 y2 + 4 Y + } bind def +/RR { + /rad exch def + normalize + /y2 exch def + /x2 exch def + normalize + /y1 exch def + /x1 exch def + newpath + x1 y1 rad add moveto + x1 y2 x2 y2 rad arcto + x2 y2 x2 y1 rad arcto + x2 y1 x1 y1 rad arcto + x1 y1 x1 y2 rad arcto + closepath + 16 {pop} repeat + } bind def +/C { + grestore + gsave + R + clip + } bind def + /FMpointsize FMLOCAL +/F { + FMfonts exch get + FMpointsize scalefont + setfont + } bind def +/Q { + /FMpointsize exch def + F + } bind def +/T { + moveto show + } bind def +/RF { + rotate + 0 ne {-1 1 scale} if + } bind def +/TF { + gsave + moveto + RF + show + grestore + } bind def +/P { + moveto + 0 32 3 2 roll widthshow + } bind def +/PF { + gsave + moveto + RF + 0 32 3 2 roll widthshow + grestore + } bind def +/S { + moveto + 0 exch ashow + } bind def +/SF { + gsave + moveto + RF + 0 exch ashow + grestore + } bind def +/B { + moveto + 0 32 4 2 roll 0 exch awidthshow + } bind def +/BF { + gsave + moveto + RF + 0 32 4 2 roll 0 exch awidthshow + grestore + } bind def +/G { + gsave + newpath + normalize translate 0.0 0.0 moveto + dnormalize scale + 0.0 0.0 1.0 5 3 roll arc + closepath fill + grestore + } bind def +/A { + gsave + savematrix + newpath + 2 index 2 div add exch 3 index 2 div sub exch + normalize 2 index 2 div sub exch 3 index 2 div add exch + translate + scale + 0.0 0.0 1.0 5 3 roll arc + restorematrix + stroke + grestore + } bind def + /x FMLOCAL + /y FMLOCAL + /w FMLOCAL + /h FMLOCAL + /xx FMLOCAL + /yy FMLOCAL + /ww FMLOCAL + /hh FMLOCAL + /FMsaveobject FMLOCAL + /FMoptop FMLOCAL + /FMdicttop FMLOCAL +/BEGINPRINTCODE { + /FMdicttop countdictstack 1 add def + /FMoptop count 4 sub def + /FMsaveobject save def + userdict begin + /showpage {} def + FMNORMALIZEGRAPHICS + 3 index neg 3 index neg translate + } bind def +/ENDPRINTCODE { + count -1 FMoptop {pop pop} for + countdictstack -1 FMdicttop {pop end} for + FMsaveobject restore + } bind def +/gn { + 0 + { 46 mul + cf read pop + 32 sub + dup 46 lt {exit} if + 46 sub add + } loop + add + } bind def + /str FMLOCAL +/cfs { + /str sl string def + 0 1 sl 1 sub {str exch val put} for + str def + } bind def +/ic [ + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 + {0 hx} {1 hx} {2 hx} {3 hx} {4 hx} {5 hx} {6 hx} {7 hx} {8 hx} {9 hx} + {10 hx} {11 hx} {12 hx} {13 hx} {14 hx} {15 hx} {16 hx} {17 hx} {18 hx} + {19 hx} {gn hx} {0} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12} + {13} {14} {15} {16} {17} {18} {19} {gn} {0 wh} {1 wh} {2 wh} {3 wh} + {4 wh} {5 wh} {6 wh} {7 wh} {8 wh} {9 wh} {10 wh} {11 wh} {12 wh} + {13 wh} {14 wh} {gn wh} {0 bl} {1 bl} {2 bl} {3 bl} {4 bl} {5 bl} {6 bl} + {7 bl} {8 bl} {9 bl} {10 bl} {11 bl} {12 bl} {13 bl} {14 bl} {gn bl} + {0 fl} {1 fl} {2 fl} {3 fl} {4 fl} {5 fl} {6 fl} {7 fl} {8 fl} {9 fl} + {10 fl} {11 fl} {12 fl} {13 fl} {14 fl} {gn fl} + ] def + /sl FMLOCAL + /val FMLOCAL + /ws FMLOCAL + /im FMLOCAL + /bs FMLOCAL + /cs FMLOCAL + /len FMLOCAL + /pos FMLOCAL +/ms { + /sl exch def + /val 255 def + /ws cfs + /im cfs + /val 0 def + /bs cfs + /cs cfs + } bind def +400 ms +/ip { + is + 0 + cf cs readline pop + { ic exch get exec + add + } forall + pop + + } bind def +/wh { + /len exch def + /pos exch def + ws 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/bl { + /len exch def + /pos exch def + bs 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/s1 1 string def +/fl { + /len exch def + /pos exch def + /val cf s1 readhexstring pop 0 get def + pos 1 pos len add 1 sub {im exch val put} for + pos len + } bind def +/hx { + 3 copy getinterval + cf exch readhexstring pop pop + } bind def + /h FMLOCAL + /w FMLOCAL + /d FMLOCAL + /lb FMLOCAL + /bitmapsave FMLOCAL + /is FMLOCAL + /cf FMLOCAL +/wbytes { + dup + 8 eq {pop} {1 eq {7 add 8 idiv} {3 add 4 idiv} ifelse} ifelse + } bind def +/BEGINBITMAPBWc { + 1 {} COMMONBITMAPc + } bind def +/BEGINBITMAPGRAYc { + 8 {} COMMONBITMAPc + } bind def +/BEGINBITMAP2BITc { + 2 {} COMMONBITMAPc + } bind def +/COMMONBITMAPc { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + r + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} image + bitmapsave restore + grestore + } bind def +/BEGINBITMAPBW { + 1 {} COMMONBITMAP + } bind def +/BEGINBITMAPGRAY { + 8 {} COMMONBITMAP + } bind def +/BEGINBITMAP2BIT { + 2 {} COMMONBITMAP + } bind def +/COMMONBITMAP { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + r + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} image + bitmapsave restore + grestore + } bind def + /proc1 FMLOCAL + /proc2 FMLOCAL + /newproc FMLOCAL +/Fmcc { + /proc2 exch cvlit def + /proc1 exch cvlit def + /newproc proc1 length proc2 length add array def + newproc 0 proc1 putinterval + newproc proc1 length proc2 putinterval + newproc cvx +} bind def +/ngrayt 256 array def +/nredt 256 array def +/nbluet 256 array def +/ngreent 256 array def + /gryt FMLOCAL + /blut FMLOCAL + /grnt FMLOCAL + /redt FMLOCAL + /indx FMLOCAL + /cynu FMLOCAL + /magu FMLOCAL + /yelu FMLOCAL + /k FMLOCAL + /u FMLOCAL +/colorsetup { + currentcolortransfer + /gryt exch def + /blut exch def + /grnt exch def + /redt exch def + 0 1 255 { + /indx exch def + /cynu 1 red indx get 255 div sub def + /magu 1 green indx get 255 div sub def + /yelu 1 blue indx get 255 div sub def + /k cynu magu min yelu min def + /u k currentundercolorremoval exec def + nredt indx 1 0 cynu u sub max sub redt exec put + ngreent indx 1 0 magu u sub max sub grnt exec put + nbluet indx 1 0 yelu u sub max sub blut exec put + ngrayt indx 1 k currentblackgeneration exec sub gryt exec put + } for + {255 mul cvi nredt exch get} + {255 mul cvi ngreent exch get} + {255 mul cvi nbluet exch get} + {255 mul cvi ngrayt exch get} + setcolortransfer + {pop 0} setundercolorremoval + {} setblackgeneration + } bind def + /tran FMLOCAL +/fakecolorsetup { + /tran 256 string def + 0 1 255 {/indx exch def + tran indx + red indx get 77 mul + green indx get 151 mul + blue indx get 28 mul + add add 256 idiv put} for + currenttransfer + {255 mul cvi tran exch get 255.0 div} + exch Fmcc settransfer +} bind def +/BITMAPCOLOR { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + colorsetup + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPCOLORc { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + colorsetup + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLORc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip} {gip} {bip} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLOR { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop } + { cf gis readhexstring pop } + { cf bis readhexstring pop } + true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUEGRAYc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip gip bip w gray} image + bitmapsave restore + grestore + } bind def +/ww FMLOCAL +/r FMLOCAL +/g FMLOCAL +/b FMLOCAL +/i FMLOCAL +/gray { + /ww exch def + /b exch def + /g exch def + /r exch def + 0 1 ww 1 sub { /i exch def r i get .299 mul g i get .587 mul + b i get .114 mul add add r i 3 -1 roll floor cvi put } for + r + } bind def +/BITMAPTRUEGRAY { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop + cf gis readhexstring pop + cf bis readhexstring pop w gray} image + bitmapsave restore + grestore + } bind def +/BITMAPGRAY { + 8 {fakecolorsetup} COMMONBITMAP + } bind def +/BITMAPGRAYc { + 8 {fakecolorsetup} COMMONBITMAPc + } bind def +/ENDBITMAP { + } bind def +end + /ALDsave FMLOCAL + /ALDmatrix matrix def ALDmatrix currentmatrix pop +/StartALD { + /ALDsave save def + savematrix + ALDmatrix setmatrix + } bind def +/InALD { + restorematrix + } bind def +/DoneALD { + ALDsave restore + } bind def +%%EndProlog +%%BeginSetup +(3.0) FMVERSION +1 1 595.3 841.9 0 1 21 FMDOCUMENT +0 0 /Times-Italic FMFONTDEFINE +1 0 /Times-Bold FMFONTDEFINE +2 0 /Times-Roman FMFONTDEFINE +3 0 /Courier FMFONTDEFINE +4 1 /Symbol FMFONTDEFINE +5 0 /Times-BoldItalic FMFONTDEFINE +6 0 /Courier-BoldOblique FMFONTDEFINE +32 FMFILLS +0 0 FMFILL +1 .1 FMFILL +2 .3 FMFILL +3 .5 FMFILL +4 .7 FMFILL +5 .9 FMFILL +6 .97 FMFILL +7 1 FMFILL +8 <0f1e3c78f0e1c387> FMFILL +9 <0f87c3e1f0783c1e> FMFILL +10 FMFILL +11 FMFILL +12 <8142241818244281> FMFILL +13 <03060c183060c081> FMFILL +14 <8040201008040201> FMFILL +16 1 FMFILL +17 .9 FMFILL +18 .7 FMFILL +19 .5 FMFILL +20 .3 FMFILL +21 .1 FMFILL +22 0.03 FMFILL +23 0 FMFILL +24 FMFILL +25 FMFILL +26 <3333333333333333> FMFILL +27 <0000ffff0000ffff> FMFILL +28 <7ebddbe7e7dbbd7e> FMFILL +29 FMFILL +30 <7fbfdfeff7fbfdfe> FMFILL +%%EndSetup +%%Page: "1" 1 +%%BeginPaperSize: A4 +%%EndPaperSize +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-1) 518.33 61.29 T +1 28 Q +(1 T) 63.65 726.29 T +(utorial) 100.75 726.29 T +2 12 Q +4.82 (M) 135.65 692.95 P +2 10 Q +4.02 (A) 146.31 692.95 P +4.02 (TLAB) 152.42 692.95 P +2 12 Q +4.82 ( has a wide variety of functions useful to the genetic algorithm) 178.51 692.95 P +1.63 (practitioner and those wishing to experiment with the genetic algorithm for the) 135.65 678.95 P +-0.03 (\336rst time. Given the versatility of M) 135.65 664.95 P +2 10 Q +-0.02 (A) 309.05 664.95 P +-0.02 (TLAB) 315.16 664.95 P +2 12 Q +-0.03 (\325) 341.26 664.95 P +-0.03 (s high-level language, problems can be) 344.59 664.95 P +0.58 (coded in m-\336les in a fraction of the time that it would take to create C or Fortran) 135.65 650.95 P +3.7 (programs for the same purpose. Couple this with M) 135.65 636.95 P +2 10 Q +3.09 (A) 412.78 636.95 P +3.09 (TLAB) 418.88 636.95 P +2 12 Q +3.7 (\325) 444.98 636.95 P +3.7 (s advanced data) 448.31 636.95 P +0.17 (analysis, visualisation tools and special purpose application domain toolboxes and) 135.65 622.95 P +2.91 (the user is presented with a uniform environment with which to explore the) 135.65 608.95 P +(potential of genetic algorithms.) 135.65 594.95 T +1.02 (The Genetic Algorithm T) 135.65 568.95 P +1.02 (oolbox uses M) 260.1 568.95 P +2 10 Q +0.85 (A) 332.76 568.95 P +0.85 (TLAB) 338.87 568.95 P +2 12 Q +1.02 ( matrix functions to build a set of) 364.97 568.95 P +0.87 (versatile tools for implementing a wide range of genetic algorithm methods. The) 135.65 554.95 P +1.04 (Genetic Algorithm T) 135.65 540.95 P +1.04 (oolbox is a collection of routines, written mostly in m-\336les,) 237.48 540.95 P +(which implement the most important functions in genetic algorithms.) 135.65 526.95 T +FMENDPAGE +%%EndPage: "1" 2 +%%Page: "2" 2 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-2) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Installation) 63.65 732.95 T +2 12 Q +2.37 (Instructions for installing the Genetic Algorithm T) 135.65 694.95 P +2.37 (oolbox can be found in the) 391.55 694.95 P +0.36 (M) 135.65 680.95 P +2 10 Q +0.3 (A) 146.31 680.95 P +0.3 (TLAB) 152.42 680.95 P +2 12 Q +0.36 ( installation instructions. It is recommended that the \336les for this toolbox) 178.51 680.95 P +(are stored in a directory named genetic of) 135.65 666.95 T +(f the main matlab/toolbox directory) 334.93 666.95 T +(.) 504.71 666.95 T +3.33 (A number of demonstrations are available. A single-population binary-coded) 135.65 640.95 P +-0.13 (genetic algorithm to solve a numerical optimization problem is implemented in the) 135.65 626.95 P +-0.25 (m-\336le) 135.65 612.95 P +3 F +-0.61 (sga.m) 167.04 612.95 P +2 F +-0.25 (. The demonstration m-\336le) 203.02 612.95 P +3 F +-0.61 (mpga.m) 332.93 612.95 P +2 F +-0.25 ( implements a real-valued multi-) 376.1 612.95 P +1.29 (population genetic algorithm to solve a dynamic control problem. Both of these) 135.65 598.95 P +(demonstration m-\336les are discussed in detail in the) 135.65 584.95 T +0 F +(Examples) 382.16 584.95 T +2 F +( Section.) 428.79 584.95 T +1.06 (Additionally) 135.65 558.95 P +1.06 (, a set of test functions, drawn from the genetic algorithm literature,) 195.51 558.95 P +2.55 (are supplied in a separate directory) 135.65 544.95 P +2.55 (,) 315.12 544.95 P +3 F +6.11 (test_fns) 323.66 544.95 P +2 F +2.55 (, from the Genetic Algorithm) 381.23 544.95 P +0.05 (T) 135.65 530.95 P +0.05 (oolbox functions. A brief description of these test functions is given at the end of) 142.14 530.95 P +0.93 (the) 135.65 516.95 P +0 F +0.93 (Examples) 154.23 516.95 P +2 F +0.93 ( Section. A further document describes the implementation and use) 200.86 516.95 P +(of these functions.) 135.65 502.95 T +FMENDPAGE +%%EndPage: "2" 3 +%%Page: "3" 3 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-3) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(An Overview of Genetic Algorithms) 63.65 732.95 T +2 12 Q +-0.06 (In this Section we give a tutorial introduction to the basic Genetic Algorithm \050GA\051) 135.65 694.95 P +(and outline the procedures for solving problems using the GA.) 135.65 680.95 T +1 16 Q +(What ar) 135.65 652.29 T +(e Genetic Algorithms?) 192.66 652.29 T +2 12 Q +0.56 (The GA is a stochastic global search method that mimics the metaphor of natural) 135.65 624.95 P +0.66 (biological evolution. GAs operate on a population of potential solutions applying) 135.65 610.95 P +2.41 (the principle of survival of the \336ttest to produce \050hopefully\051 better and better) 135.65 596.95 P +0.86 (approximations to a solution. At each generation, a new set of approximations is) 135.65 582.95 P +0.15 (created by the process of selecting individuals according to their level of \336tness in) 135.65 568.95 P +1.29 (the problem domain and breeding them together using operators borrowed from) 135.65 554.95 P +0.63 (natural genetics. This process leads to the evolution of populations of individuals) 135.65 540.95 P +2.41 (that are better suited to their environment than the individuals that they were) 135.65 526.95 P +(created from, just as in natural adaptation.) 135.65 512.95 T +3.17 (Individuals, or current approximations, are encoded as strings,) 135.65 486.95 P +0 F +3.17 (chr) 463.14 486.95 P +3.17 (omosomes) 478.68 486.95 P +2 F +3.17 (,) 528.65 486.95 P +0.8 (composed over some alphabet\050s\051, so that the) 135.65 472.95 P +0 F +0.8 (genotypes) 357.07 472.95 P +2 F +0.8 ( \050chromosome values\051 are) 405.03 472.95 P +3.66 (uniquely mapped onto the decision variable \050) 135.65 458.95 P +0 F +3.66 (phenotypic) 374.11 458.95 P +2 F +3.66 (\051 domain. The most) 426.73 458.95 P +0.03 (commonly used representation in GAs is the binary alphabet {0, 1} although other) 135.65 444.95 P +1.05 (representations can be used, e.g. ternary) 135.65 430.95 P +1.05 (, integer) 331.97 430.95 P +1.05 (, real-valued etc. For example, a) 371.85 430.95 P +2.13 (problem with two variables,) 135.65 416.95 P +0 F +2.13 (x) 281.76 416.95 P +0 10 Q +1.78 (1) 287.08 413.95 P +2 12 Q +2.13 ( and) 292.08 416.95 P +0 F +2.13 (x) 319.66 416.95 P +0 10 Q +1.78 (2) 324.98 413.95 P +2 12 Q +2.13 (, may be mapped onto the chromosome) 329.98 416.95 P +(structure in the following way:) 135.65 402.95 T +-0.3 (where) 135.65 299.98 P +0 F +-0.3 (x) 167.65 299.98 P +0 10 Q +-0.25 (1) 172.98 296.98 P +2 12 Q +-0.3 ( is encoded with 10 bits and) 177.97 299.98 P +0 F +-0.3 (x) 312.82 299.98 P +0 10 Q +-0.25 (2) 318.14 296.98 P +2 12 Q +-0.3 ( with 15 bits, possibly re\337ecting the level of) 323.14 299.98 P +-0.2 (accuracy or range of the individual decision variables. Examining the chromosome) 135.65 285.98 P +0.43 (string in isolation yields no information about the problem we are trying to solve.) 135.65 271.98 P +0.11 (It is only with the decoding of the chromosome into its phenotypic values that any) 135.65 257.98 P +1.35 (meaning can be applied to the representation. However) 135.65 243.98 P +1.35 (, as described below) 409.1 243.98 P +1.35 (, the) 509.64 243.98 P +0.55 (search process will operate on this encoding of the decision variables, rather than) 135.65 229.98 P +0.8 (the decision variables themselves, except, of course, where real-valued genes are) 135.65 215.98 P +(used.) 135.65 201.98 T +-0.19 (Having decoded the chromosome representation into the decision variable domain,) 135.65 175.98 P +1.94 (it is possible to assess the performance, or) 135.65 161.98 P +0 F +1.94 (\336tness) 356.04 161.98 P +2 F +1.94 (, of individual members of a) 386.03 161.98 P +3.53 (population. This is done through an objective function that characterises an) 135.65 147.98 P +0.6 (individual\325) 135.65 133.98 P +0.6 (s performance in the problem domain. In the natural world, this would) 187.63 133.98 P +0.08 (be an individual\325) 135.65 119.98 P +0.08 (s ability to survive in its present environment. Thus, the objective) 216.42 119.98 P +63.65 96.95 531.65 744.95 C +135.65 321.98 531.65 398.95 C +146.65 328.95 520.65 391.95 C +146.65 328.95 520.65 391.95 R +7 X +0 K +V +3 12 Q +0 X +(1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1) 157.35 369.97 T +170.49 343.64 158.95 346.95 170.49 350.26 170.49 346.95 4 Y +V +282.42 350.26 293.95 346.95 282.42 343.64 282.42 346.95 4 Y +V +170.49 346.95 282.42 346.95 2 L +0.5 H +0 Z +N +297.08 382.95 297.08 337.95 2 L +2 Z +11 X +N +311.49 343.64 299.95 346.95 311.49 350.26 311.49 346.95 4 Y +0 X +V +495.42 350.26 506.95 346.95 495.42 343.64 495.42 346.95 4 Y +V +311.49 346.95 495.42 346.95 2 L +0 Z +N +0 F +(x) 221.29 353.75 T +0 10 Q +(1) 226.62 350.75 T +0 12 Q +(x) 398.29 353.75 T +0 10 Q +(2) 403.61 350.75 T +135.65 321.98 531.65 398.95 C +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "3" 4 +%%Page: "4" 4 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-4) 518.33 61.29 T +2 12 Q +2.35 (function establishes the basis for selection of pairs of individuals that will be) 135.65 736.95 P +(mated together during reproduction.) 135.65 722.95 T +0.45 (During the reproduction phase, each individual is assigned a \336tness value derived) 135.65 696.95 P +0.94 (from its raw performance measure given by the objective function. This value is) 135.65 682.95 P +1.18 (used in the selection to bias towards more \336t individuals. Highly \336t individuals,) 135.65 668.95 P +2.11 (relative to the whole population, have a high probability of being selected for) 135.65 654.95 P +2.56 (mating whereas less \336t individuals have a correspondingly low probability of) 135.65 640.95 P +(being selected.) 135.65 626.95 T +0.54 (Once the individuals have been assigned a \336tness value, they can be chosen from) 135.65 600.95 P +5.22 (the population, with a probability according to their relative \336tness, and) 135.65 586.95 P +2.85 (recombined to produce the next generation. Genetic operators manipulate the) 135.65 572.95 P +0.61 (characters \050genes\051 of the chromosomes directly) 135.65 558.95 P +0.61 (, using the assumption that certain) 364.71 558.95 P +0.18 (individual\325) 135.65 544.95 P +0.18 (s gene codes, on average, produce \336tter individuals. The recombination) 187.63 544.95 P +0.68 (operator is used to exchange genetic information between pairs, or lar) 135.65 530.95 P +0.68 (ger groups,) 477.01 530.95 P +4.62 (of individuals. The simplest recombination operator is that of single-point) 135.65 516.95 P +(crossover) 135.65 502.95 T +(.) 180.95 502.95 T +(Consider the two parent binary strings:) 135.65 476.95 T +3 F +(P) 171.65 450.95 T +3 10 Q +(1) 178.84 447.95 T +3 12 Q +( = 1 0 0 1 0 1 1 0) 184.84 450.95 T +2 F +(, and) 314.37 450.95 T +3 F +(P) 171.65 424.95 T +3 10 Q +(2) 178.84 421.95 T +3 12 Q +( = 1 0 1 1 1 0 0 0) 184.84 424.95 T +2 F +(.) 314.37 424.95 T +0.59 (If an integer position,) 135.65 398.95 P +0 F +0.59 (i) 244.27 398.95 P +2 F +0.59 (, is selected uniformly at random between 1 and the string) 247.6 398.95 P +0.97 (length,) 135.65 384.95 P +0 F +0.97 (l) 172.6 384.95 P +2 F +0.97 (, minus one [1,) 175.93 384.95 P +0 F +0.97 (l) 254.42 384.95 P +2 F +0.97 (-1], and the genetic information exchanged between the) 257.76 384.95 P +0.15 (individuals about this point, then two new of) 135.65 370.95 P +0.15 (fspring strings are produced. The two) 351.03 370.95 P +(of) 135.65 356.95 T +(fspring below are produced when the crossover point) 145.42 356.95 T +0 F +(i = 5) 403.22 356.95 T +2 F +( is selected,) 426.64 356.95 T +3 F +(O) 171.65 330.95 T +3 10 Q +(1) 178.84 327.95 T +3 12 Q +( = 1 0 0 1 0 0 0 0) 184.84 330.95 T +2 F +(, and) 314.37 330.95 T +3 F +(O) 171.65 304.95 T +3 10 Q +(2) 178.84 301.95 T +3 12 Q +( = 1 0 1 1 1 1 1 0) 184.84 304.95 T +2 F +(.) 314.37 304.95 T +3.99 (This crossover operation is not necessarily performed on all strings in the) 135.65 278.95 P +0.87 (population. Instead, it is applied with a probability) 135.65 264.95 P +0 F +0.87 (Px) 387.77 264.95 P +2 F +0.87 ( when the pairs are chosen) 400.42 264.95 P +-0.2 (for breeding. A further genetic operator) 135.65 250.95 P +-0.2 (, called mutation, is then applied to the new) 324.02 250.95 P +1.8 (chromosomes, again with a set probability) 135.65 236.95 P +1.8 (,) 347.08 236.95 P +0 F +1.8 (Pm) 354.88 236.95 P +2 F +1.8 (. Mutation causes the individual) 370.87 236.95 P +1.06 (genetic representation to be changed according to some probabilistic rule. In the) 135.65 222.95 P +0.41 (binary) 135.65 208.95 P +0.41 (string) 172.7 208.95 P +0.41 ( representation,) 206.01 208.95 P +0.41 ( mutation will cause a single bit to change its state,) 283.36 208.95 P +0.74 (0) 135.65 194.95 P +4 F +0.74 (\336) 145.38 194.95 P +2 F +0.74 (1 or 1) 160.96 194.95 P +4 F +0.74 (\336) 194.15 194.95 P +2 F +0.74 ( 0. So, for example, mutating the fourth bit of) 205.99 194.95 P +3 F +1.77 (O) 434.89 194.95 P +3 10 Q +1.48 (1) 442.09 191.95 P +2 12 Q +0.74 ( leads to the new) 448.09 194.95 P +(string,) 135.65 180.95 T +3 F +(O) 171.65 154.95 T +3 10 Q +(1m) 178.84 151.95 T +3 12 Q +( = 1 0 0 0 0 0 0 0) 190.84 154.95 T +2 F +(.) 320.37 154.95 T +0.19 (Mutation is generally considered to be a background operator that ensures that the) 135.65 128.95 P +0.61 (probability of searching a particular subspace of the problem space is never zero.) 135.65 114.95 P +FMENDPAGE +%%EndPage: "4" 5 +%%Page: "5" 5 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-5) 518.33 61.29 T +2 12 Q +1.57 (This has the ef) 135.65 736.95 P +1.57 (fect of tending to inhibit the possibility of conver) 210.43 736.95 P +1.57 (ging to a local) 458.64 736.95 P +(optimum, rather than the global optimum.) 135.65 722.95 T +1.87 (After recombination and mutation, the individual strings are then, if necessary) 135.65 696.95 P +1.87 (,) 528.65 696.95 P +4.09 (decoded, the objective function evaluated, a \336tness value assigned to each) 135.65 682.95 P +-0.01 (individual and individuals selected for mating according to their \336tness, and so the) 135.65 668.95 P +4.08 (process continues through subsequent generations. In this way) 135.65 654.95 P +4.08 (, the average) 462.55 654.95 P +3.36 (performance of individuals in a population is expected to increase, as good) 135.65 640.95 P +0.1 (individuals are preserved and bred with one another and the less \336t individuals die) 135.65 626.95 P +-0.26 (out. The GA is terminated when some criteria are satis\336ed, e.g. a certain number of) 135.65 612.95 P +0.66 (generations, a mean deviation in the population, or when a particular point in the) 135.65 598.95 P +(search space is encountered.) 135.65 584.95 T +1 16 Q +(GAs versus T) 135.65 556.29 T +(raditional Methods) 226.86 556.29 T +2 12 Q +1.06 (From the above discussion, it can be seen that the GA dif) 135.65 528.95 P +1.06 (fers substantially from) 421.6 528.95 P +3.43 (more traditional search and optimization methods. The four most signi\336cant) 135.65 514.95 P +(dif) 135.65 500.95 T +(ferences are:) 148.76 500.95 T +(\245) 157.25 474.95 T +(GAs search a population of points in parallel, not a single point.) 171.65 474.95 T +(\245) 157.25 454.95 T +1.32 (GAs do not require derivative information or other auxiliary knowledge;) 171.65 454.95 P +1.1 (only the objective function and corresponding \336tness levels in\337uence the) 171.65 440.95 P +(directions of search.) 171.65 426.95 T +(\245) 157.25 406.95 T +(GAs use probabilistic transition rules, not deterministic ones.) 171.65 406.95 T +(\245) 157.25 386.95 T +-0.26 (GAs work on an encoding of the parameter set rather than the parameter set) 171.65 386.95 P +(itself \050except in where real-valued individuals are used\051.) 171.65 372.95 T +1.06 (It is important to note that the GA provides a number of potential solutions to a) 135.65 346.95 P +0.5 (given problem and the choice of \336nal solution is left to the user) 135.65 332.95 P +0.5 (. In cases where a) 444.75 332.95 P +0.44 (particular problem does not have one individual solution, for example a family of) 135.65 318.95 P +4.61 (Pareto-optimal solutions, as is the case in multiobjective optimization and) 135.65 304.95 P +3.39 (scheduling problems, then the GA is potentially useful for identifying these) 135.65 290.95 P +(alternative solutions simultaneously) 135.65 276.95 T +(.) 307.44 276.95 T +FMENDPAGE +%%EndPage: "5" 6 +%%Page: "6" 6 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-6) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Major Elements of the Genetic Algorithm) 63.65 732.95 T +2 12 Q +0.01 (The simple genetic algorithm \050SGA\051 is described by Goldber) 135.65 694.95 P +0.01 (g [1] and is used here) 428.67 694.95 P +0.09 (to illustrate the basic components of the GA. A pseudo-code outline of the SGA is) 135.65 680.95 P +1.58 (shown in Fig. 1. The population at time) 135.65 666.95 P +0 F +1.58 (t) 340.87 666.95 P +2 F +1.58 ( is represented by the time-dependent) 344.21 666.95 P +0.74 (variable) 135.65 652.95 P +0 F +0.74 (P) 178.02 652.95 P +2 F +0.74 (, with the initial population of random estimates being) 184.02 652.95 P +0 F +0.74 (P\0500\051) 453.87 652.95 P +2 F +0.74 (. Using this) 475.19 652.95 P +0.28 (outline of a GA, the remainder of this Section describes the major elements of the) 135.65 638.95 P +(GA.) 135.65 624.95 T +1 16 Q +(Population Repr) 135.65 336.01 T +(esentation and Initialisation) 248.64 336.01 T +2 12 Q +0.3 (GAs operate on a number of potential solutions, called a population, consisting of) 135.65 308.67 P +2.4 (some encoding of the parameter set simultaneously) 135.65 294.67 P +2.4 (. T) 395.08 294.67 P +2.4 (ypically) 409.97 294.67 P +2.4 (, a population is) 447.83 294.67 P +0.25 (composed of between 30 and 100 individuals, although, a variant called the micro) 135.65 280.67 P +1.11 (GA uses very small populations, ~10 individuals, with a restrictive reproduction) 135.65 266.67 P +(and replacement strategy in an attempt to reach real-time execution [2].) 135.65 252.67 T +0.4 (The most commonly used representation of chromosomes in the GA is that of the) 135.65 226.67 P +2.36 (single-level binary string. Here, each decision variable in the parameter set is) 135.65 212.67 P +0.23 (encoded as a binary string and these are concatenated to form a chromosome. The) 135.65 198.67 P +1.64 (use of Gray coding has been advocated as a method of overcoming the hidden) 135.65 184.67 P +4.2 (representational bias in conventional binary representation as the Hamming) 135.65 170.67 P +1.13 (distance between adjacent values is constant [3]. Empirical evidence of Caruana) 135.65 156.67 P +1.94 (and Schaf) 135.65 142.67 P +1.94 (fer [4] suggests that lar) 185 142.67 P +1.94 (ge Hamming distances in the representational) 303.11 142.67 P +5.36 (mapping between adjacent values, as is the case in the standard binary) 135.65 128.67 P +3.42 (representation, can result in the search process being deceived or unable to) 135.65 114.67 P +63.65 96.95 531.65 744.95 C +133.38 360.67 531.65 620.95 C +162.43 380.97 502.59 600.65 R +7 X +0 K +V +2 12 Q +0 X +(procedure GA) 198.43 592.65 T +(begin) 198.43 577.65 T +(t = 0;) 243.43 562.65 T +(initialize P\050t\051;) 243.43 547.65 T +(evaluate P\050t\051;) 243.43 532.65 T +(while not finished do) 243.43 517.65 T +(begin) 243.43 502.65 T +(t = t + 1;) 315.43 487.65 T +(select P\050t\051 from P\050t-1\051;) 315.43 472.65 T +(reproduce pairs in P\050t\051;) 315.43 457.65 T +(evaluate P\050t\051;) 315.43 442.65 T +(end) 243.43 427.65 T +(end.) 198.43 412.65 T +5 F +(Figure 1: A Simple Genetic Algorithm) 234.43 386.65 T +146.89 370.34 518.14 611.28 R +0.5 H +2 Z +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "6" 7 +%%Page: "7" 7 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-7) 518.33 61.29 T +2 12 Q +0.64 (ef) 135.65 736.95 P +0.64 (\336ciently locate the global minimum. A further approach of Schmitendor) 144.75 736.95 P +0.64 (gf) 496.04 736.95 P +0 F +0.64 (et-al) 509.66 736.95 P +2 F +5.3 ([5], is the use of logarithmic scaling in the conversion of binary-coded) 135.65 722.95 P +3.46 (chromosomes to their real phenotypic values. Although the precision of the) 135.65 708.95 P +1.48 (parameter values is possibly less consistent over the desired range, in problems) 135.65 694.95 P +0.3 (where the spread of feasible parameters is unknown, a lar) 135.65 680.95 P +0.3 (ger search space may be) 413.9 680.95 P +0.51 (covered with the same number of bits than a linear mapping scheme allowing the) 135.65 666.95 P +-0.2 (computational burden of exploring unknown search spaces to be reduced to a more) 135.65 652.95 P +(manageable level.) 135.65 638.95 T +0.33 (Whilst binary-coded GAs are most commonly used, there is an increasing interest) 135.65 612.95 P +0.52 (in alternative encoding strategies, such as integer and real-valued representations.) 135.65 598.95 P +1.37 (For some problem domains, it is ar) 135.65 584.95 P +1.37 (gued that the binary representation is in fact) 311.22 584.95 P +1.28 (deceptive in that it obscures the nature of the search [6]. In the subset selection) 135.65 570.95 P +0.8 (problem [7], for example, the use of an integer representation and look-up tables) 135.65 556.95 P +5.49 (provides a convenient and natural way of expressing the mapping from) 135.65 542.95 P +(representation to problem domain.) 135.65 528.95 T +0.06 (The use of real-valued genes in GAs is claimed by W) 135.65 502.95 P +0.06 (right [8] to of) 392.27 502.95 P +0.06 (fer a number of) 457.2 502.95 P +1.02 (advantages in numerical function optimization over binary encodings. Ef) 135.65 488.95 P +1.02 (\336ciency) 493.68 488.95 P +0.45 (of the GA is increased as there is no need to convert chromosomes to phenotypes) 135.65 474.95 P +-0.02 (before each function evaluation; less memory is required as ef) 135.65 460.95 P +-0.02 (\336cient \337oating-point) 433.38 460.95 P +-0.03 (internal computer representations can be used directly; there is no loss in precision) 135.65 446.95 P +1.89 (by discretisation to binary or other values; and there is greater freedom to use) 135.65 432.95 P +0.23 (dif) 135.65 418.95 P +0.23 (ferent genetic operators. The use of real-valued encodings is described in detail) 148.76 418.95 P +0.08 (by Michalewicz [9] and in the literature on Evolution Strategies \050see, for example,) 135.65 404.95 P +([10]\051.) 135.65 390.95 T +1.85 (Having decided on the representation, the \336rst step in the SGA is to create an) 135.65 364.95 P +0.93 (initial population. This is usually achieved by generating the required number of) 135.65 350.95 P +0.95 (individuals using a random number generator that uniformly distributes numbers) 135.65 336.95 P +1.57 (in the desired range. For example, with a binary population of) 135.65 322.95 P +0 F +1.57 (N) 453 322.95 P +0 10 Q +1.3 (ind) 461 319.95 P +2 12 Q +1.57 ( individuals) 473.77 322.95 P +1.57 (whose chromosomes are) 135.65 308.95 P +0 F +1.57 (L) 261.27 308.95 P +0 10 Q +1.31 (ind) 267.94 305.95 P +2 12 Q +1.57 ( bits long,) 280.71 308.95 P +0 F +1.57 (N) 336.08 308.95 P +0 10 Q +1.31 (ind) 344.08 305.95 P +4 12 Q +1.57 (\264) 361.42 308.95 P +0 F +1.57 (L) 372.58 308.95 P +0 10 Q +1.31 (ind) 379.24 305.95 P +2 12 Q +1.57 ( random numbers uniformly) 392.02 308.95 P +(distributed from the set {0, 1} would be produced.) 135.65 294.95 T +3.16 (A variation is the) 135.65 268.95 P +0 F +3.16 (extended random initialisation) 234.23 268.95 P +2 F +3.16 ( procedure of Bramlette [6]) 387.8 268.95 P +1.02 (whereby a number of random initialisations are tried for each individual and the) 135.65 254.95 P +0.74 (one with the best performance is chosen for the initial population. Other users of) 135.65 240.95 P +-0.01 (GAs have seeded the initial population with some individuals that are known to be) 135.65 226.95 P +2.31 (in the vicinity of the global minimum \050see, for example, [1) 135.65 212.95 P +2.31 (1] and [12]\051. This) 440.12 212.95 P +3.22 (approach is, of course, only applicable if the nature of the problem is well) 135.65 198.95 P +-0.16 (understood beforehand or if the GA is used in conjunction with a knowledge based) 135.65 184.95 P +(system.) 135.65 170.95 T +5.61 (The GA T) 135.65 144.95 P +5.61 (oolbox supports binary) 195.31 144.95 P +5.61 (, integer and \337oating-point chromosome) 316.35 144.95 P +3.8 (representations. Binary and integer populations may be initialised using the) 135.65 130.95 P +1.9 (T) 135.65 116.95 P +1.9 (oolbox function to create binary populations,) 142.14 116.95 P +3 F +4.55 (crtbp) 372.38 116.95 P +2 F +1.9 (. An additional function,) 408.36 116.95 P +3 F +3.25 (crtbase) 135.65 102.95 P +2 F +1.35 (, is provided that builds a vector describing the integer representation) 186.02 102.95 P +FMENDPAGE +%%EndPage: "7" 8 +%%Page: "8" 8 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-8) 518.33 61.29 T +2 12 Q +3.99 (used. Real-valued populations may be initialised with the function) 135.65 736.95 P +3 F +9.57 (crtrp) 492.67 736.95 P +2 F +3.99 (.) 528.65 736.95 P +2.54 (Conversion between binary strings and real values is provided by the routine) 135.65 722.95 P +3 F +(bs2rv) 135.65 708.95 T +2 F +( that supports the use of Gray codes and logarithmic scaling.) 171.63 708.95 T +1 16 Q +(The Objective and Fitness Functions) 135.65 680.29 T +2 12 Q +2.47 (The objective function is used to provide a measure of how individuals have) 135.65 652.95 P +-0.11 (performed in the problem domain. In the case of a minimization problem, the most) 135.65 638.95 P +1.87 (\336t individuals will have the lowest numerical value of the associated objective) 135.65 624.95 P +0.17 (function. This raw measure of \336tness is usually only used as an intermediate stage) 135.65 610.95 P +0.36 (in determining the relative performance of individuals in a GA. Another function,) 135.65 596.95 P +0.05 (the) 135.65 582.95 P +0 F +0.05 (\336tness function) 153.35 582.95 P +2 F +0.05 (, is normally used to transform the objective function value into) 225.7 582.95 P +(a measure of relative \336tness [13], thus:) 135.65 568.95 T +-0.29 (where) 135.65 514.76 P +0 F +-0.29 (f) 167.66 514.76 P +2 F +-0.29 ( is the objective function,) 170.99 514.76 P +0 F +-0.29 (g) 294.13 514.76 P +2 F +-0.29 ( transforms the value of the objective function to) 300.13 514.76 P +2.1 (a non-negative number and) 135.65 500.76 P +0 F +2.1 (F) 277.95 500.76 P +2 F +2.1 ( is the resulting relative \336tness. This mapping is) 285.28 500.76 P +1.97 (always necessary when the objective function is to be minimized as the lower) 135.65 486.76 P +3.03 (objective function values correspond to \336tter individuals. In many cases, the) 135.65 472.76 P +-0.29 (\336tness function value corresponds to the number of of) 135.65 458.76 P +-0.29 (fspring that an individual can) 392.24 458.76 P +0.33 (expect to produce in the next generation. A commonly used transformation is that) 135.65 444.76 P +1.03 (of proportional \336tness assignment \050see, for example, [1]\051. The individual \336tness,) 135.65 430.76 P +0 F +1.4 (F\050x) 135.65 416.76 P +0 10 Q +1.17 (i) 152.29 413.76 P +0 12 Q +1.4 (\051) 155.07 416.76 P +2 F +1.4 (, of each individual is computed as the individual\325) 159.07 416.76 P +1.4 (s raw performance,) 409.79 416.76 P +0 F +1.4 (f\050x) 509.22 416.76 P +0 10 Q +1.17 (i) 521.88 413.76 P +0 12 Q +1.4 (\051) 524.66 416.76 P +2 F +1.4 (,) 528.65 416.76 P +(relative to the whole population, i.e.,) 135.65 402.76 T +(,) 380.93 365.33 T +1.36 (where) 135.65 304.51 P +0 F +1.36 (N) 169.3 304.51 P +0 10 Q +1.13 (ind) 177.3 301.51 P +2 12 Q +1.36 ( is the population size and) 190.08 304.51 P +0 F +1.36 (x) 326.15 304.51 P +0 10 Q +1.13 (i) 331.47 301.51 P +2 12 Q +1.36 ( is the phenotypic value of individual) 334.25 304.51 P +0 F +1.36 (i) 525.32 304.51 P +2 F +1.36 (.) 528.65 304.51 P +1.87 (Whilst this \336tness assignment ensures that each individual has a probability of) 135.65 290.51 P +3.54 (reproducing according to its relative \336tness, it fails to account for negative) 135.65 276.51 P +(objective function values.) 135.65 262.51 T +0.15 (A linear transformation which of) 135.65 236.51 P +0.15 (fsets the objective function [1] is often used prior) 293.92 236.51 P +(to \336tness assignment, such that,) 135.65 222.51 T +0.2 (where) 135.65 168.32 P +0 F +0.2 (a) 168.15 168.32 P +2 F +0.2 ( is a positive scaling factor if the optimization is maximizing and negative) 174.14 168.32 P +-0.1 (if we are minimizing. The of) 135.65 154.32 P +-0.1 (fset) 272.83 154.32 P +0 F +-0.1 (b) 293.04 154.32 P +2 F +-0.1 ( is used to ensure that the resulting \336tness values) 299.04 154.32 P +(are non-negative.) 135.65 140.32 T +288.09 536.76 379.21 550.95 C +0 12 Q +0 X +0 K +(F) 289.09 541.75 T +(x) 304.22 541.75 T +4 F +(\050) 299.12 541.75 T +(\051) 310.16 541.75 T +0 F +(g) 334.73 541.75 T +(f) 348.54 541.75 T +(x) 359.68 541.75 T +4 F +(\050) 354.58 541.75 T +(\051) 365.61 541.75 T +(\050) 343.44 541.75 T +(\051) 372.21 541.75 T +(=) 322.15 541.75 T +-8.35 24.95 603.65 816.95 C +283.37 326.51 380.93 384.76 C +0 12 Q +0 X +0 K +(F) 284.37 365.33 T +(x) 299.5 365.33 T +0 9 Q +(i) 305.29 361.55 T +4 12 Q +(\050) 294.4 365.33 T +(\051) 308.4 365.33 T +0 F +(f) 343.44 375.55 T +(x) 354.58 375.55 T +0 9 Q +(i) 360.36 371.77 T +4 12 Q +(\050) 349.48 375.55 T +(\051) 363.47 375.55 T +0 F +(f) 352.9 343.76 T +(x) 364.04 343.76 T +0 9 Q +(i) 369.83 339.98 T +4 12 Q +(\050) 358.94 343.76 T +(\051) 372.93 343.76 T +0 9 Q +(i) 333.98 329.46 T +2 F +(1) 347.41 329.46 T +4 F +(=) 339.47 329.46 T +0 F +(N) 335.47 360.27 T +0 6 Q +(i) 341.82 357.82 T +(n) 343.94 357.82 T +(d) 347.4 357.82 T +4 18 Q +(\345) 336.52 340.55 T +4 12 Q +(=) 320.39 365.33 T +333.98 367.92 378.68 367.92 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +285.65 190.32 381.65 204.51 C +0 12 Q +0 X +0 K +(F) 286.65 195.31 T +(x) 301.79 195.31 T +4 F +(\050) 296.68 195.31 T +(\051) 307.72 195.31 T +0 F +(a) 332.3 195.31 T +(f) 339 195.31 T +(x) 350.14 195.31 T +4 F +(\050) 345.04 195.31 T +(\051) 356.07 195.31 T +0 F +(b) 374.65 195.31 T +4 F +(+) 365.07 195.31 T +(=) 319.71 195.31 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "8" 9 +%%Page: "9" 9 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-9) 518.33 61.29 T +2 12 Q +0.91 (The linear scaling and of) 135.65 736.95 P +0.91 (fsetting outlined above is, however) 258.3 736.95 P +0.91 (, susceptible to rapid) 429.66 736.95 P +6.1 (conver) 135.65 722.95 P +6.1 (gence. The) 168.07 722.95 P +0 F +6.1 (selection) 235.88 722.95 P +2 F +6.1 ( algorithm \050see below\051 selects individuals for) 278.52 722.95 P +3.81 (reproduction on the basis of their relative \336tness. Using linear scaling, the) 135.65 708.95 P +2.09 (expected number of of) 135.65 694.95 P +2.09 (fspring is approximately proportional to that individuals) 249.94 694.95 P +0.83 (performance. As there is no constraint on an individual\325) 135.65 680.95 P +0.83 (s performance in a given) 409.76 680.95 P +6.32 (generation, highly \336t individuals in early generations can dominate the) 135.65 666.95 P +5.59 (reproduction causing rapid conver) 135.65 652.95 P +5.59 (gence to possibly sub-optimal solutions.) 316.4 652.95 P +0.26 (Similarly) 135.65 638.95 P +0.26 (, if there is little deviation in the population, then scaling provides only a) 179.52 638.95 P +(small bias towards the most \336t individuals.) 135.65 624.95 T +0.33 (Baker [14] suggests that by limiting the reproductive range, so that no individuals) 135.65 598.95 P +-0.13 (generate an excessive number of of) 135.65 584.95 P +-0.13 (fspring, prevents premature conver) 304.27 584.95 P +-0.13 (gence. Here,) 471.52 584.95 P +0.97 (individuals are assigned a \336tness according to their rank in the population rather) 135.65 570.95 P +0.72 (than their raw performance. One variable,) 135.65 556.95 P +0 F +0.72 (MAX) 343.76 556.95 P +2 F +0.72 (, is used to determine the bias, or) 368.41 556.95 P +0 F +0.65 (selective pr) 135.65 542.95 P +0.65 (essur) 190.81 542.95 P +0.65 (e) 215.68 542.95 P +2 F +0.65 (, towards the most \336t individuals and the \336tness of the others is) 221.01 542.95 P +(determined by the following rules:) 135.65 528.95 T +(\245) 157.25 502.95 T +0 F +(MIN) 164.44 502.95 T +2 F +( = 2.0 -) 186.43 502.95 T +0 F +(MAX) 224.17 502.95 T +2 F +(\245) 157.25 482.95 T +0 F +(INC) 164.44 482.95 T +2 F +( = 2.0) 184.44 482.95 T +4 F +(\264) 215.19 482.95 T +2 F +( \050) 221.77 482.95 T +0 F +(MAX) 228.76 482.95 T +2 F +( -1.0\051 /) 253.41 482.95 T +0 F +(N) 288.72 482.95 T +0 10 Q +(ind) 296.72 479.95 T +2 12 Q +(\245) 157.25 462.95 T +0 F +(LOW) 164.44 462.95 T +2 F +( =) 189.76 462.95 T +0 F +(INC) 202.52 462.95 T +2 F +( / 2.0) 222.52 462.95 T +2.81 (where) 135.65 442.95 P +0 F +2.81 (MIN) 170.75 442.95 P +2 F +2.81 ( is the lower bound,) 192.74 442.95 P +0 F +2.81 (INC) 304.71 442.95 P +2 F +2.81 ( is the dif) 324.7 442.95 P +2.81 (ference between the \336tness of) 377.88 442.95 P +0.97 (adjacent individuals and) 135.65 428.95 P +0 F +0.97 (LOW) 258.13 428.95 P +2 F +0.97 ( is the expected number of trials \050number of times) 283.45 428.95 P +1.2 (selected\051 of the least \336t individual.) 135.65 414.95 P +0 F +1.2 (MAX) 311.73 414.95 P +2 F +1.2 ( is typically chosen in the interval [1.1,) 336.38 414.95 P +0.66 (2.0]. Hence, for a population size of) 135.65 400.95 P +0 F +0.66 (N) 316.12 400.95 P +0 10 Q +0.55 (ind) 324.11 397.95 P +2 12 Q +0.66 ( = 40 and) 336.89 400.95 P +0 F +0.66 (MAX) 387.59 400.95 P +2 F +0.66 ( = 1.1, we obtain) 412.24 400.95 P +0 F +0.66 (MIN) 499.24 400.95 P +2 F +0.66 ( =) 521.23 400.95 P +-0.18 (0.9,) 135.65 386.95 P +0 F +-0.18 (INC) 156.46 386.95 P +2 F +-0.18 ( = 0.05 and) 176.45 386.95 P +0 F +-0.18 (LOW) 232.81 386.95 P +2 F +-0.18 ( = 0.025. The \336tness of individuals in the population may) 258.13 386.95 P +(also be calculated directly as,) 135.65 372.95 T +(,) 439.73 335.53 T +(where) 135.65 299.28 T +0 F +(x) 167.95 299.28 T +0 10 Q +(i) 173.27 296.28 T +2 12 Q +( is the position in the ordered population of individual) 176.05 299.28 T +0 F +(i) 437.9 299.28 T +2 F +(.) 441.24 299.28 T +-0.04 (Objective functions must be created by the user) 135.65 273.28 P +-0.04 (, although a number of example m-) 363.03 273.28 P +0.7 (\336les are supplied with the T) 135.65 259.28 P +0.7 (oolbox that implement common test functions. These) 271.91 259.28 P +0.98 (objective functions all have the \336lename pre\336x) 135.65 245.28 P +3 F +2.36 (obj) 370.71 245.28 P +2 F +0.98 (. The T) 392.3 245.28 P +0.98 (oolbox supports both) 428.4 245.28 P +1.65 (linear and non-linear ranking methods,) 135.65 231.28 P +3 F +3.97 (ranking) 333.11 231.28 P +2 F +1.65 (, and includes a simple linear) 383.48 231.28 P +1.26 (scaling function,) 135.65 217.28 P +3 F +3.02 (scaling) 221.11 217.28 P +2 F +1.26 (, for completeness. It should be noted that the linear) 271.49 217.28 P +-0.14 (scaling function is not suitable for use with objective functions that return negative) 135.65 203.28 P +(\336tness values.) 135.65 189.28 T +1 16 Q +(Selection) 135.65 160.61 T +2 12 Q +0.46 (Selection is the process of determining the number of times, or) 135.65 133.28 P +0 F +0.46 (trials) 445.13 133.28 P +2 F +0.46 (, a particular) 470.46 133.28 P +1.43 (individual is chosen for reproduction and, thus, the number of of) 135.65 119.28 P +1.43 (fspring that an) 459.51 119.28 P +224.57 321.28 439.73 354.95 C +0 12 Q +0 X +0 K +(F) 225.57 335.53 T +(x) 240.7 335.53 T +0 9 Q +(i) 246.49 331.75 T +4 12 Q +(\050) 235.6 335.53 T +(\051) 249.59 335.53 T +2 F +(2) 274.17 335.53 T +0 F +(M) 292.75 335.53 T +(A) 303.45 335.53 T +(X) 311.48 335.53 T +4 F +(-) 283.17 335.53 T +2 F +(2) 331.39 335.53 T +0 F +(M) 345.2 335.53 T +(A) 355.89 335.53 T +(X) 363.93 335.53 T +2 F +(1) 383.84 335.53 T +4 F +(-) 374.26 335.53 T +(\050) 340.1 335.53 T +(\051) 390.45 335.53 T +0 F +(x) 404.51 345.75 T +0 9 Q +(i) 410.29 341.97 T +2 12 Q +(1) 425.37 345.75 T +4 F +(-) 415.79 345.75 T +0 F +(N) 398.14 327.91 T +0 9 Q +(i) 406.61 324.13 T +(n) 409.63 324.13 T +(d) 414.66 324.13 T +2 12 Q +(1) 431.73 327.91 T +4 F +(-) 422.15 327.91 T +(+) 321.81 335.53 T +(=) 261.59 335.53 T +398.14 338.12 437.48 338.12 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "9" 10 +%%Page: "10" 10 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-10) 513.33 61.29 T +2 12 Q +-0.28 (individual will produce. The selection of individuals can be viewed as two separate) 135.65 736.95 P +(processes:) 135.65 722.95 T +(1\051) 135.65 696.95 T +0.93 (determination of the number of trials an individual can expect to receive,) 171.65 696.95 P +(and) 171.65 682.95 T +(2\051) 135.65 662.95 T +2.6 (conversion of the expected number of trials into a discrete number of) 171.65 662.95 P +(of) 171.65 648.95 T +(fspring.) 181.42 648.95 T +-0.07 (The \336rst part is concerned with the transformation of raw \336tness values into a real-) 135.65 628.95 P +0.47 (valued expectation of an individual\325) 135.65 614.95 P +0.47 (s probability to reproduce and is dealt with in) 310.06 614.95 P +0.51 (the previous subsection as \336tness assignment. The second part is the probabilistic) 135.65 600.95 P +-0.19 (selection of individuals for reproduction based on the \336tness of individuals relative) 135.65 586.95 P +3.05 (to one another and is sometimes known as) 135.65 572.95 P +0 F +3.05 (sampling) 365.89 572.95 P +2 F +3.05 (. The remainder of this) 409.87 572.95 P +2.11 (subsection will review some of the more popular selection methods in current) 135.65 558.95 P +(usage.) 135.65 544.95 T +-0.17 (Baker [15] presented three measures of performance for selection algorithms,) 135.65 518.95 P +0 F +-0.17 (bias) 508.66 518.95 P +2 F +-0.17 (,) 528.65 518.95 P +0 F +3.37 (spr) 135.65 504.95 P +3.37 (ead) 150.53 504.95 P +2 F +3.37 ( and) 167.85 504.95 P +0 F +3.37 (ef\336ciency) 197.9 504.95 P +2 F +3.37 (. Bias is de\336ned as the absolute dif) 242.41 504.95 P +3.37 (ference between an) 432.34 504.95 P +4.34 (individual\325) 135.65 490.95 P +4.34 (s actual and expected selection probability) 187.63 490.95 P +4.34 (. Optimal zero bias is) 412.04 490.95 P +1.03 (therefore achieved when an individual\325) 135.65 476.95 P +1.03 (s selection probability equals its expected) 326.95 476.95 P +(number of trials.) 135.65 462.95 T +-0.05 (Spread is the range in the possible number of trials that an individual may achieve.) 135.65 436.95 P +0.71 (If) 135.65 422.95 P +0 F +0.71 (f\050i\051) 147.34 422.95 P +2 F +0.71 ( is the actual number of trials that individual) 162 422.95 P +0 F +0.71 (i) 383.91 422.95 P +2 F +0.71 ( receives, then the \322minimum) 387.24 422.95 P +(spread\323 is the smallest spread that theoretically permits zero bias, i.e.) 135.65 408.95 T +0.3 (where) 135.65 321.65 P +0 F +0.3 (et\050i\051) 168.24 321.65 P +2 F +0.3 ( is the expected number of trials of individual) 188.23 321.65 P +0 F +0.3 (i) 412.42 321.65 P +2 F +0.3 (,) 415.76 321.65 P +0.3 ( is the \337oor of) 463.16 321.65 P +1.64 (et\050i\051 and) 135.65 307.65 P +1.64 ( is the ceil. Thus, while bias is an indication of accuracy) 223.32 307.65 P +1.64 (, the) 509.36 307.65 P +(spread of a selection method measures its consistency) 135.65 293.65 T +(.) 393.02 293.65 T +0.88 (The desire for ef) 135.65 267.65 P +0.88 (\336cient selection methods is motivated by the need to maintain a) 217.67 267.65 P +1.72 (GAs overall time complexity) 135.65 253.65 P +1.72 (. It has been shown in the literature that the other) 279.61 253.65 P +4.96 (phases of a GA \050excluding the actual objective function evaluations\051 are) 135.65 239.65 P +1 (O\050L) 135.65 225.65 P +2 10 Q +0.83 (ind) 155.63 222.65 P +2 12 Q +1 (.N) 168.4 225.65 P +2 10 Q +0.83 (ind) 180.06 222.65 P +2 12 Q +1 (\051 or better time complexity) 192.83 225.65 P +1 (, where L) 324.64 225.65 P +2 10 Q +0.83 (ind) 372.27 222.65 P +2 12 Q +1 ( is the length of an individual) 385.05 225.65 P +0.71 (and N) 135.65 211.65 P +2 10 Q +0.59 (ind) 165.33 208.65 P +2 12 Q +0.71 ( is the population size. The selection algorithm should thus achieve zero) 178.1 211.65 P +1.51 (bias whilst maintaining a minimum spread and not contributing to an increased) 135.65 197.65 P +(time complexity of the GA.) 135.65 183.65 T +1 14 Q +(Roulette Wheel Selection Methods) 135.65 156.31 T +2 12 Q +8.61 (Many selection techniques employ a \322roulette wheel\323 mechanism to) 135.65 129.65 P +-0.14 (probabilistically select individuals based on some measure of their performance. A) 135.65 115.65 P +2.72 (real-valued interval,) 135.65 101.65 P +0 F +2.72 (Sum) 240.67 101.65 P +2 F +2.72 (, is determined as either the sum of the individuals\325) 261.32 101.65 P +261.26 343.65 406.04 390.95 C +0 12 Q +0 X +0 K +(f) 262.26 364.71 T +(i) 273.4 364.71 T +4 F +(\050) 268.3 364.71 T +(\051) 277.34 364.71 T +0 F +(e) 312.75 365.19 T +(t) 318.78 365.19 T +(i) 329.92 365.19 T +4 F +(\050) 324.82 365.19 T +(\051) 333.86 365.19 T +0 F +(e) 357.85 365.19 T +(t) 363.89 365.19 T +(i) 375.03 365.19 T +4 F +(\050) 369.92 365.19 T +(\051) 378.97 365.19 T +(,) 345.86 365.19 T +(\376) 394.67 350.05 T +(\375) 394.67 362.17 T +(\374) 394.67 374.29 T +(\356) 299.88 350.05 T +(\355) 299.88 362.17 T +(\354) 299.88 374.29 T +(\316) 286.33 364.71 T +307.75 362.2 307.75 373.4 2 L +0.33 H +0 Z +N +307.75 362.2 310.75 362.2 2 L +N +343.86 362.2 343.86 373.4 2 L +N +343.86 362.2 340.86 362.2 2 L +N +352.85 362.2 352.85 373.4 2 L +N +352.85 373.4 355.85 373.4 2 L +N +388.96 362.2 388.96 373.4 2 L +N +388.96 373.4 385.96 373.4 2 L +N +-8.35 24.95 603.65 816.95 C +422.05 316.65 463.16 330.85 C +0 12 Q +0 X +0 K +(e) 429.05 321.65 T +(t) 435.08 321.65 T +(i) 446.23 321.65 T +4 F +(\050) 441.12 321.65 T +(\051) 450.17 321.65 T +424.05 318.65 424.05 329.85 2 L +0.33 H +0 Z +N +424.05 318.65 427.05 318.65 2 L +N +460.16 318.65 460.16 329.85 2 L +N +460.16 318.65 457.16 318.65 2 L +N +-8.35 24.95 603.65 816.95 C +182.22 302.65 223.32 316.85 C +0 12 Q +0 X +0 K +(e) 189.22 307.65 T +(t) 195.25 307.65 T +(i) 206.39 307.65 T +4 F +(\050) 201.29 307.65 T +(\051) 210.33 307.65 T +184.22 304.65 184.22 315.85 2 L +0.33 H +0 Z +N +184.22 315.85 187.22 315.85 2 L +N +220.32 304.65 220.32 315.85 2 L +N +220.32 315.85 217.32 315.85 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "10" 11 +%%Page: "11" 11 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-11) 513.33 61.29 T +2 12 Q +1.17 (expected selection probabilities or the sum of the raw \336tness values over all the) 135.65 736.95 P +0.26 (individuals in the current population. Individuals are then mapped one-to-one into) 135.65 722.95 P +1.69 (contiguous intervals in the range [0,) 135.65 708.95 P +0 F +1.69 (Sum) 321.33 708.95 P +2 F +1.69 (]. The size of each individual interval) 341.98 708.95 P +-0.14 (corresponds to the \336tness value of the associated individual. For example, in Fig. 2) 135.65 694.95 P +1.38 (the circumference of the roulette wheel is the sum of all six individual\325) 135.65 680.95 P +1.38 (s \336tness) 491.95 680.95 P +1.76 (values. Individual 5 is the most \336t individual and occupies the lar) 135.65 666.95 P +1.76 (gest interval,) 467.93 666.95 P +1.97 (whereas individuals 6 and 4 are the least \336t and have correspondingly smaller) 135.65 652.95 P +1.31 (intervals within the roulette wheel. T) 135.65 638.95 P +1.31 (o select an individual, a random number is) 318.59 638.95 P +1.88 (generated in the interval [0,) 135.65 624.95 P +0 F +1.88 (Sum) 280.29 624.95 P +2 F +1.88 (] and the individual whose segment spans the) 300.94 624.95 P +1.11 (random number is selected. This process is repeated until the desired number of) 135.65 610.95 P +(individuals have been selected.) 135.65 596.95 T +-0.04 (The basic roulette wheel selection method is stochastic sampling with replacement) 135.65 570.95 P +4.89 (\050SSR\051. Here, the segment size and selection probability remain the same) 135.65 556.95 P +3.36 (throughout the selection phase and individuals are selected according to the) 135.65 542.95 P +0.48 (procedure outlined above. SSR gives zero bias but a potentially unlimited spread.) 135.65 528.95 P +(Any individual with a segment size > 0 could entirely \336ll the next population.) 135.65 514.95 T +3.91 (Stochastic sampling with partial replacement \050SSPR\051 extends upon SSR by) 135.65 271.94 P +3.1 (resizing an individual\325) 135.65 257.94 P +3.1 (s segment if it is selected. Each time an individual is) 249.12 257.94 P +1.33 (selected, the size of its segment is reduced by 1.0. If the segment size becomes) 135.65 243.94 P +2.15 (negative, then it is set to 0.0. This provides an upper bound on the spread of) 135.65 229.94 P +-0.2 (. However) 176.76 215.94 P +-0.2 (, the lower bound is zero and the bias is higher than that of SSR.) 226.02 215.94 P +1.29 (Remainder sampling methods involve two distinct phases. In the integral phase,) 135.65 189.94 P +2.36 (individuals are selected deterministically according to the integer part of their) 135.65 175.94 P +0.4 (expected trials. The remaining individuals are then selected probabilistically from) 135.65 161.94 P +3.95 (the fractional part of the individuals expected values. Remainder stochastic) 135.65 147.94 P +1.82 (sampling with replacement \050RSSR\051 uses roulette wheel selection to sample the) 135.65 133.94 P +3.42 (individual not assigned deterministically) 135.65 119.94 P +3.42 (. During the roulette wheel selection) 340.02 119.94 P +3.29 (phase, individual\325) 135.65 105.94 P +3.29 (s fractional parts remain unchanged and, thus, compete for) 224.22 105.94 P +63.65 96.95 531.65 744.95 C +133.38 293.94 531.65 510.95 C +0.5 H +2 Z +0 X +0 K +90 450 70.87 70.87 332.51 420.22 A +332.51 491.09 332.51 420.22 2 L +N +332.51 420.22 282.91 370.61 2 L +N +332.51 420.22 384.95 466.76 2 L +N +332.51 420.22 394.88 389.74 2 L +N +2 12 Q +(1) 358.18 462.39 T +90 450 7.09 7.09 361.18 466.48 A +(3) 350.03 366.22 T +90 450 7.09 7.09 353.03 370.31 A +(2) 382.66 416.22 T +90 450 7.09 7.09 385.66 420.31 A +(4) 299.18 370.87 T +90 450 7.09 7.09 302.18 374.96 A +332.51 420.22 303.38 484.74 2 L +N +(5) 278.18 428.87 T +90 450 7.09 7.09 281.18 432.96 A +332.38 418.74 305.38 355.74 2 L +N +(6) 319.18 469.89 T +90 450 7.09 7.09 322.18 473.98 A +5 F +(Figure 2: Roulette Wheel Selection) 245.56 316.24 T +146.49 303.24 518.54 501.66 R +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +135.65 210.95 176.75 225.15 C +0 12 Q +0 X +0 K +(e) 142.65 215.94 T +(t) 148.68 215.94 T +(i) 159.82 215.94 T +4 F +(\050) 154.72 215.94 T +(\051) 163.76 215.94 T +137.65 212.95 137.65 224.15 2 L +0.33 H +0 Z +N +137.65 224.15 140.65 224.15 2 L +N +173.76 212.95 173.76 224.15 2 L +N +173.76 224.15 170.76 224.15 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "11" 12 +%%Page: "12" 12 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-12) 513.33 61.29 T +2 12 Q +2.99 (selection between \322spins\323. RSSR provides zero bias and the spread is lower) 135.65 736.95 P +0.55 (bounded. The upper bound is limited only by the number of fractionally assigned) 135.65 722.95 P +2.87 (samples and the size of the integral part of an individual. For example, any) 135.65 708.95 P +-0.04 (individual with a fractional part > 0 could win all the samples during the fractional) 135.65 694.95 P +2.65 (phase. Remainder stochastic sampling without replacement \050RSSWR\051 sets the) 135.65 680.95 P +0.02 (fractional part of an individual\325) 135.65 666.95 P +0.02 (s expected values to zero if it is sampled during the) 285.62 666.95 P +2.51 (fractional phase. This gives RSSWR minimum spread, although this selection) 135.65 652.95 P +(method is biased in favour of smaller fractions.) 135.65 638.95 T +1 14 Q +(Stochastic Universal Sampling) 135.65 611.62 T +2 12 Q +1.84 (Stochastic universal sampling \050SUS\051 is a single-phase sampling algorithm with) 135.65 584.95 P +0.05 (minimum spread and zero bias. Instead of the single selection pointer employed in) 135.65 570.95 P +2.58 (roulette wheel methods, SUS uses) 135.65 556.95 P +0 F +2.58 (N) 315.09 556.95 P +2 F +2.58 ( equally spaced pointers, where) 323.09 556.95 P +0 F +2.58 (N) 489.84 556.95 P +2 F +2.58 ( is the) 497.84 556.95 P +1.13 (number of selections required. The population is shuf) 135.65 542.95 P +1.13 (\337ed randomly and a single) 399.86 542.95 P +1.43 (random number in the range [0) 135.65 528.95 P +0 F +1.43 (Sum) 296.11 528.95 P +2 F +1.43 (/) 316.77 528.95 P +0 F +1.43 (N) 320.1 528.95 P +2 F +1.43 (] is generated,) 328.1 528.95 P +0 F +1.43 (ptr) 402.99 528.95 P +2 F +1.43 (. The) 416.33 528.95 P +0 F +1.43 (N) 446.84 528.95 P +2 F +1.43 ( individuals are) 454.84 528.95 P +-0.2 (then chosen by generating the) 135.65 514.95 P +0 F +-0.2 (N) 280.87 514.95 P +2 F +-0.2 ( pointers spaced by 1, [) 288.87 514.95 P +0 F +-0.2 (ptr) 399.13 514.95 P +2 F +-0.2 (,) 412.64 514.95 P +0 F +-0.2 (ptr) 418.44 514.95 P +2 F +-0.2 (+1, ...,) 432.44 514.95 P +0 F +-0.2 (ptr) 465.79 514.95 P +2 F +-0.2 (+) 479.78 514.95 P +0 F +-0.2 (N) 486.55 514.95 P +2 F +-0.2 (-1], and) 494.55 514.95 P +1.84 (selecting the individuals whose \336tnesses span the positions of the pointers. An) 135.65 500.95 P +0.78 (individual is thus guaranteed to be selected a minimum of) 135.65 486.95 P +0.78 ( times and no) 465.02 486.95 P +1.34 (more than) 135.65 472.95 P +1.34 (, thus achieving minimum spread. In addition, as individuals) 230.74 472.95 P +(are selected entirely on their position in the population, SUS has zero bias.) 135.65 458.95 T +3.69 (The roulette wheel selection methods can all be implemented as O\050NlogN\051) 135.65 432.95 P +0.4 (although SUS is a simpler algorithm and has time complexity O\050N\051. The T) 135.65 418.95 P +0.4 (oolbox) 498.33 418.95 P +4.7 (supplies a stochastic universal sampling function,) 135.65 404.95 P +3 F +11.28 (sus) 404.69 404.95 P +2 F +4.7 (, and the stochastic) 426.28 404.95 P +(sampling with replacement algorithm,) 135.65 390.95 T +3 F +(rws) 321.2 390.95 T +2 F +(.) 342.79 390.95 T +1 16 Q +(Cr) 135.65 362.29 T +(ossover \050Recombination\051) 154.01 362.29 T +2 12 Q +-0.08 (The basic operator for producing new chromosomes in the GA is that of crossover) 135.65 334.95 P +-0.08 (.) 528.65 334.95 P +0.39 (Like its counterpart in nature, crossover produces new individuals that have some) 135.65 320.95 P +1.05 (parts of both parent\325) 135.65 306.95 P +1.05 (s genetic material. The simplest form of crossover is that of) 235.72 306.95 P +3.04 (single-point crossover) 135.65 292.95 P +3.04 (, described in the Overview of GAs. In this Section, a) 244.47 292.95 P +1.75 (number of variations on crossover are described and discussed and the relative) 135.65 278.95 P +(merits of each reviewed.) 135.65 264.95 T +1 14 Q +(Multi-point Cr) 135.65 237.62 T +(ossover) 224.4 237.62 T +2 12 Q +0.7 (For multi-point crossover) 135.65 210.95 P +0.7 (,) 259.16 210.95 P +0 F +0.7 (m) 265.86 210.95 P +2 F +0.7 ( crossover positions,) 274.52 210.95 P +0.7 (, where) 483.85 210.95 P +0 F +0.7 (k) 523.54 210.95 P +0 10 Q +0.58 (i) 528.87 207.95 P +2 12 Q +2.14 (are the crossover points and) 135.65 196.95 P +0 F +2.14 (l) 283.23 196.95 P +2 F +2.14 ( is the length of the chromosome, are chosen at) 286.57 196.95 P +0.08 (random with no duplicates and sorted into ascending order) 135.65 182.95 P +0.08 (. Then, the bits between) 416.75 182.95 P +-0.18 (successive crossover points are exchanged between the two parents to produce two) 135.65 168.95 P +423.91 481.96 465.02 496.16 C +0 12 Q +0 X +0 K +(e) 430.91 486.95 T +(t) 436.94 486.95 T +(i) 448.08 486.95 T +4 F +(\050) 442.98 486.95 T +(\051) 452.02 486.95 T +425.91 483.96 425.91 495.16 2 L +0.33 H +0 Z +N +425.91 483.96 428.91 483.96 2 L +N +462.02 483.96 462.02 495.16 2 L +N +462.02 483.96 459.02 483.96 2 L +N +-8.35 24.95 603.65 816.95 C +189.63 467.96 230.74 482.16 C +0 12 Q +0 X +0 K +(e) 196.63 472.95 T +(t) 202.66 472.95 T +(i) 213.8 472.95 T +4 F +(\050) 208.7 472.95 T +(\051) 217.74 472.95 T +191.63 469.96 191.63 481.16 2 L +0.33 H +0 Z +N +191.63 481.16 194.63 481.16 2 L +N +227.74 469.96 227.74 481.16 2 L +N +227.74 481.16 224.74 481.16 2 L +N +-8.35 24.95 603.65 816.95 C +377.89 204.32 483.85 220.16 C +0 12 Q +0 X +0 K +(k) 378.89 210.95 T +0 9 Q +(i) 384.68 207.17 T +2 12 Q +(1) 410.59 210.95 T +(2) 422.58 210.95 T +4 F +(\274) 434.58 210.95 T +0 F +(l) 452.57 210.95 T +2 F +(1) 468.49 210.95 T +4 F +(-) 458.91 210.95 T +(,) 416.59 210.95 T +(,) 428.58 210.95 T +(,) 446.57 210.95 T +({) 403.73 210.95 T +(}) 475.09 210.95 T +(\316) 390.17 210.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "12" 13 +%%Page: "13" 13 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-13) 513.33 61.29 T +2 12 Q +0.51 (new of) 135.65 736.95 P +0.51 (fspring. The section between the \336rst allele position and the \336rst crossover) 168.91 736.95 P +(point is not exchanged between individuals. This process is illustrated in Fig. 3.) 135.65 722.95 T +0.94 (The idea behind multi-point, and indeed many of the variations on the crossover) 135.65 557.78 P +0.7 (operator) 135.65 543.78 P +0.7 (, is that the parts of the chromosome representation that contribute to the) 175.13 543.78 P +4.05 (most to the performance of a particular individual may not necessarily be) 135.65 529.78 P +0.41 (contained in adjacent substrings [16]. Further) 135.65 515.78 P +0.41 (, the disruptive nature of multi-point) 355.05 515.78 P +1.73 (crossover appears to encourage the exploration of the search space, rather than) 135.65 501.78 P +0.29 (favoring the conver) 135.65 487.78 P +0.29 (gence to highly \336t individuals early in the search, thus making) 229.93 487.78 P +(the search more robust [17].) 135.65 473.78 T +1 14 Q +(Uniform Cr) 135.65 446.44 T +(ossover) 206.51 446.44 T +2 12 Q +0.42 (Single and multi-point crossover de\336ne cross points as places between loci where) 135.65 419.78 P +1.9 (a chromosome can be split. Uniform crossover [18] generalises this scheme to) 135.65 405.78 P +0.75 (make every locus a potential crossover point. A crossover mask, the same length) 135.65 391.78 P +0.26 (as the chromosome structures is created at random and the parity of the bits in the) 135.65 377.78 P +1.13 (mask indicates which parent will supply the of) 135.65 363.78 P +1.13 (fspring with which bits. Consider) 366.88 363.78 P +(the following two parents, crossover mask and resulting of) 135.65 349.78 T +(fspring:) 416.9 349.78 T +3 F +(P) 143.73 323.78 T +3 10 Q +(1) 150.92 320.78 T +3 12 Q +(= 1 0 1 1 0 0 0 1 1 1) 186.25 323.78 T +(P) 143.73 305.78 T +3 10 Q +(2) 150.92 302.78 T +3 12 Q +(= 0 0 0 1 1 1 1 0 0 0) 186.25 305.78 T +(Mask) 143.73 287.78 T +(= 0 0 1 1 0 0 1 1 0 0) 186.25 287.78 T +(O) 143.73 269.78 T +3 10 Q +(1) 150.92 266.78 T +3 12 Q +(= 0 0 1 1 1 1 0 1 0 0) 186.25 269.78 T +(O) 143.73 251.78 T +3 10 Q +(2) 150.92 248.78 T +3 12 Q +(= 1 0 0 1 0 0 1 0 1 1) 186.25 251.78 T +2 F +3.65 (Here, the \336rst of) 135.65 221.78 P +3.65 (fspring,) 224.98 221.78 P +3 F +8.75 (O) 268.6 221.78 P +3 10 Q +7.29 (1) 275.79 218.78 P +2 12 Q +3.65 (, is produced by taking the bit from) 281.79 221.78 P +3 F +8.75 (P) 483.18 221.78 P +3 10 Q +7.29 (1) 490.38 218.78 P +2 12 Q +3.65 ( if the) 496.38 221.78 P +0.5 (corresponding mask bit is 1 or the bit from) 135.65 207.78 P +3 F +1.21 (P) 348.37 207.78 P +3 10 Q +1 (2) 355.57 204.78 P +2 12 Q +0.5 ( if the corresponding mask bit is 0.) 361.57 207.78 P +-0.28 (Of) 135.65 193.78 P +-0.28 (fspring) 148.09 193.78 P +3 F +-0.67 (O) 184.78 193.78 P +3 10 Q +-0.56 (2) 191.98 190.78 P +2 12 Q +-0.28 ( is created using the inverse of the mask or) 197.97 193.78 P +-0.28 (, equivalently) 399.82 193.78 P +-0.28 (, swapping) 464.05 193.78 P +3 F +-0.67 (P) 518.46 193.78 P +3 10 Q +-0.56 (1) 525.65 190.78 P +2 12 Q +(and) 135.65 179.78 T +3 F +(P) 155.96 179.78 T +3 10 Q +(2) 163.16 176.78 T +2 12 Q +(.) 169.16 179.78 T +0.08 (Uniform crossover) 135.65 153.78 P +0.08 (, like multi-point crossover) 225.51 153.78 P +0.08 (, has been claimed to reduce the bias) 355.21 153.78 P +2.24 (associated with the length of the binary representation used and the particular) 135.65 139.78 P +0.79 (coding for a given parameter set. This helps to overcome the bias in single-point) 135.65 125.78 P +0.58 (crossover towards short substrings without requiring precise understanding of the) 135.65 111.78 P +63.65 96.95 531.65 744.95 C +124.27 579.78 531.65 718.95 C +151.07 674.97 307.83 682.06 R +8 X +0 K +V +0.5 H +2 Z +0 X +N +151.07 646.62 307.83 653.71 R +4 X +V +0 X +N +164.13 689.14 164.13 639.54 2 L +N +190.26 689.14 190.26 639.54 2 L +N +242.51 689.14 242.51 639.54 2 L +N +278.44 689.14 278.44 639.54 2 L +N +301.3 689.14 301.3 639.54 2 L +N +360.08 674.97 373.15 682.06 R +8 X +V +0 X +N +373.15 646.62 399.28 653.71 R +8 X +V +0 X +N +399.27 674.97 451.53 682.06 R +8 X +V +0 X +N +451.53 646.62 487.45 653.71 R +8 X +V +0 X +N +487.45 674.97 510.32 682.06 R +8 X +V +0 X +N +510.32 646.62 516.85 653.71 R +8 X +V +0 X +N +373.15 674.97 399.28 682.06 R +4 X +V +0 X +N +451.53 674.97 487.45 682.06 R +4 X +V +0 X +N +510.32 674.97 516.85 682.06 R +4 X +V +0 X +N +360.08 646.62 373.15 653.71 R +4 X +V +0 X +N +399.27 646.62 451.53 653.71 R +4 X +V +0 X +N +487.45 646.62 510.32 653.71 R +4 X +V +0 X +N +335.49 667.65 347.02 664.34 335.49 661.03 335.49 664.34 4 Y +V +320.89 664.34 335.49 664.34 2 L +N +5 12 Q +(Figure 3: Multi-point Crossover \050m=5\051) 237.91 612.02 T +138 594.44 529.92 704.29 R +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "13" 14 +%%Page: "14" 14 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-14) 513.33 61.29 T +2 12 Q +1.26 (signi\336cance of individual bits in the chromosome representation. Spears and De) 135.65 736.95 P +1.96 (Jong [19] have demonstrated how uniform crossover may be parameterised by) 135.65 722.95 P +0.09 (applying a probability to the swapping of bits. This extra parameter can be used to) 135.65 708.95 P +0.56 (control the amount of disruption during recombination without introducing a bias) 135.65 694.95 P +1.78 (towards the length of the representation used. When uniform crossover is used) 135.65 680.95 P +(with real-valued alleles, it is usually referred to as) 135.65 666.95 T +0 F +(discr) 378.13 666.95 T +(ete r) 401.67 666.95 T +(ecombination) 422.88 666.95 T +2 F +(.) 488.17 666.95 T +1 14 Q +(Other Cr) 135.65 639.62 T +(ossover Operators) 190.96 639.62 T +2 12 Q +-0.05 (A related crossover operator is that of) 135.65 612.95 P +0 F +-0.05 (shuf\337e) 319.45 612.95 P +2 F +-0.05 ( [20]. A single cross-point is selected,) 350.77 612.95 P +-0.24 (but before the bits are exchanged, they are randomly shuf) 135.65 598.95 P +-0.24 (\337ed in both parents. After) 409.03 598.95 P +-0.15 (recombination, the bits in the of) 135.65 584.95 P +-0.15 (fspring are unshuf) 287.92 584.95 P +-0.15 (\337ed. This too removes positional) 374.67 584.95 P +(bias as the bits are randomly reassigned each time crossover is performed.) 135.65 570.95 T +0.72 (The) 135.65 544.95 P +0 F +0.72 (r) 158.02 544.95 P +0.72 (educed surr) 162.24 544.95 P +0.72 (ogate) 219.47 544.95 P +2 F +0.72 ( operator [16] constrains crossover to always produce new) 246.12 544.95 P +2.89 (individuals wherever possible. Usually) 135.65 530.95 P +2.89 (, this is implemented by restricting the) 330.08 530.95 P +2.18 (location of crossover points such that crossover points only occur where gene) 135.65 516.95 P +(values dif) 135.65 502.95 T +(fer) 182.4 502.95 T +(.) 195.05 502.95 T +1 14 Q +(Intermediate Recombination) 135.65 475.62 T +2 12 Q +5.99 (Given a real-valued encoding of the chromosome structure, intermediate) 135.65 448.95 P +0.54 (recombination is a method of producing new phenotypes around and between the) 135.65 434.95 P +1.68 (values of the parents phenotypes [21]. Of) 135.65 420.95 P +1.68 (fspring are produced according to the) 343.71 420.95 P +(rule,) 135.65 406.95 T +(,) 391.24 379.75 T +2.92 (where) 135.65 351.04 P +4 F +2.92 (a) 170.87 351.04 P +2 F +2.92 ( is a scaling factor chosen uniformly at random over some interval,) 178.43 351.04 P +3.3 (typically [-0.25, 1.25] and) 135.65 337.04 P +0 F +3.3 (P) 277.1 337.04 P +0 10 Q +2.75 (1) 284.42 334.04 P +2 12 Q +3.3 ( and) 289.42 337.04 P +0 F +3.3 (P) 319.34 337.04 P +0 10 Q +2.75 (2) 326.67 334.04 P +2 12 Q +3.3 ( are the parent chromosomes \050see, for) 331.67 337.04 P +2.82 (example, [21]\051. Each variable in the of) 135.65 323.04 P +2.82 (fspring is the result of combining the) 337.52 323.04 P +-0.04 (variables in the parents according to the above expression with a new) 135.65 309.04 P +4 F +-0.04 (a) 470.88 309.04 P +2 F +-0.04 ( chosen for) 478.45 309.04 P +3.03 (each pair of parent genes. In geometric terms, intermediate recombination is) 135.65 295.04 P +273.05 373.04 391.24 388.95 C +0 12 Q +0 X +0 K +(O) 274.05 379.75 T +2 9 Q +(1) 283.17 375.99 T +0 12 Q +(P) 306.25 379.75 T +2 9 Q +(1) 314.04 375.99 T +4 12 Q +(a) 331.12 379.75 T +0 F +(P) 346.49 379.75 T +2 9 Q +(2) 354.28 375.99 T +0 12 Q +(P) 371.36 379.75 T +2 9 Q +(1) 379.15 375.99 T +4 12 Q +(-) 361.78 379.75 T +(\050) 341.39 379.75 T +(\051) 384.25 379.75 T +(\264) 321.53 379.75 T +(=) 293.67 379.75 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "14" 15 +%%Page: "15" 15 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-15) 513.33 61.29 T +2 12 Q +1.47 (capable of producing new variables within a slightly lar) 135.65 736.95 P +1.47 (ger hypercube than that) 414.33 736.95 P +(de\336ned by the parents but constrained by the range of) 135.65 722.95 T +4 F +(a) 396.12 722.95 T +2 F +(. as shown in Fig 4.) 403.69 722.95 T +1 14 Q +(Line Recombination) 135.65 481.79 T +2 12 Q +0.13 (Line recombination [21] is similar to intermediate recombination, except that only) 135.65 455.12 P +0.29 (one value of) 135.65 441.12 P +4 F +0.29 (a) 198.79 441.12 P +2 F +0.29 ( is used in the recombination. Fig. 5 shows how line recombination) 206.36 441.12 P +0.88 (can generate any point on the line de\336ned by the parents within the limits of the) 135.65 427.12 P +(perturbation,) 135.65 413.12 T +4 F +(a,) 200.27 413.12 T +2 F +(for a recombination in two variables.) 213.83 413.12 T +1 14 Q +(Discussion) 135.65 165.83 T +2 12 Q +2.58 (The binary operators discussed in this Section have all, to some extent, used) 135.65 139.16 P +0.03 (disruption in the representation to help improve exploration during recombination.) 135.65 125.16 P +1.99 (Whilst these operators may be used with real-valued populations, the resulting) 135.65 111.16 P +63.65 96.95 531.65 744.95 C +133.38 505.12 531.65 718.95 C +205.79 685.03 209.1 696.57 212.41 685.03 209.1 685.03 4 Y +0 X +0 K +V +209.1 565.46 209.1 685.03 2 L +0.5 H +2 Z +N +1 X +90 450 5.32 5.32 249.85 655.82 G +0 X +90 450 5.32 5.32 249.85 655.82 A +230.36 590.27 315.4 675.31 R +8 X +N +325.12 572.18 336.66 568.87 325.12 565.56 325.12 568.87 4 Y +0 X +V +205.56 568.87 325.12 568.87 2 L +N +1 X +90 450 5.32 5.32 295.91 609.75 G +0 X +90 450 5.32 5.32 295.91 609.75 A +4 X +90 450 5.32 5.32 271.11 662.9 G +0 X +90 450 5.32 5.32 271.11 662.9 A +4 X +90 450 5.32 5.32 260.48 631.01 G +0 X +90 450 5.32 5.32 260.48 631.01 A +4 X +90 450 5.32 5.32 242.76 602.67 G +0 X +90 450 5.32 5.32 242.76 602.67 A +4 X +90 450 5.32 5.32 285.28 641.64 G +0 X +90 450 5.32 5.32 285.28 641.64 A +1 X +90 450 5.32 5.32 356.15 634.56 G +0 X +90 450 5.32 5.32 356.15 634.56 A +4 X +90 450 5.32 5.32 356.15 609.75 G +0 X +90 450 5.32 5.32 356.15 609.75 A +2 12 Q +(Gene1) 255.46 553.89 T +(Gene 2) 0 -270 197.02 611.53 TF +(Parents) 368.55 630.47 T +(Potential of) 368.55 605.66 T +(fspring) 423.97 605.66 T +(Area of possible of) 350.83 656.65 T +(fspring) 442.21 656.65 T +330.48 657.43 318.94 660.74 330.48 664.05 330.48 660.74 4 Y +V +347.29 660.74 330.48 660.74 2 L +N +5 F +(Figure 4: Geometric Ef) 186.7 529.94 T +(fect of Intermediate Recombination) 302.75 529.94 T +141.18 514.6 523.85 709.48 R +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +63.65 96.95 531.65 744.95 C +133.38 189.16 531.65 409.12 C +196.34 372.12 199.64 383.66 202.95 372.12 199.64 372.12 4 Y +0 X +0 K +V +199.64 252.55 199.64 372.12 2 L +0.5 H +2 Z +N +1 X +90 450 5.32 5.32 228.24 352.09 G +0 X +90 450 5.32 5.32 228.24 352.09 A +315.67 259.27 327.2 255.96 315.67 252.65 315.67 255.96 4 Y +V +196.1 255.96 315.67 255.96 2 L +N +1 X +90 450 5.32 5.32 299.08 281.22 G +0 X +90 450 5.32 5.32 299.08 281.22 A +4 X +90 450 5.32 5.32 221.15 359.14 G +0 X +90 450 5.32 5.32 221.15 359.14 A +4 X +90 450 5.32 5.32 255.87 324.45 G +0 X +90 450 5.32 5.32 255.87 324.45 A +4 X +90 450 5.32 5.32 239.55 340.03 G +0 X +90 450 5.32 5.32 239.55 340.03 A +1 X +90 450 5.32 5.32 346.69 321.65 G +0 X +90 450 5.32 5.32 346.69 321.65 A +4 X +90 450 5.32 5.32 346.69 296.85 G +0 X +90 450 5.32 5.32 346.69 296.85 A +2 12 Q +(Gene1) 246 240.98 T +(Gene 2) 0 -270 187.56 298.62 TF +(Parents) 359.09 317.56 T +(Potential of) 359.09 292.76 T +(fspring) 414.51 292.76 T +5 F +(Figure 5: Geometric Ef) 197.57 217.03 T +(fect of Line Recombination) 313.62 217.03 T +141.18 201.7 523.85 396.58 R +N +4 X +90 450 5.32 5.32 270.76 309.57 G +0 X +90 450 5.32 5.32 270.76 309.57 A +4 X +90 450 5.32 5.32 286.33 293.94 G +0 X +90 450 5.32 5.32 286.33 293.94 A +4 X +90 450 5.32 5.32 306.88 273.42 G +0 X +90 450 5.32 5.32 306.88 273.42 A +4 X +90 450 5.32 5.32 314.68 265.62 G +0 X +90 450 5.32 5.32 314.68 265.62 A +4 X +90 450 5.32 5.32 214.04 366.26 G +0 X +90 450 5.32 5.32 214.04 366.26 A +213.69 366.6 312.9 267.39 2 L +V +8 X +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "15" 16 +%%Page: "16" 16 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-16) 513.33 61.29 T +2 12 Q +0.19 (changes in the genetic material after recombination would not extend to the actual) 135.65 736.95 P +0.54 (values of the decision variables, although of) 135.65 722.95 P +0.54 (fspring may) 350.19 722.95 P +0.54 (, of course, contain genes) 407.58 722.95 P +1.14 (from either parent. The intermediate and line recombination operators overcome) 135.65 708.95 P +3.39 (this limitation by acting on the decision variables themselves. Like uniform) 135.65 694.95 P +-0.23 (crossover) 135.65 680.95 P +-0.23 (, the real-valued operators may also be parameterised to provide a control) 181.13 680.95 P +4.94 (over the level of disruption introduced into of) 135.65 666.95 P +4.94 (fspring. For discrete-valued) 388.87 666.95 P +-0.07 (representations, variations on the recombination operators may be used that ensure) 135.65 652.95 P +(that only valid values are produced as a result of crossover [22].) 135.65 638.95 T +1.04 (The GA T) 135.65 612.95 P +1.04 (oolbox provides a number of crossover routines incorporating most of) 186.18 612.95 P +0.24 (the methods described above. Single-point, double-point and shuf) 135.65 598.95 P +0.24 (\337e crossover are) 452.58 598.95 P +0.73 (implemented in the T) 135.65 584.95 P +0.73 (oolbox functions) 239.92 584.95 P +3 F +1.74 (xovsp) 325.33 584.95 P +2 F +0.73 (,) 361.31 584.95 P +3 F +1.74 (xovdp) 368.03 584.95 P +2 F +0.73 ( and) 404.01 584.95 P +3 F +1.74 (xovsh) 428.77 584.95 P +2 F +0.73 (, respectively) 464.76 584.95 P +0.73 (,) 528.65 584.95 P +0.56 (and can operate on any chromosome representation. Reduced surrogate crossover) 135.65 570.95 P +3.17 (is supported with both single-point,) 135.65 556.95 P +3 F +7.62 (xovsprs) 324.77 556.95 P +2 F +3.17 (, and double-point,) 375.14 556.95 P +3 F +7.62 (xovdprs) 478.28 556.95 P +2 F +3.17 (,) 528.65 556.95 P +2.17 (crossover and with shuf) 135.65 542.95 P +2.17 (\337e crossover) 256.2 542.95 P +2.17 (,) 318.85 542.95 P +3 F +5.22 (xovshrs) 327.02 542.95 P +2 F +2.17 (. A further general multi-point) 377.39 542.95 P +1.09 (crossover routine,) 135.65 528.95 P +3 F +2.61 (xovmp) 226.75 528.95 P +2 F +1.09 (, is also provided. T) 262.73 528.95 P +1.09 (o support real-valued chromosome) 361.51 528.95 P +1.62 (representations, discrete, intermediate and line recombination operators are also) 135.65 514.95 P +1.57 (included. The discrete recombination operator) 135.65 500.95 P +1.57 (,) 362.95 500.95 P +3 F +3.77 (recdis) 370.52 500.95 P +2 F +1.57 (, performs crossover on) 413.69 500.95 P +1.86 (real-valued individuals in a similar manner to the uniform crossover operators.) 135.65 486.95 P +0.37 (Line and intermediate recombination are supported by the functions) 135.65 472.95 P +3 F +0.9 (reclin) 467.78 472.95 P +2 F +0.37 ( and) 510.96 472.95 P +3 F +0.26 (recint) 135.65 458.95 P +2 F +0.11 ( respectively) 178.82 458.95 P +0.11 (. A high-level entry function to all of the crossover operators) 239.1 458.95 P +(is provided by the function) 135.65 444.95 T +3 F +(recombin) 267.9 444.95 T +2 F +(.) 325.47 444.95 T +1 16 Q +(Mutation) 135.65 416.29 T +2 12 Q +1.09 (In natural evolution, mutation is a random process where one allele of a gene is) 135.65 388.95 P +2.75 (replaced by another to produce a new genetic structure. In GAs, mutation is) 135.65 374.95 P +0.53 (randomly applied with low probability) 135.65 360.95 P +0.53 (, typically in the range 0.001 and 0.01, and) 322.21 360.95 P +3.36 (modi\336es elements in the chromosomes. Usually considered as a background) 135.65 346.95 P +2.57 (operator) 135.65 332.95 P +2.57 (, the role of mutation is often seen as providing a guarantee that the) 175.13 332.95 P +0.45 (probability of searching any given string will never be zero and acting as a safety) 135.65 318.95 P +3.12 (net to recover good genetic material that may be lost through the action of) 135.65 304.95 P +(selection and crossover [1].) 135.65 290.95 T +2.61 (The ef) 135.65 264.95 P +2.61 (fect of mutation on a binary string is illustrated in Fig. 6 for a 10-bit) 169.01 264.95 P +0.05 (chromosome representing a real value decoded over the interval [0, 10] using both) 135.65 250.95 P +1.59 (standard and Gray coding and a mutation point of 3 in the binary string. Here,) 135.65 236.95 P +1.41 (binary mutation \337ips the value of the bit at the loci selected to be the mutation) 135.65 222.95 P +-0.23 (point. Given that mutation is generally applied uniformly to an entire population of) 135.65 208.95 P +FMENDPAGE +%%EndPage: "16" 17 +%%Page: "17" 17 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-17) 513.33 61.29 T +2 12 Q +0.82 (strings, it is possible that a given binary string may be mutated at more than one) 135.65 736.95 P +(point.) 135.65 722.95 T +2.23 (W) 135.65 580.82 P +2.23 (ith non-binary representations, mutation is achieved by either perturbing the) 146.49 580.82 P +0.87 (gene values or random selection of new values within the allowed range. W) 135.65 566.82 P +0.87 (right) 508.99 566.82 P +-0 ([8] and Janikow and Michalewicz [23] demonstrate how real-coded GAs may take) 135.65 552.82 P +0.21 (advantage of higher mutation rates than binary-coded GAs, increasing the level of) 135.65 538.82 P +5.94 (possible exploration of the search space without adversely af) 135.65 524.82 P +5.94 (fecting the) 474.74 524.82 P +1.62 (conver) 135.65 510.82 P +1.62 (gence characteristics. Indeed, T) 168.07 510.82 P +1.62 (ate and Smith [24] ar) 323.63 510.82 P +1.62 (gue that for codings) 431.17 510.82 P +-0.22 (more complex than binary) 135.65 496.82 P +-0.22 (, high mutation rates can be both desirable and necessary) 260.46 496.82 P +0.57 (and show how) 135.65 482.82 P +0.57 (, for a complex combinatorial optimization problem, high mutation) 205.29 482.82 P +0.62 (rates and non-binary coding yielded signi\336cantly better solutions than the normal) 135.65 468.82 P +(approach.) 135.65 454.82 T +2.89 (Many variations on the mutation operator have been proposed. For example,) 135.65 428.82 P +0.6 (biasing the mutation towards individuals with lower \336tness values to increase the) 135.65 414.82 P +-0.25 (exploration in the search without losing information from the \336tter individuals [25]) 135.65 400.82 P +2.48 (or parameterising the mutation such that the mutation rate decreases with the) 135.65 386.82 P +0.13 (population conver) 135.65 372.82 P +0.13 (gence [26]. M\237hlenbein [21] has introduced a mutation operator) 222.5 372.82 P +0.5 (for the real-coded GA that uses a non-linear term for the distribution of the range) 135.65 358.82 P +0.38 (of mutation applied to gene values. It is claimed that by biasing mutation towards) 135.65 344.82 P +3.96 (smaller changes in gene values, mutation can be used in conjunction with) 135.65 330.82 P +0.7 (recombination as a foreground search process. Other mutation operations include) 135.65 316.82 P +2.66 (that of) 135.65 302.82 P +0 F +2.66 (trade mutation) 174.94 302.82 P +2 F +2.66 ( [7], whereby the contribution of individual genes in a) 248.57 302.82 P +3.95 (chromosome is used to direct mutation towards weaker terms, and) 135.65 288.82 P +0 F +3.95 (r) 495.89 288.82 P +3.95 (eor) 500.12 288.82 P +3.95 (der) 515.66 288.82 P +0.71 (mutation) 135.65 274.82 P +2 F +0.71 ( [7], that swaps the positions of bits or genes to increase diversity in the) 178.3 274.82 P +(decision variable space.) 135.65 260.82 T +1.82 (Binary and integer mutation are provided in the T) 135.65 234.82 P +1.82 (oolbox by the function) 387.85 234.82 P +3 F +4.36 (mut) 507.06 234.82 P +2 F +1.82 (.) 528.65 234.82 P +0.54 (Real-valued mutation is available using the function) 135.65 220.82 P +3 F +1.29 (mutbga) 392.92 220.82 P +2 F +0.54 (. A high-level entry) 436.1 220.82 P +(function to the mutation operators is provided by the function) 135.65 206.82 T +3 F +(mutate) 434.13 206.82 T +2 F +(.) 477.3 206.82 T +63.65 96.95 531.65 744.95 C +133.42 602.82 531.65 718.95 C +5 12 Q +0 X +0 K +(Figure 6: Binary Mutation) 266.07 625.61 T +141.21 613.74 523.89 708.01 R +0.5 H +2 Z +N +2 F +( Original string -) 170.1 671.56 T +( Mutated string -) 170.1 653.69 T +(binary) 413.58 689.43 T +(Gray) 466.52 689.43 T +3 F +(0 0 0 1 1 0 0 0 1 0) 255.14 671.91 T +(0 0 1 1 1 0 0 0 1 0) 255.14 654.04 T +2 F +(0.9659) 412.41 671.56 T +(2.2146) 412.41 653.69 T +(0.6634) 462.02 671.56 T +(1.8439) 462.02 653.69 T +281.81 650.83 291.75 681.92 R +8 X +N +0 X +(mutation point) 172.34 690.39 T +279.39 694.94 285.77 684.78 274.98 690.02 277.19 692.48 4 Y +V +248.93 693.96 275.26 694.21 277.19 692.48 3 L +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "17" 18 +%%Page: "18" 18 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-18) 513.33 61.29 T +1 16 Q +(Reinsertion) 135.65 734.29 T +2 12 Q +2.42 (Once a new population has been produced by selection and recombination of) 135.65 706.95 P +2.66 (individuals from the old population, the \336tness of the individuals in the new) 135.65 692.95 P +7.66 (population may be determined. If fewer individuals are produced by) 135.65 678.95 P +4.52 (recombination than the size of the original population, then the fractional) 135.65 664.95 P +1.26 (dif) 135.65 650.95 P +1.26 (ference between the new and old population sizes is termed a generation gap) 148.76 650.95 P +-0.08 ([27]. In the case where the number of new individuals produced at each generation) 135.65 636.95 P +0.43 (is one or two, the GA is said to be steady-state [28] or incremental [29]. If one or) 135.65 622.95 P +0.6 (more of the most \336t individuals is deterministically allowed to propagate through) 135.65 608.95 P +(successive generations then the GA is said to use an) 135.65 594.95 T +0 F +(elitist strategy) 388.13 594.95 T +2 F +(.) 455.66 594.95 T +1.67 (T) 135.65 568.95 P +1.67 (o maintain the size of the original population, the new individuals have to be) 142.14 568.95 P +-0.07 (reinserted into the old population. Similarly) 135.65 554.95 P +-0.07 (, if not all the new individuals are to be) 344.4 554.95 P +0.46 (used at each generation or if more of) 135.65 540.95 P +0.46 (fspring are generated than the size of the old) 314.82 540.95 P +0.17 (population then a reinsertion scheme must be used to determine which individuals) 135.65 526.95 P +2.22 (are to exist in the new population. An important feature of not creating more) 135.65 512.95 P +5.28 (of) 135.65 498.95 P +5.28 (fspring than the current population size at each generation is that the) 145.42 498.95 P +1.12 (generational computational time is reduced, most dramatically in the case of the) 135.65 484.95 P +2.39 (steady-state GA, and that the memory requirements are smaller as fewer new) 135.65 470.95 P +(individuals need to be stored while of) 135.65 456.95 T +(fspring are produced.) 315.98 456.95 T +0.19 (When selecting which members of the old population should be replaced the most) 135.65 430.95 P +0.23 (apparent strategy is to replace the least \336t members deterministically) 135.65 416.95 P +0.23 (. However) 466.39 416.95 P +0.23 (, in) 516.09 416.95 P +2.7 (studies, Fogarty [30] has shown that no signi\336cant dif) 135.65 402.95 P +2.7 (ference in conver) 415.24 402.95 P +2.7 (gence) 503.68 402.95 P +2.15 (characteristics was found when the individuals selected for replacement where) 135.65 388.95 P +0.69 (chosen with inverse proportional selection or deterministically as the least \336t. He) 135.65 374.95 P +0.01 (further asserts that replacing the least \336t members ef) 135.65 360.95 P +0.01 (fectively implements an elitist) 386.69 360.95 P +5.91 (strategy as the most \336t will probabilistically survive through successive) 135.65 346.95 P +-0.23 (generations. Indeed, the most successful replacement scheme was one that selected) 135.65 332.95 P +-0.23 (the oldest members of a population for replacement. This is reported as being more) 135.65 318.95 P +0.03 (in keeping with generational reproduction as every member of the population will,) 135.65 304.95 P +4.87 (at some time, be replaced. Thus, for an individual to survive successive) 135.65 290.95 P +5.74 (generations, it must be suf) 135.65 276.95 P +5.74 (\336ciently \336t to ensure propagation into future) 284.66 276.95 P +(generations.) 135.65 262.95 T +-0.23 (The GA T) 135.65 236.95 P +-0.23 (oolbox provides a function for reinserting individuals into the population) 183.63 236.95 P +1.89 (after recombination,) 135.65 222.95 P +3 F +4.55 (reins) 239.69 222.95 P +2 F +1.89 (. Optional input parameters allow the use of either) 275.67 222.95 P +0.3 (uniform random or \336tness-based reinsertion. Additionally) 135.65 208.95 P +0.3 (, this routine can also be) 413.54 208.95 P +(selected to reinsert fewer of) 135.65 194.95 T +(fspring than those produced at recombination.) 268.64 194.95 T +1 16 Q +(T) 135.65 166.29 T +(ermination of the GA) 144.84 166.29 T +2 12 Q +1.32 (Because the GA is a stochastic search method, it is dif) 135.65 138.95 P +1.32 (\336cult to formally specify) 408.77 138.95 P +-0.06 (conver) 135.65 124.95 P +-0.06 (gence criteria. As the \336tness of a population may remain static for a number) 168.07 124.95 P +5.99 (of generations before a superior individual is found, the application of) 135.65 110.95 P +FMENDPAGE +%%EndPage: "18" 19 +%%Page: "19" 19 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-19) 513.33 61.29 T +2 12 Q +1.07 (conventional termination criteria becomes problematic. A common practice is to) 135.65 736.95 P +2.19 (terminate the GA after a prespeci\336ed number of generations and then test the) 135.65 722.95 P +0.17 (quality of the best members of the population against the problem de\336nition. If no) 135.65 708.95 P +-0.22 (acceptable solutions are found, the GA may be restarted or a fresh search initiated.) 135.65 694.95 P +FMENDPAGE +%%EndPage: "19" 20 +%%Page: "20" 20 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-20) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Data Structur) 63.65 732.95 T +(es) 170.74 732.95 T +2 12 Q +1.25 (M) 135.65 694.95 P +2 10 Q +1.04 (A) 146.31 694.95 P +1.04 (TLAB) 152.42 694.95 P +2 12 Q +1.25 ( essentially supports only one data type, a rectangular matrix of real or) 178.51 694.95 P +1.93 (complex numeric elements. The main data structures in the Genetic Algorithm) 135.65 680.95 P +(toolbox are:) 135.65 666.95 T +(\245) 157.25 640.95 T +(chromosomes) 171.65 640.95 T +(\245) 157.25 620.95 T +(phenotypes) 171.65 620.95 T +(\245) 157.25 600.95 T +(objective function values) 171.65 600.95 T +(\245) 157.25 580.95 T +(\336tness values) 171.65 580.95 T +(These data structures are discussed in the following subsections.) 135.65 560.95 T +1 16 Q +(Chr) 135.65 532.29 T +(omosomes) 162.9 532.29 T +2 12 Q +1.24 (The chromosome data structure stores an entire population in a single matrix of) 135.65 504.95 P +1.17 (size) 135.65 490.95 P +3 F +2.81 (Nind) 158.47 490.95 P +4 F +1.17 (\264) 191.42 490.95 P +3 F +2.81 (Lind) 202.18 490.95 P +2 F +1.17 (, where) 230.96 490.95 P +3 F +2.81 (Nind) 271.6 490.95 P +2 F +1.17 ( is the number of individuals in the population) 300.39 490.95 P +0.48 (and) 135.65 476.95 P +3 F +1.16 (Lind) 156.45 476.95 P +2 F +0.48 ( is the length of the genotypic representation of those individuals. Each) 185.23 476.95 P +-0.26 (row corresponds to an individual\325) 135.65 462.95 P +-0.26 (s genotype, consisting of base-) 295.83 462.95 P +0 F +-0.26 (n) 442.34 462.95 P +2 F +-0.26 (, typically binary) 448.34 462.95 P +-0.26 (,) 528.65 462.95 P +(values.) 135.65 448.95 T +(An example of the chromosome data structure is shown below) 135.65 422.95 T +(.) 434.32 422.95 T +1 (This data representation does not force a structure on the chromosome structure,) 135.65 262.48 P +4.56 (only requiring that all chromosomes are of equal length. Thus, structured) 135.65 248.48 P +2.9 (populations or populations with varying genotypic bases may be used in the) 135.65 234.48 P +1.08 (Genetic Algorithm T) 135.65 220.48 P +1.08 (oolbox provided that a suitable decoding function, mapping) 237.58 220.48 P +0.48 (chromosomes onto phenotypes, is employed. The role of the decoding function is) 135.65 206.48 P +(described below) 135.65 192.48 T +(.) 213.14 192.48 T +1 16 Q +(Phenotypes) 135.65 163.81 T +2 12 Q +1.57 (The decision variables, or phenotypes, in the genetic algorithm are obtained by) 135.65 136.48 P +2.06 (applying some mapping from the chromosome representation into the decision) 135.65 122.48 P +0.9 (variable space. Here, each string contained in the chromosome structure decodes) 135.65 108.48 P +154.05 284.48 513.25 404.95 C +3 12 Q +0 X +0 K +(C) 155.05 341.98 T +(h) 162.95 341.98 T +(r) 170.85 341.98 T +(o) 178.76 341.98 T +(m) 186.66 341.98 T +0 F +(g) 224.47 376.28 T +2 9 Q +(1) 230.93 372.52 T +(1) 239.92 372.52 T +4 F +(,) 235.43 372.52 T +0 12 Q +(g) 263.48 376.28 T +2 9 Q +(1) 269.94 372.52 T +(2) 278.93 372.52 T +4 F +(,) 274.44 372.52 T +0 12 Q +(g) 304.29 376.28 T +2 9 Q +(1) 310.75 372.52 T +(3) 319.74 372.52 T +4 F +(,) 315.25 372.52 T +4 12 Q +(\274) 337.57 376.28 T +0 F +(g) 362.89 376.28 T +2 9 Q +(1) 369.35 372.52 T +3 F +(L) 378.34 372.52 T +(i) 384.27 372.52 T +(n) 390.19 372.52 T +(d) 396.11 372.52 T +4 F +(,) 373.85 372.52 T +0 12 Q +(g) 224.47 358.37 T +2 9 Q +(2) 230.93 354.6 T +(1) 239.92 354.6 T +4 F +(,) 235.43 354.6 T +0 12 Q +(g) 263.48 358.37 T +2 9 Q +(2) 269.94 354.6 T +(2) 278.93 354.6 T +4 F +(,) 274.44 354.6 T +0 12 Q +(g) 304.29 358.37 T +2 9 Q +(2) 310.75 354.6 T +(3) 319.74 354.6 T +4 F +(,) 315.25 354.6 T +4 12 Q +(\274) 337.57 358.37 T +0 F +(g) 362.89 358.37 T +2 9 Q +(2) 369.35 354.6 T +3 F +(L) 378.34 354.6 T +(i) 384.27 354.6 T +(n) 390.19 354.6 T +(d) 396.11 354.6 T +4 F +(,) 373.85 354.6 T +0 12 Q +(g) 224.47 340.45 T +2 9 Q +(3) 230.93 336.69 T +(1) 239.92 336.69 T +4 F +(,) 235.43 336.69 T +0 12 Q +(g) 263.48 340.45 T +2 9 Q +(3) 269.94 336.69 T +(2) 278.93 336.69 T +4 F +(,) 274.44 336.69 T +0 12 Q +(g) 304.29 340.45 T +2 9 Q +(3) 310.75 336.69 T +(3) 319.74 336.69 T +4 F +(,) 315.25 336.69 T +4 12 Q +(\274) 337.57 340.45 T +0 F +(g) 362.89 340.45 T +2 9 Q +(3) 369.35 336.69 T +3 F +(L) 378.34 336.69 T +(i) 384.27 336.69 T +(n) 390.19 336.69 T +(d) 396.11 336.69 T +4 F +(,) 373.85 336.69 T +2 12 Q +(.) 232.45 322.56 T +(.) 271.46 322.56 T +(.) 312.27 322.56 T +4 F +(\274) 337.57 322.56 T +2 F +(.) 380.2 322.56 T +0 F +(g) 216.94 306.36 T +2 9 Q +(N) 223.4 302.6 T +(i) 230.41 302.6 T +(n) 233.44 302.6 T +(d) 238.47 302.6 T +(1) 247.46 302.6 T +4 F +(,) 242.96 302.6 T +0 12 Q +(g) 255.95 306.36 T +2 9 Q +(N) 262.41 302.6 T +(i) 269.43 302.6 T +(n) 272.45 302.6 T +(d) 277.48 302.6 T +(2) 286.47 302.6 T +4 F +(,) 281.97 302.6 T +0 12 Q +(g) 294.96 306.36 T +3 9 Q +(N) 301.42 302.6 T +(i) 307.34 302.6 T +(n) 313.26 302.6 T +(d) 319.19 302.6 T +2 F +(3) 329.08 302.6 T +4 F +(,) 324.58 302.6 T +4 12 Q +(\274) 337.57 306.36 T +0 F +(g) 353.56 306.36 T +3 9 Q +(N) 360.02 302.74 T +(i) 365.94 302.74 T +(n) 371.86 302.74 T +(d) 377.79 302.74 T +(L) 387.67 302.74 T +(i) 393.6 302.74 T +(n) 399.52 302.74 T +(d) 405.44 302.74 T +4 F +(,) 383.18 302.74 T +2 12 Q +(i) 432.35 376.89 T +(n) 435.68 376.89 T +(d) 441.68 376.89 T +(i) 447.67 376.89 T +(v) 451.01 376.89 T +(i) 457 376.89 T +(d) 460.34 376.89 T +(u) 466.33 376.89 T +(a) 472.33 376.89 T +(l) 477.66 376.89 T +(\021) 480.99 376.89 T +(1) 483.99 376.89 T +(i) 432.35 359.09 T +(n) 435.68 359.09 T +(d) 441.68 359.09 T +(i) 447.67 359.09 T +(v) 451.01 359.09 T +(i) 457 359.09 T +(d) 460.34 359.09 T +(u) 466.33 359.09 T +(a) 472.33 359.09 T +(l) 477.66 359.09 T +(\021) 480.99 359.09 T +(2) 483.99 359.09 T +(i) 432.35 341.29 T +(n) 435.68 341.29 T +(d) 441.68 341.29 T +(i) 447.67 341.29 T +(v) 451.01 341.29 T +(i) 457 341.29 T +(d) 460.34 341.29 T +(u) 466.33 341.29 T +(a) 472.33 341.29 T +(l) 477.66 341.29 T +(\021) 480.99 341.29 T +(3) 483.99 341.29 T +(.) 459.67 323.49 T +(i) 419.54 305.69 T +(n) 422.87 305.69 T +(d) 428.87 305.69 T +(i) 434.87 305.69 T +(v) 438.2 305.69 T +(i) 444.2 305.69 T +(d) 447.53 305.69 T +(u) 453.53 305.69 T +(a) 459.52 305.69 T +(l) 464.85 305.69 T +(\021) 468.18 305.69 T +3 F +(N) 472.89 305.69 T +(i) 480.79 305.69 T +(n) 488.69 305.69 T +(d) 496.6 305.69 T +4 F +(=) 199.85 341.98 T +218.44 300.65 214.44 300.65 2 L +0.33 H +0 Z +N +214.44 300.65 214.44 388.49 2 L +N +214.44 388.49 218.44 388.49 2 L +N +408.33 300.65 412.33 300.65 2 L +N +412.33 300.65 412.33 388.49 2 L +N +412.33 388.49 408.33 388.49 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "20" 21 +%%Page: "21" 21 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-21) 513.33 61.29 T +2 12 Q +1.97 (to a row vector of order) 135.65 736.95 P +3 F +4.73 (Nvar) 264.05 736.95 P +2 F +1.97 (, according to the number of dimensions in the) 292.35 736.95 P +(search space and corresponding to the decision variable vector value.) 135.65 722.95 T +1.7 (The decision variables are stored in a numerical matrix of size) 135.65 696.95 P +3 F +4.08 (Nind) 455.76 696.95 P +4 F +1.7 (\264) 489.24 696.95 P +3 F +4.08 (Nvar) 500.52 696.95 P +2 F +1.7 (.) 528.65 696.95 P +0.96 (Again, each row corresponds to a particular individual\325) 135.65 682.95 P +0.96 (s phenotype. An example) 406.85 682.95 P +-0.11 (of the phenotype data structure is given below) 135.65 668.95 P +-0.11 (, where) 355.59 668.95 P +3 F +-0.27 (DECODE) 393.66 668.95 P +2 F +-0.11 ( is used to represent) 436.83 668.95 P +0.25 (an arbitrary function, possibly from the GA T) 135.65 654.95 P +0.25 (oolbox, mapping the genotypes onto) 355.74 654.95 P +(the phenotypes.) 135.65 640.95 T +0.29 (The actual mapping between the chromosome representation and their phenotypic) 135.65 456.66 P +0.39 (values depends upon the) 135.65 442.66 P +3 F +0.94 (DECODE) 257.8 442.66 P +2 F +0.39 ( function used. It is perfectly feasible using this) 300.98 442.66 P +4.22 (representation to have vectors of decision variables of dif) 135.65 428.66 P +4.22 (ferent types. For) 444.28 428.66 P +2.81 (example, it is possible to mix integer) 135.65 414.66 P +2.81 (, real-valued and alphanumeric decision) 328.91 414.66 P +(variables in the same) 135.65 400.66 T +3 F +(Phen) 239.57 400.66 T +2 F +( data structure.) 268.36 400.66 T +1 16 Q +(Objective function values) 135.65 372 T +2 12 Q +0.05 (An objective function is used to evaluate the performance of the phenotypes in the) 135.65 344.66 P +3.4 (problem domain. Objective function values can be scalar or) 135.65 330.66 P +3.4 (, in the case of) 448.45 330.66 P +2.36 (multiobjective problems, vectorial. Note that objective function values are not) 135.65 316.66 P +(necessarily the same as the \336tness values.) 135.65 302.66 T +0.47 (Objective function values are stored in a numerical matrix of size) 135.65 276.66 P +3 F +1.12 (Nind) 457.56 276.66 P +4 F +0.47 (\264) 489.81 276.66 P +3 F +1.12 (Nobj) 499.86 276.66 P +2 F +0.47 (,) 528.65 276.66 P +1.65 (where) 135.65 262.66 P +3 F +3.96 (Nobj) 169.6 262.66 P +2 F +1.65 ( is the number of objectives. Each row corresponds to a particular) 198.38 262.66 P +1.86 (individual\325) 135.65 248.66 P +1.86 (s objective vector) 187.63 248.66 P +1.86 (. An example of the objective function values data) 275.29 248.66 P +3.98 (structure is shown below) 135.65 234.66 P +3.98 (, with) 266.4 234.66 P +3 F +9.56 (OBJFUN) 304.68 234.66 P +2 F +3.98 ( representing an arbitrary objective) 347.86 234.66 P +(function.) 135.65 220.66 T +144.97 478.66 522.32 622.95 C +3 12 Q +0 X +0 K +(P) 146.97 613.96 T +(h) 153.87 613.96 T +(e) 161.78 613.96 T +(n) 169.68 613.96 T +(D) 195.46 613.96 T +(E) 203.36 613.96 T +(C) 211.26 613.96 T +(O) 219.16 613.96 T +(D) 227.07 613.96 T +(E) 234.97 613.96 T +(C) 249.97 613.96 T +(h) 257.87 613.96 T +(r) 265.77 613.96 T +(o) 273.68 613.96 T +(m) 281.58 613.96 T +4 F +(\050) 244.87 613.96 T +(\051) 289.38 613.96 T +3 F +(%) 309.08 613.96 T +(\021) 316.28 613.96 T +(M) 323.47 613.96 T +(a) 330.67 613.96 T +(p) 337.86 613.96 T +(\021) 345.06 613.96 T +(G) 352.26 613.96 T +(e) 359.45 613.96 T +(n) 366.65 613.96 T +(o) 373.85 613.96 T +(t) 381.04 613.96 T +(y) 388.24 613.96 T +(p) 395.43 613.96 T +(e) 402.63 613.96 T +(\021) 409.83 613.96 T +(t) 417.02 613.96 T +(o) 424.22 613.96 T +(\021) 431.41 613.96 T +(P) 438.61 613.96 T +(h) 445.81 613.96 T +(e) 453 613.96 T +(n) 460.2 613.96 T +(o) 467.39 613.96 T +(t) 474.59 613.96 T +(y) 481.79 613.96 T +(p) 488.98 613.96 T +(e) 496.18 613.96 T +4 F +(=) 182.87 613.96 T +0 F +(x) 207.38 568.27 T +2 9 Q +(1) 213.17 564.51 T +(1) 222.16 564.51 T +4 F +(,) 217.67 564.51 T +0 12 Q +(x) 249.32 568.27 T +2 9 Q +(1) 255.11 564.51 T +(2) 264.1 564.51 T +4 F +(,) 259.6 564.51 T +0 12 Q +(x) 291.26 568.27 T +2 9 Q +(1) 297.04 564.51 T +(3) 306.03 564.51 T +4 F +(,) 301.54 564.51 T +4 12 Q +(\274) 323.86 568.27 T +0 F +(x) 349.18 568.27 T +2 9 Q +(1) 354.97 564.51 T +3 F +(N) 363.96 564.51 T +(v) 369.88 564.51 T +(a) 375.8 564.51 T +(r) 381.73 564.51 T +4 F +(,) 359.46 564.51 T +0 12 Q +(x) 207.38 550.35 T +2 9 Q +(2) 213.17 546.59 T +(1) 222.16 546.59 T +4 F +(,) 217.67 546.59 T +0 12 Q +(x) 249.32 550.35 T +2 9 Q +(2) 255.11 546.59 T +(2) 264.1 546.59 T +4 F +(,) 259.6 546.59 T +0 12 Q +(x) 291.26 550.35 T +2 9 Q +(2) 297.04 546.59 T +(3) 306.03 546.59 T +4 F +(,) 301.54 546.59 T +4 12 Q +(\274) 323.86 550.35 T +0 F +(x) 349.18 550.35 T +2 9 Q +(2) 354.97 546.59 T +3 F +(N) 363.96 546.59 T +(v) 369.88 546.59 T +(a) 375.8 546.59 T +(r) 381.73 546.59 T +4 F +(,) 359.46 546.59 T +0 12 Q +(x) 207.38 532.44 T +2 9 Q +(3) 213.17 528.68 T +(1) 222.16 528.68 T +4 F +(,) 217.67 528.68 T +0 12 Q +(x) 249.32 532.44 T +2 9 Q +(3) 255.11 528.68 T +(2) 264.1 528.68 T +4 F +(,) 259.6 528.68 T +0 12 Q +(x) 291.26 532.44 T +2 9 Q +(3) 297.04 528.68 T +(3) 306.03 528.68 T +4 F +(,) 301.54 528.68 T +4 12 Q +(\274) 323.86 532.44 T +0 F +(x) 349.18 532.44 T +2 9 Q +(3) 354.97 528.68 T +3 F +(N) 363.96 528.68 T +(v) 369.88 528.68 T +(a) 375.8 528.68 T +(r) 381.73 528.68 T +4 F +(,) 359.46 528.68 T +2 12 Q +(.) 215.02 514.55 T +(.) 256.96 514.55 T +(.) 298.89 514.55 T +4 F +(\274) 323.86 514.55 T +2 F +(.) 366.15 514.55 T +0 F +(x) 198.05 498.35 T +3 9 Q +(N) 203.84 494.59 T +(i) 209.76 494.59 T +(n) 215.68 494.59 T +(d) 221.6 494.59 T +2 F +(1) 231.49 494.59 T +4 F +(,) 227 494.59 T +0 12 Q +(x) 239.99 498.35 T +3 9 Q +(N) 245.77 494.59 T +(i) 251.7 494.59 T +(n) 257.62 494.59 T +(d) 263.54 494.59 T +2 F +(2) 273.43 494.59 T +4 F +(,) 268.93 494.59 T +0 12 Q +(x) 281.92 498.35 T +3 9 Q +(N) 287.71 494.59 T +(i) 293.63 494.59 T +(n) 299.55 494.59 T +(d) 305.48 494.59 T +2 F +(3) 315.36 494.59 T +4 F +(,) 310.87 494.59 T +4 12 Q +(\274) 323.86 498.35 T +0 F +(x) 339.85 498.35 T +3 9 Q +(N) 345.64 494.73 T +(i) 351.56 494.73 T +(n) 357.48 494.73 T +(d) 363.4 494.73 T +(N) 373.29 494.73 T +(v) 379.21 494.73 T +(a) 385.14 494.73 T +(r) 391.06 494.73 T +4 F +(,) 368.8 494.73 T +2 12 Q +(i) 417.96 568.88 T +(n) 421.3 568.88 T +(d) 427.29 568.88 T +(i) 433.29 568.88 T +(v) 436.62 568.88 T +(i) 442.62 568.88 T +(d) 445.96 568.88 T +(u) 451.95 568.88 T +(a) 457.95 568.88 T +(l) 463.27 568.88 T +(\021) 466.61 568.88 T +(1) 469.61 568.88 T +(i) 417.96 551.08 T +(n) 421.3 551.08 T +(d) 427.29 551.08 T +(i) 433.29 551.08 T +(v) 436.62 551.08 T +(i) 442.62 551.08 T +(d) 445.96 551.08 T +(u) 451.95 551.08 T +(a) 457.95 551.08 T +(l) 463.27 551.08 T +(\021) 466.61 551.08 T +(2) 469.61 551.08 T +(i) 417.96 533.28 T +(n) 421.3 533.28 T +(d) 427.29 533.28 T +(i) 433.29 533.28 T +(v) 436.62 533.28 T +(i) 442.62 533.28 T +(d) 445.96 533.28 T +(u) 451.95 533.28 T +(a) 457.95 533.28 T +(l) 463.27 533.28 T +(\021) 466.61 533.28 T +(3) 469.61 533.28 T +(.) 445.28 515.48 T +(i) 405.16 497.68 T +(n) 408.49 497.68 T +(d) 414.49 497.68 T +(i) 420.48 497.68 T +(v) 423.82 497.68 T +(i) 429.82 497.68 T +(d) 433.15 497.68 T +(u) 439.15 497.68 T +(a) 445.14 497.68 T +(l) 450.47 497.68 T +(\021) 453.8 497.68 T +3 F +(N) 458.51 497.68 T +(i) 466.41 497.68 T +(n) 474.31 497.68 T +(d) 482.21 497.68 T +4 F +(=) 180.97 533.96 T +199.55 492.64 195.55 492.64 2 L +0.33 H +0 Z +N +195.55 492.64 195.55 580.48 2 L +N +195.55 580.48 199.55 580.48 2 L +N +393.95 492.64 397.95 492.64 2 L +N +397.95 492.64 397.95 580.48 2 L +N +397.95 580.48 393.95 580.48 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "21" 22 +%%Page: "22" 22 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-22) 513.33 61.29 T +1 16 Q +(Fitness values) 135.65 577.51 T +2 12 Q +2.12 (Fitness values are derived from objective function values through a scaling or) 135.65 550.18 P +2.59 (ranking function. Fitnesses are non-negative scalars and are stored in column) 135.65 536.18 P +0.07 (vectors of length) 135.65 522.18 P +3 F +0.17 (Nind) 219.46 522.18 P +2 F +0.07 (, an example of which is shown below) 248.25 522.18 P +0.07 (. Again, FITNESS is) 431.82 522.18 P +(an arbitrary \336tness function.) 135.65 508.18 T +1.6 (Note that for multiobjective functions, the \336tness of a particular individual is a) 135.65 335.63 P +2.33 (function of a vector of objective function values. Multiobjective problems are) 135.65 321.62 P +2.49 (characterised by having no single unique solution, but a family of equally \336t) 135.65 307.62 P +2.42 (solutions with dif) 135.65 293.62 P +2.42 (ferent values of decision variables. Care should therefore be) 224.23 293.62 P +0.26 (taken to adopt some mechanism to ensure that the population is able to evolve the) 135.65 279.62 P +1.35 (set of Pareto optimal solutions, for example by using \336tness sharing [31] in the) 135.65 265.62 P +-0.04 (selection method. Although not supported in this version of the Genetic Algorithm) 135.65 251.62 P +1.73 (T) 135.65 237.62 P +1.73 (oolbox, it is planned that multiobjective search will be implemented in future) 142.14 237.62 P +(versions.) 135.65 223.62 T +152.42 602.18 514.87 744.95 C +3 12 Q +0 X +0 K +(O) 162.01 735.96 T +(b) 169.91 735.96 T +(j) 177.82 735.96 T +(V) 185.72 735.96 T +(O) 211.5 735.96 T +(B) 219.4 735.96 T +(J) 227.3 735.96 T +(F) 235.2 735.96 T +(U) 243.1 735.96 T +(N) 251.01 735.96 T +(P) 266.01 735.96 T +(h) 273.91 735.96 T +(e) 281.81 735.96 T +(n) 289.72 735.96 T +4 F +(\050) 260.91 735.96 T +(\051) 297.52 735.96 T +3 F +(%) 317.22 735.96 T +(\021) 324.42 735.96 T +(O) 331.61 735.96 T +(b) 338.81 735.96 T +(j) 346 735.96 T +(e) 353.2 735.96 T +(c) 360.39 735.96 T +(t) 367.59 735.96 T +(i) 374.79 735.96 T +(v) 381.98 735.96 T +(e) 389.18 735.96 T +(\021) 396.38 735.96 T +(F) 403.57 735.96 T +(u) 410.77 735.96 T +(n) 417.96 735.96 T +(c) 425.16 735.96 T +(t) 432.36 735.96 T +(i) 439.55 735.96 T +(o) 446.75 735.96 T +(n) 453.94 735.96 T +4 F +(=) 198.91 735.96 T +0 F +(y) 223.43 690.27 T +2 9 Q +(1) 229.21 686.51 T +(1) 238.2 686.51 T +4 F +(,) 233.71 686.51 T +0 12 Q +(y) 265.36 690.27 T +2 9 Q +(1) 271.15 686.51 T +(2) 280.14 686.51 T +4 F +(,) 275.64 686.51 T +0 12 Q +(y) 307.3 690.27 T +2 9 Q +(1) 313.08 686.51 T +(3) 322.07 686.51 T +4 F +(,) 317.58 686.51 T +4 12 Q +(\274) 339.9 690.27 T +0 F +(y) 365.22 690.27 T +2 9 Q +(1) 371.01 686.51 T +3 F +(N) 380 686.51 T +(v) 385.92 686.51 T +(a) 391.85 686.51 T +(r) 397.77 686.51 T +4 F +(,) 375.5 686.51 T +0 12 Q +(y) 223.43 672.36 T +2 9 Q +(2) 229.21 668.59 T +(1) 238.2 668.59 T +4 F +(,) 233.71 668.59 T +0 12 Q +(y) 265.36 672.36 T +2 9 Q +(2) 271.15 668.59 T +(2) 280.14 668.59 T +4 F +(,) 275.64 668.59 T +0 12 Q +(y) 307.3 672.36 T +2 9 Q +(2) 313.08 668.59 T +(3) 322.07 668.59 T +4 F +(,) 317.58 668.59 T +4 12 Q +(\274) 339.9 672.36 T +0 F +(y) 365.22 672.36 T +2 9 Q +(2) 371.01 668.59 T +3 F +(N) 380 668.59 T +(v) 385.92 668.59 T +(a) 391.85 668.59 T +(r) 397.77 668.59 T +4 F +(,) 375.5 668.59 T +0 12 Q +(y) 223.43 654.44 T +2 9 Q +(3) 229.21 650.68 T +(1) 238.2 650.68 T +4 F +(,) 233.71 650.68 T +0 12 Q +(y) 265.36 654.44 T +2 9 Q +(3) 271.15 650.68 T +(2) 280.14 650.68 T +4 F +(,) 275.64 650.68 T +0 12 Q +(y) 307.3 654.44 T +2 9 Q +(3) 313.08 650.68 T +(3) 322.07 650.68 T +4 F +(,) 317.58 650.68 T +4 12 Q +(\274) 339.9 654.44 T +0 F +(y) 365.22 654.44 T +2 9 Q +(3) 371.01 650.68 T +3 F +(N) 380 650.68 T +(v) 385.92 650.68 T +(a) 391.85 650.68 T +(r) 397.77 650.68 T +4 F +(,) 375.5 650.68 T +2 12 Q +(.) 231.06 636.55 T +(.) 273 636.55 T +(.) 314.93 636.55 T +4 F +(\274) 339.9 636.55 T +2 F +(.) 382.19 636.55 T +0 F +(y) 214.09 620.35 T +3 9 Q +(N) 219.88 616.59 T +(i) 225.8 616.59 T +(n) 231.72 616.59 T +(d) 237.65 616.59 T +2 F +(1) 247.53 616.59 T +4 F +(,) 243.04 616.59 T +0 12 Q +(y) 256.03 620.35 T +3 9 Q +(N) 261.82 616.59 T +(i) 267.74 616.59 T +(n) 273.66 616.59 T +(d) 279.58 616.59 T +2 F +(2) 289.47 616.59 T +4 F +(,) 284.97 616.59 T +0 12 Q +(y) 297.96 620.35 T +3 9 Q +(N) 303.75 616.59 T +(i) 309.67 616.59 T +(n) 315.59 616.59 T +(d) 321.52 616.59 T +2 F +(3) 331.4 616.59 T +4 F +(,) 326.91 616.59 T +4 12 Q +(\274) 339.9 620.35 T +0 F +(y) 355.89 620.35 T +3 9 Q +(N) 361.68 616.73 T +(i) 367.6 616.73 T +(n) 373.52 616.73 T +(d) 379.44 616.73 T +(N) 389.33 616.73 T +(v) 395.26 616.73 T +(a) 401.18 616.73 T +(r) 407.1 616.73 T +4 F +(,) 384.84 616.73 T +2 12 Q +(i) 434 690.88 T +(n) 437.34 690.88 T +(d) 443.33 690.88 T +(i) 449.33 690.88 T +(v) 452.66 690.88 T +(i) 458.66 690.88 T +(d) 461.99 690.88 T +(u) 467.99 690.88 T +(a) 473.99 690.88 T +(l) 479.31 690.88 T +(\021) 482.65 690.88 T +(1) 485.65 690.88 T +(i) 434 673.08 T +(n) 437.34 673.08 T +(d) 443.33 673.08 T +(i) 449.33 673.08 T +(v) 452.66 673.08 T +(i) 458.66 673.08 T +(d) 461.99 673.08 T +(u) 467.99 673.08 T +(a) 473.99 673.08 T +(l) 479.31 673.08 T +(\021) 482.65 673.08 T +(2) 485.65 673.08 T +(i) 434 655.28 T +(n) 437.34 655.28 T +(d) 443.33 655.28 T +(i) 449.33 655.28 T +(v) 452.66 655.28 T +(i) 458.66 655.28 T +(d) 461.99 655.28 T +(u) 467.99 655.28 T +(a) 473.99 655.28 T +(l) 479.31 655.28 T +(\021) 482.65 655.28 T +(3) 485.65 655.28 T +(.) 461.32 637.48 T +(i) 421.2 619.68 T +(n) 424.53 619.68 T +(d) 430.53 619.68 T +(i) 436.52 619.68 T +(v) 439.86 619.68 T +(i) 445.86 619.68 T +(d) 449.19 619.68 T +(u) 455.19 619.68 T +(a) 461.18 619.68 T +(l) 466.51 619.68 T +(\021) 469.84 619.68 T +3 F +(N) 474.55 619.68 T +(i) 482.45 619.68 T +(n) 490.35 619.68 T +(d) 498.25 619.68 T +4 F +(=) 197.01 655.96 T +215.59 614.64 211.59 614.64 2 L +0.33 H +0 Z +N +211.59 614.64 211.59 702.48 2 L +N +211.59 702.48 215.59 702.48 2 L +N +409.99 614.64 413.99 614.64 2 L +N +413.99 614.64 413.99 702.48 2 L +N +413.99 702.48 409.99 702.48 2 L +N +-8.35 24.95 603.65 816.95 C +182.59 357.63 484.7 488.74 C +3 12 Q +0 X +0 K +(F) 195.87 479.75 T +(i) 203.77 479.75 T +(t) 211.68 479.75 T +(n) 219.58 479.75 T +(F) 245.36 479.75 T +(I) 253.26 479.75 T +(T) 261.16 479.75 T +(N) 269.07 479.75 T +(E) 276.97 479.75 T +(S) 284.87 479.75 T +(S) 292.77 479.75 T +(O) 307.77 479.75 T +(b) 315.68 479.75 T +(j) 323.58 479.75 T +(V) 331.48 479.75 T +4 F +(\050) 302.67 479.75 T +(\051) 339.28 479.75 T +3 F +(\021) 345.98 479.75 T +(%) 353.18 479.75 T +(\021) 360.37 479.75 T +(F) 367.57 479.75 T +(i) 374.77 479.75 T +(t) 381.96 479.75 T +(n) 389.16 479.75 T +(e) 396.36 479.75 T +(s) 403.55 479.75 T +(s) 410.75 479.75 T +(\021) 417.94 479.75 T +(F) 425.14 479.75 T +(u) 432.33 479.75 T +(n) 439.53 479.75 T +(c) 446.73 479.75 T +(t) 453.92 479.75 T +(i) 461.12 479.75 T +(o) 468.32 479.75 T +(n) 475.51 479.75 T +4 F +(=) 232.77 479.75 T +0 F +(f) 259.74 442.24 T +2 9 Q +(1) 263.54 438.48 T +0 12 Q +(f) 259.74 424.33 T +2 9 Q +(2) 263.54 420.56 T +0 12 Q +(f) 259.74 406.41 T +2 9 Q +(3) 263.54 402.65 T +2 12 Q +(.) 261.89 388.52 T +0 F +(f) 250.41 373.71 T +3 9 Q +(N) 254.2 370.09 T +(i) 260.13 370.09 T +(n) 266.05 370.09 T +(d) 271.97 370.09 T +2 12 Q +(i) 298.32 442.15 T +(n) 301.65 442.15 T +(d) 307.64 442.15 T +(i) 313.64 442.15 T +(v) 316.98 442.15 T +(i) 322.97 442.15 T +(d) 326.31 442.15 T +(u) 332.3 442.15 T +(a) 338.3 442.15 T +(l) 343.63 442.15 T +(\021) 346.96 442.15 T +(1) 349.96 442.15 T +(i) 298.32 424.35 T +(n) 301.65 424.35 T +(d) 307.64 424.35 T +(i) 313.64 424.35 T +(v) 316.98 424.35 T +(i) 322.97 424.35 T +(d) 326.31 424.35 T +(u) 332.3 424.35 T +(a) 338.3 424.35 T +(l) 343.63 424.35 T +(\021) 346.96 424.35 T +(2) 349.96 424.35 T +(i) 298.32 406.55 T +(n) 301.65 406.55 T +(d) 307.64 406.55 T +(i) 313.64 406.55 T +(v) 316.98 406.55 T +(i) 322.97 406.55 T +(d) 326.31 406.55 T +(u) 332.3 406.55 T +(a) 338.3 406.55 T +(l) 343.63 406.55 T +(\021) 346.96 406.55 T +(3) 349.96 406.55 T +(.) 328.11 388.75 T +(i) 286.07 373.97 T +(n) 289.4 373.97 T +(d) 295.4 373.97 T +(i) 301.39 373.97 T +(v) 304.73 373.97 T +(i) 310.73 373.97 T +(d) 314.06 373.97 T +(u) 320.06 373.97 T +(a) 326.05 373.97 T +(l) 331.38 373.97 T +(\021) 334.71 373.97 T +3 F +(N) 339.42 373.97 T +(i) 346.61 373.97 T +(n) 353.81 373.97 T +(d) 361.01 373.97 T +4 F +(=) 233.32 408.75 T +251.91 368.23 247.91 368.23 2 L +0.33 H +0 Z +N +247.91 368.23 247.91 454.45 2 L +N +247.91 454.45 251.91 454.45 2 L +N +274.86 368.23 278.86 368.23 2 L +N +278.86 368.23 278.86 454.45 2 L +N +278.86 454.45 274.86 454.45 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "22" 23 +%%Page: "23" 23 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-23) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Support for Multiple Populations) 63.65 732.95 T +2 12 Q +0.49 (The GA T) 135.65 694.95 P +0.49 (oolbox provides support for multiple subpopulations through the use of) 185.09 694.95 P +2.44 (high-level genetic operator functions and a routine for exchanging individuals) 135.65 680.95 P +0.12 (between subpopulations. In the literature, the use of multiple populations has been) 135.65 666.95 P +1.48 (shown, in most cases, to improve the quality of the results obtained using GAs) 135.65 652.95 P +(compared to the single population GA \050see, for example, [32] and [33]\051.) 135.65 638.95 T +0.36 (The GA T) 135.65 612.95 P +0.36 (oolbox supports the use of a single population divided into a number of) 184.83 612.95 P +3.75 (subpopulations or) 135.65 598.95 P +0 F +3.75 (demes) 231.76 598.95 P +2 F +3.75 ( by modifying the use of data structures such that) 261.74 598.95 P +4.05 (subpopulations are stored in contiguous blocks within a single matrix. For) 135.65 584.95 P +5.76 (example, the chromosome data structure,) 135.65 570.95 P +3 F +13.81 (Chrom) 364.61 570.95 P +2 F +5.76 (, composed of) 400.59 570.95 P +3 F +13.81 (SUBPOP) 488.47 570.95 P +2 F +(subpopulations each of length) 135.65 556.95 T +3 F +(N) 282.22 556.95 T +2 F +( individuals is stored as:) 289.42 556.95 T +2.16 (This is known as the) 135.65 242.2 P +0 F +2.16 (Migration) 248.04 242.2 P +2 F +2.16 (, or) 296.69 242.2 P +0 F +2.16 (Island) 319.99 242.2 P +2 F +2.16 (, model [34]. Each subpopulation is) 349.97 242.2 P +1.3 (evolved over generations by a traditional GA and from time to time individuals) 135.65 228.2 P +5.19 (migrate from one subpopulation to another) 135.65 214.2 P +5.19 (. The amount of migration of) 366.46 214.2 P +3.82 (individuals and the pattern of that migration determines how much genetic) 135.65 200.2 P +(diversity can occur) 135.65 186.2 T +(.) 226.25 186.2 T +2.83 (T) 135.65 160.2 P +2.83 (o allow the T) 142.14 160.2 P +2.83 (oolbox routines to operate independently on subpopulations, a) 213.4 160.2 P +-0.29 (number of high-level entry functions are provided that accept an optional ar) 135.65 146.2 P +-0.29 (gument) 495.67 146.2 P +1.24 (that determines the number of subpopulations contained in a data structure. The) 135.65 132.2 P +0.5 (low-level routines are then called independently) 135.65 118.2 P +0.5 (, in turn, with each subpopulation) 368.22 118.2 P +238.13 264.2 429.16 548.95 C +3 12 Q +0 X +0 K +(C) 239.13 402.93 T +(h) 246.33 402.93 T +(r) 253.52 402.93 T +(o) 260.72 402.93 T +(m) 267.92 402.93 T +(I) 317.18 515.29 T +(n) 324.38 515.29 T +(d) 331.58 515.29 T +(1) 340.23 509.8 T +(S) 349.14 515.29 T +(u) 356.33 515.29 T +(b) 363.53 515.29 T +(P) 370.73 515.29 T +(o) 377.92 515.29 T +(p) 385.12 515.29 T +(1) 393.77 509.8 T +(I) 317.68 495.33 T +(n) 324.88 495.33 T +(d) 332.08 495.33 T +(2) 340.73 489.85 T +(S) 348.64 495.33 T +(u) 355.83 495.33 T +(b) 363.03 495.33 T +(P) 370.23 495.33 T +(o) 377.42 495.33 T +(p) 384.62 495.33 T +(1) 393.27 489.85 T +4 F +(\274) 353.58 475.38 T +3 F +(I) 317.18 459.4 T +(n) 324.38 459.4 T +(d) 331.58 459.4 T +(N) 340.23 453.92 T +(S) 349.14 459.4 T +(u) 356.33 459.4 T +(b) 363.53 459.4 T +(P) 370.73 459.4 T +(o) 377.92 459.4 T +(p) 385.12 459.4 T +(1) 393.77 453.92 T +(I) 317.68 439.45 T +(n) 324.88 439.45 T +(d) 332.08 439.45 T +(1) 340.73 433.96 T +(S) 349.64 439.45 T +(u) 356.83 439.45 T +(b) 364.03 439.45 T +(P) 371.23 439.45 T +(o) 378.42 439.45 T +(p) 385.62 439.45 T +(2) 394.27 433.96 T +(I) 317.68 419.49 T +(n) 324.88 419.49 T +(d) 332.08 419.49 T +(2) 340.73 414.01 T +(S) 348.64 419.49 T +(u) 355.83 419.49 T +(b) 363.03 419.49 T +(P) 370.23 419.49 T +(o) 377.42 419.49 T +(p) 384.62 419.49 T +(2) 393.27 414.01 T +4 F +(\274) 353.58 399.54 T +3 F +(I) 317.18 383.56 T +(n) 324.38 383.56 T +(d) 331.58 383.56 T +(N) 340.23 378.07 T +(S) 349.14 383.56 T +(u) 356.33 383.56 T +(b) 363.53 383.56 T +(P) 370.73 383.56 T +(o) 377.92 383.56 T +(p) 385.12 383.56 T +(2) 393.77 378.07 T +4 F +(\274) 353.58 363.6 T +3 F +(I) 299.2 347.62 T +(n) 306.39 347.62 T +(d) 313.59 347.62 T +(1) 322.24 342.14 T +(S) 331.15 347.62 T +(u) 338.34 347.62 T +(b) 345.54 347.62 T +(P) 352.73 347.62 T +(o) 359.93 347.62 T +(p) 367.13 347.62 T +(S) 375.79 342.14 T +(U) 382.98 342.14 T +(B) 390.18 342.14 T +(P) 397.37 342.14 T +(O) 404.57 342.14 T +(P) 411.77 342.14 T +(I) 299.7 327.67 T +(n) 306.89 327.67 T +(d) 314.09 327.67 T +(2) 322.74 322.18 T +(S) 330.65 327.67 T +(u) 337.84 327.67 T +(b) 345.04 327.67 T +(P) 352.23 327.67 T +(o) 359.43 327.67 T +(p) 366.63 327.67 T +(S) 375.29 322.18 T +(U) 382.48 322.18 T +(B) 389.68 322.18 T +(P) 396.87 322.18 T +(O) 404.07 322.18 T +(P) 411.27 322.18 T +4 F +(\274) 353.58 307.72 T +3 F +(I) 299.2 291.73 T +(n) 306.39 291.73 T +(d) 313.59 291.73 T +(N) 322.24 286.25 T +(S) 331.15 291.73 T +(u) 338.34 291.73 T +(b) 345.54 291.73 T +(P) 352.73 291.73 T +(o) 359.93 291.73 T +(p) 367.13 291.73 T +(S) 375.79 286.25 T +(U) 382.98 286.25 T +(B) 390.18 286.25 T +(P) 397.37 286.25 T +(O) 404.57 286.25 T +(P) 411.77 286.25 T +2 F +(.) 424.17 402.93 T +4 F +(=) 282.11 402.93 T +300.7 283.77 296.7 283.77 2 L +0.33 H +0 Z +N +296.7 283.77 296.7 527.27 2 L +N +296.7 527.27 300.7 527.27 2 L +N +417.46 283.77 421.46 283.77 2 L +N +421.46 283.77 421.46 527.27 2 L +N +421.46 527.27 417.46 527.27 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "23" 24 +%%Page: "24" 24 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-24) 513.33 61.29 T +2 12 Q +0.1 (to perform functions such as selection, crossover and reinsertion. These high-level) 135.65 736.95 P +(functions are listed in the T) 135.65 722.95 T +(able below) 266.39 722.95 T +(.) 317.9 722.95 T +1 F +(Note:) 135.65 570.95 T +2 F +( As currently implemented, all subpopulations must be of equal size.) 163.62 570.95 T +0.04 (The transfer of individuals between subpopulations is implemented in the T) 135.65 544.95 P +0.04 (oolbox) 498.33 544.95 P +0.57 (function) 135.65 530.95 P +3 F +1.37 (migrate) 179.19 530.95 P +2 F +0.57 (. A single scalar is used to determine the amount of migration) 229.56 530.95 P +3.62 (of individuals from one subpopulation to another) 135.65 516.95 P +3.62 (. Thus, given a population) 391.9 516.95 P +1.6 (comprised of a number of subpopulations, the same number of individuals will) 135.65 502.95 P +1.86 (always be transferred from a subpopulation as the number it will receive from) 135.65 488.95 P +0.15 (another subpopulation. A second parameter to the function) 135.65 474.95 P +3 F +0.37 (migrate) 421.67 474.95 P +2 F +0.15 ( controls the) 472.05 474.95 P +3.59 (manner in which individuals are selected for migration, either uniformly or) 135.65 460.95 P +4.25 (according to \336tness. Uniform selection picks individuals for migration and) 135.65 446.95 P +2.52 (replaces individuals in a subpopulation with immigrants in a random manner) 135.65 432.95 P +2.52 (.) 528.65 432.95 P +2.4 (Fitness-based migration selects individuals according to their \336tness level, the) 135.65 418.95 P +0.08 (most \336t individuals being the ones selected for migration, and replaces individuals) 135.65 404.95 P +(in a subpopulation uniformly at random.) 135.65 390.95 T +1.09 (A further parameter speci\336es the population topology over which migration will) 135.65 364.95 P +-0.26 (take place. Fig. 7 shows the most basic migration paths implemented in) 135.65 350.95 P +3 F +-0.63 (migrate) 478.28 350.95 P +2 F +-0.26 (,) 528.65 350.95 P +0.71 (the ring topology) 135.65 336.95 P +0.71 (. Here individuals are transferred between directionally adjacent) 218.92 336.95 P +1.69 (subpopulations. For example, individuals from subpopulation 6 migrate only to) 135.65 322.95 P +6.65 (subpopulation 1 and individuals from subpopulation 1 only migrate to) 135.65 308.95 P +(subpopulation 2.) 135.65 294.95 T +(SUBPOPULA) 222.4 690.95 T +(TION SUPPOR) 291.04 690.95 T +(T FUNCTIONS) 367.28 690.95 T +3 F +(mutate) 141.65 666.95 T +2 F +(mutation operators) 249.65 666.95 T +3 F +(recombin) 141.65 644.95 T +2 F +(crossover and recombination operators) 249.65 644.95 T +3 F +(reins) 141.65 622.95 T +2 F +(uniform random and \336tness-based reinsertion) 249.65 622.95 T +3 F +(select) 141.65 600.95 T +2 F +(independent subpopulation selection) 249.65 600.95 T +135.65 706.7 135.65 593.2 2 L +V +0.5 H +0 Z +N +243.65 679.45 243.65 592.7 2 L +V +N +531.65 706.7 531.65 593.2 2 L +V +N +135.4 706.95 531.9 706.95 2 L +V +N +135.9 682.2 531.4 682.2 2 L +V +N +135.9 679.7 531.4 679.7 2 L +V +N +135.4 592.95 531.9 592.95 2 L +V +N +63.65 96.95 531.65 744.95 C +133.38 126.4 531.65 290.95 C +314.34 259.94 354.02 279.78 9.92 RR +7 X +0 K +V +0.5 H +2 Z +0 X +N +2 9 Q +(SubPop 1) 316.82 266.16 T +373.86 190.49 413.55 210.33 9.92 RR +7 X +V +0 X +N +(SubPop 3) 376.35 196.71 T +254.81 190.49 294.49 210.33 9.92 RR +7 X +V +0 X +N +(SubPop 5) 257.3 196.71 T +254.81 230.17 294.49 250.02 9.92 RR +7 X +V +0 X +N +(SubPop 6) 257.3 236.4 T +373.86 230.17 413.55 250.02 9.92 RR +7 X +V +0 X +N +(SubPop 2) 376.35 236.4 T +314.34 160.72 354.02 180.57 9.92 RR +7 X +V +0 X +N +(SubPop 4) 316.82 166.95 T +308.7 272.85 314.34 269.86 308.93 266.48 308.81 269.67 4 Y +V +98 180 39.68 19.84 314.34 250.02 A +395.27 255.94 393.69 250.02 389.35 254.35 392.31 255.15 4 Y +V +15 90 39.68 19.84 354.02 250.02 A +273.07 184.57 274.65 190.49 278.99 186.17 276.03 185.37 4 Y +V +195 270 39.68 19.84 314.34 190.49 A +359.65 167.65 354.02 170.65 359.43 174.03 359.54 170.84 4 Y +V +278 360 39.68 19.84 354.02 190.49 A +396.7 215.53 393.7 210.33 390.7 215.53 393.7 215.53 4 Y +V +393.7 230.17 393.7 215.53 2 L +N +271.65 224.98 274.65 230.17 277.65 224.98 274.65 224.98 4 Y +V +274.65 210.33 274.65 224.98 2 L +N +5 12 Q +(Figure 7: Ring Migration T) 246.77 143.55 T +(opology) 382.95 143.55 T +142.84 130.96 525.52 287.44 R +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "24" 25 +%%Page: "25" 25 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-25) 513.33 61.29 T +2 12 Q +1.18 (A similar strategy to the ring topology is the neighbourhood migration of Fig.8.) 135.65 736.95 P +3.3 (Like the ring topology) 135.65 722.95 P +3.3 (, migration is made only between nearest neighbours,) 252.38 722.95 P +2.19 (however) 135.65 708.95 P +2.19 (, migration may occur in either direction between subpopulations. For) 176.46 708.95 P +2.73 (each subpopulation, the possible immigrants are determined, according to the) 135.65 694.95 P +0.13 (desired selection method, from adjacent subpopulations and a \336nal selection made) 135.65 680.95 P +0.07 (from this pool of individuals. This ensures that individuals will not migrate from a) 135.65 666.95 P +(subpopulation to the same subpopulation.) 135.65 652.95 T +-0.1 (The most general migration strategy supported by) 135.65 458.75 P +3 F +-0.25 (migrate) 377.1 458.75 P +2 F +-0.1 ( is that of unrestricted) 427.47 458.75 P +3.36 (migration, Fig. 9. Here, individuals may migrate from any subpopulation to) 135.65 444.75 P +2.16 (another) 135.65 430.75 P +2.16 (. For each subpopulation, a pool of potential immigrants is constructed) 170.96 430.75 P +3.58 (from the other subpopulations. The individual migrants are then determined) 135.65 416.75 P +(according to the appropriate selection strategy) 135.65 402.75 T +(.) 356.36 402.75 T +0.63 (An example of a GA with multiple subpopulations is considered in the) 135.65 215.11 P +0 F +0.63 (Examples) 485.02 215.11 P +2 F +(Section.) 135.65 201.11 T +63.65 96.95 531.65 744.95 C +133.38 470.75 531.65 648.95 C +312.67 609.34 352.35 629.18 9.92 RR +7 X +0 K +V +0.5 H +0 Z +0 X +N +2 9 Q +(SubPop 1) 315.16 615.56 T +372.2 539.9 411.88 559.74 9.92 RR +7 X +V +0 X +N +(SubPop 3) 374.68 546.12 T +253.14 539.9 292.83 559.74 9.92 RR +7 X +V +0 X +N +(SubPop 5) 255.63 546.12 T +253.14 579.58 292.83 599.42 9.92 RR +7 X +V +0 X +N +(SubPop 6) 255.63 585.8 T +372.2 579.58 411.88 599.42 9.92 RR +7 X +V +0 X +N +(SubPop 2) 374.68 585.8 T +312.67 510.13 352.35 529.97 9.92 RR +7 X +V +0 X +N +(SubPop 4) 315.16 516.35 T +277.32 603.75 272.98 599.42 271.4 605.35 274.36 604.55 4 Y +V +307.04 622.26 312.67 619.26 307.26 615.88 307.15 619.07 4 Y +V +98 165 39.68 19.84 312.67 599.42 A +357.77 615.88 352.36 619.26 357.99 622.26 357.88 619.07 4 Y +V +393.6 605.35 392.03 599.42 387.68 603.75 390.64 604.55 4 Y +V +15 82 39.68 19.84 352.35 599.42 A +307.26 523.43 312.67 520.05 307.04 517.06 307.15 520.25 4 Y +V +271.4 533.98 272.98 539.9 277.32 535.57 274.36 534.77 4 Y +V +195 262 39.68 19.84 312.67 539.9 A +387.68 535.57 392.03 539.9 393.6 533.98 390.64 534.77 4 Y +V +357.99 517.06 352.36 520.05 357.77 523.43 357.88 520.25 4 Y +V +278 345 39.68 19.84 352.35 539.9 A +389.04 574.38 392.04 579.58 395.04 574.38 392.04 574.38 4 Y +V +395.04 564.93 392.04 559.74 389.04 564.93 392.04 564.93 4 Y +V +392.04 574.38 392.04 564.93 2 L +N +275.99 564.93 272.99 559.74 269.99 564.93 272.99 564.93 4 Y +V +269.99 574.38 272.99 579.58 275.99 574.38 272.99 574.38 4 Y +V +272.99 564.93 272.99 574.38 2 L +N +5 12 Q +(Figure 8: Neighbourhood Migration T) 218.12 492.95 T +(opology) 408.27 492.95 T +141.18 481.15 523.85 638.55 R +2 Z +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +63.65 96.95 531.65 744.95 C +133.38 227.11 531.65 398.75 C +311.25 362.42 353.77 382.26 9.92 RR +7 X +0 K +V +0.5 H +0 Z +0 X +N +2 9 Q +(SubPop 1) 315.16 369.28 T +382.12 291.56 424.64 311.4 9.92 RR +7 X +V +0 X +N +(SubPop 3) 386.02 298.41 T +311.25 263.21 353.77 283.05 9.92 RR +7 X +V +0 X +N +(SubPop 4) 315.16 270.07 T +240.39 334.08 282.91 353.92 9.92 RR +7 X +V +0 X +N +(SubPop 6) 244.29 340.93 T +382.12 334.08 424.64 353.92 9.92 RR +7 X +V +0 X +N +(SubPop 2) 386.02 340.93 T +240.39 291.56 282.91 311.4 9.92 RR +7 X +V +0 X +N +(SubPop 5) 244.29 298.41 T +288.1 339.74 282.91 342.74 288.1 345.74 288.1 342.74 4 Y +V +376.92 345.74 382.12 342.74 376.92 339.74 376.92 342.74 4 Y +V +288.1 342.74 376.92 342.74 2 L +N +288.1 297.22 282.91 300.22 288.1 303.22 288.1 300.22 4 Y +V +376.92 303.22 382.12 300.22 376.92 297.22 376.92 300.22 4 Y +V +288.1 300.22 376.92 300.22 2 L +N +259.27 328.82 262.45 333.91 265.27 328.61 262.27 328.72 4 Y +V +264.83 316.48 261.64 311.4 258.83 316.7 261.83 316.59 4 Y +V +262.27 328.71 261.83 316.59 2 L +N +400.7 328.77 403.79 333.91 406.69 328.66 403.69 328.71 4 Y +V +406.47 316.54 403.38 311.4 400.47 316.65 403.47 316.59 4 Y +V +403.7 328.71 403.48 316.59 2 L +N +335.55 288.23 332.51 283.05 329.55 288.27 332.55 288.25 4 Y +V +330.08 357.4 333.12 362.57 336.08 357.36 333.08 357.38 4 Y +V +332.55 288.25 333.08 357.38 2 L +N +265.7 357.93 261.12 353.91 259.92 359.88 262.81 358.91 4 Y +V +304.36 376.57 310.45 373.24 304.52 369.63 304.44 373.1 4 Y +V +97 165 49.33 19.33 310.46 353.91 A +358.95 369.45 353.79 372.57 359.07 375.49 359.01 372.47 4 Y +V +404.8 360.17 403.78 353.91 398.86 357.93 401.83 359.05 4 Y +V +16 84 50 18.67 353.79 353.91 A +398.23 287.21 403.12 291.24 404.17 284.99 401.2 286.1 4 Y +V +359.87 269.25 353.78 272.58 359.71 276.19 359.79 272.72 4 Y +V +277 344 49.33 18.67 353.79 291.24 A +305.19 275.53 311.12 271.91 305.02 268.58 305.11 272.05 4 Y +V +260.59 285.27 261.79 291.24 266.36 287.22 263.48 286.24 4 Y +V +195 263 49.33 19.33 311.12 291.24 A +377.29 310.28 382.45 306.58 376.66 303.96 376.97 307.12 4 Y +V +339.96 356.6 343.12 362.57 346.72 356.84 343.34 356.72 4 Y +V +186 262 39.33 56 382.46 362.57 A +314.84 356.76 318.45 362.57 321.68 356.54 318.26 356.65 4 Y +V +289.05 303.42 283.12 305.91 288.24 309.8 288.64 306.61 4 Y +V +279 354 35.33 56.67 283.12 362.57 A +286.86 334.27 281.79 337.91 287.48 340.48 287.17 337.37 4 Y +V +323.54 289.08 320.45 283.24 316.94 288.83 320.24 288.96 4 Y +V +6 82 38.67 54.67 281.79 283.24 A +343.9 289.35 340.45 283.91 337.47 289.62 340.69 289.49 4 Y +V +378.27 339.89 383.78 337.24 378.73 333.79 378.5 336.84 4 Y +V +97 174 43.33 53.33 383.79 283.91 A +5 12 Q +(Figure 9: Unrestricted Migration T) 226.45 246.03 T +(opology) 399.93 246.03 T +141.18 238.52 523.85 387.34 R +2 Z +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "25" 26 +%%Page: "26" 26 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-26) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Examples) 63.65 732.95 T +2 12 Q +2.91 (This Section contains two detailed examples using the GA T) 135.65 694.95 P +2.91 (oolbox to solve) 451.86 694.95 P +(optimization problems:) 135.65 680.95 T +(\245) 157.25 654.95 T +(A simple binary GA to solve De Jong\325) 171.65 654.95 T +(s \336rst test function [13].) 355.87 654.95 T +(\245) 157.25 634.95 T +(A real-valued multi-population GA to solve the Harvest problem [9].) 171.65 634.95 T +1 16 Q +(The Simple GA) 135.65 598.29 T +2 12 Q +1.33 (This example demonstrates how a simple GA can be constructed using routines) 135.65 570.95 P +0.28 (from the GA T) 135.65 556.95 P +0.28 (oolbox to solve an optimization problem. The objective function to) 207.28 556.95 P +(be minimized is an extended version of De Jong\325) 135.65 542.95 T +(s \336rst test function [13]:) 370.15 542.95 T +(,) 315.32 503.13 T +0.97 (where) 135.65 463.88 P +0 F +0.97 (n) 168.91 463.88 P +2 F +0.97 ( de\336nes the number of dimensions of the problem. For this example, we) 174.91 463.88 P +(choose) 135.65 449.88 T +0 F +(n) 171.95 449.88 T +2 F +( = 20. The minimum of this function is, of course, located at) 177.95 449.88 T +0 F +(x) 469.87 449.88 T +0 10 Q +(i) 475.19 446.88 T +2 12 Q +( = 0.) 477.97 449.88 T +1 (The computational element of the M) 135.65 423.88 P +2 10 Q +0.84 (A) 316.21 423.88 P +0.84 (TLAB) 322.32 423.88 P +2 12 Q +1 ( objective function is encapsulated in) 348.42 423.88 P +(the code segment below) 135.65 409.88 T +(.) 250.45 409.88 T +3 F +(function ObjVal = objfun1\050 Phen \051) 171.65 383.88 T +(ObjVal = sum\050\050Phen .* Phen\051\325\051\325;) 171.65 363.88 T +2 F +1.32 (An m-\336le implementing this objective function,) 135.65 337.88 P +3 F +3.15 (objfun1) 375.74 337.88 P +2 F +1.32 (, is included with the) 426.11 337.88 P +(GA T) 135.65 323.88 T +(oolbox software.) 162.45 323.88 T +1.92 (Having written an m-\336le for the objective function, the GA code may now be) 135.65 297.88 P +-0.07 (constructed. This can be done directly from the M) 135.65 283.88 P +2 10 Q +-0.06 (A) 375.22 283.88 P +-0.06 (TLAB) 381.33 283.88 P +2 12 Q +-0.07 ( command line, in a script) 407.42 283.88 P +2.05 (\336le or as a M) 135.65 269.88 P +2 10 Q +1.71 (A) 207.13 269.88 P +1.71 (TLAB) 213.24 269.88 P +2 12 Q +2.05 ( function. Fig. 10 shows an outline of the script \336le) 239.33 269.88 P +3 F +4.92 (sga) 510.06 269.88 P +2 F +(supplied with the toolbox that implements a simple GA to solve this problem.) 135.65 255.88 T +3.3 (The \336rst \336ve lines describe the major variables of the GA. The number of) 135.65 229.88 P +1.5 (individuals is set to) 135.65 215.88 P +3 F +3.6 (NIND = 40) 237.61 215.88 P +2 F +1.5 ( and the number of generations) 309.58 215.88 P +3 F +3.6 (MAXGEN =) 470.48 215.88 P +-0.31 (300) 135.65 201.88 P +2 F +-0.13 (. The number of variables used is) 157.24 201.88 P +3 F +-0.31 (NVAR = 20) 318.87 201.88 P +2 F +-0.13 ( and each variable uses a 20 bit) 383.01 201.88 P +1.58 (representation,) 135.65 187.88 P +3 F +3.8 (PRECI = 20) 211.17 187.88 P +2 F +1.58 (. This example uses a generation gap,) 290.73 187.88 P +3 F +3.8 (GGAP =) 484.67 187.88 P +4.4 (0.9) 135.65 173.88 P +2 F +1.83 (, and \336tness-based reinsertion to implement an elitist strategy whereby the) 157.24 173.88 P +2.92 (four most \336t individuals always propagate through to successive generations.) 135.65 159.88 P +(Thus, 36 \050) 135.65 145.88 T +3 F +(NIND) 184.62 145.88 T +4 F +(\264) 216.4 145.88 T +3 F +(GGAP) 225.98 145.88 T +2 F +(\051 new individuals are produced at each generation.) 254.77 145.88 T +237.51 485.88 315.32 524.95 C +0 12 Q +0 X +0 K +(f) 238.51 503.13 T +2 9 Q +(1) 242.31 499.36 T +0 12 Q +(x) 254.61 503.13 T +4 F +(\050) 249.51 503.13 T +(\051) 260.54 503.13 T +0 F +(x) 304.04 503.13 T +0 9 Q +(i) 309.83 499.35 T +2 F +(2) 309.83 509.24 T +0 F +(i) 285.12 488.83 T +2 F +(1) 298.55 488.83 T +4 F +(=) 290.62 488.83 T +0 F +(n) 291.83 517.81 T +4 18 Q +(\345) 287.67 499.93 T +4 12 Q +(=) 272.53 503.13 T +-8.35 24.95 603.65 816.95 C +351.3 496.49 429.79 512.33 C +2 12 Q +0 X +0 K +(5) 359.35 503.13 T +(1) 365.35 503.13 T +(2) 371.34 503.13 T +4 F +(-) 352.3 503.13 T +0 F +(x) 389.92 503.13 T +0 9 Q +(i) 395.71 499.35 T +2 12 Q +(5) 410.8 503.13 T +(1) 416.79 503.13 T +(2) 422.79 503.13 T +4 F +(\243) 380.34 503.13 T +(\243) 401.21 503.13 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "26" 27 +%%Page: "27" 27 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-27) 513.33 61.29 T +2 12 Q +1.06 (The \336eld descriptor is constructed using the matrix replication function,) 135.65 178.42 P +3 F +2.54 (rep) 493.67 178.42 P +2 F +1.06 (, to) 515.26 178.42 P +3.96 (build the matrix,) 135.65 164.42 P +3 F +9.51 (FieldD) 230.16 164.42 P +2 F +3.96 (, describing the chromosomes\325 representation and) 273.34 164.42 P +-0.2 (interpretation. In this case,) 135.65 150.42 P +3 F +-0.49 (FieldD) 265.41 150.42 P +2 F +-0.2 ( describes 20 variables, each Gray coded using) 308.59 150.42 P +0.35 (20 bits over the interval [-512, 512]. An initial population is then created with the) 135.65 136.42 P +(function) 135.65 122.42 T +3 F +(crtbp) 178.62 122.42 T +2 F +( thus,) 214.6 122.42 T +63.65 96.95 531.65 744.95 C +136.44 200.42 531.65 732.95 C +142.71 234 525.38 722.98 R +7 X +0 K +V +3 12 Q +0 X +(NIND = 40;) 142.71 714.98 T +(% Number of individuals) 305.86 714.98 T +(MAXGEN = 300;) 142.71 700.98 T +(% Maximum no. of generations) 305.86 700.98 T +(NVAR = 20;) 142.71 686.98 T +(% No. of variables) 305.86 686.98 T +(PRECI = 20;) 142.71 672.98 T +(% Precision of variables) 305.86 672.98 T +(GGAP = 0.9;) 142.71 658.98 T +(% Generation gap) 305.86 658.98 T +(% Build f) 142.71 639.98 T +(ield descriptor) 207.47 639.98 T +(FieldD = [rep\050[PRECI],[1,NVAR]\051;...) 142.71 625.98 T +(rep\050[-512;512],[1,NVAR]\051; rep\050[1;0;1;1],[1,NVAR]\051];) 157.1 611.98 T +(% Initialise population) 142.71 592.98 T +(Chrom = crtbp\050NIND, NVAR*PRECI\051;) 142.71 578.98 T +(gen = 0;) 142.71 559.98 T +(% Counter) 305.86 559.98 T +(% Evaluate initial population) 142.71 540.98 T +(ObjV = objfun1\050bs2rv\050Chrom,FieldD\051\051;) 142.71 526.98 T +(% Generational loop) 142.71 507.98 T +(while gen < MAXGEN,) 142.71 493.98 T +(% Assign f) 167.91 474.98 T +(itness values to entire population) 239.87 474.98 T +(FitnV = ranking\050ObjV\051;) 167.91 460.98 T +(% Select individuals for breeding) 167.91 441.98 T +(SelCh = select\050\325sus\325, Chrom, FitnV, GGAP\051;) 167.91 427.98 T +(% Recombine individuals \050crossover\051) 167.91 408.98 T +(SelCh = recombin\050\325xovsp\325,SelCh,0.7\051;) 167.91 394.98 T +(% Apply mutation) 167.91 375.98 T +(SelCh = mut\050SelCh\051;) 167.91 361.98 T +(% Evaluate offspring, call objective function) 167.91 342.98 T +(ObjVSel = objfun1\050bs2rv\050SelCh,FieldD\051\051;) 167.91 328.98 T +(% Reinsert offspring into population) 167.91 309.98 T +([Chrom ObjV]=reins\050Chrom,SelCh,1,1,ObjV,ObjVSel\051;) 167.91 295.98 T +(% Increment counter) 167.91 276.98 T +(gen = gen+1;) 167.91 262.98 T +(end) 142.71 243.98 T +139.16 204.48 528.92 728.89 R +0.5 H +2 Z +N +5 F +(Figure 10: The Simple GA in M) 238.91 212.83 T +5 10 Q +(A) 397.51 212.83 T +(TLAB) 403.63 212.83 T +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "27" 28 +%%Page: "28" 28 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-28) 513.33 61.29 T +3 12 Q +(Chrom = crtbp\050NIND, NVAR*PRECI\051;) 171.65 736.95 T +2 F +0.14 (producing a matrix,) 135.65 710.95 P +3 F +0.35 (Chrom) 233.35 710.95 P +2 F +0.14 (, of) 269.33 710.95 P +3 F +0.35 (NIND) 288.6 710.95 P +2 F +0.14 ( uniformly distributed random binary strings) 317.39 710.95 P +(of length) 135.65 696.95 T +3 F +(NVAR) 181.62 696.95 T +4 F +(\264) 213.4 696.95 T +3 F +(PRECI) 222.98 696.95 T +2 F +(.) 258.96 696.95 T +0.86 (The generation counter) 135.65 670.95 P +0.86 (,) 248.12 670.95 P +3 F +2.06 (gen) 254.98 670.95 P +2 F +0.86 (, is set to zero. The following line then converts the) 276.57 670.95 P +0.12 (binary strings to real-values using the function) 135.65 656.95 P +3 F +0.28 (bs2rv) 362.64 656.95 P +2 F +0.12 ( and evaluates the objective) 398.62 656.95 P +1.26 (function,) 135.65 642.95 P +3 F +3.03 (objfun1) 182.88 642.95 P +2 F +1.26 (, for all of the individuals in the initial population as shown) 233.25 642.95 P +(below) 135.65 628.95 T +(.) 164.18 628.95 T +3 F +(ObjV = objfun1\050bs2rv\050Chrom, FieldD\051\051;) 171.65 602.95 T +2 F +2.08 (The function) 135.65 576.95 P +3 F +4.98 (bs2rv) 204.42 576.95 P +2 F +2.08 ( converts the binary strings in the matrix) 240.4 576.95 P +3 F +4.98 (Chrom) 454.22 576.95 P +2 F +2.08 ( to real-) 490.2 576.95 P +1.74 (values according to the \336eld descriptor) 135.65 562.95 P +1.74 (,) 330.07 562.95 P +3 F +4.18 (FieldD) 337.81 562.95 P +2 F +1.74 (, and returns a matrix of real-) 380.99 562.95 P +1.05 (valued phenotypes. The return value matrix of) 135.65 548.95 P +3 F +2.52 (bs2rv) 368.17 548.95 P +2 F +1.05 ( is then passed directly as) 404.15 548.95 P +4.34 (the input ar) 135.65 534.95 P +4.34 (gument to the objective function,) 198.74 534.95 P +3 F +10.41 (objfun1) 382.32 534.95 P +2 F +4.34 (, and the resulting) 432.69 534.95 P +0.18 (objective function values are returned in the matrix) 135.65 520.95 P +3 F +0.44 (ObjV) 385.59 520.95 P +2 F +0.18 (. The GA then enters the) 412.83 520.95 P +(generational) 135.65 506.95 T +3 F +(while) 197.93 506.95 T +2 F +( loop.) 233.91 506.95 T +1.49 (The \336rst step in the generational loop is the assignment of \336tness values to the) 135.65 480.95 P +3.02 (individuals. In this example, rank-based \336tness assignment is used as shown) 135.65 466.95 P +(below) 135.65 452.95 T +(,) 164.18 452.95 T +3 F +(FitnV = ranking\050ObjV\051;) 171.65 426.95 T +2 F +2.36 (Here, the objective function values, ObjV) 135.65 400.95 P +2.36 (, are passed to the T) 346.1 400.95 P +2.36 (oolbox function) 452.99 400.95 P +3 F +1.32 (ranking) 135.65 386.95 P +2 F +0.55 ( with no other ar) 186.02 386.95 P +0.55 (guments. The default setting for the ranking algorithm) 267.29 386.95 P +-0.1 (assume a selective pressure of 2 and linear ranking, giving the most \336t individual a) 135.65 372.95 P +1.62 (\336tness value of 2 and the least \336t individual a \336tness value of 0. Note that the) 135.65 358.95 P +1.78 (ranking algorithm assumes that the objective function is to be) 135.65 344.95 P +1 F +1.78 (minimised) 451.91 344.95 P +2 F +1.78 (. The) 505.22 344.95 P +(resulting \336tness values are returned in the vector) 135.65 330.95 T +3 F +(FitnV) 371.47 330.95 T +2 F +(.) 405.91 330.95 T +2.13 (The selection stage uses the high-level function) 135.65 304.95 P +3 F +5.1 (select) 381.37 304.95 P +2 F +2.13 ( to call the low-level) 424.55 304.95 P +(stochastic universal sampling routine,) 135.65 290.95 T +3 F +(sus) 319.87 290.95 T +2 F +(, as follows,) 341.45 290.95 T +3 F +(SelCh = select\050\325sus\325, Chrom, FitnV, GGAP\051;) 171.65 264.95 T +2 F +2.64 (After selection,) 135.65 238.95 P +3 F +6.33 (SelCh) 217.86 238.95 P +2 F +2.64 ( contains) 253.84 238.95 P +3 F +6.33 (GGAP) 305.09 238.95 P +4 F +2.64 (\264) 339.51 238.95 P +3 F +6.33 (NIND) 351.73 238.95 P +2 F +2.64 ( individuals from the original) 380.51 238.95 P +1.73 (population) 135.65 224.95 P +3 F +4.16 (Chrom) 191.68 224.95 P +2 F +1.73 (. These individuals are now recombined using the high-level) 227.67 224.95 P +(function) 135.65 210.95 T +3 F +(recombin) 178.62 210.95 T +2 F +( as shown below) 236.19 210.95 T +(.) 315.02 210.95 T +3 F +(SelCh = recombin\050\325xovsp\325, SelCh, 0.7\051;) 171.65 184.95 T +1.76 (recombin) 135.65 158.95 P +2 F +0.73 ( takes the individuals selected for reproduction,) 193.22 158.95 P +3 F +1.76 (SelCh) 428.85 158.95 P +2 F +0.73 (, and uses the) 464.83 158.95 P +-0.27 (single-point crossover routine,) 135.65 144.95 P +3 F +-0.65 (xovsp) 284.07 144.95 P +2 F +-0.27 (, to perform crossover with probability) 320.05 144.95 P +-0.27 (,) 503.78 144.95 P +0 F +-0.27 (Px) 509.5 144.95 P +2 F +-0.27 ( =) 522.16 144.95 P +-0.21 (0.7. The individuals in the input matrix) 135.65 130.95 P +3 F +-0.51 (SelCh) 325.06 130.95 P +2 F +-0.21 ( are ordered such that individuals in) 361.04 130.95 P +2.9 (odd numbered positions are crossed with the individual in the adjacent even) 135.65 116.95 P +1.66 (numbered position. If the number of individuals in) 135.65 102.95 P +3 F +3.98 (SelCh) 394.43 102.95 P +2 F +1.66 ( is odd then the last) 430.41 102.95 P +FMENDPAGE +%%EndPage: "28" 29 +%%Page: "29" 29 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-29) 513.33 61.29 T +2 12 Q +0.28 (individual is always returned uncrossed. The of) 135.65 736.95 P +0.28 (fspring produced by this crossover) 364.63 736.95 P +-0.05 (are returned in the same matrix,) 135.65 722.95 P +3 F +-0.13 (SelCh) 290.87 722.95 P +2 F +-0.05 (. The actual crossover routine used may be) 326.85 722.95 P +5.34 (changed by supplying a dif) 135.65 708.95 P +5.34 (ferent function name in the string passed to) 286.72 708.95 P +3 F +(recombin) 135.65 694.95 T +2 F +(.) 193.22 694.95 T +2.79 (Having produced a set of of) 135.65 668.95 P +2.79 (fspring, mutation may now be applied using the) 282.93 668.95 P +(mutation function) 135.65 654.95 T +3 F +(mut) 224.27 654.95 T +2 F +(:) 245.85 654.95 T +3 F +(SelCh = mut\050SelCh\051;) 171.65 628.95 T +2 F +2.71 (Again, the of) 135.65 602.95 P +2.71 (fspring are returned in the matrix) 203.8 602.95 P +3 F +6.49 (SelCh) 381.91 602.95 P +2 F +2.71 (. As no probability of) 417.89 602.95 P +-0.08 (mutation has been speci\336ed in the function call, the default value of) 135.65 588.95 P +0 F +-0.08 (Pm) 462.74 588.95 P +2 F +-0.08 ( = 0.7/) 478.73 588.95 P +0 F +-0.08 (Lind) 509.65 588.95 P +2 F +(= 0.0017, where) 135.65 574.95 T +0 F +(Lind) 216.69 574.95 T +2 F +( is the length of an individual, is assumed.) 238.68 574.95 T +-0.02 (The objective function values for the of) 135.65 548.95 P +-0.02 (fspring,) 325.16 548.95 P +3 F +-0.05 (ObjVSel) 365.12 548.95 P +2 F +-0.02 (, may now be calculated) 415.49 548.95 P +(thus:) 135.65 534.95 T +3 F +(ObjVSel = objfun1\050bs2rv\050SelCh, FieldD\051\051;) 171.65 508.95 T +2 F +0.92 (Because we have used a generation gap, the number of of) 135.65 482.95 P +0.92 (fspring is less than the) 420.71 482.95 P +1.1 (size of the population. Therefore, we must reinsert the of) 135.65 468.95 P +1.1 (fspring into the current) 418.1 468.95 P +(population. This is achieved using the reinsertion function,) 135.65 454.95 T +3 F +(reins) 420.8 454.95 T +2 F +(, as follows:) 456.78 454.95 T +3 F +([Chrom,ObjV]=reins\050Chrom, SelCh,1,1,ObjV,ObjVSel\051;) 171.65 428.95 T +2 F +0.57 (Here,) 135.65 402.95 P +3 F +1.37 (Chrom) 165.52 402.95 P +2 F +0.57 ( and) 201.5 402.95 P +3 F +1.37 (SelCh) 225.95 402.95 P +2 F +0.57 ( are matrices containing the original population and the) 261.93 402.95 P +1.36 (resulting of) 135.65 388.95 P +1.36 (fspring. The two occurrences of the numeral) 191.76 388.95 P +3 F +3.26 (1) 417.09 388.95 P +2 F +1.36 ( indicate that a single) 424.28 388.95 P +2.69 (population is used and that \336tness-based reinsertion be applied. Fitness-based) 135.65 374.95 P +3.38 (reinsertion replaces the least \336t members of) 135.65 360.95 P +3 F +8.12 (Chrom) 371.51 360.95 P +2 F +3.38 ( with the individuals in) 407.49 360.95 P +3 F +2.11 (SelCh) 135.65 346.95 P +2 F +0.88 (. The objective function values of the original population,) 171.63 346.95 P +3 F +2.11 (ObjV) 459.02 346.95 P +2 F +0.88 (, are thus) 486.26 346.95 P +2.41 (required as a parameter to) 135.65 332.95 P +3 F +5.79 (reins) 275.25 332.95 P +2 F +2.41 (. In addition, so that the objective function) 311.23 332.95 P +1.58 (values of the new population can be returned without having to re-evaluate the) 135.65 318.95 P +0.74 (objective function for the entire population, the objective values of the of) 135.65 304.95 P +0.74 (fspring,) 494.67 304.95 P +3 F +-0.64 (ObjVSel) 135.65 290.95 P +2 F +-0.27 (, are also supplied.) 186.02 290.95 P +3 F +-0.64 (reins) 277.56 290.95 P +2 F +-0.27 ( returns the new population with the of) 313.54 290.95 P +-0.27 (fspring) 497.67 290.95 P +(inserted,) 135.65 276.95 T +3 F +(Chrom) 179.62 276.95 T +2 F +(, and the objective function values for this population,) 215.6 276.95 T +3 F +(ObjV) 477.76 276.95 T +2 F +(.) 505 276.95 T +0.09 (Finally) 135.65 250.95 P +0.09 (, the generational counter) 168.86 250.95 P +0.09 (,) 290.54 250.95 P +3 F +0.21 (gen) 296.62 250.95 P +2 F +0.09 (, is incremented. The GA iterates around the) 318.21 250.95 P +0.49 (loop until) 135.65 236.95 P +3 F +1.17 (gen = MAXGEN) 185.94 236.95 P +2 F +0.49 (, in this case 300, and then terminates. The results of) 274.62 236.95 P +1.28 (the genetic optimization are contained in the matrix ObjV and the values of the) 135.65 222.95 P +(decision variables may be obtained by:) 135.65 208.95 T +3 F +(Phen = bs2rv\050Chrom, FieldD\051;) 171.65 182.95 T +FMENDPAGE +%%EndPage: "29" 30 +%%Page: "30" 30 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-30) 513.33 61.29 T +1 16 Q +(A Multi-population GA) 135.65 734.29 T +2 12 Q +3.7 (This example shows how functions from the GA T) 135.65 706.95 P +3.7 (oolbox may be used to) 408.25 706.95 P +1.76 (implement a real-valued, multi-population GA. A M) 135.65 692.95 P +2 10 Q +1.47 (A) 398.07 692.95 P +1.47 (TLAB) 404.18 692.95 P +2 12 Q +1.76 ( m-\336le script) 430.27 692.95 P +3 F +4.24 (mpga) 499.86 692.95 P +2 F +1.76 (,) 528.65 692.95 P +0.49 (supplied with the T) 135.65 678.95 P +0.49 (oolbox, implements the code described in this subsection. The) 229.23 678.95 P +2.82 (objective function chosen is that of the harvest problem [9] which is a one-) 135.65 664.95 P +(dimensional equation of growth:) 135.65 650.95 T +(,) 378.2 623.75 T +(with one equality constraint,) 135.65 595.02 T +(,) 353.47 567.81 T +0.35 (where) 135.65 539.1 P +0 F +0.35 (x) 168.29 539.1 P +0 10 Q +0.29 (0) 173.62 536.1 P +2 12 Q +0.35 ( is the initial condition of the state,) 178.62 539.1 P +0 F +0.35 (a) 350.98 539.1 P +2 F +0.35 ( is a scalar constant, and) 356.98 539.1 P +0 F +0.35 (x) 478.65 539.1 P +0 10 Q +0.29 (k) 483.97 536.1 P +4 12 Q +0.35 (\316) 491.76 539.1 P +0 F +0.35 (R) 503.65 539.1 P +2 F +0.35 (and) 514.33 539.1 P +0 F +0.25 (u) 135.65 525.1 P +0 10 Q +0.21 (k) 141.65 522.1 P +4 12 Q +0.25 (\316) 149.33 525.1 P +0 F +0.25 ( R) 157.88 525.1 P +0 10 Q +0.21 (+) 168.46 529.9 P +2 12 Q +0.25 ( are the state and nonnegative control respectively) 175.2 525.1 P +0.25 (. The objective function) 416.31 525.1 P +(is de\336ned as:) 135.65 511.1 T +(,) 375.47 471.18 T +0.04 (where) 135.65 431.93 P +0 F +0.04 (N) 167.98 431.93 P +2 F +0.04 ( is the number of control steps over which the problem is to be solved. An) 175.98 431.93 P +1.19 (m-\336le implementing this objective function,) 135.65 417.93 P +3 F +2.86 (objharv) 356.16 417.93 P +2 F +1.19 (, is supplied with the GA) 405.75 417.93 P +1.41 (T) 135.65 403.93 P +1.41 (oolbox software. Note that as this is a maximisation problem and the T) 142.14 403.93 P +1.41 (oolbox) 498.33 403.93 P +5.62 (routines are implemented to minimise, the objective function,) 135.65 389.93 P +3 F +13.48 (objharv) 479.06 389.93 P +2 F +5.62 (,) 528.65 389.93 P +-0.25 (multiplies) 135.65 375.93 P +0 F +-0.25 (J) 186.38 375.93 P +2 F +-0.25 ( by -1 to produce a minimisation problem. The initial condition is set to) 191.71 375.93 P +0 F +2.3 (x) 135.65 361.93 P +0 10 Q +1.92 (0) 140.97 358.93 P +2 12 Q +2.3 ( = 100 and the scalar is chosen as) 145.97 361.93 P +0 F +2.3 (a) 329.64 361.93 P +2 F +2.3 ( = 1.1. Additionally) 335.64 361.93 P +2.3 (, the exact optimal) 436.14 361.93 P +(solution for this problem can be determined analytically as:) 135.65 347.93 T +(.) 384.8 299.39 T +2.08 (The number of control steps for this problem is) 135.65 260.73 P +0 F +2.08 (N) 383.86 260.73 P +2 F +2.08 ( = 20, thus,) 391.86 260.73 P +3 F +4.99 (NVAR = 20) 456.91 260.73 P +2 F +2.9 (decision variables will be used, one for each control input,) 135.65 246.73 P +0 F +2.9 (u) 447.79 246.73 P +0 10 Q +2.42 (k) 453.79 243.73 P +2 12 Q +2.9 (. The decision) 458.23 246.73 P +-0.02 (variables are bounded in the range) 135.65 232.73 P +3 F +-0.04 (RANGE = [0, 200]) 303.4 232.73 P +2 F +-0.02 (, limiting the maximum) 418.41 232.73 P +0.99 (control input, at any time-step, to 200. The \336eld descriptor) 135.65 218.73 P +0.99 (,) 424.54 218.73 P +3 F +2.37 (FieldD) 431.52 218.73 P +2 F +0.99 (, describing) 474.7 218.73 P +1.46 (the decision variables may be constructed using the matrix replication function,) 135.65 204.73 P +3 F +(rep) 135.65 190.73 T +2 F +(, thus:) 157.24 190.73 T +3 F +(NVAR = 20;) 171.65 164.73 T +(RANGE = [0; 200];) 171.65 149.73 T +(FieldD = rep\050RANGE,[1,NVAR]\051;) 171.65 134.73 T +286.1 617.02 378.2 632.95 C +0 12 Q +0 X +0 K +(x) 287.1 623.75 T +0 9 Q +(k) 292.89 619.97 T +2 F +(1) 306.31 619.97 T +4 F +(+) 299.13 619.97 T +0 12 Q +(a) 329.39 623.75 T +(x) 344.39 623.75 T +4 F +(\327) 338.39 623.75 T +0 9 Q +(k) 350.17 619.97 T +0 12 Q +(u) 366.75 623.75 T +0 9 Q +(k) 373.21 619.97 T +4 12 Q +(-) 357.16 623.75 T +(=) 316.81 623.75 T +-8.35 24.95 603.65 816.95 C +310.83 561.1 353.47 577.02 C +0 12 Q +0 X +0 K +(x) 311.83 567.81 T +2 9 Q +(0) 317.61 564.05 T +0 12 Q +(x) 340.69 567.81 T +0 9 Q +(N) 346.48 564.03 T +4 12 Q +(=) 328.11 567.81 T +-8.35 24.95 603.65 816.95 C +288.83 453.93 375.47 493.1 C +0 12 Q +0 X +0 K +(J) 289.83 471.18 T +2 F +(m) 313.74 471.18 T +(a) 323.07 471.18 T +(x) 328.39 471.18 T +0 F +(u) 364.02 471.18 T +0 9 Q +(k) 370.48 467.4 T +(k) 336.35 456.88 T +2 F +(0) 351.27 456.88 T +4 F +(=) 343.34 456.88 T +0 F +(N) 336.1 485.95 T +2 F +(1) 351.53 485.95 T +4 F +(-) 344.34 485.95 T +4 18 Q +(\345) 339.64 467.97 T +4 12 Q +(=) 301.15 471.18 T +374.47 482.38 364.02 482.38 2 L +0.33 H +0 Z +N +364.02 482.38 361.02 467.54 2 L +N +361.02 467.54 359.02 471.75 2 L +N +359.02 471.75 358.02 469.65 2 L +N +-8.35 24.95 603.65 816.95 C +279.49 282.73 384.8 329.93 C +0 12 Q +0 X +0 K +(J) 280.49 299.39 T +2 9 Q +(*) 285.82 305.5 T +0 12 Q +(x) 320.47 309.69 T +2 9 Q +(0) 326.26 305.93 T +0 12 Q +(a) 338.56 309.69 T +0 9 Q +(N) 344.56 315.75 T +2 12 Q +(1) 363.14 309.69 T +4 F +(-) 353.55 309.69 T +(\050) 333.46 309.69 T +(\051) 369.74 309.69 T +2 9 Q +(2) 375.73 319.8 T +0 12 Q +(a) 317.9 287.73 T +0 9 Q +(N) 323.89 293.83 T +2 F +(1) 339.32 293.83 T +4 F +(-) 332.14 293.83 T +0 12 Q +(a) 351.62 287.73 T +2 F +(1) 370.2 287.73 T +4 F +(-) 360.62 287.73 T +(\050) 346.52 287.73 T +(\051) 376.81 287.73 T +(=) 297.31 299.39 T +317.9 301.98 382.55 301.98 2 L +0.33 H +0 Z +N +383.8 328.93 316.9 328.93 2 L +N +316.9 328.93 313.9 285.73 2 L +N +313.9 285.73 311.9 297.03 2 L +N +311.9 297.03 310.9 291.38 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "30" 31 +%%Page: "31" 31 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-31) 513.33 61.29 T +2 12 Q +1.59 (The parameters for the GA may be speci\336ed using M) 135.65 736.95 P +2 10 Q +1.32 (A) 405.4 736.95 P +1.32 (TLAB) 411.51 736.95 P +2 12 Q +1.59 ( variables. For this) 437.61 736.95 P +(example the following parameters are de\336ned:) 135.65 722.95 T +3 F +(% Def) 171.65 696.95 T +(ine GA Parameters) 207.63 696.95 T +(GGAP = 0.8;) 171.65 681.95 T +(% Generation gap) 315.65 681.95 T +(XOVR = 1;) 171.65 666.95 T +(% Crossover rate) 315.65 666.95 T +(MUTR = 1/NVAR;) 171.65 651.95 T +(% Mutation rate) 315.65 651.95 T +(MAXGEN = 1200;) 171.65 636.95 T +(% Maximum no. of generations) 315.65 636.95 T +(INSR = 0.9;) 171.65 621.95 T +(% Insertion rate) 315.65 621.95 T +(SUBPOP = 8;) 171.65 606.95 T +(% No. of subpopulations) 315.65 606.95 T +(MIGR = 0.2;) 171.65 591.95 T +(% Migration rate) 315.65 591.95 T +(MIGGEN = 20;) 171.65 576.95 T +(% No. of gens / migration) 315.65 576.95 T +(NIND = 20;) 171.65 561.95 T +(% No. of individuals / subpop) 315.65 561.95 T +2 F +1.04 (As well as the conventional GA parameters, such as generation gap \050) 135.65 535.95 P +3 F +2.5 (GGAP) 477.51 535.95 P +2 F +1.04 (\051 and) 506.3 535.95 P +3.32 (crossover rate \050) 135.65 521.95 P +3 F +7.96 (XOVR) 216.21 521.95 P +2 F +3.32 (\051, a number of other parameters associated with multi-) 244.99 521.95 P +0.71 (population GAs are de\336ned. Here,) 135.65 507.95 P +3 F +1.71 (INSR = 0.9) 306.75 507.95 P +2 F +0.71 ( speci\336es that only 90% of the) 382.13 507.95 P +4.47 (individuals produced at each generation are reinserted into the population,) 135.65 493.95 P +3 F +2.2 (SUBPOP = 8) 135.65 479.95 P +2 F +0.92 ( subpopulations are to be used with a migration rate of) 212.01 479.95 P +3 F +2.2 (MIGR =) 486.27 479.95 P +1.31 (0.2) 135.65 465.95 P +2 F +0.55 (, or 20%, between subpopulations and migration occurring at every) 157.24 465.95 P +3 F +1.31 (MIGGEN) 488.47 465.95 P +(= 20) 135.65 451.95 T +2 F +(generations. Each subpopulation contains) 171.63 451.95 T +3 F +(NIND = 20) 373.83 451.95 T +2 F +( individuals.) 438.59 451.95 T +(The functions used by the script-\336le are speci\336ed using M) 135.65 425.95 T +2 10 Q +(A) 414.46 425.95 T +(TLAB) 420.57 425.95 T +2 12 Q +( strings:) 446.66 425.95 T +3 F +(% Specify other functions as strings) 171.65 399.95 T +(SEL_F = \325sus\325;) 171.65 384.95 T +(% Name of selection function) 315.65 384.95 T +(XOV_F = \325recdis\325;) 171.65 369.95 T +(% Name of recombination fun.) 315.65 369.95 T +(MUT_F = \325mutbga\325;) 171.65 354.95 T +(% Name of mutation function) 315.65 354.95 T +(OBJ_F = \325objharv\325;) 171.65 339.95 T +(% Name of objective function) 315.65 339.95 T +2 F +3.51 (Because we are using discrete recombination,) 135.65 313.95 P +3 F +8.42 (recdis) 378.85 313.95 P +2 F +3.51 (, for the breeding of) 422.03 313.95 P +(of) 135.65 299.95 T +(fspring, the crossover rate is not used and, hence) 145.42 299.95 T +3 F +(XOVR = 1) 381.57 299.95 T +2 F +( above.) 439.14 299.95 T +2.11 (The initial population is created using the function) 135.65 273.95 P +3 F +5.07 (crtrp) 397.73 273.95 P +2 F +2.11 ( and the generation) 433.71 273.95 P +(counter) 135.65 259.95 T +(,) 171.14 259.95 T +3 F +(gen) 177.13 259.95 T +2 F +(, set to zero:) 198.72 259.95 T +3 F +(Chrom = crtrp\050SUBPOP*NIND,FieldD\051;) 171.65 233.95 T +(gen = 0;) 171.65 218.95 T +2 F +4.09 (This will consist of) 135.65 192.95 P +3 F +9.82 (SUBPOP) 247.3 192.95 P +4 F +4.09 (\264) 297.57 192.95 P +3 F +9.82 (NIND) 311.25 192.95 P +2 F +4.09 ( individuals with individual decision) 340.03 192.95 P +2.1 (variables chosen uniformly at random in the range speci\336ed by) 135.65 178.95 P +3 F +5.03 (FieldD) 461.73 178.95 P +2 F +2.1 (. The) 504.9 178.95 P +3 F +-0.02 (Chrom) 135.65 164.95 P +2 F +-0.01 ( matrix contains all of the subpopulations and the objective function values) 171.63 164.95 P +(for all the individuals in all the subpopulations may be calculated directly) 135.65 150.95 T +(,) 487.64 150.95 T +3 F +(ObjV = feval\050OBJ_F, Chrom\051;) 171.65 124.95 T +FMENDPAGE +%%EndPage: "31" 32 +%%Page: "32" 32 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-32) 513.33 61.29 T +2 12 Q +0 (using the M) 135.65 736.95 P +2 10 Q +0 (A) 192.96 736.95 P +0 (TLAB) 199.07 736.95 P +3 12 Q +0.01 (feval) 228.16 736.95 P +2 F +0 ( command.) 264.14 736.95 P +3 F +0.01 (feval) 320.45 736.95 P +2 F +0 ( performs function evaluation taking) 356.42 736.95 P +-0.19 (the \336rst input ar) 135.65 722.95 P +-0.19 (gument, in this case the name of our objective function,) 211.15 722.95 P +3 F +-0.46 (objharv) 479.06 722.95 P +2 F +-0.19 (,) 528.65 722.95 P +-0.13 (contained in) 135.65 708.95 P +3 F +-0.3 (OBJ_F) 197.35 708.95 P +2 F +-0.13 (, as the function to be evaluated and calls that function with all) 232.37 708.95 P +(the remaining parameters as its input ar) 135.65 694.95 T +(guments. In this case, the function call is:) 324.63 694.95 T +3 F +(ObjV = objharv\050Chrom\051;) 171.65 668.95 T +2 F +0.28 (As a real-valued coding is used, there is no need to convert the chromosomes into) 135.65 642.95 P +2.3 (a phenotypic representation. Like the previous example, the GA now enters a) 135.65 628.95 P +(generational) 135.65 614.95 T +3 F +(while) 197.93 614.95 T +2 F +( loop.) 233.91 614.95 T +0.39 (The M) 135.65 588.95 P +2 10 Q +0.33 (A) 168.35 588.95 P +0.33 (TLAB) 174.46 588.95 P +2 12 Q +0.39 ( code for the generational loop of the multi-population GA is shown) 200.55 588.95 P +(in Fig. 1) 135.65 574.95 T +(1 below) 175.53 574.95 T +(.) 213.05 574.95 T +63.65 96.95 531.65 744.95 C +136.44 123.46 531.65 570.95 C +142.71 164.04 525.38 558 R +7 X +0 K +V +3 12 Q +0 X +(% Generational loop) 142.71 550 T +(while gen < MAXGEN,) 142.71 536 T +(% Fitness assignment to whole population) 167.91 514 T +(FitnV = ranking\050ObjV,2,SUBPOP\051;) 167.91 500 T +(% Select individuals from population) 167.91 478 T +-0.39 (SelCh = select\050SEL_F, Chrom, FitnV, GGAP, SUBPOP\051;) 167.91 464 P +(% Recombine selected individuals) 167.91 442 T +(SelCh=recombin\050XOV_F, SelCh, XOVR, SUBPOP\051;) 167.91 428 T +(% Mutate offspring) 167.91 406 T +(SelCh = mutate\050MUT_F,SelCh,FieldD,[MUTR],SUBPOP\051;) 167.91 392 T +(% Calculate objective function for offsprings) 167.91 370 T +(ObjVOff = feval\050OBJ_F,SelCh\051;) 167.91 356 T +(% Insert best offspring replacing worst parents) 167.91 334 T +([Chrom, ObjV] = reins\050Chrom, SelCh, SUBPOP, ...) 167.91 320 T +([1 INSR], ObjV, ObjVOff\051;) 203.89 306 T +(% Increment counter) 167.91 284 T +(gen=gen+1;) 167.91 270 T +(% Migrate individuals between subpopulations) 167.91 248 T +(if \050rem\050gen,MIGGEN\051 == 0\051) 167.91 234 T +([Chrom, ObjV] = ...) 189.49 220 T +-0.47 (migrate\050Chrom, SUBPOP, [MIGR, 1, 1], ObjV\051;) 218.28 206 P +(end) 167.91 192 T +(end) 142.71 170 T +139.16 129.55 528.92 564.86 R +0.5 H +2 Z +N +5 F +(Figure 1) 196.93 138.85 T +(1: Generational Loop of a Multipopulation GA) 239.25 138.85 T +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "32" 33 +%%Page: "33" 33 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-33) 513.33 61.29 T +2 12 Q +2.91 (The \336rst step of the generational loop is the assignment of \336tness values to) 135.65 736.95 P +(individuals:) 135.65 722.95 T +3 F +(FitnV = ranking\050ObjV, 2, SUBPOP\051;) 171.65 696.95 T +2 F +1.22 (Because we are using multiple subpopulations,) 135.65 670.95 P +3 F +2.92 (ranking) 371.15 670.95 P +2 F +1.22 ( requires us to specify) 421.52 670.95 P +2.2 (the selective pressure required, here we use a selective pressure of 2, and the) 135.65 656.95 P +0.96 (number of subpopulations,) 135.65 642.95 P +3 F +2.3 (SUBPOP) 269.77 642.95 P +2 F +0.96 (. Each subpopulation\325) 311.62 642.95 P +0.96 (s individuals\325 objective) 417.8 642.95 P +2.68 (values in) 135.65 628.95 P +3 F +6.43 (ObjV) 186.97 628.95 P +2 F +2.68 ( are ranked separately and the resulting sets of \336tness values) 215.76 628.95 P +(returned in the vector) 135.65 614.95 T +3 F +(FitnV) 241.56 614.95 T +2 F +(.) 275.99 614.95 T +1.97 (W) 135.65 588.95 P +1.97 (ithin each subpopulation, individuals are selected for breeding independently) 146.49 588.95 P +(using the high-level selection function,) 135.65 574.95 T +3 F +(select) 325.53 574.95 T +2 F +(:) 368.7 574.95 T +3 F +(SelCh = select\050SEL_F, Chrom, FitnV, GGAP, SUBPOP\051;) 171.65 548.95 T +5.96 (select) 135.65 522.95 P +2 F +2.48 ( calls the low-level selection function,) 178.82 522.95 P +3 F +5.96 (SEL_F = \325sus\325) 379.26 522.95 P +2 F +2.48 ( for each) 484.73 522.95 P +0.23 (subpopulation and builds the matrix) 135.65 508.95 P +3 F +0.56 (SelCh) 312.38 508.95 P +2 F +0.23 ( containing all the pairs of individuals) 348.36 508.95 P +0.24 (to be recombined. Like the previous example, the generation gap,) 135.65 494.95 P +3 F +0.59 (GGAP = 0.8) 455.52 494.95 P +2 F +0.24 (,) 528.65 494.95 P +2.22 (means that 0.8) 135.65 480.95 P +4 F +2.22 (\264) 214.92 480.95 P +2 F +2.22 ( 20 = 16,) 221.5 480.95 P +3 F +5.32 (GGAP) 276.11 480.95 P +4 F +2.22 (\264) 310.11 480.95 P +3 F +5.32 (NIND) 321.92 480.95 P +2 F +2.22 (, individuals are selected from each) 350.7 480.95 P +-0.03 (subpopulation. Thus,) 135.65 466.95 P +3 F +-0.07 (SelCh) 239.54 466.95 P +2 F +-0.03 ( contains a total of) 275.52 466.95 P +3 F +-0.07 (GGAP) 366.98 466.95 P +4 F +-0.03 (\264) 398.73 466.95 P +3 F +-0.07 (NIND) 408.29 466.95 P +4 F +-0.03 (\264) 440.04 466.95 P +3 F +-0.07 (SUBPOP) 449.59 466.95 P +-0.07 (= 128) 495.74 466.95 P +2 F +(individuals.) 135.65 452.95 T +0.04 (In a similar manner) 135.65 426.95 P +0.04 (, the high-level recombination function,) 228.89 426.95 P +3 F +0.1 (recombin) 422.64 426.95 P +2 F +0.04 (, is used to) 480.21 426.95 P +(recombine the pairs of individuals within each subpopulation of) 135.65 412.95 T +3 F +(SelCh) 445.11 412.95 T +2 F +(:) 481.09 412.95 T +3 F +(SelCh = recombin\050XOV_F, SelCh, XOVR, SUBPOP\051;) 171.65 386.95 T +2 F +5.24 (The recombination function,) 135.65 360.95 P +3 F +12.58 (XOV_F = \325recdis\325) 291.28 360.95 P +2 F +5.24 (, performs discrete) 431.57 360.95 P +1.73 (recombination between pairs of individuals for each subpopulation. As discrete) 135.65 346.95 P +0.6 (recombination does not require the speci\336cation of a conventional crossover rate,) 135.65 332.95 P +(the variable) 135.65 318.95 T +3 F +(XOVR = 1.0) 194.93 318.95 T +2 F +( is used only for compatibility) 266.89 318.95 T +(.) 410.37 318.95 T +(The of) 135.65 292.95 T +(fspring are now mutated:) 167.07 292.95 T +3 F +(SelCh = mutate\050MUT_F,SelCh,FieldD,MUTR,SUBPOP\051;) 171.65 266.95 T +2 F +0.16 (Here, the breeder genetic algorithm mutation function,) 135.65 240.95 P +3 F +0.39 (MUT_F = \325mutbga\325) 401.58 240.95 P +2 F +0.16 (, is) 517.49 240.95 P +2 (called using the high-level mutation routine,) 135.65 226.95 P +3 F +4.81 (mutate) 363.2 226.95 P +2 F +2 (, with a mutation rate of) 406.38 226.95 P +3 F +1.94 (MUTR = 1/NIND = 0.05) 135.65 212.95 P +2 F +0.81 (. The breeder genetic algorithm mutation function) 287.31 212.95 P +2.68 (requires the \336eld descriptor) 135.65 198.95 P +2.68 (,) 274.78 198.95 P +3 F +6.43 (FieldD) 283.45 198.95 P +2 F +2.68 (, so that the result of mutation will not) 326.63 198.95 P +(produce values outside the bounds of the decision variables.) 135.65 184.95 T +0.23 (The objective values of all the of) 135.65 158.95 P +0.23 (fspring,) 294.7 158.95 P +3 F +0.55 (ObjVOff) 334.9 158.95 P +2 F +0.23 ( may now be calculated, again) 385.28 158.95 P +(using) 135.65 144.95 T +3 F +(feval) 164.64 144.95 T +2 F +(:) 200.62 144.95 T +3 F +(ObjVOff = feval\050OBJ_F, SelCh\051;) 171.65 118.95 T +FMENDPAGE +%%EndPage: "33" 34 +%%Page: "34" 34 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-34) 513.33 61.29 T +2 12 Q +(Of) 135.65 736.95 T +(fspring may now be reinserted into the appropriate subpopulations:) 148.09 736.95 T +3 F +([Chrom, ObjV] = reins\050Chrom, SelCh, SUBPOP,...) 171.65 710.95 T +([1, INSR], ObjV, ObjVOff\051;) 337.16 695.95 T +2 F +1.72 (Fitness-based reinsertion is used, but the addition of the extra parameter to the) 135.65 669.95 P +1.81 (fourth ar) 135.65 655.95 P +1.81 (gument of) 178.87 655.95 P +3 F +4.34 (reins) 234.46 655.95 P +2 F +1.81 ( speci\336es an insertion rate of) 270.44 655.95 P +3 F +4.34 (INSR = 0.9) 421.87 655.95 P +2 F +1.81 (. This) 502.52 655.95 P +3.04 (means that for each subpopulation the least-\336t 10% of the of) 135.65 641.95 P +3.04 (fspring are not) 455.62 641.95 P +(reinserted.) 135.65 627.95 T +4.78 (Individuals in Multi-population GAs migrate between populations at some) 135.65 601.95 P +2.63 (interval. The T) 135.65 587.95 P +2.63 (oolbox routine) 211.69 587.95 P +3 F +6.32 (migrate) 290.25 587.95 P +2 F +2.63 ( is used to swap individuals between) 340.62 587.95 P +1.84 (subpopulations according to some migration strategy) 135.65 573.95 P +1.84 (. In this example, at every) 398.23 573.95 P +3 F +(MIGGEN = 20) 135.65 559.95 T +2 F +( generations, migration takes place between subpopulations.) 214.8 559.95 T +3 F +(% Migration between subpopulations) 171.65 533.95 T +(if\050rem\050gen, MIGGEN\051 == 0\051) 171.65 518.95 T +([Chrom, ObjV] = migrate\050Chrom, SUBPOP, ...) 200.43 503.95 T +([MIGR, 1, 1], ObjV\051;) 380.33 488.95 T +(end) 171.65 473.95 T +2 F +1.79 (Here, the most \336t 20%,) 135.65 447.95 P +3 F +4.29 (MIGR = 0.2) 258.85 447.95 P +2 F +1.79 (, of each subpopulation is selected for) 339.39 447.95 P +3.37 (migration. Nearest neighbour subpopulations then exchange these individuals) 135.65 433.95 P +2.79 (amongst their subpopulations, uniformly reinserting the immigrant individuals) 135.65 419.95 P +0.32 (\050see the) 135.65 405.95 P +0 F +0.32 (Support for Multiple Populations) 176.26 405.95 P +2 F +0.32 ( Section\051. The return matrix) 336.83 405.95 P +3 F +0.78 (Chrom) 475.02 405.95 P +2 F +0.32 ( and) 511.01 405.95 P +0.24 (vector) 135.65 391.95 P +3 F +0.58 (ObjV) 168.86 391.95 P +2 F +0.24 ( re\337ect the changes of individuals in the subpopulations as a result of) 197.64 391.95 P +(migration.) 135.65 377.95 T +1.39 (The GA iterates around the generational loop until) 135.65 351.95 P +3 F +3.33 (gen = MAXGEN) 391.9 351.95 P +2 F +1.39 ( and then) 484.91 351.95 P +1.41 (terminates. Fig. 12 shows a typical solution of the harvest problem obtained by) 135.65 337.95 P +3 F +(mpga) 135.65 323.95 T +2 F +(.) 164.43 323.95 T +63.65 96.95 531.65 744.95 C +133.38 101.21 531.65 319.95 C +0 77 211 550 590 191.56 153.49 240.81 153.36 FMBEGINEPSF +%%BeginDocument: +%!PS-Adobe-2.0 EPSF-1.2 +%%Creator: MATLAB, The Mathworks, Inc. +%%Title: MATLAB graph +%%CreationDate: 04/13/94 22:48:14 +%%DocumentFonts: Times-Roman +%%DocumentNeededFonts: Times-Roman +%%DocumentProcessColors: Cyan Magenta Yellow Black +%%Pages: 1 +%%BoundingBox: 77 211 550 590 +%%EndComments + +%%BeginProlog + +% MathWorks dictionary +/MathWorks 120 dict begin + +% definition operators +/bdef {bind def} bind def +/ldef {load def} bind def +/xdef {exch def} bdef +/xstore {exch store} bdef + +% operator abbreviations +/c /clip ldef +/cc /concat ldef +/cp /closepath ldef +/gr /grestore ldef +/gs /gsave ldef +/mt /moveto ldef +/np /newpath ldef +/cm /currentmatrix ldef +/sm /setmatrix ldef +/rc {rectclip} bdef 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+%%BeginObject: graph1 1 +bplot + +/dpi2point 12 def +portraitMode 0216 7344 csm + + 710 260 5677 4549 MR c np +76 dict begin %Colortable dictionary +/c0 { 0 0 0 sc} bdef +/c1 { 1 1 1 sc} bdef +/c2 { 1 0 0 sc} bdef +/c3 { 0 1 0 sc} bdef +/c4 { 0 0 1 sc} bdef +/c5 { 1 1 0 sc} bdef +/c6 { 1 0 1 sc} bdef +/c7 { 0 1 1 sc} bdef + +/Helvetica 144 FMS + +c1 + 0 0 6917 5187 PR +6 w +DO +4 w +SO +6 w +c0 + 899 4615 mt 6258 4615 L + 899 389 mt 6258 389 L + 899 4615 mt 899 389 L +6258 4615 mt 6258 389 L + 899 4615 mt 899 4615 L +6258 4615 mt 6258 4615 L + 899 4615 mt 6258 4615 L + 899 4615 mt 899 389 L + 899 4615 mt 899 4615 L + 899 4615 mt 899 4561 L + 899 389 mt 899 443 L + 859 4776 mt +(0) s +1435 4615 mt 1435 4561 L +1435 389 mt 1435 443 L +1395 4776 mt +(2) s +1971 4615 mt 1971 4561 L +1971 389 mt 1971 443 L +1931 4776 mt +(4) s +2507 4615 mt 2507 4561 L +2507 389 mt 2507 443 L +2467 4776 mt +(6) s +3043 4615 mt 3043 4561 L +3043 389 mt 3043 443 L +3003 4776 mt +(8) s +3579 4615 mt 3579 4561 L +3579 389 mt 3579 443 L +3499 4776 mt +(10) s +4114 4615 mt 4114 4561 L +4114 389 mt 4114 443 L +4034 4776 mt +(12) s +4650 4615 mt 4650 4561 L +4650 389 mt 4650 443 L +4570 4776 mt +(14) s +5186 4615 mt 5186 4561 L +5186 389 mt 5186 443 L +5106 4776 mt +(16) s +5722 4615 mt 5722 4561 L +5722 389 mt 5722 443 L +5642 4776 mt +(18) s +6258 4615 mt 6258 4561 L +6258 389 mt 6258 443 L +6178 4776 mt +(20) s + 899 4615 mt 953 4615 L +6258 4615 mt 6204 4615 L + 792 4668 mt +(0) s + 899 3911 mt 953 3911 L +6258 3911 mt 6204 3911 L + 712 3964 mt +(10) s + 899 3206 mt 953 3206 L +6258 3206 mt 6204 3206 L + 712 3259 mt +(20) s + 899 2502 mt 953 2502 L +6258 2502 mt 6204 2502 L + 712 2555 mt +(30) s + 899 1798 mt 953 1798 L +6258 1798 mt 6204 1798 L + 712 1851 mt +(40) s + 899 1093 mt 953 1093 L +6258 1093 mt 6204 1093 L + 712 1146 mt +(50) s + 899 389 mt 953 389 L +6258 389 mt 6204 389 L + 712 442 mt +(60) s + 899 4615 mt 6258 4615 L + 899 389 mt 6258 389 L + 899 4615 mt 899 389 L +6258 4615 mt 6258 389 L + 899 389 mt 899 389 L +6258 389 mt 6258 389 L +gs 899 389 5360 4227 MR c np +268 -498 268 -691 268 -535 268 -415 268 -274 268 -381 268 -226 268 -159 +268 -204 267 -157 268 -95 268 -80 268 -95 268 -56 268 -33 268 -59 +268 -34 268 -28 268 -21 1167 4500 20 MP stroke +gr +gs 0 0 256 192 MR c np + +end + +eplot +%%EndObject graph 1 + +epage +end + +showpage + +%%Trailer +%%EOF + +%%EndDocument +FMENDEPSF +0 12 Q +0 X +0 K +(u) 334.85 146.66 T +0 10 Q +(k) 340.85 143.66 T +0 12 Q +(J) 232.65 228.4 T +5 F +(Figure 12: Optimal Solution Obtained by) 214.83 124 T +6 F +(mpga) 421.42 124 T +137.63 114.44 527.4 313.33 R +0.5 H +2 Z +N +63.65 96.95 531.65 744.95 C +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "34" 35 +%%Page: "35" 35 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-35) 513.33 61.29 T +2 12 Q +0.02 (Again, like the previous example, the results of the GA search are contained in the) 135.65 736.95 P +0.13 (matrix) 135.65 722.95 P +3 F +0.31 (ObjV) 170.09 722.95 P +2 F +0.13 (. The objective value and index of the best individual are found using) 197.33 722.95 P +(the function) 135.65 708.95 T +3 F +(min) 196.27 708.95 T +2 F +(, for example:) 217.86 708.95 T +3 F +([Y, I] = min\050ObjV\051) 171.65 682.95 T +(Y =) 171.65 667.95 T +(-73.2370) 200.43 652.95 T +(I =) 171.65 637.95 T +(50) 200.43 622.95 T +2 F +0.87 (Remembering that the sign of the objective function has been changed to form a) 135.65 596.95 P +0.99 (minimisation problem, these results correspond to an objective function value of) 135.65 582.95 P +2.46 (73.2370. The exact solution is given as 73.2376. The GA optimal solution is) 135.65 568.95 P +1.59 (therefore accurate within a 10) 135.65 554.95 P +2 10 Q +1.32 (-5) 285.2 559.75 P +2 12 Q +1.59 (error bound on the exact optimal solution. The) 297.35 554.95 P +(chromosome values are displayed in Fig. 12 using:) 135.65 540.95 T +3 F +(plot\050Chrom\050I,:\051\051) 171.65 514.95 T +FMENDPAGE +%%EndPage: "35" 36 +%%Page: "36" 36 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-36) 513.33 61.29 T +1 16 Q +(Demonstration Scripts) 135.65 734.29 T +2 12 Q +-0.03 (A number of test functions have been implemented for use with the GA script \336les) 135.65 706.95 P +4.04 (supplied with the T) 135.65 692.95 P +4.04 (oolbox. These test functions are supplied in a separate) 239.87 692.95 P +1.62 (directory) 135.65 678.95 P +1.62 (,) 178.16 678.95 P +3 F +3.89 (test_fns) 185.78 678.95 P +2 F +1.62 (, from the main demonstrations and T) 243.35 678.95 P +1.62 (oolbox routines and) 433.13 678.95 P +1.58 (are accompanied by a postscript \336le,) 135.65 664.95 P +3 F +3.79 (test_fns.ps) 323.33 664.95 P +2 F +1.58 (, giving full details of the) 402.48 664.95 P +1.23 (problems implemented. The T) 135.65 650.95 P +1.23 (able below summarises the test functions supplied) 283.74 650.95 P +(with the T) 135.65 636.95 T +(oolbox.) 184.11 636.95 T +(No.) 179.02 604.95 T +(m-\336le name) 232.83 604.95 T +(Description) 379.47 604.95 T +(1) 163.25 580.95 T +3 F +(objfun1) 224.45 580.95 T +2 F +(De Jong\325) 310.85 580.95 T +(s function 1) 353.82 580.95 T +(2) 163.25 558.95 T +3 F +(objfun1a) 224.45 558.95 T +2 F +(axis parallel hyper) 310.85 558.95 T +(-ellipsoid) 399.2 558.95 T +(3) 163.25 536.95 T +3 F +(objfun1b) 224.45 536.95 T +2 F +(rotated hyper) 310.85 536.95 T +(-ellipsoid) 374.22 536.95 T +(4) 163.25 514.95 T +3 F +(objfun2) 224.45 514.95 T +2 F +(Rosenbrock\325) 310.85 514.95 T +(s valley \050banana function\051) 371.48 514.95 T +(5) 163.25 492.95 T +3 F +(objfun6) 224.45 492.95 T +2 F +(Rastrigin\325) 310.85 492.95 T +(s function) 358.16 492.95 T +(6) 163.25 470.95 T +3 F +(objfun7) 224.45 470.95 T +2 F +(Schwefel\325) 310.85 470.95 T +(s function) 358.81 470.95 T +(7) 163.25 448.95 T +3 F +(objfun8) 224.45 448.95 T +2 F +(Griewangk\325) 310.85 448.95 T +(s function) 367.47 448.95 T +(8) 163.25 426.95 T +3 F +(objfun9) 224.45 426.95 T +2 F +(sum of dif) 310.85 426.95 T +(ferent powers) 359.94 426.95 T +(9) 163.25 404.95 T +3 F +(objdopi) 224.45 404.95 T +2 F +(double integrator) 310.85 404.95 T +(10) 163.25 382.95 T +3 F +(objharv) 224.45 382.95 T +2 F +(harvest problem) 310.85 382.95 T +(1) 163.25 360.95 T +(1) 168.8 360.95 T +3 F +(objlinq) 224.45 360.95 T +2 F +(discrete linear) 310.85 360.95 T +(-quadratic problem) 378.21 360.95 T +(12) 163.25 338.95 T +3 F +(objlinq2) 224.45 338.95 T +2 F +(continuous linear) 310.85 338.95 T +(-quadratic problem) 393.55 338.95 T +(13) 163.25 316.95 T +3 F +(objpush) 224.45 316.95 T +2 F +(push-cart problem) 310.85 316.95 T +157.25 620.7 157.25 309.2 2 L +V +0.5 H +0 Z +N +218.45 621.2 218.45 308.7 2 L +V +N +304.85 621.2 304.85 308.7 2 L +V +N +510.05 620.7 510.05 309.2 2 L +V +N +157 620.95 510.3 620.95 2 L +V +N +157.5 596.2 509.8 596.2 2 L +V +N +157.5 593.7 509.8 593.7 2 L +V +N +157 572.95 510.3 572.95 2 L +V +N +157 550.95 510.3 550.95 2 L +V +N +157 528.95 510.3 528.95 2 L +V +N +157 506.95 510.3 506.95 2 L +V +N +157 484.95 510.3 484.95 2 L +V +N +157 462.95 510.3 462.95 2 L +V +N +157 440.95 510.3 440.95 2 L +V +N +157 418.95 510.3 418.95 2 L +V +2 H +N +157 396.95 510.3 396.95 2 L +V +0.5 H +N +157 374.95 510.3 374.95 2 L +V +N +157 352.95 510.3 352.95 2 L +V +N +157 330.95 510.3 330.95 2 L +V +N +157 308.95 510.3 308.95 2 L +V +N +FMENDPAGE +%%EndPage: "36" 37 +%%Page: "37" 37 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-37) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(Refer) 63.65 732.95 T +(ences) 106.27 732.95 T +2 12 Q +2.36 ([1] D. E. Goldber) 135.65 694.95 P +2.36 (g,) 226.77 694.95 P +0 F +2.36 (Genetic Algorithms in Sear) 241.12 694.95 P +2.36 (ch, Optimization and Machine) 378.67 694.95 P +(Learning) 150.05 680.95 T +2 F +(, Addison W) 194.03 680.95 T +(esley Publishing Company) 254.03 680.95 T +(, January 1989.) 381.86 680.95 T +1.14 ([2] C. L. Karr) 135.65 658.95 P +1.14 (, \322Design of an Adaptive Fuzzy Logic Controller Using a Genetic) 204.85 658.95 P +(Algorithm\323,) 150.05 644.95 T +0 F +(Pr) 211.35 644.95 T +(oc. ICGA 4) 222.9 644.95 T +2 F +(, pp. 450-457, 1991.) 277.19 644.95 T +1.8 ([3] R. B. Holstien,) 135.65 622.95 P +0 F +1.8 (Arti\336cial Genetic Adaptation in Computer Contr) 234.46 622.95 P +1.8 (ol Systems) 476.55 622.95 P +2 F +1.8 (,) 528.65 622.95 P +7.26 (PhD Thesis, Department of Computer and Communication Sciences,) 150.05 608.95 P +(University of Michigan, Ann Arbor) 150.05 594.95 T +(, 1971.) 320.45 594.95 T +0.67 ([4] R. A. Caruana and J. D. Schaf) 135.65 572.95 P +0.67 (fer) 301.64 572.95 P +0.67 (, \322Representation and Hidden Bias: Gray vs.) 314.47 572.95 P +(Binary Coding\323,) 150.05 558.95 T +0 F +(Pr) 232.34 558.95 T +(oc. 6) 243.88 558.95 T +274.98 562.79 267.2 562.79 2 L +V +0.48 H +0 Z +N +0 10 Q +(th) 267.2 563.75 T +0 12 Q +( Int. Conf. Machine Learning) 274.98 558.95 T +2 F +(, pp153-161, 1988.) 415.56 558.95 T +2.14 ([5] W) 135.65 536.95 P +2.14 (. E. Schmitendor) 164.99 536.95 P +2.14 (gf, O. Shaw) 249.67 536.95 P +2.14 (, R. Benson and S. Forrest, \322Using Genetic) 310.46 536.95 P +1.16 (Algorithms for Controller Design: Simultaneous Stabilization and Eigenvalue) 150.05 522.95 P +4.21 (Placement in a Region\323,) 150.05 508.95 P +0 F +4.21 (T) 286.49 508.95 P +4.21 (echnical Report No. CS92-9) 292.05 508.95 P +2 F +4.21 (, Dept. Computer) 439.94 508.95 P +(Science, College of Engineering, University of New Mexico, 1992.) 150.05 494.95 T +1.52 ([6] M. F) 135.65 472.95 P +1.52 (. Bramlette, \322Initialization, Mutation and Selection Methods in Genetic) 178.04 472.95 P +(Algorithms for Function Optimization\323,) 150.05 458.95 T +0 F +(Pr) 344.94 458.95 T +(oc ICGA 4) 356.49 458.95 T +2 F +(, pp. 100-107, 1991.) 407.79 458.95 T +0.31 ([7] C. B. Lucasius and G. Kateman, \322T) 135.65 436.95 P +0.31 (owards Solving Subset Selection Problems) 324.51 436.95 P +2.37 (with the Aid of the Genetic Algorithm\323, In) 150.05 422.95 P +0 F +2.37 (Parallel Pr) 377.18 422.95 P +2.37 (oblem Solving fr) 433.41 422.95 P +2.37 (om) 516.99 422.95 P +2.89 (Natur) 150.05 408.95 P +2.89 (e 2) 177.6 408.95 P +2 F +2.89 (, R. M\212nner and B. Manderick, \050Eds.\051, pp. 239-247, Amsterdam:) 194.81 408.95 P +(North-Holland, 1992.) 150.05 394.95 T +2.88 ([8] A. H. W) 135.65 372.95 P +2.88 (right, \322Genetic Algorithms for Real Parameter Optimization\323, In) 201.41 372.95 P +0 F +-0.29 (Foundations of Genetic Algorithms) 150.05 358.95 P +2 F +-0.29 (, J. E. Rawlins \050Ed.\051, Mor) 318.74 358.95 P +-0.29 (gan Kaufmann, pp.) 440.31 358.95 P +(205-218, 1991.) 150.05 344.95 T +-0.01 ([9] Z. Michalewicz,) 135.65 322.95 P +0 F +-0.01 (Genetic Algorithms + Data Structur) 233.88 322.95 P +-0.01 (es = Evolution Pr) 407.41 322.95 P +-0.01 (ograms) 492.67 322.95 P +2 F +-0.01 (,) 528.65 322.95 P +(Springer V) 150.05 308.95 T +(erlag, 1992.) 201.68 308.95 T +4.12 ([10] T) 135.65 286.95 P +4.12 (. B\212ck, F) 169.19 286.95 P +4.12 (. Hof) 219.77 286.95 P +4.12 (fmeister and H.-P) 248.32 286.95 P +4.12 (. Schwefel, \322A Survey of Evolution) 340.17 286.95 P +(Strategies\323,) 150.05 272.95 T +0 F +(Pr) 208.67 272.95 T +(oc. ICGA 4) 220.22 272.95 T +2 F +(, pp. 2-10, 1991.) 274.52 272.95 T +1.27 ([1) 135.65 250.95 P +1.27 (1] J. J. Grefenstette, \322Incorporating Problem Speci\336c Knowledge into Genetic) 145.2 250.95 P +1.83 (Algorithms\323, In) 150.05 236.95 P +0 F +1.83 (Genetic Algorithms and Simulated Annealing) 232.66 236.95 P +2 F +1.83 (, pp. 42-60, L.) 457.86 236.95 P +(Davis \050Ed.\051, Mor) 150.05 222.95 T +(gan Kaufmann, 1987.) 231.77 222.95 T +0.89 ([12] D. Whitley) 135.65 200.95 P +0.89 (, K. Mathias and P) 212.93 200.95 P +0.89 (. Fitzhorn, \322Delta Coding: An Iterative Search) 304.45 200.95 P +(Strategy for Genetic Algorithms\323,) 150.05 186.95 T +0 F +(Pr) 316.27 186.95 T +(oc. ICGA 4) 327.81 186.95 T +2 F +(, pp. 77-84, 1991.) 382.11 186.95 T +1.8 ([13] K. A. De Jong,) 135.65 164.95 P +0 F +1.8 (Analysis of the Behaviour of a Class of Genetic Adaptive) 242.59 164.95 P +4.64 (Systems) 150.05 150.95 P +2 F +4.64 (, PhD Thesis, Dept. of Computer and Communication Sciences,) 188.02 150.95 P +(University of Michigan, Ann Arbor) 150.05 136.95 T +(, 1975.) 320.45 136.95 T +2.09 ([14] J. E. Baker) 135.65 114.95 P +2.09 (, \322Adaptive Selection Methods for Genetic Algorithms\323,) 217.03 114.95 P +0 F +2.09 (Pr) 505.78 114.95 P +2.09 (oc.) 517.33 114.95 P +(ICGA 1) 150.05 100.95 T +2 F +(, pp. 101-1) 187.02 100.95 T +(1) 238.55 100.95 T +(1, 1985.) 244.1 100.95 T +FMENDPAGE +%%EndPage: "37" 38 +%%Page: "38" 38 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-38) 513.33 61.29 T +2 12 Q +-0.08 ([15] J. E. Baker) 135.65 736.95 P +-0.08 (, \322Reducing bias and inef) 210.55 736.95 P +-0.08 (\336ciency in the selection algorithm\323,) 331.61 736.95 P +0 F +-0.08 (Pr) 505.78 736.95 P +-0.08 (oc.) 517.33 736.95 P +(ICGA 2) 150.05 722.95 T +2 F +(, pp. 14-21, 1987.) 187.02 722.95 T +0.71 ([16] L. Booker) 135.65 700.95 P +0.71 (, \322Improving search in genetic algorithms,\323 In) 208.2 700.95 P +0 F +0.71 (Genetic Algorithms) 437.33 700.95 P +4.04 (and Simulated Annealing) 150.05 686.95 P +2 F +4.04 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 279.4 686.95 P +4.04 (gan Kaufmann) 456.66 686.95 P +(Publishers, 1987.) 150.05 672.95 T +0 ([17] W) 135.65 650.95 P +0 (. M. Spears and K. A. De Jong, \322An Analysis of Multi-Point Crossover\323, In) 168.85 650.95 P +0 F +(Foundations of Genetic Algorithms) 150.05 636.95 T +2 F +(, J. E. Rawlins \050Ed.\051, pp. 301-315, 1991.) 319.62 636.95 T +0.66 ([18] G. Syswerda, \322Uniform crossover in genetic algorithms\323, Proc. ICGA 3, pp.) 135.65 614.95 P +(2-9, 1989.) 150.05 600.95 T +0.46 ([19] W) 135.65 578.95 P +0.46 (. M. Spears and K. A. De Jong, \322On the V) 169.31 578.95 P +0.46 (irtues of Parameterised Uniform) 375.38 578.95 P +(Crossover\323,) 150.05 564.95 T +0 F +(Pr) 210 564.95 T +(oc. ICGA 4) 221.55 564.95 T +2 F +(, pp.230-236, 1991.) 275.85 564.95 T +1.05 ([20] R. A. Caruana, L. A. Eshelman, J. D. Schaf) 135.65 542.95 P +1.05 (fer) 376.42 542.95 P +1.05 (, \322Representation and hidden) 389.25 542.95 P +-0.3 (bias II: Eliminating de\336ning length bias in genetic search via shuf) 150.05 528.95 P +-0.3 (\337e crossover\323,) 462.67 528.95 P +2.77 (In) 150.05 514.95 P +0 F +2.77 (Eleventh International Joint Confer) 165.81 514.95 P +2.77 (ence on Arti\336cial Intelligence) 345.24 514.95 P +2 F +2.77 (, N. S.) 495.79 514.95 P +(Sridharan \050Ed.\051, V) 150.05 500.95 T +(ol. 1, pp. 750-755, Mor) 237.1 500.95 T +(gan Kaufmann Publishers, 1989.) 348.82 500.95 T +3.24 ([21] H. M\237hlenbein and D. Schlierkamp-V) 135.65 478.95 P +3.24 (oosen, \322Predictive Models for the) 357.14 478.95 P +0.37 (Breeder Genetic Algorithm\323,) 150.05 464.95 P +0 F +0.37 (Evolutionary Computation) 293.72 464.95 P +2 F +0.37 (, V) 422.36 464.95 P +0.37 (ol. 1, No. 1, pp. 25-) 435.84 464.95 P +(49, 1993.) 150.05 450.95 T +1.26 ([22] H. Furuya and R. T) 135.65 428.95 P +1.26 (. Haftka, \322Genetic Algorithms for Placing Actuators on) 257.33 428.95 P +(Space Structures\323,) 150.05 414.95 T +0 F +(Pr) 241.64 414.95 T +(oc. ICGA 5) 253.19 414.95 T +2 F +(, pp. 536-542, 1993.) 307.48 414.95 T +0.3 ([23] C. Z. Janikow and Z. Michalewicz, \322An Experimental Comparison of Binary) 135.65 392.95 P +0.49 (and Floating Point Representations in Genetic Algorithms\323,) 150.05 378.95 P +0 F +0.49 (Pr) 443.33 378.95 P +0.49 (oc. ICGA 4) 454.89 378.95 P +2 F +0.49 (, pp.) 510.17 378.95 P +(31-36, 1991.) 150.05 364.95 T +0.74 ([24] D. M. T) 135.65 342.95 P +0.74 (ate and A. E. Smith, \322Expected Allele Conver) 198.65 342.95 P +0.74 (gence and the Role of) 424.11 342.95 P +(Mutation in Genetic Algorithms\323,) 150.05 328.95 T +0 F +(Pr) 315.62 328.95 T +(oc. ICGA) 327.17 328.95 T +2 F +( 5, pp.31-37, 1993.) 372.47 328.95 T +2.12 ([25] L. Davis, \322Adapting Operator Probabilities in Genetic Algorithms\323,) 135.65 306.95 P +0 F +2.12 (Pr) 505.78 306.95 P +2.12 (oc.) 517.33 306.95 P +(ICGA 3) 150.05 292.95 T +2 F +(, pp. 61-69, 1989.) 187.02 292.95 T +5.14 ([26] T) 135.65 270.95 P +5.14 (. C. Fogarty) 170.21 270.95 P +5.14 (, \322V) 237.02 270.95 P +5.14 (arying the Probability of Mutation in the Genetic) 260.81 270.95 P +(Algorithm\323,) 150.05 256.95 T +0 F +(Pr) 211.35 256.95 T +(oc. ICGA 3) 222.9 256.95 T +2 F +(, pp. 104-109, 1989.) 277.19 256.95 T +0.12 ([27] K. A. De Jong and J. Sarma, \322Generation Gaps Revisited\323, In) 135.65 234.95 P +0 F +0.12 ( Foundations of) 455.43 234.95 P +2.86 (Genetic Algorithms 2) 150.05 220.95 P +2 F +2.86 (, L. D. Whitley \050Ed.\051, Mor) 258.37 220.95 P +2.86 (gan Kaufmann Publishers,) 399.02 220.95 P +(1993.) 150.05 206.95 T +2.13 ([28] D. Whitley) 135.65 184.95 P +2.13 (, \322The GENIT) 215.4 184.95 P +2.13 (OR algorithm and selection pressure: why rank-) 288.38 184.95 P +1.7 (based allocations of reproductive trials is best\323,) 150.05 170.95 P +0 F +1.7 ( Pr) 387.77 170.95 P +1.7 (oc. ICGA 3) 404.02 170.95 P +2 F +1.7 (, pp. 1) 461.73 170.95 P +1.7 (16-121,) 494.67 170.95 P +(1989.) 150.05 156.95 T +2.82 ([29] R. Huang and T. C. Fogarty, \322Adaptive Classification and Control-Rule) 135.65 134.95 P +1.46 (Optimization Via a Learning Algorithm for Controlling a Dynamic System\323,) 150.05 120.95 P +0 F +(Proc. 30th Conf. Decision and Control) 150.05 106.95 T +2 F +(, Brighton, England, pp. 867-868, 1991.) 336.95 106.95 T +FMENDPAGE +%%EndPage: "38" 39 +%%Page: "39" 39 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(1-39) 513.33 61.29 T +2 12 Q +0.5 ([30] T) 135.65 736.95 P +0.5 (. C. Fogarty) 165.57 736.95 P +0.5 (, \322An Incremental Genetic Algorithm for Real-T) 223.11 736.95 P +0.5 (ime Learning\323,) 458.53 736.95 P +0 F +(Pr) 150.05 722.95 T +(oc. 6th Int. W) 161.6 722.95 T +(orkshop on Machine Learning) 225.45 722.95 T +2 F +(, pp. 416-419, 1989.) 371.03 722.95 T +2.13 ([31] D. E. Goldber) 135.65 700.95 P +2.13 (g and J. Richardson, \322Genetic Algorithms with Sharing for) 232.1 700.95 P +(Multimodal Function Optimization\323,) 150.05 686.95 T +0 F +(Pr) 329.96 686.95 T +(oc. ICGA 2) 341.51 686.95 T +2 F +(, pp.41-49, 1987.) 395.8 686.95 T +0.39 ([32] H. M\237hlenbein, M. Schomisch and J. Born, \322The Parallel Genetic Algorithm) 135.65 664.95 P +(as a Function Optimizer\323,) 150.05 650.95 T +0 F +(Parallel Computing) 276.96 650.95 T +2 F +(, No. 17, pp. 619-632, 1991.) 372.59 650.95 T +-0.14 ([33] T) 135.65 628.95 P +-0.14 (. Starkweather) 164.93 628.95 P +-0.14 (, D. Whitley and K. Mathias, \322Optimization Using Distributed) 233.59 628.95 P +0.85 (Genetic Algorithms\323,) 150.05 614.95 P +0 F +0.85 (Pr) 258 614.95 P +0.85 (oc. Parallel Pr) 269.55 614.95 P +0.85 (oblem Solving Fr) 342.43 614.95 P +0.85 (om Natur) 426.96 614.95 P +0.85 (e 1) 473.01 614.95 P +2 F +0.85 (, Lecture) 488.18 614.95 P +(Notes in Computer Science No. 496, pp. 176-185, Springer) 150.05 600.95 T +(-V) 434.29 600.95 T +(erlag, 1990.) 445.61 600.95 T +0.22 ([34] M. Geor) 135.65 578.95 P +0.22 (ges-Schleuter) 199.48 578.95 P +0.22 (, \322Comparison of Local Mating Strategies in Massively) 264.28 578.95 P +1.35 (Parallel Genetic Algorithms\323, In) 150.05 564.95 P +0 F +1.35 ( Parallel Pr) 309.98 564.95 P +1.35 (oblem Solving fr) 369.54 564.95 P +1.35 (om Natur) 451.08 564.95 P +1.35 (e 2) 497.64 564.95 P +2 F +1.35 (, R.) 513.3 564.95 P +1.77 (M\212nner and B. 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/icircumflex /idieresis /ntilde /oacute /ograve +/ocircumflex /odieresis /otilde /uacute /ugrave /ucircumflex +/udieresis /dagger /.notdef /cent /sterling /section /bullet +/paragraph /germandbls /registered /copyright /trademark /acute +/dieresis /.notdef /AE /Oslash /.notdef /.notdef /.notdef /.notdef +/yen /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef +/ordfeminine /ordmasculine /.notdef /ae /oslash /questiondown +/exclamdown /logicalnot /.notdef /florin /.notdef /.notdef +/guillemotleft /guillemotright /ellipsis /.notdef /Agrave /Atilde +/Otilde /OE /oe /endash /emdash /quotedblleft /quotedblright +/quoteleft /quoteright /.notdef /.notdef /ydieresis /Ydieresis +/fraction /currency /guilsinglleft /guilsinglright /fi /fl /daggerdbl +/periodcentered /quotesinglbase /quotedblbase /perthousand +/Acircumflex /Ecircumflex /Aacute /Edieresis /Egrave /Iacute +/Icircumflex /Idieresis /Igrave /Oacute /Ocircumflex /.notdef /Ograve +/Uacute /Ucircumflex /Ugrave /dotlessi /circumflex /tilde /macron +/breve /dotaccent /ring /cedilla /hungarumlaut /ogonek /caron +] def +/ReEncode { + dup + length + dict begin + { + 1 index /FID ne + {def} + {pop pop} ifelse + } forall + 0 eq {/Encoding DiacriticEncoding def} if + currentdict + end + } bind def +/graymode true def + /bwidth FMLOCAL + /bpside FMLOCAL + /bstring FMLOCAL + /onbits FMLOCAL + /offbits FMLOCAL + /xindex FMLOCAL + /yindex FMLOCAL + /x FMLOCAL + /y FMLOCAL +/setpattern { + /bwidth exch def + /bpside exch def + /bstring exch def + /onbits 0 def /offbits 0 def + freq sangle landscape {90 add} if + {/y exch def + /x exch def + /xindex x 1 add 2 div bpside mul cvi def + /yindex y 1 add 2 div bpside mul cvi def + bstring yindex bwidth mul xindex 8 idiv add get + 1 7 xindex 8 mod sub bitshift and 0 ne + {/onbits onbits 1 add def 1} + {/offbits offbits 1 add def 0} + ifelse + } + setscreen + {} settransfer + offbits offbits onbits add div FMsetgray + /graymode false def + } bind def +/grayness { + FMsetgray + graymode not { + /graymode true def + orgxfer cvx settransfer + orgfreq organgle orgproc cvx setscreen + } if + } bind def + /HUE FMLOCAL + /SAT FMLOCAL + /BRIGHT FMLOCAL + /Colors FMLOCAL +FMPrintInColor + + { + /HUE 0 def + /SAT 0 def + /BRIGHT 0 def + % array of arrays Hue and Sat values for the separations [HUE BRIGHT] + /Colors + [[0 0 ] % black + [0 0 ] % white + [0.00 1.0] % red + [0.37 1.0] % green + [0.60 1.0] % blue + [0.50 1.0] % cyan + [0.83 1.0] % magenta + [0.16 1.0] % comment / yellow + ] def + + /BEGINBITMAPCOLOR { + BITMAPCOLOR} def + /BEGINBITMAPCOLORc { + BITMAPCOLORc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUECOLOR } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUECOLORc } def + /K { + Colors exch get dup + 0 get /HUE exch store + 1 get /BRIGHT exch store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } def + /FMsetgray { + /SAT exch 1.0 exch sub store + HUE 0 eq BRIGHT 0 eq and + {1.0 SAT sub setgray} + {HUE SAT BRIGHT sethsbcolor} + ifelse + } bind def + } + + { + /BEGINBITMAPCOLOR { + BITMAPGRAY} def + /BEGINBITMAPCOLORc { + BITMAPGRAYc} def + /BEGINBITMAPTRUECOLOR { + BITMAPTRUEGRAY } def + /BEGINBITMAPTRUECOLORc { + BITMAPTRUEGRAYc } def + /FMsetgray {setgray} bind def + /K { + pop + } def + } +ifelse +/normalize { + transform round exch round exch itransform + } bind def +/dnormalize { + dtransform round exch round exch idtransform + } bind def +/lnormalize { + 0 dtransform exch cvi 2 idiv 2 mul 1 add exch idtransform pop + } bind def +/H { + lnormalize setlinewidth + } bind def +/Z { + setlinecap + } bind def + /fillvals FMLOCAL +/X { + fillvals exch get + dup type /stringtype eq + {8 1 setpattern} + {grayness} + ifelse + } bind def +/V { + gsave eofill grestore + } bind def +/N { + stroke + } bind def +/M {newpath moveto} bind def +/E {lineto} bind def +/D {curveto} bind def +/O {closepath} bind def + /n FMLOCAL +/L { + /n exch def + newpath + normalize + moveto + 2 1 n {pop normalize lineto} for + } bind def +/Y { + L + closepath + } bind def + /x1 FMLOCAL + /x2 FMLOCAL + /y1 FMLOCAL + /y2 FMLOCAL + /rad FMLOCAL +/R { + /y2 exch def + /x2 exch def + /y1 exch def + /x1 exch def + x1 y1 + x2 y1 + x2 y2 + x1 y2 + 4 Y + } bind def +/RR { + /rad exch def + normalize + /y2 exch def + /x2 exch def + normalize + /y1 exch def + /x1 exch def + newpath + x1 y1 rad add moveto + x1 y2 x2 y2 rad arcto + x2 y2 x2 y1 rad arcto + x2 y1 x1 y1 rad arcto + x1 y1 x1 y2 rad arcto + closepath + 16 {pop} repeat + } bind def +/C { + grestore + gsave + R + clip + } bind def + /FMpointsize FMLOCAL +/F { + FMfonts exch get + FMpointsize scalefont + setfont + } bind def +/Q { + /FMpointsize exch def + F + } bind def +/T { + moveto show + } bind def +/RF { + rotate + 0 ne {-1 1 scale} if + } bind def +/TF { + gsave + moveto + RF + show + grestore + } bind def +/P { + moveto + 0 32 3 2 roll widthshow + } bind def +/PF { + gsave + moveto + RF + 0 32 3 2 roll widthshow + grestore + } bind def +/S { + moveto + 0 exch ashow + } bind def +/SF { + gsave + moveto + RF + 0 exch ashow + grestore + } bind def +/B { + moveto + 0 32 4 2 roll 0 exch awidthshow + } bind def +/BF { + gsave + moveto + RF + 0 32 4 2 roll 0 exch awidthshow + grestore + } bind def +/G { + gsave + newpath + normalize translate 0.0 0.0 moveto + dnormalize scale + 0.0 0.0 1.0 5 3 roll arc + closepath fill + grestore + } bind def +/A { + gsave + savematrix + newpath + 2 index 2 div add exch 3 index 2 div sub exch + normalize 2 index 2 div sub exch 3 index 2 div add exch + translate + scale + 0.0 0.0 1.0 5 3 roll arc + restorematrix + stroke + grestore + } bind def + /x FMLOCAL + /y FMLOCAL + /w FMLOCAL + /h FMLOCAL + /xx FMLOCAL + /yy FMLOCAL + /ww FMLOCAL + /hh FMLOCAL + /FMsaveobject FMLOCAL + /FMoptop FMLOCAL + /FMdicttop FMLOCAL +/BEGINPRINTCODE { + /FMdicttop countdictstack 1 add def + /FMoptop count 4 sub def + /FMsaveobject save def + userdict begin + /showpage {} def + FMNORMALIZEGRAPHICS + 3 index neg 3 index neg translate + } bind def +/ENDPRINTCODE { + count -1 FMoptop {pop pop} for + countdictstack -1 FMdicttop {pop end} for + FMsaveobject restore + } bind def +/gn { + 0 + { 46 mul + cf read pop + 32 sub + dup 46 lt {exit} if + 46 sub add + } loop + add + } bind def + /str FMLOCAL +/cfs { + /str sl string def + 0 1 sl 1 sub {str exch val put} for + str def + } bind def +/ic [ + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0223 + 0 + {0 hx} {1 hx} {2 hx} {3 hx} {4 hx} {5 hx} {6 hx} {7 hx} {8 hx} {9 hx} + {10 hx} {11 hx} {12 hx} {13 hx} {14 hx} {15 hx} {16 hx} {17 hx} {18 hx} + {19 hx} {gn hx} {0} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12} + {13} {14} {15} {16} {17} {18} {19} {gn} {0 wh} {1 wh} {2 wh} {3 wh} + {4 wh} {5 wh} {6 wh} {7 wh} {8 wh} {9 wh} {10 wh} {11 wh} {12 wh} + {13 wh} {14 wh} {gn wh} {0 bl} {1 bl} {2 bl} {3 bl} {4 bl} {5 bl} {6 bl} + {7 bl} {8 bl} {9 bl} {10 bl} {11 bl} {12 bl} {13 bl} {14 bl} {gn bl} + {0 fl} {1 fl} {2 fl} {3 fl} {4 fl} {5 fl} {6 fl} {7 fl} {8 fl} {9 fl} + {10 fl} {11 fl} {12 fl} {13 fl} {14 fl} {gn fl} + ] def + /sl FMLOCAL + /val FMLOCAL + /ws FMLOCAL + /im FMLOCAL + /bs FMLOCAL + /cs FMLOCAL + /len FMLOCAL + /pos FMLOCAL +/ms { + /sl exch def + /val 255 def + /ws cfs + /im cfs + /val 0 def + /bs cfs + /cs cfs + } bind def +400 ms +/ip { + is + 0 + cf cs readline pop + { ic exch get exec + add + } forall + pop + + } bind def +/wh { + /len exch def + /pos exch def + ws 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/bl { + /len exch def + /pos exch def + bs 0 len getinterval im pos len getinterval copy pop + pos len + } bind def +/s1 1 string def +/fl { + /len exch def + /pos exch def + /val cf s1 readhexstring pop 0 get def + pos 1 pos len add 1 sub {im exch val put} for + pos len + } bind def +/hx { + 3 copy getinterval + cf exch readhexstring pop pop + } bind def + /h FMLOCAL + /w FMLOCAL + /d FMLOCAL + /lb FMLOCAL + /bitmapsave FMLOCAL + /is FMLOCAL + /cf FMLOCAL +/wbytes { + dup + 8 eq {pop} {1 eq {7 add 8 idiv} {3 add 4 idiv} ifelse} ifelse + } bind def +/BEGINBITMAPBWc { + 1 {} COMMONBITMAPc + } bind def +/BEGINBITMAPGRAYc { + 8 {} COMMONBITMAPc + } bind def +/BEGINBITMAP2BITc { + 2 {} COMMONBITMAPc + } bind def +/COMMONBITMAPc { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + r + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} image + bitmapsave restore + grestore + } bind def +/BEGINBITMAPBW { + 1 {} COMMONBITMAP + } bind def +/BEGINBITMAPGRAY { + 8 {} COMMONBITMAP + } bind def +/BEGINBITMAP2BIT { + 2 {} COMMONBITMAP + } bind def +/COMMONBITMAP { + /r exch def + /d exch def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + r + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} image + bitmapsave restore + grestore + } bind def + /proc1 FMLOCAL + /proc2 FMLOCAL + /newproc FMLOCAL +/Fmcc { + /proc2 exch cvlit def + /proc1 exch cvlit def + /newproc proc1 length proc2 length add array def + newproc 0 proc1 putinterval + newproc proc1 length proc2 putinterval + newproc cvx +} bind def +/ngrayt 256 array def +/nredt 256 array def +/nbluet 256 array def +/ngreent 256 array def + /gryt FMLOCAL + /blut FMLOCAL + /grnt FMLOCAL + /redt FMLOCAL + /indx FMLOCAL + /cynu FMLOCAL + /magu FMLOCAL + /yelu FMLOCAL + /k FMLOCAL + /u FMLOCAL +/colorsetup { + currentcolortransfer + /gryt exch def + /blut exch def + /grnt exch def + /redt exch def + 0 1 255 { + /indx exch def + /cynu 1 red indx get 255 div sub def + /magu 1 green indx get 255 div sub def + /yelu 1 blue indx get 255 div sub def + /k cynu magu min yelu min def + /u k currentundercolorremoval exec def + nredt indx 1 0 cynu u sub max sub redt exec put + ngreent indx 1 0 magu u sub max sub grnt exec put + nbluet indx 1 0 yelu u sub max sub blut exec put + ngrayt indx 1 k currentblackgeneration exec sub gryt exec put + } for + {255 mul cvi nredt exch get} + {255 mul cvi ngreent exch get} + {255 mul cvi nbluet exch get} + {255 mul cvi ngrayt exch get} + setcolortransfer + {pop 0} setundercolorremoval + {} setblackgeneration + } bind def + /tran FMLOCAL +/fakecolorsetup { + /tran 256 string def + 0 1 255 {/indx exch def + tran indx + red indx get 77 mul + green indx get 151 mul + blue indx get 28 mul + add add 256 idiv put} for + currenttransfer + {255 mul cvi tran exch get 255.0 div} + exch Fmcc settransfer +} bind def +/BITMAPCOLOR { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + colorsetup + /is w d wbytes string def + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {cf is readhexstring pop} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPCOLORc { + /d 8 def + gsave + translate rotate scale /h exch def /w exch def + /lb w d wbytes def + sl lb lt {lb ms} if + /bitmapsave save def + colorsetup + /is im 0 lb getinterval def + ws 0 lb getinterval is copy pop + /cf currentfile def + w h d [w 0 0 h neg 0 h] + {ip} {is} {is} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLORc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip} {gip} {bip} true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUECOLOR { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop } + { cf gis readhexstring pop } + { cf bis readhexstring pop } + true 3 colorimage + bitmapsave restore + grestore + } bind def +/BITMAPTRUEGRAYc { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + + /is w string def + + ws 0 w getinterval is copy pop + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + {ip gip bip w gray} image + bitmapsave restore + grestore + } bind def +/ww FMLOCAL +/r FMLOCAL +/g FMLOCAL +/b FMLOCAL +/i FMLOCAL +/gray { + /ww exch def + /b exch def + /g exch def + /r exch def + 0 1 ww 1 sub { /i exch def r i get .299 mul g i get .587 mul + b i get .114 mul add add r i 3 -1 roll floor cvi put } for + r + } bind def +/BITMAPTRUEGRAY { + gsave + translate rotate scale /h exch def /w exch def + /bitmapsave save def + /is w string def + /gis w string def + /bis w string def + /cf currentfile def + w h 8 [w 0 0 h neg 0 h] + { cf is readhexstring pop + cf gis readhexstring pop + cf bis readhexstring pop w gray} image + bitmapsave restore + grestore + } bind def +/BITMAPGRAY { + 8 {fakecolorsetup} COMMONBITMAP + } bind def +/BITMAPGRAYc { + 8 {fakecolorsetup} COMMONBITMAPc + } bind def +/ENDBITMAP { + } bind def +end + /ALDsave FMLOCAL + /ALDmatrix matrix def ALDmatrix currentmatrix pop +/StartALD { + /ALDsave save def + savematrix + ALDmatrix setmatrix + } bind def +/InALD { + restorematrix + } bind def +/DoneALD { + ALDsave restore + } bind def +%%EndProlog +%%BeginSetup +(3.0) FMVERSION +1 1 595.3 841.9 0 1 15 FMDOCUMENT +0 0 /Times-Italic FMFONTDEFINE +1 0 /Times-Bold FMFONTDEFINE +2 0 /Courier FMFONTDEFINE +3 0 /Times-Roman FMFONTDEFINE +4 1 /Symbol FMFONTDEFINE +32 FMFILLS +0 0 FMFILL +1 .1 FMFILL +2 .3 FMFILL +3 .5 FMFILL +4 .7 FMFILL +5 .9 FMFILL +6 .97 FMFILL +7 1 FMFILL +8 <0f1e3c78f0e1c387> FMFILL +9 <0f87c3e1f0783c1e> FMFILL +10 FMFILL +11 FMFILL +12 <8142241818244281> FMFILL +13 <03060c183060c081> FMFILL +14 <8040201008040201> FMFILL +16 1 FMFILL +17 .9 FMFILL +18 .7 FMFILL +19 .5 FMFILL +20 .3 FMFILL +21 .1 FMFILL +22 0.03 FMFILL +23 0 FMFILL +24 FMFILL +25 FMFILL +26 <3333333333333333> FMFILL +27 <0000ffff0000ffff> FMFILL +28 <7ebddbe7e7dbbd7e> FMFILL +29 FMFILL +30 <7fbfdfeff7fbfdfe> FMFILL +%%EndSetup +%%Page: "1" 1 +%%BeginPaperSize: A4 +%%EndPaperSize +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-1) 518.33 61.29 T +1 28 Q +(2 Refer) 63.65 726.29 T +(ence) 150.98 726.29 T +2 12 Q +(bs2rv) 135.65 692.95 T +3 F +(.......................................................................................................) 178.82 692.95 T +(2-5) 487.65 692.95 T +2 F +(crtbase) 135.65 672.95 T +3 F +( ...................................................................................................) 186.02 672.95 T +(2-7) 486.65 672.95 T +2 F +(crtbp) 135.65 652.95 T +3 F +( ........................................................................................................) 171.63 652.95 T +(2-8) 486.65 652.95 T +2 F +(crtrp) 135.65 632.95 T +3 F +( ........................................................................................................) 171.63 632.95 T +(2-10) 486.65 632.95 T +2 F +(migrate) 135.65 612.95 T +3 F +( ...................................................................................................) 186.02 612.95 T +(2-1) 486.65 612.95 T +(1) 502.19 612.95 T +2 F +(mut) 135.65 592.95 T +3 F +( ............................................................................................................) 157.24 592.95 T +(2-14) 486.65 592.95 T +2 F +(mutate) 135.65 572.95 T +3 F +( .....................................................................................................) 178.82 572.95 T +(2-16) 486.65 572.95 T +2 F +(mutbga) 135.65 552.95 T +3 F +( .....................................................................................................) 178.82 552.95 T +(2-17) 486.65 552.95 T +2 F +(ranking) 135.65 532.95 T +3 F +( ...................................................................................................) 186.02 532.95 T +(2-20) 486.65 532.95 T +2 F +(recdis) 135.65 512.95 T +3 F +( .....................................................................................................) 178.82 512.95 T +(2-24) 486.65 512.95 T +2 F +(recint) 135.65 492.95 T +3 F +( .....................................................................................................) 178.82 492.95 T +(2-26) 486.65 492.95 T +2 F +(reclin) 135.65 472.95 T +3 F +( .....................................................................................................) 178.82 472.95 T +(2-28) 486.65 472.95 T +2 F +(recmut) 135.65 452.95 T +3 F +( .....................................................................................................) 178.82 452.95 T +(2-30) 486.65 452.95 T +2 F +(recombin) 135.65 432.95 T +3 F +( .................................................................................................) 193.22 432.95 T +(2-33) 487.05 432.95 T +2 F +(reins) 135.65 412.95 T +3 F +( ........................................................................................................) 171.63 412.95 T +(2-34) 486.65 412.95 T +2 F +(rep) 135.65 392.95 T +3 F +( .............................................................................................................) 157.24 392.95 T +(2-37) 487.05 392.95 T +2 F +(rws) 135.65 372.95 T +3 F +( .............................................................................................................) 157.24 372.95 T +(2-38) 487.05 372.95 T +2 F +(scaling) 135.65 352.95 T +3 F +( ...................................................................................................) 186.02 352.95 T +(2-40) 486.65 352.95 T +2 F +(select) 135.65 332.95 T +3 F +( .....................................................................................................) 178.82 332.95 T +(2-41) 486.65 332.95 T +2 F +(sus) 135.65 312.95 T +3 F +( ............................................................................................................) 157.24 312.95 T +(2-44) 486.65 312.95 T +2 F +(xovdp) 135.65 292.95 T +3 F +( ........................................................................................................) 171.63 292.95 T +(2-46) 486.65 292.95 T +2 F +(xovdprs) 135.65 272.95 T +3 F +( ...................................................................................................) 186.02 272.95 T +(2-47) 486.65 272.95 T +2 F +(xovmp) 135.65 252.95 T +3 F +( ........................................................................................................) 171.63 252.95 T +(2-48) 486.65 252.95 T +2 F +(xovsh) 135.65 232.95 T +3 F +( ........................................................................................................) 171.63 232.95 T +(2-49) 486.65 232.95 T +2 F +(xovshrs) 135.65 212.95 T +3 F +( ...................................................................................................) 186.02 212.95 T +(2-50) 486.65 212.95 T +2 F +(xovsp) 135.65 192.95 T +3 F +( ........................................................................................................) 171.63 192.95 T +(2-51) 486.65 192.95 T +2 F +(xovsprs) 135.65 172.95 T +3 F +( ...................................................................................................) 186.02 172.95 T +(2-52) 486.65 172.95 T +FMENDPAGE +%%EndPage: "1" 2 +%%Page: "2" 2 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-2) 518.33 61.29 T +1 28 Q +(2 Refer) 63.65 726.29 T +(ence) 150.98 726.29 T +3 12 Q +1.19 (This Section contains detailed descriptions of all of the functions in the Genetic) 135.65 692.95 P +0.55 (Algorithm T) 135.65 678.95 P +0.55 (oolbox. It begins with a list of functions grouped by subject area and) 195.66 678.95 P +5.8 (continues with) 135.65 664.95 P +0 F +5.8 (Refer) 220.53 664.95 P +5.8 (ence) 246.07 664.95 P +3 F +5.8 (entries in alphabetical order) 276.83 664.95 P +5.8 (. Information about) 427.12 664.95 P +(individual functions is also available through the on-line) 135.65 650.95 T +2 F +(Help) 409.48 650.95 T +3 F +( facility) 438.27 650.95 T +(.) 474.46 650.95 T +FMENDPAGE +%%EndPage: "2" 3 +%%Page: "3" 3 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-3) 518.33 61.29 T +3 12 Q +(CREA) 262.19 696.95 T +(TING POPULA) 292.85 696.95 T +(TIONS) 369.8 696.95 T +2 F +(crtbase) 141.65 672.95 T +3 F +(create a base vector) 249.65 672.95 T +2 F +(crtbp) 141.65 650.95 T +3 F +(create arbitrary discrete random populations) 249.65 650.95 T +2 F +(crtrp) 141.65 628.95 T +3 F +(create real-valued initial population) 249.65 628.95 T +(FITNESS ASSIGNMENT) 269.85 558.95 T +2 F +(ranking) 141.65 534.95 T +3 F +(generalised rank-based \336tness assignment) 249.65 534.95 T +2 F +(scaling) 141.65 512.95 T +3 F +(proportional \336tness scaling) 249.65 512.95 T +(SELECTION FUNCTIONS) 265.86 442.95 T +2 F +(reins) 141.65 418.95 T +3 F +(uniform random and \336tness-based reinsertion) 249.65 418.95 T +2 F +(rws) 141.65 396.95 T +3 F +(roulette wheel selection) 249.65 396.95 T +2 F +(select) 141.65 374.95 T +3 F +(high-level selection routine) 249.65 374.95 T +2 F +(sus) 141.65 352.95 T +3 F +(stochastic universal sampling) 249.65 352.95 T +(MUT) 267.11 282.95 T +(A) 292.8 282.95 T +(TION OPERA) 300.13 282.95 T +(T) 369.75 282.95 T +(ORS) 376.86 282.95 T +2 F +(mut) 141.65 258.95 T +3 F +(discrete mutation) 249.65 258.95 T +2 F +(mutate) 141.65 236.95 T +3 F +(high-level mutation function) 249.65 236.95 T +2 F +(mutbga) 141.65 214.95 T +3 F +(real-value mutation) 249.65 214.95 T +135.65 712.7 135.65 621.2 2 L +V +0.5 H +0 Z +N +243.65 685.45 243.65 620.7 2 L +V +N +531.65 712.7 531.65 621.2 2 L +V +N +135.4 712.95 531.9 712.95 2 L +V +N +135.9 688.2 531.4 688.2 2 L +V +N +135.9 685.7 531.4 685.7 2 L +V +N +135.4 620.95 531.9 620.95 2 L +V +N +135.65 574.7 135.65 505.2 2 L +V +N +243.65 547.45 243.65 504.7 2 L +V +N +531.65 574.7 531.65 505.2 2 L +V +N +135.4 574.95 531.9 574.95 2 L +V +N +135.9 550.2 531.4 550.2 2 L +V +N +135.9 547.7 531.4 547.7 2 L +V +N +135.4 504.95 531.9 504.95 2 L +V +N +135.65 458.7 135.65 345.2 2 L +V +N +243.65 431.45 243.65 344.7 2 L +V +N +531.65 458.7 531.65 345.2 2 L +V +N +135.4 458.95 531.9 458.95 2 L +V +N +135.9 434.2 531.4 434.2 2 L +V +N +135.9 431.7 531.4 431.7 2 L +V +N +135.4 344.95 531.9 344.95 2 L +V +N +135.65 298.7 135.65 207.2 2 L +V +N +243.65 271.45 243.65 206.7 2 L +V +N +531.65 298.7 531.65 207.2 2 L +V +N +135.4 298.95 531.9 298.95 2 L +V +N +135.9 274.2 531.4 274.2 2 L +V +N +135.9 271.7 531.4 271.7 2 L +V +N +135.4 206.95 531.9 206.95 2 L +V +N +FMENDPAGE +%%EndPage: "3" 4 +%%Page: "4" 4 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-4) 518.33 61.29 T +3 12 Q +(CROSSOVER OPERA) 262.62 696.95 T +(T) 374.24 696.95 T +(ORS) 381.35 696.95 T +2 F +(recdis) 141.65 672.95 T +3 F +(discrete recombination) 249.65 672.95 T +2 F +(recint) 141.65 650.95 T +3 F +(intermediate recombination) 249.65 650.95 T +2 F +(reclin) 141.65 628.95 T +3 F +(line recombination) 249.65 628.95 T +2 F +(recmut) 141.65 606.95 T +3 F +(line recombination with mutation features) 249.65 606.95 T +2 F +(recombin) 141.65 584.95 T +3 F +(high-level recombination operator) 249.65 584.95 T +2 F +(xovdp) 141.65 562.95 T +3 F +(double-point crossover) 249.65 562.95 T +2 F +(xovdprs) 141.65 540.95 T +3 F +(double-point reduced surrogate crossover) 249.65 540.95 T +2 F +(xovmp) 141.65 518.95 T +3 F +(general multi-point crossover) 249.65 518.95 T +2 F +(xovsh) 141.65 496.95 T +3 F +(shuf) 249.65 496.95 T +(\337e crossover) 270.08 496.95 T +2 F +(xovshrs) 141.65 474.95 T +3 F +(shuf) 249.65 474.95 T +(\337e reduced surrogate crossover) 270.08 474.95 T +2 F +(xovsp) 141.65 452.95 T +3 F +(single-point crossover) 249.65 452.95 T +2 F +(xovsprs) 141.65 430.95 T +3 F +(single-point reduced surrogate crossover) 249.65 430.95 T +(SUBPOPULA) 257.54 360.95 T +(TION SUPPOR) 326.18 360.95 T +(T) 402.42 360.95 T +2 F +(migrate) 141.65 336.95 T +3 F +(exchange individuals between subpopulations) 249.65 336.95 T +(UTILITY FUNCTIONS) 274.86 266.95 T +2 F +(bs2rv) 141.65 242.95 T +3 F +(binary string to real-value conversion) 249.65 242.95 T +2 F +(rep) 141.65 220.95 T +3 F +(matrix replication) 249.65 220.95 T +135.65 712.7 135.65 423.2 2 L +V +0.5 H +0 Z +N +243.65 685.45 243.65 422.7 2 L +V +N +531.65 712.7 531.65 423.2 2 L +V +N +135.4 712.95 531.9 712.95 2 L +V +N +135.9 688.2 531.4 688.2 2 L +V +N +135.9 685.7 531.4 685.7 2 L +V +N +135.4 422.95 531.9 422.95 2 L +V +N +135.65 376.7 135.65 329.2 2 L +V +N +243.65 349.45 243.65 328.7 2 L +V +N +531.65 376.7 531.65 329.2 2 L +V +N +135.4 376.95 531.9 376.95 2 L +V +N +135.9 352.2 531.4 352.2 2 L +V +N +135.9 349.7 531.4 349.7 2 L +V +N +135.4 328.95 531.9 328.95 2 L +V +N +135.65 282.7 135.65 213.2 2 L +V +N +243.65 255.45 243.65 212.7 2 L +V +N +531.65 282.7 531.65 213.2 2 L +V +N +135.4 282.95 531.9 282.95 2 L +V +N +135.9 258.2 531.4 258.2 2 L +V +N +135.9 255.7 531.4 255.7 2 L +V +N +135.4 212.95 531.9 212.95 2 L +V +N +FMENDPAGE +%%EndPage: "4" 5 +%%Page: "5" 5 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-5) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(bs2rv) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(binary string to real value conversion) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(Phen = bs2rv\050Chrom, FieldD\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +1.31 (Phen = bs2rv\050Chrom, FieldD\051) 135.65 588.95 P +3 F +0.55 ( decodes the binary representation of the) 333.87 588.95 P +5.26 (population,) 135.65 574.95 P +2 F +12.62 (Chrom) 198.21 574.95 P +3 F +5.26 (, into vectors of reals. The chromosomes are seen as) 234.19 574.95 P +0.28 (concatenated binary strings of given length, and decoded into real numbers over a) 135.65 560.95 P +1.93 (speci\336ed interval using either standard binary or Gray coding according to the) 135.65 546.95 P +8.28 (decoding matrix,) 135.65 532.95 P +2 F +19.86 (FieldD) 236.48 532.95 P +3 F +8.28 (. The resulting matrix,) 279.65 532.95 P +2 F +19.86 (Phen) 422.69 532.95 P +3 F +8.28 (, contains the) 451.47 532.95 P +(corresponding population phenotypes.) 135.65 518.95 T +0.12 (The use of Gray coding for binary chromosome representation is recommended as) 135.65 492.95 P +-0.23 (the regular Hamming distance between quantization intervals reportedly makes the) 135.65 478.95 P +-0.12 (genetic search less deceptive \050see, for example, [1, 2]\051. An option to set the scaling) 135.65 464.95 P +2.54 (between quantization points can be used to select either linear or logarithmic) 135.65 450.95 P +-0.17 (decoding to real values from binary strings. Logarithmic scaling is useful when the) 135.65 436.95 P +0.26 (range of decision variable is unknown at the outset as a wider range of parametric) 135.65 422.95 P +3.55 (values can be searched with fewer bits [3], thus reducing the memory and) 135.65 408.95 P +(computational requirements of the GA.) 135.65 394.95 T +(The matrix) 135.65 368.95 T +2 F +(FieldD) 191.61 368.95 T +3 F +( has the following structure:) 234.79 368.95 T +(,) 356.55 294.72 T +(where the rows of the matrix are composed as follows:) 135.65 221.66 T +2 F +3.26 (len) 135.65 195.66 P +3 F +1.36 (, a row vector containing the length of each substring in) 157.24 195.66 P +2 F +3.26 (Chrom) 442.65 195.66 P +3 F +1.36 (. Note that) 478.63 195.66 P +2 F +(sum\050len\051) 135.65 181.66 T +3 F +( should equal) 193.22 181.66 T +2 F +(length\050Chrom\051) 260.18 181.66 T +3 F +(.) 353.72 181.66 T +2 F +-0.15 (lb) 135.65 155.66 P +3 F +-0.06 ( and) 150.04 155.66 P +2 F +-0.15 (ub) 173.23 155.66 P +3 F +-0.06 ( are row vectors containing the lower and upper bounds respectively for) 187.62 155.66 P +(each variable used.) 135.65 141.66 T +2 F +4.76 (code) 135.65 115.66 P +3 F +1.98 ( is a binary row vector indicating how each substring is decoded. Select) 164.43 115.66 P +2 F +(code\050i\051 = 0) 135.65 101.66 T +3 F +( for standard binary and) 214.8 101.66 T +2 F +(code\050i\051 = 1) 332.38 101.66 T +3 F +( for Gray coding.) 411.53 101.66 T +307.75 243.66 356.55 350.95 C +2 12 Q +0 X +0 K +(l) 321.15 335.96 T +(e) 329.05 335.96 T +(n) 336.95 335.96 T +(l) 325.1 321.49 T +(b) 333 321.49 T +(u) 325.1 307.02 T +(b) 333 307.02 T +(c) 317.2 292.55 T +(o) 325.1 292.55 T +(d) 333 292.55 T +(e) 340.9 292.55 T +(s) 313.25 278.08 T +(c) 321.15 278.08 T +(a) 329.05 278.08 T +(l) 336.95 278.08 T +(e) 344.86 278.08 T +(l) 317.2 263.61 T +(b) 325.1 263.61 T +(i) 333 263.61 T +(n) 340.9 263.61 T +(u) 317.2 249.14 T +(b) 325.1 249.14 T +(i) 333 249.14 T +(n) 340.9 249.14 T +314.75 246.66 310.75 246.66 2 L +0.33 H +0 Z +N +310.75 246.66 310.75 347.95 2 L +N +310.75 347.95 314.75 347.95 2 L +N +349.55 246.66 353.55 246.66 2 L +N +353.55 246.66 353.55 347.95 2 L +N +353.55 347.95 349.55 347.95 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "5" 6 +%%Page: "6" 6 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-6) 518.33 61.29 T +2 12 Q +9.44 (scale) 135.65 736.95 P +3 F +3.93 ( is a binary row vector indicating whether to use arithmetic and/or) 171.63 736.95 P +1.68 (logarithmic scaling for each substring. Select) 135.65 722.95 P +2 F +4.03 (scale\050i\051 = 0) 365.25 722.95 P +3 F +1.68 ( for arithmetic) 459.67 722.95 P +(scaling and) 135.65 708.95 T +2 F +(scale\050i\051 = 1) 192.94 708.95 T +3 F +( for logarithmic scaling.) 279.29 708.95 T +2 F +0.93 (lbin) 135.65 682.95 P +3 F +0.39 ( and) 164.43 682.95 P +2 F +0.93 (ubin) 188.52 682.95 P +3 F +0.39 ( are binary row vectors indicating whether or not to include each) 217.3 682.95 P +2.86 (bound in the representation range. Select) 135.65 668.95 P +2 F +6.86 ({l|u}bin\050i\051 = 0) 351.65 668.95 P +3 F +2.86 ( to exclude) 473.3 668.95 P +2 F +0.9 ({l|u}b\050i\051) 135.65 654.95 P +3 F +0.38 ( from the representation range and) 200.41 654.95 P +2 F +0.9 ({l|u}bin\050i\051 = 1) 370.52 654.95 P +3 F +0.38 ( to include) 480.26 654.95 P +2 F +({l|u}b\050i\051) 135.65 640.95 T +3 F +( in the representation range.) 200.41 640.95 T +1 16 Q +(Example) 117.65 612.29 T +3 12 Q +2.8 (Consider the following binary population, created using the) 135.65 594.95 P +2 F +6.73 (crtbp) 446.89 594.95 P +3 F +2.8 ( function,) 482.87 594.95 P +2.25 (representing a set of single decision variables in the range [-1, 10]. The code) 135.65 580.95 P +1.74 (extract shows how the function) 135.65 566.95 P +2 F +4.17 (bs2rv) 297.24 566.95 P +3 F +1.74 ( may be used to convert the Gray code) 333.22 566.95 P +(binary representation to real-valued phenotypes using arithmetic scaling.) 135.65 552.95 T +2 F +(Chrom = crtbp\0504,8\051 % create random chromosomes) 135.65 532.95 T +(Chrom =) 135.65 512.95 T +(0 0 0 0 0 1 1 1) 153.65 498.95 T +(1 0 0 0 1 0 0 1) 153.65 484.95 T +(0 0 1 0 1 0 0 0) 153.65 470.95 T +(1 1 0 1 1 0 1 1) 153.65 456.95 T +(FieldD = [8; -1; 10; 1; 0; 1; 1]; % representation) 135.65 436.95 T +(Phen = bs2rv\050Chrom,FieldD\051 % convert binary to real) 135.65 416.95 T +(Phen =) 135.65 396.95 T +(-0.7843) 153.65 382.95 T +(9.3961) 160.84 368.95 T +(1.0706) 160.84 354.95 T +(5.2980) 160.84 340.95 T +1 16 Q +(Algorithm) 117.65 318.29 T +2 12 Q +2.04 (bs2rv) 135.65 300.95 P +3 F +0.85 ( is implemented as an m-\336le in the GA T) 171.63 300.95 P +0.85 (oolbox. If logarithmic scaling is) 374.67 300.95 P +(used then the range must not include zero.) 135.65 286.95 T +1 16 Q +(Refer) 117.65 258.29 T +(ence) 155.53 258.29 T +3 12 Q +1.8 ([1] R. B. Holstien,) 135.65 240.95 P +0 F +1.8 (Arti\336cial Genetic Adaptation in Computer Contr) 234.46 240.95 P +1.8 (ol Systems) 476.55 240.95 P +3 F +1.8 (,) 528.65 240.95 P +0.7 (Ph.D. Thesis, Department of Computer and Communication Sciences, University) 135.65 226.95 P +(of Michigan, Ann Arbor) 135.65 212.95 T +(, 1971.) 252.42 212.95 T +0.67 ([2] R. A. Caruana and J. D. Schaf) 135.65 186.95 P +0.67 (fer) 301.64 186.95 P +0.67 (, \322Representation and Hidden Bias: Gray vs.) 314.47 186.95 P +(Binary Coding\323,) 135.65 172.95 T +0 F +(Pr) 217.93 172.95 T +(oc. 6) 229.48 172.95 T +260.58 176.79 252.8 176.79 2 L +V +0.48 H +0 Z +N +0 10 Q +(th) 252.8 177.75 T +0 12 Q +( Int. Conf. Machine Learning) 260.58 172.95 T +3 F +(, pp153-161, 1988.) 401.16 172.95 T +2.14 ([3] W) 135.65 146.95 P +2.14 (. E. Schmitendor) 164.99 146.95 P +2.14 (gf, O. Shaw) 249.67 146.95 P +2.14 (, R. Benson and S. Forrest, \322Using Genetic) 310.46 146.95 P +3.22 (Algorithms for Controller Design: Simultaneous Stabilization and Eigenvalue) 135.65 132.95 P +0.9 (Placement in a Region\323,) 135.65 118.95 P +0 F +0.9 (T) 258.84 118.95 P +0.9 (echnical Report No. CS92-9) 264.41 118.95 P +3 F +0.9 (, Dept. Computer Science,) 402.36 118.95 P +(College of Engineering, University of New Mexico, 1992.) 135.65 104.95 T +FMENDPAGE +%%EndPage: "6" 7 +%%Page: "7" 7 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-7) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(crtbase) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Create a base vector) 135.65 674.95 T +(.) 231.9 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(BaseVec = crtbase\050Lind, Base\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.66 (crtbase) 135.65 588.95 P +3 F +0.27 ( produces a vector whose elements correspond to the base of the loci of) 186.02 588.95 P +1.48 (a chromosome structure. This function can be used in conjunction with) 135.65 574.95 P +2 F +3.55 (crtbp) 495.67 574.95 P +3 F +(when creating populations using representations in dif) 135.65 560.95 T +(ferent bases.) 395.26 560.95 T +2 F +-0.28 (BaseVec = crtbase\050Lind, Base\051) 135.65 534.95 P +3 F +-0.12 ( creates a vector of length) 343.49 534.95 P +2 F +-0.28 (Lind) 469.34 534.95 P +3 F +-0.12 ( whose) 498.12 534.95 P +8.25 (individual elements are of base) 135.65 520.95 P +2 F +19.8 (Base) 329.13 520.95 P +3 F +8.25 (. If) 357.91 520.95 P +2 F +19.8 (Lind) 391.4 520.95 P +3 F +8.25 ( is a vector) 420.18 520.95 P +8.25 (, then) 496.75 520.95 P +2 F +13.9 (length\050BaseVec\051 = sum\050Lind\051) 135.65 506.95 P +3 F +5.79 (. If) 357.74 506.95 P +2 F +13.9 (Base) 386.31 506.95 P +3 F +5.79 ( is also a vector of) 415.09 506.95 P +2 F +7.3 (length\050Lind\051) 135.65 492.95 P +3 F +3.04 (, then) 222 492.95 P +2 F +7.3 (BaseVec) 257.73 492.95 P +3 F +3.04 ( is composed of groups of bases of length) 308.11 492.95 P +1.43 (determined by the elements of) 135.65 478.95 P +2 F +3.44 (Lind) 291.04 478.95 P +3 F +1.43 ( and base) 319.83 478.95 P +2 F +3.44 (Base) 371.76 478.95 P +3 F +1.43 (. This last option is useful) 400.54 478.95 P +(when describing populations with structure.) 135.65 464.95 T +1 16 Q +(Example) 117.65 436.29 T +3 12 Q +0.03 (T) 135.65 418.95 P +0.03 (o create a basevector for a population containing four elements in base 8 and \336ve) 142.14 418.95 P +(elements in base four:) 135.65 404.95 T +2 F +(BaseV = crtbase\050[4 5], [8 4]\051) 135.65 384.95 T +(BaseV =) 135.65 364.95 T +(8 8 8 8 4 4 4 4 4) 153.65 350.95 T +1 16 Q +(See Also) 117.65 328.29 T +2 12 Q +(crtbp) 135.65 310.95 T +3 F +(,) 171.63 310.95 T +2 F +(bs2rv) 177.62 310.95 T +FMENDPAGE +%%EndPage: "7" 8 +%%Page: "8" 8 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-8) 518.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(crtbp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Create an initial population.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +([Chrom, Lind, BaseV] = crtbp\050Nind, Lind\051) 135.65 628.95 T +([Chrom, Lind, BaseV] = crtbp\050Nind, Lind, Base\051) 135.65 608.95 T +([Chrom, Lind, BaseV] = crtbp\050Nind, BaseV\051) 135.65 588.95 T +1 16 Q +(Description) 117.65 566.29 T +3 12 Q +0.45 (The \336rst step in a genetic algorithm is to create an initial population consisting of) 135.65 548.95 P +2.57 (random chromosomes.) 135.65 534.95 P +2 F +6.18 (crtbp) 253.05 534.95 P +3 F +2.57 ( produces a matrix,) 289.03 534.95 P +2 F +6.18 (Chrom) 394.25 534.95 P +3 F +2.57 (, containing random) 430.23 534.95 P +(values in its elements.) 135.65 520.95 T +2 F +4.94 (Chrom = crtbp\050Nind, Lind\051) 135.65 494.95 P +3 F +2.06 ( creates a random binary matrix of size) 330.38 494.95 P +-0.26 (, where) 212.04 480.95 P +2 F +-0.64 (Nind) 249.8 480.95 P +3 F +-0.26 ( speci\336es the number of individuals in the population) 278.58 480.95 P +8.37 (and) 135.65 466.95 P +2 F +20.1 (Lind) 164.34 466.95 P +3 F +8.37 ( the length of the individuals. Additionally) 193.12 466.95 P +8.37 (,) 446.81 466.95 P +2 F +20.1 (Chrom =) 461.18 466.95 P +9.35 (crtbp\050[Nind, Lind]\051) 135.65 452.95 P +3 F +3.9 ( can be used to specify the dimensions of the) 281.73 452.95 P +(chromosome matrix.) 135.65 438.95 T +2 F +0.99 (Chrom = crtbp\050Nind, Lind, Base\051) 135.65 412.95 P +3 F +0.41 ( produces a chromosome matrix of) 362.7 412.95 P +-0.27 (base) 135.65 398.95 P +2 F +-0.64 (Base) 159.69 398.95 P +3 F +-0.27 (. If) 188.48 398.95 P +2 F +-0.64 (Base) 204.92 398.95 P +3 F +-0.27 ( is a vector) 233.71 398.95 P +-0.27 (, then the value of the elements of) 284.71 398.95 P +2 F +-0.64 (Base) 448.11 398.95 P +3 F +-0.27 ( specify the) 476.89 398.95 P +2.26 (base of the loci of the chromosomes. In this case, the second right hand side) 135.65 384.95 P +(ar) 135.65 370.95 T +(gument may be omitted,) 144.75 370.95 T +2 F +(Chrom = crtbp\050Nind, BaseV\051) 264.35 370.95 T +3 F +(.) 451.45 370.95 T +2 F +3.95 ([Chrom, Lind, BaseV] = crtbp\050Nind, BaseV\051) 135.65 344.95 P +3 F +1.65 ( also returns the) 450.43 344.95 P +-0.27 (length of the chromosome structure,) 135.65 330.95 P +2 F +-0.65 (Lind) 310.83 330.95 P +3 F +-0.27 (, and the base of the chromosome loci in) 339.62 330.95 P +(the vector) 135.65 316.95 T +2 F +(BaseV) 186.27 316.95 T +3 F +(.) 220.71 316.95 T +1 16 Q +(Example) 117.65 288.29 T +3 12 Q +0.05 (T) 135.65 270.95 P +0.05 (o create a random population of 6 individuals of length 8 where the \336rst four loci) 142.14 270.95 P +(are base eight and the last \336ve loci are base four:) 135.65 256.95 T +2 F +(BaseV = crtbase\050[4 5], [8 4]\051) 135.65 236.95 T +(Chrom = crtbp\0506, BaseV\051) 135.65 216.95 T +3 F +(or) 135.65 196.95 T +2 F +(Chrom = crtbp\050[6,8],[8 8 8 8 4 4 4 4 4]\051) 135.65 176.95 T +135.65 477.47 212.04 489.94 C +2 12 Q +0 X +0 K +(N) 136.65 480.95 T +(i) 144.55 480.95 T +(n) 152.45 480.95 T +(d) 160.35 480.95 T +(L) 180.13 480.95 T +(i) 188.04 480.95 T +(n) 195.94 480.95 T +(d) 203.84 480.95 T +4 F +(\264) 170.55 480.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "8" 9 +%%Page: "9" 9 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-9) 518.33 61.29 T +2 12 Q +(Chrom =) 135.65 736.95 T +(4 3 1 1 2 0 2 0 3) 153.65 722.95 T +(1 4 7 5 2 1 1 1 0) 153.65 708.95 T +(1 3 0 1 0 0 0 0 2) 153.65 694.95 T +(1 5 5 7 2 0 2 3 1) 153.65 680.95 T +(4 5 7 7 0 1 3 0 3) 153.65 666.95 T +(4 2 4 0 3 3 1 1 0) 153.65 652.95 T +1 16 Q +(Algorithm) 117.65 630.29 T +2 12 Q +(crtbp) 135.65 612.95 T +3 F +( is an m-\336le in the GA T) 171.63 612.95 T +(oolbox that uses the M) 288.38 612.95 T +3 10 Q +(A) 397.66 612.95 T +(TLAB) 403.76 612.95 T +3 12 Q +( function) 429.86 612.95 T +2 F +(rand) 475.83 612.95 T +3 F +(.) 504.61 612.95 T +1 16 Q +(See Also) 117.65 584.29 T +2 12 Q +(crtbase) 135.65 566.95 T +3 F +(,) 186.02 566.95 T +2 F +(crtrp) 192.02 566.95 T +FMENDPAGE +%%EndPage: "9" 10 +%%Page: "10" 10 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-10) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(crtrp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Create a real-valued initial population) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(Chrom = crtrp\050Nind, FieldDR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +3 12 Q +0.45 (The \336rst step in a genetic algorithm is to create an initial population consisting of) 135.65 588.95 P +2.82 (random individuals.) 135.65 574.95 P +2 F +6.77 (crtrp) 240.23 574.95 P +3 F +2.82 ( produces a matrix,) 276.21 574.95 P +2 F +6.77 (Chrom) 382.42 574.95 P +3 F +2.82 (, containing uniformly) 418.4 574.95 P +(distributed random values in its elements.) 135.65 560.95 T +2 F +2.4 (Chrom = crtrp\050Nind, FiedDR\051) 135.65 534.95 P +3 F +1 ( creates a random real-valued matrix of) 337.14 534.95 P +3 (size) 135.65 520.95 P +3 (, where) 236.68 520.95 P +2 F +7.2 (Nind) 280.98 520.95 P +3 F +3 ( speci\336es the number of individuals in the) 309.77 520.95 P +0.14 (population and) 135.65 506.95 P +2 F +0.33 (Nvar) 210.55 506.95 P +3 F +0.14 ( the number of variables of each individual.) 239.33 506.95 P +2 F +0.33 (Nvar) 452.62 506.95 P +3 F +0.14 ( is derived) 481.4 506.95 P +(from) 135.65 492.95 T +2 F +(FieldDR) 161.96 492.95 T +3 F +( with) 212.33 492.95 T +2 F +(Nvar = size\050FieldDR,2\051) 239.65 492.95 T +3 F +(.) 397.97 492.95 T +2 F +0 (FieldDR) 135.65 466.95 P +3 F +0 ( \050FieldDescriptionRealvalue\051 is a matrix of size) 186.02 466.95 P +0 ( and contains) 468.35 466.95 P +0.64 (the boundaries of each variable of an individual. The \336rst row contains the lower) 135.65 452.95 P +(bounds, the second row the upper bounds.) 135.65 438.95 T +2 F +(FieldDR) 135.65 412.95 T +3 F +( is used in other functions \050mutation\051.) 186.02 412.95 T +1 16 Q +(Example) 117.65 384.29 T +3 12 Q +(T) 135.65 366.95 T +(o create a random population of 6 individuals with 4 variables each:) 142.14 366.95 T +(De\336ne boundaries on the variables,) 135.65 346.95 T +2 F +(FieldDR = [) 135.65 326.95 T +(-100 -50 -30 -20;) 153.65 312.95 T +( % lower bound) 283.18 312.95 T +( 100) 153.65 298.95 T +(50) 196.82 298.95 T +(30) 225.61 298.95 T +(20]; % upper bound) 254.39 298.95 T +3 F +(Create initial population) 135.65 278.95 T +2 F +(Chrom = crtrp\0506, FieldDR\051) 135.65 258.95 T +(Chrom =) 135.65 238.95 T +(40.23 -17.17) 168.04 224.95 T +(28.95) 268.79 224.95 T +(15.38) 319.16 224.95 T +(82.06) 168.04 210.95 T +(13.26) 218.41 210.95 T +(13.35) 268.79 210.95 T +(-9.09) 319.16 210.95 T +(52.43) 168.04 196.95 T +(25.64) 218.41 196.95 T +(15.20) 268.79 196.95 T +(-2.54) 319.16 196.95 T +( -47.50) 153.65 182.95 T +( 49.10) 211.22 182.95 T +( 9.09) 268.79 182.95 T +(10.65) 319.16 182.95 T +( -90.50 -13.46 -25.63) 153.65 168.95 T +(-0.89) 319.16 168.95 T +(47.21 -25.29) 168.04 154.95 T +( 7.89 -10.48) 268.79 154.95 T +1 16 Q +(See Also) 117.65 132.29 T +2 12 Q +(mutbga) 138.65 114.95 T +3 F +(,) 181.82 114.95 T +2 F +(recdis) 187.82 114.95 T +3 F +(,) 231 114.95 T +2 F +(recint) 236.99 114.95 T +3 F +(,) 280.17 114.95 T +2 F +(reclin) 286.17 114.95 T +160.3 517.47 236.68 529.94 C +2 12 Q +0 X +0 K +(N) 161.3 520.95 T +(i) 169.2 520.95 T +(n) 177.1 520.95 T +(d) 185 520.95 T +(N) 204.78 520.95 T +(v) 212.68 520.95 T +(a) 220.59 520.95 T +(r) 228.49 520.95 T +4 F +(\264) 195.2 520.95 T +-8.35 24.95 603.65 816.95 C +416.87 463.35 468.35 476.13 C +3 12 Q +0 X +0 K +(2) 417.87 466.95 T +2 F +(N) 436.45 466.95 T +(v) 444.35 466.95 T +(a) 452.26 466.95 T +(r) 460.16 466.95 T +4 F +(\264) 426.87 466.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "10" 11 +%%Page: "11" 11 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-11) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(migrate) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +( Migrate individuals between subpopulations) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(Chrom = migrate\050Chrom, SUBPOP\051) 135.65 628.95 T +(Chrom = migrate\050Chrom, SUBPOP, MigOpt\051) 135.65 608.95 T +(Chrom = migrate\050Chrom, SUBPOP, MigOpt, ObjV\051) 135.65 588.95 T +([Chrom, ObjV] = migrate\050Chrom, SUBPOP, MigOpt, ObjV\051) 135.65 568.95 T +1 16 Q +(Description) 117.65 546.29 T +2 12 Q +9.55 (migrate) 135.65 528.95 P +3 F +3.98 ( performs migration of individuals between subpopulations in the) 186.02 528.95 P +1.62 (current population,) 135.65 514.95 P +2 F +3.89 (Chrom) 233.16 514.95 P +3 F +1.62 (, and returns the population after migration,) 269.14 514.95 P +2 F +3.89 (Chrom) 492.67 514.95 P +3 F +1.62 (.) 528.65 514.95 P +0.02 (Each row of) 135.65 500.95 P +2 F +0.06 (Chrom) 197.33 500.95 P +3 F +0.02 ( corresponds to one individual. The number of subpopulations) 233.31 500.95 P +0.88 (is indicated by) 135.65 486.95 P +2 F +2.12 (SUBPOP) 211.26 486.95 P +3 F +0.88 (. The subpopulations in) 253.1 486.95 P +2 F +2.12 (Chrom) 372.24 486.95 P +3 F +0.88 ( are ordered according to) 408.22 486.95 P +(the following scheme:) 135.65 472.95 T +(All subpopulations must have the same number of individuals.) 135.65 146.46 T +2 F +(MigOpt) 135.65 120.46 T +3 F +( is an optional vector with a maximum of 3 parameters:) 178.82 120.46 T +230.9 168.46 436.39 454.95 C +2 12 Q +0 X +0 K +(C) 239.23 312.73 T +(h) 246.42 312.73 T +(r) 253.62 312.73 T +(o) 260.82 312.73 T +(m) 268.01 312.73 T +(I) 317.28 425.09 T +(n) 324.48 425.09 T +(d) 331.67 425.09 T +(1) 340.33 419.61 T +(S) 349.23 425.09 T +(u) 356.43 425.09 T +(b) 363.63 425.09 T +(P) 370.82 425.09 T +(o) 378.02 425.09 T +(p) 385.21 425.09 T +(1) 393.87 419.61 T +(I) 317.78 405.14 T +(n) 324.98 405.14 T +(d) 332.17 405.14 T +(2) 340.83 399.65 T +(S) 348.73 405.14 T +(u) 355.93 405.14 T +(b) 363.13 405.14 T +(P) 370.32 405.14 T +(o) 377.52 405.14 T +(p) 384.71 405.14 T +(1) 393.37 399.65 T +4 F +(\274) 353.68 385.18 T +2 F +(I) 317.28 369.2 T +(n) 324.48 369.2 T +(d) 331.67 369.2 T +(N) 340.33 363.72 T +(S) 349.23 369.2 T +(u) 356.43 369.2 T +(b) 363.63 369.2 T +(P) 370.82 369.2 T +(o) 378.02 369.2 T +(p) 385.21 369.2 T +(1) 393.87 363.72 T +(I) 317.78 349.25 T +(n) 324.98 349.25 T +(d) 332.17 349.25 T +(1) 340.83 343.77 T +(S) 349.73 349.25 T +(u) 356.93 349.25 T +(b) 364.13 349.25 T +(P) 371.32 349.25 T +(o) 378.52 349.25 T +(p) 385.71 349.25 T +(2) 394.37 343.77 T +(I) 317.78 329.3 T +(n) 324.98 329.3 T +(d) 332.17 329.3 T +(2) 340.83 323.81 T +(S) 348.73 329.3 T +(u) 355.93 329.3 T +(b) 363.13 329.3 T +(P) 370.32 329.3 T +(o) 377.52 329.3 T +(p) 384.71 329.3 T +(2) 393.37 323.81 T +4 F +(\274) 353.68 309.34 T +2 F +(I) 317.28 293.36 T +(n) 324.48 293.36 T +(d) 331.67 293.36 T +(N) 340.33 287.88 T +(S) 349.23 293.36 T +(u) 356.43 293.36 T +(b) 363.63 293.36 T +(P) 370.82 293.36 T +(o) 378.02 293.36 T +(p) 385.21 293.36 T +(2) 393.87 287.88 T +4 F +(\274) 353.68 273.41 T +2 F +(I) 299.29 257.43 T +(n) 306.49 257.43 T +(d) 313.68 257.43 T +(1) 322.34 251.94 T +(S) 331.24 257.43 T +(u) 338.44 257.43 T +(b) 345.64 257.43 T +(P) 352.83 257.43 T +(o) 360.03 257.43 T +(p) 367.22 257.43 T +(S) 375.88 251.94 T +(U) 383.08 251.94 T +(B) 390.27 251.94 T +(P) 397.47 251.94 T +(O) 404.67 251.94 T +(P) 411.86 251.94 T +(I) 299.79 237.47 T +(n) 306.99 237.47 T +(d) 314.18 237.47 T +(2) 322.84 231.99 T +(S) 330.74 237.47 T +(u) 337.94 237.47 T +(b) 345.14 237.47 T +(P) 352.33 237.47 T +(o) 359.53 237.47 T +(p) 366.72 237.47 T +(S) 375.38 231.99 T +(U) 382.58 231.99 T +(B) 389.77 231.99 T +(P) 396.97 231.99 T +(O) 404.17 231.99 T +(P) 411.36 231.99 T +4 F +(\274) 353.68 217.52 T +2 F +(I) 299.29 201.54 T +(n) 306.49 201.54 T +(d) 313.68 201.54 T +(N) 322.34 196.05 T +(S) 331.24 201.54 T +(u) 338.44 201.54 T +(b) 345.64 201.54 T +(P) 352.83 201.54 T +(o) 360.03 201.54 T +(p) 367.22 201.54 T +(S) 375.88 196.05 T +(U) 383.08 196.05 T +(B) 390.27 196.05 T +(P) 397.47 196.05 T +(O) 404.67 196.05 T +(P) 411.86 196.05 T +4 F +(=) 282.21 312.73 T +300.79 193.57 296.79 193.57 2 L +0.33 H +0 Z +N +296.79 193.57 296.79 437.08 2 L +N +296.79 437.08 300.79 437.08 2 L +N +417.56 193.57 421.56 193.57 2 L +N +421.56 193.57 421.56 437.08 2 L +N +421.56 437.08 417.56 437.08 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "11" 12 +%%Page: "12" 12 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-12) 513.33 61.29 T +2 12 Q +(MigOpt\0501\051) 135.65 736.95 T +3 F +(:) 200.41 736.95 T +8.11 (scalar containing the rate of migration of individuals between) 171.65 722.95 P +(subpopulations in the range) 171.65 708.95 T +2 F +([0, 1]) 306.9 708.95 T +3 F +(If omitted or) 171.65 694.95 T +2 F +(NaN) 235.27 694.95 T +3 F +(,) 256.86 694.95 T +2 F +(MigOpt\0501\051 = 0.2) 262.86 694.95 T +3 F +( \05020%\051 is assumed.) 370.8 694.95 T +4.74 (If the migration rate is greater than 0 at least one individual per) 171.65 680.95 P +(subpopulation will migrate.) 171.65 666.95 T +2 F +(MigOpt\0502\051) 135.65 646.95 T +3 F +(:) 200.41 646.95 T +(scalar specifying the migration selection method) 171.65 632.95 T +(0 - uniform migration) 171.65 618.95 T +(1 - \336tness-based migration) 171.65 604.95 T +(If omitted or NaN,) 171.65 590.95 T +2 F +(MigOpt\0502\051 = 0) 263.91 590.95 T +3 F +( is assumed.) 357.46 590.95 T +2 F +(MigOpt\0503\051) 135.65 570.95 T +3 F +(:) 200.41 570.95 T +(scalar indicating the structure of the subpopulations for migration) 171.65 556.95 T +(0 - complete net structure) 171.65 542.95 T +(1 - neighbourhood structure) 171.65 528.95 T +(2 - ring structure) 171.65 514.95 T +(If omitted or) 171.65 500.95 T +2 F +(NaN,) 235.27 500.95 T +(MigOpt\0503\051 = 0) 267.06 500.95 T +3 F +( is assumed) 360.6 500.95 T +(If) 135.65 480.95 T +2 F +(MigOpt) 146.63 480.95 T +3 F +( is omitted or) 189.81 480.95 T +2 F +(NaN) 256.45 480.95 T +3 F +(, then the default values are assumed.) 278.03 480.95 T +2 F +0.25 (ObjV) 135.65 454.95 P +3 F +0.1 ( is an optional column vector with as many rows as) 164.43 454.95 P +2 F +0.25 (Chrom) 414.41 454.95 P +3 F +0.1 ( and contains the) 450.39 454.95 P +2.17 (corresponding objective values for all individuals in) 135.65 440.95 P +2 F +5.22 (Chrom) 403.71 440.95 P +3 F +2.17 (. For \336tness-based) 439.69 440.95 P +1.14 (selection of individuals \050) 135.65 426.95 P +2 F +2.73 (MigOpt\0502\051 = 1) 257.99 426.95 P +3 F +1.14 (\051) 356.99 426.95 P +2 F +2.73 (ObjV) 365.12 426.95 P +3 F +1.14 ( is necessary) 393.9 426.95 P +1.14 (. If) 456.01 426.95 P +2 F +2.73 (ObjV) 475.27 426.95 P +3 F +1.14 ( is an) 504.05 426.95 P +2.98 (input and output parameter) 135.65 412.95 P +2.98 (, the objective values are copied according to the) 273.68 412.95 P +0.45 (migration of the individuals. This saves the recomputation of the objective values) 135.65 398.95 P +(for the whole population.) 135.65 384.95 T +1 16 Q +(Example) 117.65 356.29 T +2 12 Q +2.59 (Chrom = migrate\050Chrom, SUBPOP\051) 135.65 338.95 P +3 F +1.08 ( chooses 20% of the individuals of) 359.29 338.95 P +6.2 (one subpopulation and replaces these individuals with uniformly chosen) 135.65 324.95 P +5.26 (individuals from all other subpopulations. This process is done for each) 135.65 310.95 P +(subpopulation. \050) 135.65 296.95 T +2 F +(MigOpt = [0.2, 0, 0]) 213.6 296.95 T +3 F +(\051) 357.53 296.95 T +2 F +-0.64 (Chrom = migrate\050Chrom, SUBPOP, [NaN 1 NaN], ObjV]\051) 135.65 270.95 P +3 F +-0.27 ( chooses) 490.95 270.95 P +0.3 (20% of the individuals of one subpopulation and replaces these individuals with a) 135.65 256.95 P +1.11 (selection of the \336ttest individuals \050smaller) 135.65 242.95 P +2 F +2.66 (ObjV) 346.85 242.95 P +3 F +1.11 (\051 from all other subpopulations.) 375.64 242.95 P +(\050net structure\051 This process is repeated for each subpopulation.) 135.65 228.95 T +2 F +5.45 ([Chrom,ObjV] = migrate\050Chrom,SUBPOP,[0.3 1 2],ObjV]\051) 135.65 202.95 P +3 F +5.16 (chooses 30% of the individuals of one subpopulation and replaces these) 135.65 188.95 P +5.9 (individuals with the \336ttest individuals \050smaller) 135.65 174.95 P +2 F +14.15 (ObjV) 397.58 174.95 P +3 F +5.9 (\051 from an adjacent) 426.37 174.95 P +0.69 (subpopulation in a unidirectional ring structure. This process is repeated for each) 135.65 160.95 P +1.12 (subpopulation. The \336rst subpopulation receives its new individuals from the last) 135.65 146.95 P +4.69 (subpopulation \050) 135.65 132.95 P +2 F +11.26 (SUBPOP) 215.3 132.95 P +3 F +4.69 (\051.) 258.48 132.95 P +2 F +11.26 (ObjV) 273.16 132.95 P +3 F +4.69 ( is returned according to the migration of) 301.94 132.95 P +(individuals.) 135.65 118.95 T +FMENDPAGE +%%EndPage: "12" 13 +%%Page: "13" 13 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-13) 513.33 61.29 T +3 12 Q +(The migration scheme employed:) 135.65 736.95 T +(subpop1-->subpop2-->subpop3-->...-->subpop) 135.65 722.95 T +2 F +(SUBPOP) 360.24 722.95 T +3 F +(--> subpop1) 403.41 722.95 T +2 F +1.85 ([Chrom,ObjV] = migrate\050Chrom,SUBPOP,[NaN NaN 1],ObjV]\051) 135.65 696.95 P +3 F +5.16 (chooses 20% of the individuals of one subpopulation and replaces these) 135.65 682.95 P +0.69 (individuals with uniformly chosen individuals from both adjacent subpopulations) 135.65 668.95 P +1.18 (in an one dimensional neighborhood structure. This process is repeated for each) 135.65 654.95 P +1.12 (subpopulation. The \336rst subpopulation receives its new individuals from the last) 135.65 640.95 P +2.3 (\050) 135.65 626.95 P +2 F +5.53 (SUBPOP) 139.64 626.95 P +3 F +2.3 (\051 and second subpopulation the last subpopulation from the \336rst and) 182.82 626.95 P +2 F +9.55 (SUBPOP-1) 135.65 612.95 P +3 F +3.98 ( subpopulation.) 193.22 612.95 P +2 F +9.55 (ObjV) 278.14 612.95 P +3 F +3.98 ( is returned according to the migration of) 306.92 612.95 P +(individuals.) 135.65 598.95 T +(The migration scheme employed:) 135.65 584.95 T +(subpop) 135.65 570.95 T +2 F +(SUBPOP) 170.3 570.95 T +3 F +(-->subpop1<-->subpop2<-->...<-->subpop) 213.47 570.95 T +2 F +(SUBPOP) 417.71 570.95 T +3 F +(<--subpop1) 460.89 570.95 T +1 16 Q +(See Also) 117.65 542.29 T +2 12 Q +(select) 135.65 524.95 T +3 F +(,) 178.82 524.95 T +2 F +(recombin) 184.82 524.95 T +3 F +(,) 242.39 524.95 T +2 F +(mutate) 248.39 524.95 T +3 F +(,) 291.56 524.95 T +2 F +(reins) 297.56 524.95 T +1 16 Q +(Refer) 117.65 502.29 T +(ence) 155.53 502.29 T +3 12 Q +-0.23 ([1] H. M) 135.65 484.95 P +-0.23 (\237) 177.49 484.95 P +-0.23 (hlenbein, M. Schomisch and J. Born, \322The Parallel Genetic Algorithm as) 183.49 484.95 P +(a Function Optimizer\323,) 135.65 470.95 T +0 F +(Parallel Computing) 249.57 470.95 T +3 F +(, No. 17, pp.619-632, 1991.) 345.2 470.95 T +0.73 ([2] T) 135.65 444.95 P +0.73 (. Starkweather) 159.8 444.95 P +0.73 (, D. Whitley and K. Mathias, \322Optimization using Distributed) 229.32 444.95 P +0.29 (Genetic Algorithms\323, In) 135.65 430.95 P +0 F +0.29 (Parallel Pr) 255.77 430.95 P +0.29 (oblems Solving fr) 309.93 430.95 P +0.29 (om Natur) 394.02 430.95 P +0.29 (e) 439.52 430.95 P +3 F +0.29 (, Lecture Notes in) 444.84 430.95 P +(Computer Science, V) 135.65 416.95 T +(ol. 496, pp. 176-185, Springer) 237.03 416.95 T +(, 1991.) 381.13 416.95 T +2.45 ([3] R. T) 135.65 390.95 P +2.45 (anese, \322Distributed Genetic Algorithms\323,) 178.02 390.95 P +0 F +2.45 (Pr) 389.03 390.95 P +2.45 (oc. ICGA 3) 400.58 390.95 P +3 F +2.45 (, pp. 434-439,) 459.78 390.95 P +(Mor) 135.65 376.95 T +(gan Kaufmann Publishers, 1989.) 156.09 376.95 T +1.1 ([4] H.-M. V) 135.65 350.95 P +1.1 (oigt, J. Born and I. Santibanez-Koref, \322Modelling and Simulation of) 194.26 350.95 P +2.04 (Distributed Evolutionary Search Processes for Function Optimization\323, Parallel) 135.65 336.95 P +0.35 (Problems Solving from Nature, Lecture Notes in Computer Science, V) 135.65 322.95 P +0.35 (ol. 496, pp.) 476.65 322.95 P +(373-380, Springer V) 135.65 308.95 T +(erlag, 1991.) 233.25 308.95 T +FMENDPAGE +%%EndPage: "13" 14 +%%Page: "14" 14 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-14) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(mut) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Discrete mutation operator) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = mut\050OldChrom, Pm, BaseV\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +2.12 (mut) 135.65 588.95 P +3 F +0.88 ( takes the representation of the current population and mutates each element) 157.24 588.95 P +2.74 (with a given probability) 135.65 574.95 P +2.74 (. T) 258.02 574.95 P +2.74 (o allow for varying bases in the chromosome and) 273.24 574.95 P +1.06 (structured populations,) 135.65 560.95 P +2 F +2.54 (mut) 250.69 560.95 P +3 F +1.06 ( allows an additional ar) 272.28 560.95 P +1.06 (gument) 388.22 560.95 P +2 F +2.54 (BaseV) 428.26 560.95 P +3 F +1.06 ( that speci\336es) 464.24 560.95 P +(the base of the individual elements of a chromosome.) 135.65 546.95 T +2 F +11.77 (NewChrom = mut\050OldChrom, Pm\051) 135.65 520.95 P +3 F +4.91 ( takes the current population,) 372.46 520.95 P +2 F +5.12 (OldChrom) 135.65 506.95 P +3 F +2.13 (, with each row corresponding to an individuals, and mutates each) 193.22 506.95 P +-0.17 (element with probability) 135.65 492.95 P +2 F +-0.41 (Pm) 256.07 492.95 P +3 F +-0.17 (. If the mutation probability) 270.46 492.95 P +-0.17 (,) 401.92 492.95 P +2 F +-0.41 (Pm) 407.75 492.95 P +3 F +-0.17 (, is omitted,) 422.14 492.95 P +2 F +-0.41 (Pm=0.7/) 481.27 492.95 P +3.06 (Lind) 135.65 478.95 P +3 F +1.28 ( is assumed, where) 164.43 478.95 P +2 F +3.06 (Lind) 263.13 478.95 P +3 F +1.28 ( is the length of the chromosome structure. This) 291.92 478.95 P +3.3 (value is selected as it implies that the probability of any one element of a) 135.65 464.95 P +1.07 (chromosome being mutated is approximately 0.5 \050see [1]\051. W) 135.65 450.95 P +1.07 (ithout a third input) 438.82 450.95 P +(ar) 135.65 436.95 T +(gument,) 144.75 436.95 T +2 F +(mut) 186.73 436.95 T +3 F +( assumes that the population is binary coded.) 208.32 436.95 T +2 F +1.55 (NewChrom = \050OldChrom, Pm, BaseV\051) 135.65 410.95 P +3 F +0.64 ( uses a third ar) 372.11 410.95 P +0.64 (gument to specify) 444.41 410.95 P +1.25 (the base of the mutation of the individual elements of the chromosomes. In this) 135.65 396.95 P +0.08 (case,) 135.65 382.95 P +2 F +0.2 (length\050BaseV\051 = Lind) 162.37 382.95 P +3 F +0.08 (, where) 306.68 382.95 P +2 F +0.2 (Lind) 345.14 382.95 P +3 F +0.08 ( is the length of the chromosome) 373.92 382.95 P +(structure.) 135.65 368.95 T +2 F +(mut) 135.65 342.95 T +3 F +( is a low-level mutation function normally called by) 157.24 342.95 T +2 F +(mutate) 409.41 342.95 T +3 F +(.) 452.59 342.95 T +1 16 Q +(Example) 117.65 314.29 T +3 12 Q +(Consider a binary population) 135.65 296.95 T +2 F +(OldChrom) 278.23 296.95 T +3 F +( with 4 individuals each of length 8:) 335.79 296.95 T +2 F +(OldChrom =[) 135.65 276.95 T +(0 0 0 0 0 1 1 1;) 153.65 262.95 T +(1 0 0 0 1 0 0 1;) 153.65 248.95 T +(0 0 1 0 1 0 0 0;) 153.65 234.95 T +(1 1 0 1 1 0 1 1]) 153.65 220.95 T +3 F +(Mutate) 135.65 200.95 T +2 F +(OldChrom) 172.62 200.95 T +3 F +( with default probability:) 230.19 200.95 T +2 F +(NewChrom = mut\050OldChrom\051) 135.65 180.95 T +3 F +(Thus,) 135.65 160.95 T +2 F +(NewChrom) 165.63 160.95 T +3 F +( can become:) 223.2 160.95 T +FMENDPAGE +%%EndPage: "14" 15 +%%Page: "15" 15 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-15) 513.33 61.29 T +2 12 Q +(NewChrom =) 135.65 736.95 T +(0 0 1 0 0 1 1 1) 153.65 722.95 T +(1 1 0 0 0 0 0 1) 153.65 708.95 T +(0 0 0 0 1 0 0 0) 153.65 694.95 T +(1 1 0 1 1 0 1 1) 153.65 680.95 T +3 F +4.05 (The complement of a binary string is obtained by applying mutation with) 135.65 660.95 P +(probability 1.) 135.65 646.95 T +2 F +(mut\050[1 0 1 0 1 1 1 0], 1\051) 135.65 626.95 T +(ans =) 135.65 606.95 T +(0 1 0 1 0 0 0 1) 153.65 592.95 T +1 16 Q +(See Also) 117.65 570.29 T +2 12 Q +(mutate) 135.65 552.95 T +3 F +(,) 178.82 552.95 T +2 F +(mutbga) 184.82 552.95 T +1 16 Q +(Refer) 117.65 530.29 T +(ence) 155.53 530.29 T +3 12 Q +2.35 ([1] J\237r) 135.65 512.95 P +2.35 (gen Hesser and Reinhard M\212nner) 169.42 512.95 P +2.35 (, \322T) 338.86 512.95 P +2.35 (owards an Optimal Mutation Rate) 359.02 512.95 P +1.91 (Probability for Genetic Algorithms\323, In) 135.65 498.95 P +0 F +1.91 (Parallel Pr) 337.76 498.95 P +1.91 (oblem Solving fr) 393.54 498.95 P +1.91 (om Natur) 476.21 498.95 P +1.91 (e) 523.32 498.95 P +3 F +1.91 (,) 528.65 498.95 P +(Lecture Notes in Computer Science, V) 135.65 484.95 T +(ol. 496, pp23-32, 1990.) 319.96 484.95 T +FMENDPAGE +%%EndPage: "15" 16 +%%Page: "16" 16 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-16) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(mutate) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Mutation of individuals \050high-level function\051.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = mutate\050MUT_F, OldChrom, FieldDR\051) 135.65 628.95 T +(NewChrom = mutate\050MUT_F, OldChrom, FieldDR, MutOpt\051) 135.65 608.95 T +(NewChrom = mutate\050MUT_F, OldChrom, FieldDR, MutOpt,) 135.65 588.95 T +(SUBPOP\051) 153.65 574.95 T +1 16 Q +(Description) 117.65 552.29 T +2 12 Q +4.2 (mutate) 135.65 534.95 P +3 F +1.75 ( performs mutation of individuals from a population,) 178.82 534.95 P +2 F +4.2 (OldChrom) 449.01 534.95 P +3 F +1.75 (, and) 506.58 534.95 P +1.91 (returns the mutated individuals in a new population,) 135.65 520.95 P +2 F +4.58 (NewChrom) 403.75 520.95 P +3 F +1.91 (. Each row of) 461.32 520.95 P +2 F +(OldChrom) 135.65 506.95 T +3 F +( and) 193.22 506.95 T +2 F +(NewChrom) 216.53 506.95 T +3 F +( corresponds to one individual.) 274.1 506.95 T +2 F +1.64 (MUT_F) 135.65 480.95 P +3 F +0.69 ( is a string that contains the name of the low-level mutation function, e.g.) 171.63 480.95 P +2 F +(mutbga) 135.65 466.95 T +3 F +( or) 178.82 466.95 T +2 F +(mut) 194.81 466.95 T +3 F +(.) 216.4 466.95 T +2 F +0.87 (FieldDR) 135.65 440.95 P +3 F +0.36 ( is a matrix of size) 186.02 440.95 P +0.36 ( and contains the bounds of each variable) 330.94 440.95 P +3.43 (of an individual \050real-valued variables\051 or a matrix of size) 135.65 426.95 P +3.43 ( and) 507.9 426.95 P +2.56 (contains the base of each variable \050discrete-valued variables\051. If) 135.65 412.95 P +2 F +6.14 (FieldDR) 467.72 412.95 P +3 F +2.56 ( is) 518.09 412.95 P +(omitted, empty or) 135.65 398.95 T +2 F +(NaN) 224.27 398.95 T +3 F +(, a binary representation of the variables is assumed) 245.85 398.95 T +2 F +(.) 494 398.95 T +1.54 (MutOpt) 135.65 372.95 P +3 F +0.64 ( is an optional parameter containing the mutation rate, the probability of) 178.82 372.95 P +1.35 (mutating a variable of an individual. If) 135.65 358.95 P +2 F +3.23 (MutOpt) 333.62 358.95 P +3 F +1.35 ( is omitted) 376.79 358.95 P +2 F +3.23 (,) 430.14 358.95 P +3 F +1.35 ( a default mutation) 437.33 358.95 P +0.34 (rate is assumed. For real-value mutation) 135.65 344.95 P +2 F +0.82 (MutOpt) 333.23 344.95 P +3 F +0.34 ( can contain a second parameter) 376.41 344.95 P +(specifying a scalar for shrinking the mutation range \050see) 135.65 330.95 T +2 F +(mutbga) 408.44 330.95 T +3 F +(\051.) 451.61 330.95 T +2 F +0.01 (SUBPOP) 135.65 304.95 P +3 F +0.01 ( is an optional parameter and determines the number of subpopulations in) 178.82 304.95 P +2 F +5.07 (OldChrom) 135.65 290.95 P +3 F +2.11 (. If) 193.22 290.95 P +2 F +5.07 (SUBPOP) 214.42 290.95 P +3 F +2.11 ( is omitted or) 257.6 290.95 P +2 F +5.07 (NaN,) 332.69 290.95 P +5.07 (SUBPOP = 1) 366.58 290.95 P +3 F +2.11 ( is assumed. All) 448.68 290.95 P +(subpopulations in) 135.65 276.95 T +2 F +(OldChrom) 223.61 276.95 T +3 F +( must have the same size.) 281.18 276.95 T +1 16 Q +(Example) 117.65 248.29 T +3 12 Q +4.98 (For examples, see) 135.65 230.95 P +2 F +11.94 (mutbga) 239.84 230.95 P +3 F +4.98 ( \050real-value mutation\051 and) 283.02 230.95 P +2 F +11.94 (mut) 430.82 230.95 P +3 F +4.98 ( \050discrete-value) 452.41 230.95 P +(mutation\051.) 135.65 216.95 T +1 16 Q +(Algorithm) 117.65 194.29 T +2 12 Q +3.36 (mutate) 135.65 176.95 P +3 F +1.4 ( checks the consistency of the input parameters and calls the low-level) 178.82 176.95 P +-0.05 (mutation function. If) 135.65 162.95 P +2 F +-0.12 (mutate) 238.1 162.95 P +3 F +-0.05 ( is called with more than one subpopulation then the) 281.27 162.95 P +(low-level mutation function is called separately for each subpopulation.) 135.65 148.95 T +1 16 Q +(See Also) 117.65 126.29 T +2 12 Q +(mutbga) 135.65 108.95 T +3 F +(,) 178.82 108.95 T +2 F +(mut) 184.82 108.95 T +3 F +(,) 206.41 108.95 T +2 F +(recombin) 212.41 108.95 T +3 F +(,) 269.97 108.95 T +2 F +(select) 275.97 108.95 T +279.46 437.35 330.94 450.13 C +3 12 Q +0 X +0 K +(2) 280.46 440.95 T +2 F +(N) 299.04 440.95 T +(v) 306.94 440.95 T +(a) 314.84 440.95 T +(r) 322.74 440.95 T +4 F +(\264) 289.45 440.95 T +-8.35 24.95 603.65 816.95 C +450.42 423.35 507.9 436.13 C +3 12 Q +0 X +0 K +(1) 454.42 426.95 T +2 F +(N) 473 426.95 T +(v) 480.9 426.95 T +(a) 488.8 426.95 T +(r) 496.7 426.95 T +4 F +(\264) 463.41 426.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "16" 17 +%%Page: "17" 17 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-17) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(mutbga) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +3.11 (Mutation of real-valued population \050mutation operator of the breeder genetic) 135.65 674.95 P +(algorithm\051.) 135.65 660.95 T +1 16 Q +(Synopsis) 117.65 632.29 T +2 12 Q +(NewChrom = mutbga\050OldChrom, FieldDR\051) 135.65 614.95 T +(NewChrom = mutbga\050OldChrom, FieldDR, MutOpt\051) 135.65 594.95 T +1 16 Q +(Description) 117.65 572.29 T +2 12 Q +-0.41 (mutbga) 135.65 554.95 P +3 F +-0.17 ( takes the real-valued population,) 178.82 554.95 P +2 F +-0.41 (OldChrom) 340.52 554.95 P +3 F +-0.17 (, mutates each variable with) 398.09 554.95 P +(given probability and returns the population after mutation,) 135.65 540.95 T +2 F +(NewChrom) 423.13 540.95 T +3 F +(.) 480.7 540.95 T +2 F +-0.55 (NewChrom = mutbga\050OldChrom, FieldDR, MutOpt\051) 135.65 514.95 P +3 F +-0.23 ( takes the current) 450.07 514.95 P +3.3 (population, stored in the matrix) 135.65 500.95 P +2 F +7.91 (OldChrom) 306.05 500.95 P +3 F +3.3 ( and mutates each variable with) 363.61 500.95 P +0.1 (probability) 135.65 486.95 P +2 F +0.24 (MutOpt\0501\051) 191.39 486.95 P +3 F +0.1 ( by addition of small random values \050size of the mutation) 256.15 486.95 P +(step\051. The mutation step can be shrunk with) 135.65 472.95 T +2 F +(MutOpt\0502\051) 348.51 472.95 T +3 F +(.) 413.27 472.95 T +2 F +1.31 (FieldDR) 135.65 446.95 P +3 F +0.55 ( is a matrix containing the boundaries of each variable of an individual) 186.02 446.95 P +(\050see) 135.65 432.95 T +2 F +(crtrp) 157.96 432.95 T +3 F +(\051.) 193.94 432.95 T +2 F +(MutOpt) 135.65 406.95 T +3 F +( is an optional vector with a maximum of two parameters:) 178.82 406.95 T +2 F +(MutOpt\0501\051) 135.65 386.95 T +3 F +(:) 200.41 386.95 T +(scalar containing the mutation rate in the range) 171.65 372.95 T +2 F +([0, 1].) 400.15 372.95 T +3 F +0.43 (If omitted or) 171.65 358.95 P +2 F +1.02 (NaN) 236.55 358.95 P +3 F +0.43 (,) 258.14 358.95 P +2 F +1.02 (MutOpt\0501\051 = 1/Nvar) 264.56 358.95 P +3 F +0.43 ( is assumed, where) 396.14 358.95 P +2 F +1.02 (Nvar) 491.44 358.95 P +3 F +0.43 ( is) 520.22 358.95 P +0.63 (the number of variables per individual de\336ned by) 171.65 344.95 P +2 F +1.51 (size\050FieldDR,2\051.) 416.51 344.95 P +3 F +3.35 (This value is selected as it implies that the number of variables per) 171.65 330.95 P +(individual mutated is approximately 1.) 171.65 316.95 T +2 F +(MutOpt\0502\051) 135.65 296.95 T +3 F +(:) 200.41 296.95 T +1.99 (scalar containing a value in the range [0, 1] for shrinking the mutation) 171.65 282.95 P +(range.) 171.65 268.95 T +(If omitted or) 171.65 254.95 T +2 F +(NaN) 235.27 254.95 T +3 F +(,) 256.86 254.95 T +2 F +(MutOpt\0502\051 = 1) 262.86 254.95 T +3 F +( is assumed \050no shrinking\051.) 356.41 254.95 T +2 F +(mutbga) 135.65 234.95 T +3 F +( is a low-level mutation function normally called by) 178.82 234.95 T +2 F +(mutate) 431 234.95 T +3 F +(.) 474.17 234.95 T +1 16 Q +(Example) 117.65 206.29 T +3 12 Q +(Consider the following population with three real-valued individuals:) 135.65 188.95 T +2 F +(OldChrom = [) 135.65 168.95 T +(40.2381 -17.1766) 153.65 154.95 T +( 28.9530) 275.98 154.95 T +(15.3883;) 347.94 154.95 T +(82.0642) 153.65 140.95 T +(13.2639) 218.41 140.95 T +(13.3596) 283.18 140.95 T +(-9.0916;) 347.94 140.95 T +(52.4396) 153.65 126.95 T +(25.6410) 218.41 126.95 T +(15.2014) 283.18 126.95 T +(-2.5435]) 347.94 126.95 T +3 F +(The bounds are de\336ned as:) 135.65 106.95 T +FMENDPAGE +%%EndPage: "17" 18 +%%Page: "18" 18 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-18) 513.33 61.29 T +2 12 Q +(FieldDR = [) 135.65 736.95 T +(-100 -50 -30 -20;) 153.65 722.95 T +( 100) 153.65 708.95 T +(50) 196.82 708.95 T +( 30) 218.41 708.95 T +(20]) 254.39 708.95 T +3 F +2.08 (T) 135.65 688.95 P +2.08 (o mutate) 142.14 688.95 P +2 F +4.99 (OldChrom) 190.93 688.95 P +3 F +2.08 ( with mutation probability) 248.5 688.95 P +2 F +4.99 (1/4) 385.41 688.95 P +3 F +2.08 ( and no shrinking of the) 407 688.95 P +(mutation range:) 135.65 674.95 T +2 F +(NewChrom = mutbga\050OldChrom, FieldDR, [1/4 1.0]\051) 135.65 654.95 T +1.38 (mutbga) 135.65 634.95 P +3 F +0.57 ( produces an internal mask table,) 178.82 634.95 P +2 F +1.38 (MutMx) 343.14 634.95 P +3 F +0.57 (, determining which variable to) 379.12 634.95 P +(mutate and the sign for adding) 135.65 620.95 T +2 F +(delta) 284.88 620.95 T +3 F +( \050see Algorithm\051, e.g.) 320.86 620.95 T +2 F +(MutMx = [) 135.65 600.95 T +(0) 153.65 586.95 T +(0) 175.24 586.95 T +( 0) 189.63 586.95 T +(1;) 218.41 586.95 T +(0) 153.65 572.95 T +(0) 175.24 572.95 T +(-1) 189.63 572.95 T +(0;) 218.41 572.95 T +(0) 153.65 558.95 T +( 0) 168.04 558.95 T +(-1) 189.63 558.95 T +(-1]) 211.22 558.95 T +3 F +(An second internal table,) 135.65 538.95 T +2 F +(delta) 258.56 538.95 T +3 F +(, speci\336es the normalized mutation step size, e.g.) 294.54 538.95 T +2 F +(delta = [) 135.65 518.95 T +(0.2500) 153.65 504.95 T +(0.2500 0.2500 0.2500;) 204.02 504.95 T +(0.0001 0.0001 0.0001 0.0001;) 153.65 490.95 T +(0.2505 0.2505 0.2505 0.2505]) 153.65 476.95 T +3 F +(Thus, after mutation) 135.65 456.95 T +2 F +(NewChrom) 236.25 456.95 T +3 F +( becomes:) 293.82 456.95 T +2 F +(NewChrom =) 135.65 436.95 T +(40.2381 -17.1766 28.9530 20.0000) 153.65 422.95 T +(82.0642) 153.65 408.95 T +(13.2638 13.3559 -9.0916) 218.41 408.95 T +(52.4396) 153.65 394.95 T +(25.6410 -7.6858 -7.5539) 218.41 394.95 T +(NewChrom - OldChrom) 135.65 374.95 T +3 F +( shows the mutation steps) 272.37 374.95 T +2 F +(NewChrom - OldChrom =) 135.65 354.95 T +(0) 196.82 340.95 T +(0) 254.39 340.95 T +(0) 311.96 340.95 T +(4.6117) 333.55 340.95 T +(0) 196.82 326.95 T +(0) 254.39 326.95 T +(-0.0037) 268.79 326.95 T +(0) 369.53 326.95 T +(0) 196.82 312.95 T +( 0) 247.2 312.95 T +(-7.5156 -5.0104) 268.79 312.95 T +1 16 Q +(Algorithm) 117.65 290.29 T +3 12 Q +(The mutation of a variable is computed as follows:) 135.65 272.95 T +(mutated variable = variable +) 135.65 252.95 T +2 F +(MutMx) 135.65 232.95 T +3 F +(=) 180.62 232.95 T +( with probability) 202.43 232.95 T +2 F +(MutOpt\0501\051) 285.39 232.95 T +3 F +(, \050+ or - with equal probability\051) 350.15 232.95 T +(else 0) 171.65 218.95 T +2 F +(range =) 135.65 198.95 T +3 F +( domain of variable \050search interval de\336ned by) 228.79 198.95 T +2 F +(FieldDR) 455.94 198.95 T +3 F +(\051.) 506.32 198.95 T +2 F +(delta =) 135.65 165.03 T +3 F +(,) 237.45 165.03 T +( with probability 1/m, else 0, m = 20.) 281.05 165.03 T +0.1 (W) 135.65 131.79 P +0.1 (ith m = 20, the mutation operator is able to locate the optimum up to a precision) 146.49 131.79 P +(of) 135.65 117.79 T +(.) 303.18 117.79 T +280.07 247.96 504.55 261.94 C +2 12 Q +0 X +0 K +(M) 281.07 252.95 T +(u) 288.98 252.95 T +(t) 296.88 252.95 T +(M) 304.78 252.95 T +(x) 312.68 252.95 T +(r) 332.46 252.95 T +(a) 340.36 252.95 T +(n) 348.27 252.95 T +(g) 356.17 252.95 T +(e) 364.07 252.95 T +(M) 383.85 252.95 T +(u) 391.75 252.95 T +(t) 399.65 252.95 T +(O) 407.55 252.95 T +(p) 415.46 252.95 T +(t) 423.36 252.95 T +(2) 438.36 252.95 T +4 F +(\050) 433.26 252.95 T +(\051) 446.16 252.95 T +2 F +(d) 464.74 252.95 T +(e) 472.64 252.95 T +(l) 480.55 252.95 T +(t) 488.45 252.95 T +(a) 496.35 252.95 T +4 F +(\264) 374.26 252.95 T +(\264) 455.16 252.95 T +(\264) 322.88 252.95 T +-8.35 24.95 603.65 816.95 C +187.39 229.43 202.43 241.99 C +3 12 Q +0 X +0 K +(1) 195.43 232.95 T +4 F +(\261) 188.39 232.95 T +-8.35 24.95 603.65 816.95 C +193.22 195.35 228.79 208.13 C +3 12 Q +0 X +0 K +(0) 194.22 198.95 T +(.) 200.21 198.95 T +(5) 203.21 198.95 T +4 F +(\264) 212.21 198.95 T +-8.35 24.95 603.65 816.95 C +189.02 147.79 237.44 186.95 C +4 12 Q +0 X +0 K +(a) 211.43 165.03 T +0 9 Q +(i) 219.46 160.38 T +3 12 Q +(2) 222.67 165.03 T +0 9 Q +(i) 233.95 171.06 T +4 F +(-) 228.67 171.06 T +0 F +(i) 191.26 150.74 T +3 F +(0) 204.7 150.74 T +4 F +(=) 196.76 150.74 T +0 F +(m) 190.02 179.81 T +3 F +(1) 205.94 179.81 T +4 F +(-) 198.76 179.81 T +4 18 Q +(\345) 193.81 161.83 T +-8.35 24.95 603.65 816.95 C +243.44 157.53 281.04 174.21 C +4 12 Q +0 X +0 K +(a) 244.69 165.03 T +0 9 Q +(i) 252.72 160.38 T +3 12 Q +(1) 273.8 165.03 T +4 F +(=) 261.22 165.03 T +-8.35 24.95 603.65 816.95 C +148.64 112.79 303.18 131.01 C +2 12 Q +0 X +0 K +(r) 149.64 117.79 T +(a) 157.54 117.79 T +(n) 165.44 117.79 T +(g) 173.34 117.79 T +(e) 181.24 117.79 T +(M) 201.02 117.79 T +4 F +(\264) 191.44 117.79 T +2 F +(u) 208.93 117.79 T +(t) 216.83 117.79 T +(O) 224.73 117.79 T +(p) 232.63 117.79 T +(t) 240.54 117.79 T +(2) 255.54 117.79 T +4 F +(\050) 250.44 117.79 T +(\051) 263.34 117.79 T +3 F +(2) 281.92 117.79 T +3 9 Q +(1) 293.2 123.88 T +(9) 297.69 123.88 T +4 F +(-) 287.92 123.88 T +4 12 Q +(\264) 272.33 117.79 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "18" 19 +%%Page: "19" 19 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-19) 513.33 61.29 T +3 12 Q +0.92 (The mutation operator) 135.65 736.95 P +2 F +2.21 (mutbga) 248.67 736.95 P +3 F +0.92 ( is able to generate most points in the hypercube) 291.84 736.95 P +0.24 (de\336ned by the variables of the individual and the range of the mutation. However) 135.65 722.95 P +0.24 (,) 528.65 722.95 P +0.93 (it tests more often near the variable, that is, the probability of small step sizes is) 135.65 708.95 P +(greater than that of lar) 135.65 694.95 T +(ger step sizes.) 242.01 694.95 T +1 16 Q +(See Also) 117.65 666.29 T +2 12 Q +(mutate) 135.65 648.95 T +3 F +(,) 178.82 648.95 T +2 F +(recdis) 184.82 648.95 T +3 F +(,) 228 648.95 T +2 F +(recint) 233.99 648.95 T +3 F +(,) 277.17 648.95 T +2 F +(reclin) 283.17 648.95 T +1 16 Q +(Refer) 117.65 626.29 T +(ence) 155.53 626.29 T +3 12 Q +3.9 ([1] H. M) 135.65 608.95 P +3.9 (\237) 185.76 608.95 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 608.95 P +3.9 (oosen, \322Predictive Models for the) 354.48 608.95 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 594.95 P +0 F +0.18 (Evolutionary) 469.02 594.95 P +(Computation) 135.65 580.95 T +3 F +(, V) 198.29 580.95 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 580.95 T +FMENDPAGE +%%EndPage: "19" 20 +%%Page: "20" 20 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-20) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(ranking) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Rank-based \336tness assignment) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(FitnV = ranking\050ObjV\051) 135.65 628.95 T +(FitnV = ranking\050ObjV, RFun\051) 135.65 608.95 T +(FitnV = ranking\050ObjV, RFun, SUBPOP\051) 135.65 588.95 T +1 16 Q +(Description) 117.65 566.29 T +2 12 Q +-0.17 (ranking) 135.65 548.95 P +3 F +-0.07 ( ranks individuals according to their objective values,) 186.02 548.95 P +2 F +-0.17 (ObjV) 444.93 548.95 P +3 F +-0.07 (, and returns) 472.17 548.95 P +1.5 (a column vector containing the corresponding individual \336tness values,) 135.65 534.95 P +2 F +3.59 (FitnV) 494.22 534.95 P +3 F +1.5 (.) 528.65 534.95 P +(This function ranks individuals for) 135.65 520.95 T +1 F +(minimisation) 305.21 520.95 T +3 F +(.) 372.52 520.95 T +2 F +(RFun) 135.65 494.95 T +3 F +( is an optional vector with 1, 2 or) 164.43 494.95 T +2 F +(length\050ObjV\051) 326.33 494.95 T +3 F +( parameters:) 412.68 494.95 T +0.28 (If) 135.65 474.95 P +2 F +0.68 (RFun) 146.92 474.95 P +3 F +0.28 ( is a scalar in) 175.7 474.95 P +2 F +0.68 ([1, 2]) 242.72 474.95 P +3 F +0.28 (, linear ranking is assumed and the scalar indicates) 286.58 474.95 P +(the selective pressure.) 135.65 460.95 T +(If) 135.65 440.95 T +2 F +(RFun) 146.63 440.95 T +3 F +( is a vector with 2 parameters:) 175.42 440.95 T +2 F +(RFun\0501\051) 135.65 420.95 T +3 F +(:) 186.02 420.95 T +(scalar indicating the selective pressure) 171.65 406.95 T +(for linear ranking) 171.65 392.95 T +2 F +(RFun\0501\051) 258.58 392.95 T +3 F +( must be in) 308.95 392.95 T +2 F +([1, 2]) 364.92 392.95 T +3 F +(for non-linear ranking) 171.65 378.95 T +2 F +(RFun\0501\051) 280.56 378.95 T +3 F +( must be in) 330.93 378.95 T +2 F +([1, length\050ObjV\051-2]) 386.91 378.95 T +3 F +(If) 171.65 364.95 T +2 F +(NaN) 182.63 364.95 T +3 F +(,) 204.22 364.95 T +2 F +(RFun\0501\051 = 2) 210.22 364.95 T +3 F +( is assumed.) 289.38 364.95 T +2 F +(RFun\0502\051) 135.65 344.95 T +3 F +(:) 186.02 344.95 T +(ranking method) 171.65 330.95 T +(0 - linear ranking) 171.65 316.95 T +(1 - non-linear ranking) 171.65 302.95 T +0.29 (If) 135.65 282.95 P +2 F +0.69 (RFun) 146.92 282.95 P +3 F +0.29 ( is a vector of) 175.71 282.95 P +2 F +0.69 (length\050ObjV\051) 245.43 282.95 P +3 F +0.29 (, it should contain the \336tness values to be) 331.78 282.95 P +(assigned to each rank.) 135.65 268.95 T +2.78 (If) 135.65 242.95 P +2 F +6.66 (RFun) 149.41 242.95 P +3 F +2.78 ( is omitted or) 178.2 242.95 P +2 F +6.66 (NaN) 255.94 242.95 P +3 F +2.78 (, linear ranking and a selective pressure of 2 are) 277.52 242.95 P +(assumed.) 135.65 228.95 T +2 F +2.19 (SUBPOP) 135.65 202.95 P +3 F +0.91 ( is an optional parameter and indicates the number of subpopulations in) 178.82 202.95 P +2 F +10.67 (ObjV) 135.65 188.95 P +3 F +4.45 (. If) 162.88 188.95 P +2 F +10.67 (SUBPOP) 188.76 188.95 P +3 F +4.45 ( is omitted or) 231.93 188.95 P +2 F +10.67 (NaN) 316.35 188.95 P +3 F +4.45 (,) 337.94 188.95 P +2 F +10.67 (SUBPOP = 1) 348.38 188.95 P +3 F +4.45 ( is assumed. All) 441.68 188.95 P +(subpopulations in) 135.65 174.95 T +2 F +(ObjV) 223.61 174.95 T +3 F +( must have the same size.) 252.39 174.95 T +2.76 (If) 135.65 148.95 P +2 F +6.63 (ranking) 149.4 148.95 P +3 F +2.76 ( is called with more than one subpopulation then the ranking is) 199.77 148.95 P +(performed separately for each subpopulation.) 135.65 134.95 T +FMENDPAGE +%%EndPage: "20" 21 +%%Page: "21" 21 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-21) 513.33 61.29 T +1 16 Q +(Example) 117.65 734.29 T +3 12 Q +(Consider a population with 10 individuals. The current objective values are:) 135.65 716.95 T +2 F +(ObjV = [1; 2; 3; 4; 5; 10; 9; 8; 7; 6]) 135.65 696.95 T +3 F +(Evaluate the \336tness with linear ranking and selective pressure 2:) 135.65 676.95 T +2 F +(FitnV = ranking\050ObjV\051) 135.65 656.95 T +(FitnV =) 135.65 636.95 T +(2.00) 153.65 622.95 T +(1.77) 153.65 608.95 T +(1.55) 153.65 594.95 T +(1.33) 153.65 580.95 T +(1.11) 153.65 566.95 T +(0) 153.65 552.95 T +(0.22) 153.65 538.95 T +(0.44) 153.65 524.95 T +(0.66) 153.65 510.95 T +(0.88) 153.65 496.95 T +3 F +(Evaluate the \336tness with non-linear ranking and selective pressure 2:) 135.65 476.95 T +2 F +(FitnV = ranking\050ObjV, [2 1]\051) 135.65 456.95 T +(FitnV =) 135.65 436.95 T +(2.00) 153.65 422.95 T +(1.66) 153.65 408.95 T +(1.38) 153.65 394.95 T +(1.15) 153.65 380.95 T +(0.95) 153.65 366.95 T +(0.38) 153.65 352.95 T +(0.45) 153.65 338.95 T +(0.55) 153.65 324.95 T +(0.66) 153.65 310.95 T +(0.79) 153.65 296.95 T +3 F +(Evaluate the \336tness with the values in RFun:) 135.65 276.95 T +2 F +(RFun = [3; 5; 7; 10; 14; 18; 25; 30; 40; 50]) 135.65 256.95 T +(FitnV = ranking\050ObjV, RFun\051) 135.65 236.95 T +FMENDPAGE +%%EndPage: "21" 22 +%%Page: "22" 22 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-22) 513.33 61.29 T +2 12 Q +(FitnV =) 135.65 736.95 T +(50) 153.65 722.95 T +(40) 153.65 708.95 T +(30) 153.65 694.95 T +(25) 153.65 680.95 T +(18) 153.65 666.95 T +( 3) 153.65 652.95 T +( 5) 153.65 638.95 T +( 7) 153.65 624.95 T +(10) 153.65 610.95 T +(14) 153.65 596.95 T +3 F +3.93 (Evaluate the \336tness with non-linear ranking and selective pressure 2 for 2) 135.65 576.95 P +(subpopulations in) 135.65 562.95 T +2 F +(ObjV) 223.61 562.95 T +3 F +(:) 251.5 562.95 T +2 F +(FitnV = ranking\050ObjV, [2 1], 2\051) 135.65 542.95 T +(FitnV =) 135.65 522.95 T +(2.00) 153.65 508.95 T +(1.28) 153.65 494.95 T +(0.83) 153.65 480.95 T +(0.53) 153.65 466.95 T +(0.34) 153.65 452.95 T +(0.34) 153.65 438.95 T +(0.53) 153.65 424.95 T +(0.83) 153.65 410.95 T +(1.28) 153.65 396.95 T +(2.00) 153.65 382.95 T +1 16 Q +(Algorithm) 117.65 360.29 T +3 12 Q +2.48 (The algorithms for both linear and non-linear ranking \336rst sorts the objective) 135.65 342.95 P +0.21 (function values into descending order) 135.65 328.95 P +0.21 (. The least \336t individual is placed in position) 316.38 328.95 P +1 (1 in the sorted list of objective values and the most \336t individual position) 135.65 314.95 P +2 F +2.41 (Nind) 502.86 314.95 P +3 F +0.08 (where) 135.65 300.95 P +2 F +0.19 (Nind) 168.02 300.95 P +3 F +0.08 ( is the number of individuals in the population. A \336tness value is then) 196.81 300.95 P +4.45 (assigned to each individual depending on its position,) 135.65 286.95 P +2 F +10.68 (Pos) 431.42 286.95 P +3 F +4.45 (, in the sorted) 453.01 286.95 P +(population.) 135.65 272.95 T +(For linear ranking individuals are assigned \336tness values according to:) 135.65 252.95 T +2 F +(FitnV\050Pos\051 =) 135.65 231.96 T +3 F +(, and) 484.28 231.96 T +(for non-linear ranking according to:) 135.65 210.97 T +2 F +(FitnV\050Pos\051 =) 135.65 178.65 T +3 F +(,) 308.28 178.65 T +(where) 135.65 121.83 T +0 F +( X) 164.95 121.83 T +3 F +( is computed as the root of the polynomial:) 175.27 121.83 T +225 226.97 484.28 240.95 C +2 12 Q +0 X +0 K +(2) 226 231.96 T +(S) 245.78 231.96 T +(P) 253.68 231.96 T +4 F +(-) 236.2 231.96 T +2 F +(2) 273.46 231.96 T +(S) 300.34 231.96 T +(P) 308.24 231.96 T +(1) 328.02 231.96 T +4 F +(-) 318.44 231.96 T +(\050) 295.24 231.96 T +(\051) 335.83 231.96 T +2 F +(P) 361.51 231.96 T +(o) 369.41 231.96 T +(s) 377.31 231.96 T +(1) 397.09 231.96 T +4 F +(-) 387.51 231.96 T +(\050) 356.41 231.96 T +(\051) 404.89 231.96 T +(\264) 344.82 231.96 T +(\264) 283.66 231.96 T +2 F +(N) 425.99 231.96 T +(i) 433.89 231.96 T +(n) 441.8 231.96 T +(d) 449.7 231.96 T +(1) 469.48 231.96 T +4 F +(-) 459.89 231.96 T +(\050) 420.89 231.96 T +(\051) 477.28 231.96 T +(\244) 413.89 231.96 T +(+) 263.88 231.96 T +-8.35 24.95 603.65 816.95 C +225 137.83 308.28 198.97 C +2 12 Q +0 X +0 K +(N) 227 185.72 T +(i) 234.9 185.72 T +(n) 242.8 185.72 T +(d) 250.71 185.72 T +0 F +(X) 270.48 185.72 T +0 9 Q +(P) 277.81 191.82 T +(o) 283.83 191.82 T +(s) 288.86 191.82 T +3 F +(1) 301.79 191.82 T +4 F +(-) 294.6 191.82 T +4 12 Q +(\264) 260.9 185.72 T +0 F +(X) 267.86 156.94 T +2 F +(i) 282.99 156.94 T +4 F +(\050) 277.89 156.94 T +(\051) 290.8 156.94 T +2 F +(i) 239.01 141.31 T +(1) 257.14 141.31 T +4 9 Q +(=) 249.21 141.31 T +2 12 Q +(N) 236.49 172.25 T +(i) 244.21 172.25 T +(n) 251.94 172.25 T +(d) 259.66 172.25 T +4 18 Q +(\345) 245.26 153.74 T +227 181.24 306.03 181.24 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "22" 23 +%%Page: "23" 23 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-23) 513.33 61.29 T +3 12 Q +(.) 473.9 730.99 T +0.08 (The vector) 135.65 709.99 P +2 F +0.19 (FitnV) 190.42 709.99 P +3 F +0.08 ( is then unsorted to re\337ect the order of the original input vector) 226.4 709.99 P +0.08 (,) 528.65 709.99 P +2 F +(ObjV) 135.65 695.99 T +3 F +(.) 162.88 695.99 T +1 16 Q +(See Also) 117.65 673.32 T +2 12 Q +(select) 135.65 655.99 T +3 F +(,) 178.82 655.99 T +2 F +(rws) 184.82 655.99 T +3 F +(,) 206.41 655.99 T +2 F +(sus) 212.41 655.99 T +1 16 Q +(Refer) 117.65 633.32 T +(ence) 155.53 633.32 T +3 12 Q +1.46 ([1] D. Whitley) 135.65 615.99 P +1.46 (, \322The GENIT) 208.07 615.99 P +1.46 (OR Algorithm and Selection Pressure: Why Rank-) 279.71 615.99 P +2.08 (Based Allocation of Reproductive T) 135.65 601.99 P +2.08 (rials is Best\323,) 317.43 601.99 P +0 F +2.08 (Pr) 390.97 601.99 P +2.08 (oc. ICGA 3) 402.52 601.99 P +3 F +2.08 (, pp. 1) 460.97 601.99 P +2.08 (16-121,) 494.67 601.99 P +(Mor) 135.65 587.99 T +(gan Kaufmann Publishers, 1989.) 156.09 587.99 T +135.65 725.99 473.9 744.95 C +2 12 Q +0 X +0 K +(0) 136.65 730.99 T +(S) 169.53 730.99 T +(P) 177.43 730.99 T +(1) 197.21 730.99 T +4 F +(-) 187.63 730.99 T +(\050) 164.43 730.99 T +(\051) 205.01 730.99 T +2 F +(X) 223.59 730.99 T +(N) 231.25 736.47 T +(i) 238.98 736.47 T +(n) 246.7 736.47 T +(d) 254.43 736.47 T +(1) 271.06 736.47 T +4 9 Q +(-) 263.87 736.47 T +4 12 Q +(\264) 214.01 730.99 T +2 F +(S) 290.84 730.99 T +(P) 298.74 730.99 T +(X) 318.52 730.99 T +(N) 326.18 736.47 T +(i) 333.9 736.47 T +(n) 341.63 736.47 T +(d) 349.35 736.47 T +(2) 365.98 736.47 T +4 9 Q +(-) 358.8 736.47 T +4 12 Q +(\264) 308.94 730.99 T +(\274) 385.76 730.99 T +2 F +(S) 410.34 730.99 T +(P) 418.24 730.99 T +(X) 438.02 730.99 T +(S) 457.8 730.99 T +(P) 465.71 730.99 T +4 F +(+) 448.22 730.99 T +(\264) 428.44 730.99 T +(+) 281.25 730.99 T +(+) 376.18 730.99 T +(+) 400.76 730.99 T +(=) 149.84 730.99 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "23" 24 +%%Page: "24" 24 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-24) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ecdis) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Discrete recombination) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = recdis\050OldChrom\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +6.77 (recdis) 135.65 588.95 P +3 F +2.82 ( performs discrete recombination between pairs of individuals in the) 178.82 588.95 P +3.85 (current population,) 135.65 574.95 P +2 F +9.24 (OldChrom) 237.62 574.95 P +3 F +3.85 (, and returns a new population after mating,) 295.18 574.95 P +2 F +(NewChrom) 135.65 560.95 T +3 F +(. Each row of) 193.22 560.95 T +2 F +(OldChrom) 260.82 560.95 T +3 F +( corresponds to one individual.) 318.39 560.95 T +1.18 (The pairs are mated in order) 135.65 534.95 P +1.18 (, odd row with the next even row) 276.62 534.95 P +1.18 (. If the number of) 442.66 534.95 P +0.5 (rows in the matrix) 135.65 520.95 P +2 F +1.2 (OldChrom) 228.25 520.95 P +3 F +0.5 ( is odd then the last row is not mated and added at) 285.82 520.95 P +4.19 (the end of) 135.65 506.95 P +2 F +10.05 (NewChrom) 199.16 506.95 P +3 F +4.19 (. The population should therefore be or) 256.73 506.95 P +4.19 (ganised into) 469.16 506.95 P +0.94 (contiguous pairs that require mating. This can be achieved by using the function) 135.65 492.95 P +2 F +0.28 (ranking) 135.65 478.95 P +3 F +0.12 ( to assign a \336tness level to each individual and a selection function \050e.g.) 186.02 478.95 P +2 F +5 (select) 135.65 464.95 P +3 F +2.09 (\051 to select individuals with a probability related to their \336tness in the) 178.82 464.95 P +(current population.) 135.65 450.95 T +2 F +(recdis) 135.65 424.95 T +3 F +( is a low-level recombination function normally called by) 178.82 424.95 T +2 F +(recombin) 457.64 424.95 T +3 F +(.) 515.2 424.95 T +1 16 Q +(Example) 117.65 396.29 T +3 12 Q +(Consider the following population with \336ve real-value individuals:) 135.65 378.95 T +2 F +(OldChrom = [) 135.65 358.95 T +( 40.23 -17.17) 153.65 344.95 T +( 28.95) 254.39 344.95 T +(15.38; % parent1) 311.96 344.95 T +( 82.06) 153.65 330.95 T +( 13.26) 204.02 330.95 T +(13.35) 261.59 330.95 T +(-9.09; % parent2) 311.96 330.95 T +( 52.43) 153.65 316.95 T +(25.64) 211.22 316.95 T +(15.20) 261.59 316.95 T +(-2.54; % parent3) 311.96 316.95 T +(-47.50) 153.65 302.95 T +(49.10) 211.22 302.95 T +(9.09) 268.79 302.95 T +( 10.65; % parent4) 304.77 302.95 T +(-90.50 -13.46 -25.63) 153.65 288.95 T +(-0.89] % parent5) 311.96 288.95 T +3 F +(T) 135.65 268.95 T +(o perform discrete recombination:) 142.14 268.95 T +2 F +(NewChrom = recdis\050OldChrom\051) 135.65 248.95 T +4.11 (recdis) 135.65 228.95 P +3 F +1.71 ( produces an internal mask table determining which parents contribute) 178.82 228.95 P +(which variables to the of) 135.65 214.95 T +(fspring, e.g.) 254.01 214.95 T +2 F +(Mask = [) 135.65 194.95 T +(1 2 1 2; % for producing offspring1) 160.84 180.95 T +( 2 2 1 1; % for producing offspring2) 153.65 166.95 T +( 2 1 2 1; % for producing offspring3) 153.65 152.95 T +( 1 1 2 2] % for producing offspring4) 153.65 138.95 T +3 F +(Thus, after recombination) 135.65 118.95 T +2 F +(NewChrom) 262.89 118.95 T +3 F +( would become:) 320.45 118.95 T +FMENDPAGE +%%EndPage: "24" 25 +%%Page: "25" 25 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-25) 513.33 61.29 T +2 12 Q +(NewChrom = [) 135.65 736.95 T +(40.23) 160.84 722.95 T +(13.26) 211.22 722.95 T +(28.95) 261.59 722.95 T +( -9.09; % Mask\0501,:\051 parent1&2) 304.77 722.95 T +(82.06) 160.84 708.95 T +(13.26) 211.22 708.95 T +(28.95) 261.59 708.95 T +( 15.38; % Mask\0502,:\051 parent1&2) 304.77 708.95 T +(-47.50) 153.65 694.95 T +(25.64) 211.22 694.95 T +( 9.09) 261.59 694.95 T +(-2.54; % Mask\0503,:\051 parent3&4) 311.96 694.95 T +(52.43) 160.84 680.95 T +( 25.64) 204.02 680.95 T +( 9.09) 261.59 680.95 T +( 10.65] % Mask\0504,:\051 parent3&4) 304.77 680.95 T +3 F +0.75 (As the number of individuals in the parent population,) 135.65 660.95 P +2 F +1.79 (OldChrom) 405.55 660.95 P +3 F +0.75 (, was odd, the) 463.12 660.95 P +-0.18 (last individual is appended without recombination to) 135.65 646.95 P +2 F +-0.43 (NewChrom) 389.9 646.95 P +3 F +-0.18 ( and the of) 447.47 646.95 P +-0.18 (fspring) 497.67 646.95 P +(returned to the users workspace, thus) 135.65 632.95 T +2 F +(NewChrom =) 135.65 612.95 T +(40.23) 160.84 598.95 T +( 13.26) 204.02 598.95 T +(28.95) 261.59 598.95 T +( -9.09) 304.77 598.95 T +(82.06) 160.84 584.95 T +(13.26) 211.22 584.95 T +(28.95) 261.59 584.95 T +( 15.38) 304.77 584.95 T +(-47.50) 153.65 570.95 T +(25.64) 211.22 570.95 T +( 9.09) 261.59 570.95 T +( -2.54) 304.77 570.95 T +(52.43) 160.84 556.95 T +( 25.64) 204.02 556.95 T +(9.09) 268.79 556.95 T +(10.65) 311.96 556.95 T +(-90.50 -13.46 -25.63) 153.65 542.95 T +( -0.89) 304.77 542.95 T +1 16 Q +(Algorithm) 117.65 520.29 T +3 12 Q +1.99 (Discrete recombination exchanges variable values between the individuals. For) 135.65 502.95 P +2.43 (each variable the parent who contributes its variable value to the of) 135.65 488.95 P +2.43 (fspring is) 484.24 488.95 P +(chosen randomly with equal probability) 135.65 474.95 T +(.) 326.08 474.95 T +0.91 (Discrete recombination can generate the corners of the hypercube de\336ned by the) 135.65 448.95 P +(parents.) 135.65 434.95 T +1 16 Q +(See Also) 117.65 406.29 T +2 12 Q +(recombin) 135.65 388.95 T +3 F +(,) 193.22 388.95 T +2 F +(recint) 199.21 388.95 T +3 F +(,) 242.39 388.95 T +2 F +(reclin) 248.39 388.95 T +3 F +(,) 291.56 388.95 T +2 F +(ranking) 297.56 388.95 T +3 F +(,) 347.93 388.95 T +2 F +(sus) 353.93 388.95 T +3 F +(,) 375.52 388.95 T +2 F +(rws) 381.51 388.95 T +1 16 Q +(Refer) 117.65 366.29 T +(ence) 155.53 366.29 T +3 12 Q +3.9 ([1] H. M) 135.65 348.95 P +3.9 (\237) 185.76 348.95 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 348.95 P +3.9 (oosen, \322Predictive Models for the) 354.48 348.95 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 334.95 P +0 F +0.18 (Evolutionary) 469.02 334.95 P +(Computation) 135.65 320.95 T +3 F +(, V) 198.29 320.95 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 320.95 T +FMENDPAGE +%%EndPage: "25" 26 +%%Page: "26" 26 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-26) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ecint) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Intermediate recombination) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = recint\050OldChrom\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.73 (recint) 135.65 588.95 P +3 F +0.3 ( performs intermediate recombination between pairs of individuals in the) 178.82 588.95 P +3.85 (current population,) 135.65 574.95 P +2 F +9.24 (OldChrom) 237.62 574.95 P +3 F +3.85 (, and returns a new population after mating,) 295.18 574.95 P +2 F +(NewChrom) 135.65 560.95 T +3 F +(. Each row of) 193.22 560.95 T +2 F +(OldChrom) 260.82 560.95 T +3 F +( corresponds to one individual.) 318.39 560.95 T +2 F +1.76 (recint) 135.65 534.95 P +3 F +0.73 ( is a function only applicable to populations of real-value variables \050and) 178.82 534.95 P +(not binary or integer\051.) 135.65 520.95 T +1.18 (The pairs are mated in order) 135.65 494.95 P +1.18 (, odd row with the next even row) 276.62 494.95 P +1.18 (. If the number of) 442.66 494.95 P +0.5 (rows in the matrix) 135.65 480.95 P +2 F +1.2 (OldChrom) 228.25 480.95 P +3 F +0.5 ( is odd then the last row is not mated and added at) 285.82 480.95 P +4.19 (the end of) 135.65 466.95 P +2 F +10.05 (NewChrom) 199.16 466.95 P +3 F +4.19 (. The population should therefore be or) 256.73 466.95 P +4.19 (ganised into) 469.16 466.95 P +0.94 (contiguous pairs that require mating. This can be achieved by using the function) 135.65 452.95 P +2 F +0.28 (ranking) 135.65 438.95 P +3 F +0.12 ( to assign a \336tness level to each individual and a selection function \050e.g.) 186.02 438.95 P +2 F +5 (select) 135.65 424.95 P +3 F +2.09 (\051 to select individuals with a probability related to their \336tness in the) 178.82 424.95 P +(current population.) 135.65 410.95 T +2 F +(recint) 135.65 384.95 T +3 F +( is a low-level recombination function normally called by) 178.82 384.95 T +2 F +(recombin) 457.64 384.95 T +3 F +(.) 515.2 384.95 T +1 16 Q +(Example) 117.65 356.29 T +3 12 Q +(Consider the following population with three real-value individuals:) 135.65 338.95 T +2 F +(OldChrom = [) 135.65 318.95 T +(40.23 -17.17) 153.65 304.95 T +( 28.95) 247.2 304.95 T +(15.38; % parent1) 304.77 304.95 T +(82.06) 153.65 290.95 T +( 13.26) 196.82 290.95 T +(13.35) 254.39 290.95 T +(-9.09; % parent2) 304.77 290.95 T +(52.43) 153.65 276.95 T +(25.64) 204.02 276.95 T +(15.20) 254.39 276.95 T +(-2.54] % parent3) 304.77 276.95 T +3 F +(T) 135.65 256.95 T +(o perform intermediate recombination:) 142.14 256.95 T +2 F +(NewChrom = recint\050OldChrom\051) 135.65 236.95 T +3 F +2.57 (New values are produced by adding the scaled dif) 135.65 216.95 P +2.57 (ference between the parent) 395.08 216.95 P +1.05 (values to the \336rst parent \050see) 135.65 202.95 P +0 F +1.05 (Algorithm) 282.51 202.95 P +3 F +1.05 ( subsection\051. An internal table of scaling) 331.15 202.95 P +(factors,) 135.65 188.95 T +2 F +(Alpha) 174.28 188.95 T +3 F +(, is produced, e.g.) 210.26 188.95 T +2 F +(Alpha = [) 135.65 168.95 T +(-0.13 0.50 0.32 0.16; % for offspring1) 153.65 154.95 T +( 1.12 0.54 0.44 1.16] % for offspring2) 153.65 140.95 T +3 F +(Thus, after recombination) 135.65 120.95 T +2 F +(NewChrom) 262.89 120.95 T +3 F +( would become:) 320.45 120.95 T +FMENDPAGE +%%EndPage: "26" 27 +%%Page: "27" 27 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-27) 513.33 61.29 T +2 12 Q +(NewChrom = [) 135.65 736.95 T +(34.40) 153.65 722.95 T +( -1.92) 196.82 722.95 T +( 23.86) 247.2 722.95 T +( 11.33; % Alpha\0501,:\051 parent1&2) 297.57 722.95 T +(87.11) 153.65 708.95 T +( -0.59) 196.82 708.95 T +(21.98 -13.04] % Alpha\0502,:\051 parent1&2) 254.39 708.95 T +3 F +0.75 (As the number of individuals in the parent population,) 135.65 688.95 P +2 F +1.79 (OldChrom) 405.55 688.95 P +3 F +0.75 (, was odd, the) 463.12 688.95 P +-0.18 (last individual is appended without recombination to) 135.65 674.95 P +2 F +-0.43 (NewChrom) 389.9 674.95 P +3 F +-0.18 ( and the of) 447.47 674.95 P +-0.18 (fspring) 497.67 674.95 P +(returned to the users workspace, thus:) 135.65 660.95 T +2 F +(NewChrom =) 135.65 640.95 T +(34.40) 153.65 626.95 T +(-1.92) 204.02 626.95 T +(23.86) 254.39 626.95 T +( 11.33) 297.57 626.95 T +(87.11) 153.65 612.95 T +(-0.59) 204.02 612.95 T +(21.98 -13.04) 254.39 612.95 T +(52.43) 153.65 598.95 T +(25.64) 204.02 598.95 T +(15.20) 254.39 598.95 T +(-2.54) 304.77 598.95 T +1 16 Q +(Algorithm) 117.65 576.29 T +3 12 Q +(Intermediate recombination combines parent values using the following rule:) 135.65 558.95 T +2 F +(offspring = parent1 +) 135.65 532.95 T +3 F +(where) 135.65 506.95 T +2 F +(Alpha) 167.95 506.95 T +3 F +( is a scaling factor chosen uniformly at random in the interval) 203.93 506.95 T +2 F +1.08 ([-0.25, 1.25]) 135.65 492.95 P +3 F +0.45 (.) 230.28 492.95 P +2 F +1.08 (recint) 236.73 492.95 P +3 F +0.45 ( produces a new Alpha for each pair of values to be) 279.9 492.95 P +(combined.) 135.65 478.95 T +1.99 (Intermediate recombination can generate any point within a hypercube slightly) 135.65 452.95 P +(lar) 135.65 438.95 T +(ger than that de\336ned by the parents.) 148.09 438.95 T +2.01 (Intermediate recombination is similar to line recombination) 135.65 412.95 P +2 F +4.82 (reclin) 438.51 412.95 P +3 F +2.01 (. Whereas) 481.69 412.95 P +2 F +5.85 (recint) 135.65 398.95 P +3 F +2.44 ( uses a new Alpha factor for each pair of values combined together) 178.82 398.95 P +2.44 (,) 528.65 398.95 P +2 F +(reclin) 135.65 384.95 T +3 F +( uses one) 178.82 384.95 T +2 F +(Alpha) 225.79 384.95 T +3 F +( factor for each pair of parents.) 261.77 384.95 T +1 16 Q +(See Also) 117.65 356.29 T +2 12 Q +(recombin) 135.65 338.95 T +3 F +(,) 193.22 338.95 T +2 F +(recdis) 199.21 338.95 T +3 F +(,) 242.39 338.95 T +2 F +(reclin) 248.39 338.95 T +3 F +(,) 291.56 338.95 T +2 F +(ranking) 297.56 338.95 T +3 F +(,) 347.93 338.95 T +2 F +(sus) 353.93 338.95 T +3 F +(,) 375.52 338.95 T +2 F +(rws) 381.51 338.95 T +1 16 Q +(Refer) 117.65 316.29 T +(ence) 155.53 316.29 T +3 12 Q +3.9 ([1] H. M) 135.65 298.95 P +3.9 (\237) 185.76 298.95 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 298.95 P +3.9 (oosen, \322Predictive Models for the) 354.48 298.95 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 284.95 P +0 F +0.18 (Evolutionary) 469.02 284.95 P +(Computation) 135.65 270.95 T +3 F +(, V) 198.29 270.95 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 270.95 T +293.96 527.96 482.85 541.94 C +2 12 Q +0 X +0 K +(A) 294.96 532.95 T +(l) 302.86 532.95 T +(p) 310.77 532.95 T +(h) 318.67 532.95 T +(a) 326.57 532.95 T +(p) 353.45 532.95 T +(a) 361.35 532.95 T +(r) 369.25 532.95 T +(e) 377.16 532.95 T +(n) 385.06 532.95 T +(t) 392.96 532.95 T +(2) 400.86 532.95 T +(p) 420.64 532.95 T +(a) 428.54 532.95 T +(r) 436.45 532.95 T +(e) 444.35 532.95 T +(n) 452.25 532.95 T +(t) 460.15 532.95 T +(1) 468.05 532.95 T +4 F +(-) 411.06 532.95 T +(\050) 348.35 532.95 T +(\051) 475.86 532.95 T +(\264) 336.77 532.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "27" 28 +%%Page: "28" 28 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-28) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(eclin) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Line recombination) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = reclin\050OldChrom\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +1.86 (reclin) 135.65 588.95 P +3 F +0.77 ( performs line recombination between pairs of individuals in the current) 178.82 588.95 P +0.89 (population,) 135.65 574.95 P +2 F +2.15 (OldChrom) 193.85 574.95 P +3 F +0.89 (, and returns a new population after mating,) 251.41 574.95 P +2 F +2.15 (NewChrom) 471.08 574.95 P +3 F +0.89 (.) 528.65 574.95 P +(Each row of) 135.65 560.95 T +2 F +(OldChrom) 197.26 560.95 T +3 F +( corresponds to one individual.) 254.83 560.95 T +2 F +1.9 (reclin) 135.65 534.95 P +3 F +0.79 ( is a function only applicable to populations of real-value variables \050) 178.82 534.95 P +1 F +0.79 (not) 514.99 534.95 P +3 F +(binary or integer\051.) 135.65 520.95 T +1.18 (The pairs are mated in order) 135.65 494.95 P +1.18 (, odd row with the next even row) 276.62 494.95 P +1.18 (. If the number of) 442.66 494.95 P +0.5 (rows in the matrix) 135.65 480.95 P +2 F +1.2 (OldChrom) 228.25 480.95 P +3 F +0.5 ( is odd then the last row is not mated and added at) 285.82 480.95 P +4.19 (the end of) 135.65 466.95 P +2 F +10.05 (NewChrom) 199.16 466.95 P +3 F +4.19 (. The population should therefore be or) 256.73 466.95 P +4.19 (ganised into) 469.16 466.95 P +0.94 (contiguous pairs that require mating. This can be achieved by using the function) 135.65 452.95 P +2 F +0.28 (ranking) 135.65 438.95 P +3 F +0.12 ( to assign a \336tness level to each individual and a selection function \050e.g.) 186.02 438.95 P +2 F +5 (select) 135.65 424.95 P +3 F +2.09 (\051 to select individuals with a probability related to their \336tness in the) 178.82 424.95 P +(current population.) 135.65 410.95 T +2 F +(reclin) 135.65 384.95 T +3 F +( is a low-level recombination function normally called by) 178.82 384.95 T +2 F +(recombin) 457.64 384.95 T +3 F +(.) 515.2 384.95 T +1 16 Q +(Example) 117.65 356.29 T +3 12 Q +(Consider the following population with three real-value individuals:) 135.65 338.95 T +2 F +(OldChrom = [) 135.65 318.95 T +( 40.23 -17.17) 153.65 304.95 T +(28.95) 261.59 304.95 T +(15.38; % parent1) 311.96 304.95 T +( 82.06) 153.65 290.95 T +( 13.26) 204.02 290.95 T +(13.35) 261.59 290.95 T +(-9.09; % parent2) 311.96 290.95 T +( 52.43) 153.65 276.95 T +(25.64) 211.22 276.95 T +(15.20) 261.59 276.95 T +(-2.54] % parent3) 311.96 276.95 T +3 F +(T) 135.65 256.95 T +(o perform line recombination:) 142.14 256.95 T +2 F +(NewChrom = reclin\050OldChrom\051) 135.65 236.95 T +3 F +2.57 (New values are produced by adding the scaled dif) 135.65 216.95 P +2.57 (ference between the parent) 395.08 216.95 P +2.19 (values to the \336rst parent \050see Algorithm\051. An internal table of scaling factors,) 135.65 202.95 P +2 F +(Alpha) 135.65 188.95 T +3 F +(, is produced, e.g.) 171.63 188.95 T +2 F +(Alpha = [) 135.65 168.95 T +(0.78; % for producing offspring1) 153.65 154.95 T +(1.05] % for producing offspring2) 153.65 140.95 T +3 F +(Thus, after recombination NewChrom would become:) 135.65 120.95 T +FMENDPAGE +%%EndPage: "28" 29 +%%Page: "29" 29 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-29) 513.33 61.29 T +2 12 Q +(NewChrom = [) 135.65 736.95 T +(72.97) 153.65 722.95 T +( 6.64 16.74) 196.82 722.95 T +(-3.77; % Alpha\0501\051 parent1&2) 290.37 722.95 T +(84.25 14.85 12.54 -10.37] % Alpha\0502\051 parent1&2) 153.65 708.95 T +3 F +0.75 (As the number of individuals in the parent population,) 135.65 688.95 P +2 F +1.79 (OldChrom) 405.55 688.95 P +3 F +0.75 (, was odd, the) 463.12 688.95 P +-0.18 (last individual is appended without recombination to) 135.65 674.95 P +2 F +-0.43 (NewChrom) 389.9 674.95 P +3 F +-0.18 ( and the of) 447.47 674.95 P +-0.18 (fspring) 497.67 674.95 P +(returned to the users workspace, thus:) 135.65 660.95 T +2 F +(NewChrom =) 135.65 640.95 T +(72.97) 153.65 626.95 T +(6.64 16.74) 204.02 626.95 T +( -3.77) 283.18 626.95 T +(84.25 14.85 12.54 -10.37) 153.65 612.95 T +(52.43 25.64 15.20) 153.65 598.95 T +( -2.54) 283.18 598.95 T +1 16 Q +(Algorithm) 117.65 576.29 T +3 12 Q +(Line recombination combines parent values using the following rule:) 135.65 558.95 T +2 F +(offspring = parent1 +) 135.65 532.95 T +3 F +(where) 135.65 506.95 T +2 F +(Alpha) 167.95 506.95 T +3 F +( is a scaling factor chosen uniformly at random in the interval) 203.93 506.95 T +2 F +0.42 ([-0.25, 1.25]) 135.65 492.95 P +3 F +0.17 (.) 229.61 492.95 P +2 F +0.42 (reclin) 235.78 492.95 P +3 F +0.17 ( produces a new Alpha for each pair of parents to be) 278.96 492.95 P +(combined.) 135.65 478.95 T +2.41 (Line recombination can generate any point on a slightly longer line than that) 135.65 452.95 P +(de\336ned by the parents.) 135.65 438.95 T +1.59 (Line recombination is similar to intermediate recombination) 135.65 412.95 P +2 F +3.82 (recint) 438.93 412.95 P +3 F +1.59 (. Whereas) 482.11 412.95 P +2 F +7.91 (reclin) 135.65 398.95 P +3 F +3.29 ( uses one Alpha factor for each pair of parents combined together) 178.82 398.95 P +3.29 (,) 528.65 398.95 P +2 F +(recint) 135.65 384.95 T +3 F +( uses a new) 178.82 384.95 T +2 F +(Alpha) 236.78 384.95 T +3 F +( factor for each pair of values.) 272.76 384.95 T +1 16 Q +(See Also) 117.65 356.29 T +2 12 Q +(recombin) 135.65 338.95 T +3 F +(,) 193.22 338.95 T +2 F +(recdis) 199.21 338.95 T +3 F +(,) 242.39 338.95 T +2 F +(recint) 248.39 338.95 T +3 F +(,) 291.56 338.95 T +2 F +(ranking) 297.56 338.95 T +3 F +(,) 347.93 338.95 T +2 F +(sus) 353.93 338.95 T +3 F +(,) 375.52 338.95 T +2 F +(rws) 381.51 338.95 T +1 16 Q +(Refer) 117.65 316.29 T +(ence) 155.53 316.29 T +3 12 Q +3.9 ([1] H. M) 135.65 298.95 P +3.9 (\237) 185.76 298.95 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 298.95 P +3.9 (oosen, \322Predictive Models for the) 354.48 298.95 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 284.95 P +0 F +0.18 (Evolutionary) 469.02 284.95 P +(Computation) 135.65 270.95 T +3 F +(, V) 198.29 270.95 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 270.95 T +293.96 527.96 482.85 541.94 C +2 12 Q +0 X +0 K +(A) 294.96 532.95 T +(l) 302.86 532.95 T +(p) 310.77 532.95 T +(h) 318.67 532.95 T +(a) 326.57 532.95 T +(p) 353.45 532.95 T +(a) 361.35 532.95 T +(r) 369.25 532.95 T +(e) 377.16 532.95 T +(n) 385.06 532.95 T +(t) 392.96 532.95 T +(2) 400.86 532.95 T +(p) 420.64 532.95 T +(a) 428.54 532.95 T +(r) 436.45 532.95 T +(e) 444.35 532.95 T +(n) 452.25 532.95 T +(t) 460.15 532.95 T +(1) 468.05 532.95 T +4 F +(-) 411.06 532.95 T +(\050) 348.35 532.95 T +(\051) 475.86 532.95 T +(\264) 336.77 532.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "29" 30 +%%Page: "30" 30 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-30) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ecmut) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Line recombination with mutation features) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = recmut\050OldChrom, FieldDR\051) 135.65 628.95 T +(NewChrom = recmut\050OldChrom, FieldDR, MutOpt\051) 135.65 608.95 T +1 16 Q +(Description) 117.65 586.29 T +2 12 Q +5.35 (recmut) 135.65 568.95 P +3 F +2.23 ( performs line recombination with mutation features between pairs of) 178.82 568.95 P +1.26 (individuals in the current population,) 135.65 554.95 P +2 F +3.03 (OldChrom) 322.53 554.95 P +3 F +1.26 (, and returns a new population) 380.1 554.95 P +(after mating,) 135.65 540.95 T +2 F +(NewChrom) 199.93 540.95 T +3 F +(. Each row of) 257.5 540.95 T +2 F +(OldChrom) 325.11 540.95 T +3 F +( corresponds to one individual.) 382.68 540.95 T +2 F +1.31 (FieldDR) 135.65 514.95 P +3 F +0.55 ( is a matrix containing the boundaries of each variable of an individual) 186.02 514.95 P +(\050see) 135.65 500.95 T +2 F +(crtrp) 157.96 500.95 T +3 F +(\051.) 193.94 500.95 T +2 F +(MutOpt) 135.65 474.95 T +3 F +( is an optional vector with a maximum of 2 parameters:) 178.82 474.95 T +2 F +(MutOpt\0501\051) 135.65 454.95 T +3 F +(:) 200.41 454.95 T +(scalar containing the recombination rate in the range) 171.65 440.95 T +2 F +([0, 1].) 426.78 440.95 T +3 F +(If omitted or) 171.65 426.95 T +2 F +(NaN) 235.27 426.95 T +3 F +(,) 256.86 426.95 T +2 F +(MutOpt\0501\051 = 1) 262.86 426.95 T +3 F +( is assumed.) 356.41 426.95 T +2 F +(MutOpt\0502\051) 135.65 406.95 T +3 F +(:) 200.41 406.95 T +-0.23 (scalar containing a value in the range [0, 1] for shrinking the recombination) 171.65 392.95 P +(range.) 171.65 378.95 T +(If omitted or) 171.65 364.95 T +2 F +(NaN) 235.27 364.95 T +3 F +(,) 256.86 364.95 T +2 F +(MutOpt\0502\051 = 1) 262.86 364.95 T +3 F +( is assumed \050no shrinking\051.) 356.41 364.95 T +2 F +1.76 (recmut) 135.65 344.95 P +3 F +0.73 ( is a function only applicable to populations of real-value variables \050and) 178.82 344.95 P +(not binary or integer\051.) 135.65 330.95 T +1.18 (The pairs are mated in order) 135.65 304.95 P +1.18 (, odd row with the next even row) 276.62 304.95 P +1.18 (. If the number of) 442.66 304.95 P +0.5 (rows in the matrix) 135.65 290.95 P +2 F +1.2 (OldChrom) 228.25 290.95 P +3 F +0.5 ( is odd then the last row is not mated and added at) 285.82 290.95 P +4.19 (the end of) 135.65 276.95 P +2 F +10.05 (NewChrom) 199.16 276.95 P +3 F +4.19 (. The population should therefore be or) 256.73 276.95 P +4.19 (ganised into) 469.16 276.95 P +0.94 (contiguous pairs that require mating. This can be achieved by using the function) 135.65 262.95 P +2 F +-0.51 (ranking) 135.65 248.95 P +3 F +-0.21 ( to assign a \336tness level to each individual and a selection function \050) 186.02 248.95 P +2 F +-0.51 (sus) 510.06 248.95 P +3 F +-0.24 (or) 135.65 234.95 P +2 F +-0.57 (rws) 148.4 234.95 P +3 F +-0.24 (\051 to select individuals with a probability related to their \336tness in the current) 169.99 234.95 P +(population.) 135.65 220.95 T +2 F +0.89 (recmut) 135.65 194.95 P +3 F +0.37 ( uses features of the mutation operator of the Breeder Genetic Algorithm) 178.82 194.95 P +2.31 (\050see) 135.65 180.95 P +2 F +5.53 (mutbga) 160.26 180.95 P +3 F +2.31 (\051. Therefore, the calling syntax of this recombination function is) 203.44 180.95 P +(identical to this of the mutation function) 135.65 166.95 T +2 F +(mutbga) 331.87 166.95 T +3 F +(.) 375.05 166.95 T +2 F +(recmut) 135.65 140.95 T +3 F +( is a low-level recombination function normally called by) 178.82 140.95 T +2 F +(mutate) 457.64 140.95 T +3 F +(.) 500.81 140.95 T +FMENDPAGE +%%EndPage: "30" 31 +%%Page: "31" 31 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-31) 513.33 61.29 T +1 16 Q +(Example) 117.65 734.29 T +3 12 Q +(Consider the following population with four real-valued individuals:) 135.65 716.95 T +2 F +(OldChrom = [) 135.65 696.95 T +(40.2381 -17.1766) 160.84 682.95 T +( 28.9530) 283.18 682.95 T +(15.3883; % parent1) 355.14 682.95 T +(82.0642) 160.84 668.95 T +(13.2639) 225.61 668.95 T +(13.3596) 290.37 668.95 T +(-9.0916; % parent2) 355.14 668.95 T +(52.4396) 160.84 654.95 T +(25.6410) 225.61 654.95 T +(15.2014) 290.37 654.95 T +(-2.5435; % parent3) 355.14 654.95 T +(-47.5381) 153.65 640.95 T +(49.1963) 225.61 640.95 T +(9.0954) 297.57 640.95 T +(10.6521] % parent4) 355.14 640.95 T +3 F +(The boundaries are de\336ned as:) 135.65 620.95 T +2 F +(FieldDR = [) 135.65 600.95 T +(-100 -50 -30 -20;) 153.65 586.95 T +( 100) 153.65 572.95 T +(50) 196.82 572.95 T +( 30) 218.41 572.95 T +(20]) 254.39 572.95 T +3 F +(T) 135.65 552.95 T +(o perform line recombination with mutation features:) 142.14 552.95 T +2 F +(NewChrom = recmut\050OldChrom, FieldDR\051) 135.65 532.95 T +4.89 (recmut) 135.65 512.95 P +3 F +2.04 ( produces an internal mask table,) 178.82 512.95 P +2 F +4.89 (RecMx) 351.94 512.95 P +3 F +2.04 (, determining which pairs of) 387.92 512.95 P +2.56 (parents to recombine \050here recombine all pairs\051 and the sign for adding) 135.65 498.95 P +2 F +6.14 (the) 510.06 498.95 P +3 F +(recombination step) 135.65 484.95 T +(\050see Algorithm\051, e.g.) 234.45 484.95 T +2 F +(RecMx = [) 135.65 464.95 T +( 1) 153.65 450.95 T +(-1) 175.24 450.95 T +(-1) 196.82 450.95 T +(-1; % for producing offspring1 & 2) 218.41 450.95 T +(-1) 153.65 436.95 T +(-1) 175.24 436.95 T +(-1) 196.82 436.95 T +(-1] % for producing offspring3 & 4) 218.41 436.95 T +3 F +6.59 (T) 135.65 416.95 P +6.59 (wo further internal tables,) 142.14 416.95 P +2 F +15.81 (delta) 295.39 416.95 P +3 F +6.59 ( and) 331.37 416.95 P +2 F +15.81 (Diff) 367.86 416.95 P +3 F +6.59 (, specify the normalized) 396.64 416.95 P +(recombination step size, e.g.) 135.65 402.95 T +2 F +(delta = [) 135.65 382.95 T +(0.1250) 153.65 368.95 T +(0.1250 0.1250 0.1250; % for offspring1 & 2) 204.02 368.95 T +(0.0005 0.0005 0.0005 0.0005] % for offspring3 & 4) 153.65 354.95 T +(Diff = [) 135.65 334.95 T +-0.68 (1.3937) 168.04 320.95 P +-0.68 (1.0143) 218.41 320.95 P +-0.68 (-0.5196) 268.79 320.95 P +-0.68 (-0.8157; % for offspring1 & 2) 326.35 320.95 P +-0.68 (-10.5712) 153.65 306.95 P +-0.68 (2.4906) 218.41 306.95 P +-0.68 (-0.6456) 268.79 306.95 P +-0.68 (1.3952] % for offspring3 & 4) 333.55 306.95 P +3 F +(Thus, after recombination NewChrom becomes:) 135.65 286.95 T +2 F +(NewChrom =) 135.65 266.95 T +(57.6637) 160.84 252.95 T +(-23.5177) 218.41 252.95 T +(30.0000) 290.37 252.95 T +(17.4281) 355.14 252.95 T +(64.6386) 160.84 238.95 T +(19.6050) 225.61 238.95 T +(11.4106) 290.37 238.95 T +(-11.1314) 347.94 238.95 T +(52.9719) 160.84 224.95 T +(25.5783) 225.61 224.95 T +(15.2112) 290.37 224.95 T +(-2.5576) 355.14 224.95 T +(-48.0704) 153.65 210.95 T +(49.2590) 225.61 210.95 T +(9.0856) 297.57 210.95 T +(10.6662) 355.14 210.95 T +1 16 Q +(Algorithm) 117.65 188.29 T +3 12 Q +(The of) 135.65 170.95 T +(fsprings of a pair of two parents are computed as follows:) 167.07 170.95 T +(of) 135.65 150.95 T +(fspring1=parent1 +) 145.42 150.95 T +(of) 135.65 130.95 T +(fspring2=parent2 +) 145.42 130.95 T +240.89 145.96 508.85 159.94 C +2 12 Q +0 X +0 K +(R) 241.89 150.95 T +(e) 249.79 150.95 T +(c) 257.69 150.95 T +(M) 265.6 150.95 T +(x) 273.5 150.95 T +(r) 293.28 150.95 T +(a) 301.18 150.95 T +(n) 309.08 150.95 T +(g) 316.98 150.95 T +(e) 324.89 150.95 T +(M) 344.67 150.95 T +(u) 352.57 150.95 T +(t) 360.47 150.95 T +(O) 368.37 150.95 T +(p) 376.27 150.95 T +(t) 384.18 150.95 T +(2) 399.18 150.95 T +4 F +(\050) 394.08 150.95 T +(\051) 406.98 150.95 T +2 F +(d) 425.56 150.95 T +(e) 433.46 150.95 T +(l) 441.36 150.95 T +(t) 449.27 150.95 T +(a) 457.17 150.95 T +4 F +(\264) 335.08 150.95 T +(\264) 415.98 150.95 T +(\264) 283.69 150.95 T +2 F +(D) 476.95 150.95 T +(i) 484.85 150.95 T +(f) 492.75 150.95 T +(f) 500.65 150.95 T +4 F +(\264) 467.36 150.95 T +-8.35 24.95 603.65 816.95 C +240.89 125.96 529.6 139.94 C +2 12 Q +0 X +0 K +(R) 241.89 130.95 T +(e) 249.79 130.95 T +(c) 257.69 130.95 T +(M) 265.6 130.95 T +(x) 273.5 130.95 T +(r) 293.28 130.95 T +(a) 301.18 130.95 T +(n) 309.08 130.95 T +(g) 316.98 130.95 T +(e) 324.89 130.95 T +(M) 344.67 130.95 T +(u) 352.57 130.95 T +(t) 360.47 130.95 T +(O) 368.37 130.95 T +(p) 376.27 130.95 T +(t) 384.18 130.95 T +(2) 399.18 130.95 T +4 F +(\050) 394.08 130.95 T +(\051) 406.98 130.95 T +2 F +(d) 425.56 130.95 T +(e) 433.46 130.95 T +(l) 441.36 130.95 T +(t) 449.27 130.95 T +(a) 457.17 130.95 T +4 F +(\264) 335.08 130.95 T +(\264) 415.98 130.95 T +(\264) 283.69 130.95 T +2 F +(D) 491.1 130.95 T +(i) 499 130.95 T +(f) 506.9 130.95 T +(f) 514.8 130.95 T +4 F +(-) 484.05 130.95 T +(\050) 478.95 130.95 T +(\051) 522.6 130.95 T +(\264) 467.36 130.95 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "31" 32 +%%Page: "32" 32 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-32) 513.33 61.29 T +2 12 Q +(RecMx) 135.65 736.95 T +3 F +(=) 180.62 736.95 T +( with probability) 202.43 736.95 T +2 F +(MutOpt\0501\051) 285.39 736.95 T +3 F +(, \050- with probability 0.9\051) 350.15 736.95 T +(else 0) 171.65 722.95 T +2 F +(range =) 135.65 702.95 T +3 F +( domain of variable \050search interval de\336ned by) 228.79 702.95 T +2 F +(FieldDR) 455.94 702.95 T +3 F +(\051.) 506.32 702.95 T +2 F +(delta =) 135.65 669.03 T +3 F +(,) 237.45 669.03 T +( with probability 1/m, else 0, m = 20.) 281.05 669.03 T +0.13 (The recombination operator) 135.65 600.85 P +2 F +0.31 (recmut) 272.93 600.85 P +3 F +0.13 ( generates of) 316.11 600.85 P +0.13 (fspring in a direction de\336ned by) 377.43 600.85 P +0.02 (the parents \050line recombination\051. It tests more often outside the area de\336ned by the) 135.65 586.85 P +1.11 (parents and in the direction of parent1. The point for the of) 135.65 572.85 P +1.11 (fspring is de\336ned by) 430.05 572.85 P +-0.18 (features of the mutation operator) 135.65 558.85 P +-0.18 (. The probability of small step sizes is greater than) 291.46 558.85 P +(that of bigger steps \050see) 135.65 544.85 T +2 F +(mutbga) 252.56 544.85 T +3 F +(\051.) 295.74 544.85 T +1 16 Q +(See Also) 117.65 516.18 T +2 12 Q +(mutate) 135.65 498.85 T +3 F +(,) 178.82 498.85 T +2 F +(mutbga) 184.82 498.85 T +3 F +(,) 228 498.85 T +2 F +(reclin) 233.99 498.85 T +1 16 Q +(Refer) 117.65 476.18 T +(ence) 155.53 476.18 T +3 12 Q +0.79 ([1] H. M) 135.65 458.85 P +0.79 (\237) 179.52 458.85 P +0.79 (hlenbein, \322The Breeder Genetic Algorithm - a provable optimal search) 185.52 458.85 P +6.19 (algorithm and its application\323,) 135.65 444.85 P +0 F +6.19 (IEE Colloquium, Applications of Genetic) 309.33 444.85 P +(Algorithms) 135.65 430.85 T +3 F +(, Digest No. 94/067, London, 15) 188.96 430.85 T +352.31 434.56 344.54 434.56 2 L +V +0.49 H +0 Z +N +3 10 Q +(th) 344.54 435.65 T +3 12 Q +( March 1994.) 352.31 430.85 T +3.9 ([2] H. M) 135.65 404.85 P +3.9 (\237) 185.76 404.85 P +3.9 (hlenbein and D. Schlierkamp-V) 191.76 404.85 P +3.9 (oosen, \322Predictive Models for the) 354.48 404.85 P +0.18 (Breeder Genetic Algorithm: I. Continuous Parameter Optimization\323,) 135.65 390.85 P +0 F +0.18 (Evolutionary) 469.02 390.85 P +(Computation) 135.65 376.85 T +3 F +(, V) 198.29 376.85 T +(ol. 1, No. 1, pp.25-49, 1993.) 211.4 376.85 T +187.39 733.43 202.43 745.99 C +3 12 Q +0 X +0 K +(1) 195.43 736.95 T +4 F +(\261) 188.39 736.95 T +-8.35 24.95 603.65 816.95 C +193.22 699.35 228.79 712.13 C +3 12 Q +0 X +0 K +(0) 194.22 702.95 T +(.) 200.21 702.95 T +(5) 203.21 702.95 T +4 F +(\264) 212.21 702.95 T +-8.35 24.95 603.65 816.95 C +189.02 651.79 237.44 690.95 C +4 12 Q +0 X +0 K +(a) 211.43 669.03 T +0 9 Q +(i) 219.46 664.38 T +3 12 Q +(2) 222.67 669.03 T +0 9 Q +(i) 233.95 675.06 T +4 F +(-) 228.67 675.06 T +0 F +(i) 191.26 654.74 T +3 F +(0) 204.7 654.74 T +4 F +(=) 196.76 654.74 T +0 F +(m) 190.02 683.81 T +3 F +(1) 205.94 683.81 T +4 F +(-) 198.76 683.81 T +4 18 Q +(\345) 193.81 665.83 T +-8.35 24.95 603.65 816.95 C +243.44 661.53 281.04 678.21 C +4 12 Q +0 X +0 K +(a) 244.69 669.03 T +0 9 Q +(i) 252.72 664.38 T +3 12 Q +(1) 273.8 669.03 T +4 F +(=) 261.22 669.03 T +-8.35 24.95 603.65 816.95 C +135.65 616.85 322.93 643.79 C +2 12 Q +0 X +0 K +(D) 136.65 627.72 T +(i) 144.55 627.72 T +(f) 152.45 627.72 T +(f) 160.35 627.72 T +(p) 193.13 634.8 T +(a) 201.04 634.8 T +(r) 208.94 634.8 T +(e) 216.84 634.8 T +(n) 224.74 634.8 T +(t) 232.64 634.8 T +(2) 240.55 634.8 T +(p) 260.33 634.8 T +(a) 268.23 634.8 T +(r) 276.13 634.8 T +(e) 284.03 634.8 T +(n) 291.93 634.8 T +(t) 299.84 634.8 T +(1) 307.74 634.8 T +4 F +(-) 250.74 634.8 T +2 F +(p) 193.13 620.33 T +(a) 201.04 620.33 T +(r) 208.94 620.33 T +(e) 216.84 620.33 T +(n) 224.74 620.33 T +(t) 232.64 620.33 T +(1) 240.55 620.33 T +(p) 260.33 620.33 T +(a) 268.23 620.33 T +(r) 276.13 620.33 T +(e) 284.03 620.33 T +(n) 291.93 620.33 T +(t) 299.84 620.33 T +(2) 307.74 620.33 T +4 F +(-) 250.74 620.33 T +(=) 173.55 627.72 T +188.13 618.85 188.13 628.32 2 L +0.33 H +0 Z +N +190.13 618.85 190.13 628.32 2 L +N +318.93 618.85 318.93 628.32 2 L +N +316.93 618.85 316.93 628.32 2 L +N +187.13 630.32 320.68 630.32 2 L +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "32" 33 +%%Page: "33" 33 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-33) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ecombin) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Recombination of individuals \050high-level function\051.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = recombin\050REC_F, Chrom\051) 135.65 628.95 T +(NewChrom = recombin\050REC_F, Chrom, RecOpt\051) 135.65 608.95 T +(NewChrom = recombin\050REC_F, Chrom, RecOpt, SUBPOP\051) 135.65 588.95 T +1 16 Q +(Description) 117.65 566.29 T +2 12 Q +4.99 (recombin) 135.65 548.95 P +3 F +2.08 ( performs recombination of individuals from a population,) 193.22 548.95 P +2 F +4.99 (Chrom) 492.67 548.95 P +3 F +2.08 (,) 528.65 548.95 P +1.73 (and returns the recombined individuals in a new population,) 135.65 534.95 P +2 F +4.16 (NewChrom) 442.38 534.95 P +3 F +1.73 (. Each) 499.94 534.95 P +(row of) 135.65 520.95 T +2 F +(Chrom) 170.29 520.95 T +3 F +( and) 206.26 520.95 T +2 F +(NewChrom) 229.58 520.95 T +3 F +( corresponds to one individual.) 287.15 520.95 T +2 F +0.52 (REC_F) 135.65 494.95 P +3 F +0.22 ( is a string that contains the name of the low-level recombination function,) 171.63 494.95 P +(e.g.) 135.65 480.95 T +2 F +(recdis) 155.96 480.95 T +3 F +( or) 199.14 480.95 T +2 F +(xovsp) 215.13 480.95 T +3 F +(.) 251.11 480.95 T +2 F +4.92 (RecOpt) 135.65 454.95 P +3 F +2.05 ( is an optional parameter specifying the crossover rate. If) 178.82 454.95 P +2 F +4.92 (RecOpt) 475.42 454.95 P +3 F +2.05 ( is) 518.6 454.95 P +(omitted or) 135.65 440.95 T +2 F +(NaN,) 188.29 440.95 T +3 F +( a default value is assumed.) 217.07 440.95 T +2 F +0.01 (SUBPOP) 135.65 414.95 P +3 F +0.01 ( is an optional parameter and determines the number of subpopulations in) 178.82 414.95 P +2 F +8.57 (Chrom) 135.65 400.95 P +3 F +3.57 (. If) 171.63 400.95 P +2 F +8.57 (SUBPOP) 195.75 400.95 P +3 F +3.57 ( is omitted or) 238.93 400.95 P +2 F +8.57 (NaN,) 319.85 400.95 P +8.57 (SUBPOP = 1) 355.2 400.95 P +3 F +3.57 ( is assumed. All) 444.31 400.95 P +(subpopulations in) 135.65 386.95 T +2 F +(Chrom) 223.61 386.95 T +3 F +( must have the same size.) 259.59 386.95 T +1 16 Q +(Example) 117.65 358.29 T +3 12 Q +( For examples see) 135.65 340.95 T +2 F +(recdis) 224.91 340.95 T +3 F +(,) 268.09 340.95 T +2 F +(recint) 274.09 340.95 T +3 F +(,) 317.26 340.95 T +2 F +(reclin) 323.26 340.95 T +3 F +(,) 366.44 340.95 T +2 F +(xovsp) 372.43 340.95 T +3 F +(,) 408.41 340.95 T +2 F +(xovdp) 414.41 340.95 T +3 F +( and) 450.39 340.95 T +2 F +(xovmp) 473.71 340.95 T +3 F +(.) 509.69 340.95 T +1 16 Q +(Algorithm) 117.65 318.29 T +2 12 Q +0.22 (recombin) 135.65 300.95 P +3 F +0.09 ( checks the consistency of the input parameters and calls the low-level) 193.22 300.95 P +-0.04 (recombination function. If) 135.65 286.95 P +2 F +-0.08 (recombin) 264.79 286.95 P +3 F +-0.04 ( is called with more than one subpopulation) 322.35 286.95 P +6.44 (then the low-level recombination function is called separately for each) 135.65 272.95 P +(subpopulation.) 135.65 258.95 T +1 16 Q +(See Also) 117.65 236.29 T +2 12 Q +(recdis) 135.65 218.95 T +3 F +(,) 178.82 218.95 T +2 F +(recint) 184.82 218.95 T +3 F +(,) 228 218.95 T +2 F +(reclin) 233.99 218.95 T +3 F +(,) 277.17 218.95 T +2 F +(xovsp) 283.17 218.95 T +3 F +(,) 319.15 218.95 T +2 F +(xovdp) 325.14 218.95 T +3 F +(,) 361.12 218.95 T +2 F +(xovsh) 367.12 218.95 T +3 F +(,) 403.1 218.95 T +2 F +(mutate) 409.1 218.95 T +3 F +(,) 452.27 218.95 T +2 F +(select) 458.27 218.95 T +FMENDPAGE +%%EndPage: "33" 34 +%%Page: "34" 34 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-34) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(eins) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Reinsertion of of) 135.65 674.95 T +(fspring in the population.) 216.71 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(Chrom = reins\050Chrom, SelCh\051) 135.65 628.95 T +(Chrom = reins\050Chrom, SelCh, SUBPOP\051) 135.65 608.95 T +(Chrom = reins\050Chrom, SelCh, SUBPOP, InsOpt, ObjVCh\051) 135.65 588.95 T +([Chrom, ObjVCh]= reins\050Chrom, SelCh, SUBPOP, InsOpt,) 135.65 568.95 T +(ObjVCh, ObjVSel\051) 153.65 554.95 T +1 16 Q +(Description) 117.65 532.29 T +2 12 Q +7.41 (reins) 135.65 514.95 P +3 F +3.09 ( performs insertion of of) 171.63 514.95 P +3.09 (fspring into the current population, replacing) 301.02 514.95 P +1.7 (parents with of) 135.65 500.95 P +1.7 (fspring and returning the resulting population. The of) 210.79 500.95 P +1.7 (fspring are) 478.33 500.95 P +0.23 (contained in the matrix) 135.65 486.95 P +2 F +0.56 (SelCh) 250.51 486.95 P +3 F +0.23 ( and the parents in the matrix) 286.49 486.95 P +2 F +0.56 (Chrom) 431.02 486.95 P +3 F +0.23 (. Each row in) 467 486.95 P +2 F +(Chrom) 135.65 472.95 T +3 F +( and) 171.63 472.95 T +2 F +(Selch) 194.94 472.95 T +3 F +( corresponds to one individual.) 230.92 472.95 T +2 F +2.19 (SUBPOP) 135.65 446.95 P +3 F +0.91 ( is an optional parameter and indicates the number of subpopulations in) 178.82 446.95 P +2 F +-0.32 (Chrom) 135.65 432.95 P +3 F +-0.13 ( and) 171.63 432.95 P +2 F +-0.32 (SelCh) 194.68 432.95 P +3 F +-0.13 (. If) 230.66 432.95 P +2 F +-0.32 (SUBPOP) 247.37 432.95 P +3 F +-0.13 ( is omitted or) 290.55 432.95 P +2 F +-0.32 (NaN) 356.65 432.95 P +3 F +-0.13 (,) 378.24 432.95 P +2 F +-0.32 (SUBPOP = 1) 384.1 432.95 P +3 F +-0.13 ( is assumed. All) 455.42 432.95 P +(subpopulations in) 135.65 418.95 T +2 F +(Chrom) 223.61 418.95 T +3 F +( and) 259.59 418.95 T +2 F +(SelCh) 282.9 418.95 T +3 F +( each must have the same size.) 318.88 418.95 T +2 F +(InsOpt) 135.65 392.95 T +3 F +( is an optional vector with a maximum of 2 parameters:) 178.82 392.95 T +2 F +(InsOpt\0501\051) 135.65 372.95 T +3 F +(:) 200.41 372.95 T +(scalar indicating the selection method for replacing parents with of) 171.65 358.95 T +(fspring:) 492.2 358.95 T +(0 - uniform selection, of) 171.65 344.95 T +(fspring replace parents uniformly at random) 287.68 344.95 T +(1 - \336tness-based selection, of) 171.65 330.95 T +(fspring replace least \336t parents) 311 330.95 T +(If omitted or) 171.65 316.95 T +2 F +(NaN) 235.27 316.95 T +3 F +(,) 256.86 316.95 T +2 F +(InsOpt\0501\051 = 0) 262.86 316.95 T +3 F +( is assumed) 356.41 316.95 T +2 F +(InsOpt\0502\051) 135.65 296.95 T +3 F +(:) 200.41 296.95 T +0.2 (scalar containing the rate of reinsertion of of) 171.65 282.95 P +0.2 (fspring per subpopulation as a) 386.3 282.95 P +(fraction of subpopulation size in the range) 171.65 268.95 T +2 F +([0, 1]) 377.17 268.95 T +3 F +(.) 420.34 268.95 T +(If omitted or) 171.65 254.95 T +2 F +(NaN) 235.27 254.95 T +3 F +(,) 256.86 254.95 T +2 F +(InsOpt\0502\051 = 1.0) 262.86 254.95 T +3 F +( is assumed.) 370.8 254.95 T +(If) 171.65 240.95 T +2 F +(INSR = 0) 182.63 240.95 T +3 F +( no insertion takes place.) 240.2 240.95 T +0.41 (If) 171.65 226.95 P +2 F +0.97 (INSR) 183.04 226.95 P +3 F +0.41 ( is not 1.0) 211.82 226.95 P +2 F +0.97 (ObjVSel) 263.75 226.95 P +3 F +0.41 ( is needed for selecting the best of) 314.12 226.95 P +0.41 (fspring for) 480.28 226.95 P +(insertion \050truncation selection between of) 171.65 212.95 T +(fspring\051.) 370.62 212.95 T +(If) 135.65 192.95 T +2 F +(InsOpt) 146.63 192.95 T +3 F +( is omitted or) 189.81 192.95 T +2 F +(NaN) 256.45 192.95 T +3 F +(, then the default values are assumed.) 278.03 192.95 T +2 F +6.7 (ObjVCh) 135.65 166.95 P +3 F +2.79 ( is an optional column vector containing the objective values of the) 178.82 166.95 P +(individuals in) 135.65 152.95 T +2 F +(Chrom) 204.29 152.95 T +3 F +(.) 240.27 152.95 T +2 F +(ObjVCh) 246.26 152.95 T +3 F +( is needed for \336tness-based reinsertion.) 289.44 152.95 T +2 F +5.13 (ObjVSel) 135.65 126.95 P +3 F +2.14 ( is an optional column vector containing the objective values of the) 186.02 126.95 P +0.53 (individuals in) 135.65 112.95 P +2 F +1.28 (SelCh) 205.35 112.95 P +3 F +0.53 (.) 241.33 112.95 P +2 F +1.28 (ObjVSel) 247.87 112.95 P +3 F +0.53 ( is required if the number of of) 298.24 112.95 P +0.53 (fspring is greater) 449.31 112.95 P +FMENDPAGE +%%EndPage: "34" 35 +%%Page: "35" 35 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-35) 513.33 61.29 T +3 12 Q +1.91 (than the number of of) 135.65 736.95 P +1.91 (fspring to be reinserted into the population. In this case,) 246.99 736.95 P +(of) 135.65 722.95 T +(fspring are selected for reinsertion according to their \336tness.) 145.42 722.95 T +2.6 (If) 135.65 696.95 P +2 F +6.24 (ObjVCh) 149.23 696.95 P +3 F +2.6 ( is output parameter) 192.41 696.95 P +2.6 (,) 295.33 696.95 P +2 F +6.24 (ObjVCh) 303.93 696.95 P +3 F +2.6 ( and) 347.11 696.95 P +2 F +6.24 (ObjVSel) 375.62 696.95 P +3 F +2.6 ( are needed as input) 425.99 696.95 P +0.25 (parameters. The objective values are then copied, according to the insertion of the) 135.65 682.95 P +4.68 (of) 135.65 668.95 P +4.68 (fspring, saving the recomputation of the objective values for the whole) 145.42 668.95 P +(population.) 135.65 654.95 T +1 16 Q +(Example) 117.65 626.29 T +3 12 Q +2.57 (Consider a population of 8 parents,) 135.65 608.95 P +2 F +6.16 (Chrom) 322.6 608.95 P +3 F +2.57 (, and a population of 6 of) 358.58 608.95 P +2.57 (fspring,) 494.67 608.95 P +2 F +(SelCh) 135.65 594.95 T +3 F +(:) 171.63 594.95 T +2 F +(Chrom = [1; 2; 3; 4; 5; 6; 7; 8]) 135.65 574.95 T +(SelCh = [11; 12; 13; 14; 15; 16]) 135.65 560.95 T +3 F +(Insert all of) 135.65 540.95 T +(fspring in the population:) 190.72 540.95 T +2 F +(Chrom = reins\050Chrom, SelCh\051) 135.65 520.95 T +3 F +(Thus, a new population) 135.65 500.95 T +2 F +(Chrom) 251.24 500.95 T +3 F +( is produced, e.g.:) 287.22 500.95 T +2 F +(Chrom =) 135.65 480.95 T +(12) 153.65 466.95 T +(11) 153.65 452.95 T +(15) 153.65 438.95 T +(16) 153.65 424.95 T +( 5) 153.65 410.95 T +(13) 153.65 396.95 T +(14) 153.65 382.95 T +( 8) 153.65 368.95 T +3 F +2.5 (Consider the following) 135.65 348.95 P +2 F +6.01 (ObjVCh) 256.76 348.95 P +3 F +2.5 ( vector for the parent population) 299.94 348.95 P +2 F +6.01 (Chrom) 472.85 348.95 P +3 F +2.5 ( and) 508.83 348.95 P +2 F +(ObjVSel) 135.65 334.95 T +3 F +( for the of) 186.02 334.95 T +(fspring,) 233.43 334.95 T +2 F +(SelCh) 273.4 334.95 T +3 F +(:) 309.39 334.95 T +2 F +(ObjVCh = [21; 22; 23; 24; 25; 26; 27; 28];) 135.65 314.95 T +(ObjVSel= [31; 32; 33; 34; 35; 36]) 135.65 300.95 T +3 F +(Insert all of) 135.65 280.95 T +(fspring \336tness-based, i.e. replace least \336t parents:) 190.72 280.95 T +2 F +(Chrom = reins\050Chrom, SelCh, 1, 1, ObjVCh\051) 135.65 260.95 T +(Chrom =) 135.65 240.95 T +( 1) 153.65 226.95 T +( 2) 153.65 212.95 T +(16) 153.65 198.95 T +(15) 153.65 184.95 T +(14) 153.65 170.95 T +(13) 153.65 156.95 T +(12) 153.65 142.95 T +(11) 153.65 128.95 T +FMENDPAGE +%%EndPage: "35" 36 +%%Page: "36" 36 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-36) 513.33 61.29 T +3 12 Q +0.56 (Insert 50% of the of) 135.65 736.95 P +0.56 (fspring \336tness-based and copy the objective values according) 233.6 736.95 P +(the insertion of of) 135.65 722.95 T +(fspring:) 221.04 722.95 T +2 F +([Chrom, ObjVCh] = reins\050Chrom, SelCh, 1, [1 0.5],...) 135.65 702.95 T +(ObjVCh, ObjVSel\051) 153.65 688.95 T +(Chrom =) 135.65 668.95 T +( 1) 153.65 654.95 T +( 2) 153.65 640.95 T +( 3) 153.65 626.95 T +( 4) 153.65 612.95 T +( 5) 153.65 598.95 T +(13) 153.65 584.95 T +(12) 153.65 570.95 T +(11) 153.65 556.95 T +(ObjVCh =) 135.65 536.95 T +(21) 153.65 522.95 T +(22) 153.65 508.95 T +(23) 153.65 494.95 T +(24) 153.65 480.95 T +(25) 153.65 466.95 T +(33) 153.65 452.95 T +(32) 153.65 438.95 T +(31) 153.65 424.95 T +3 F +0.4 (Consider Chrom and SelCh consist of 2 subpopulations. Insert all of) 135.65 404.95 P +0.4 (fspring in the) 466.89 404.95 P +(appropriate subpopulations:) 135.65 390.95 T +2 F +(Chrom = reins\050Chrom, SelCh, 2\051) 135.65 370.95 T +(Chrom =) 135.65 350.95 T +(12) 153.65 336.95 T +( 2) 153.65 322.95 T +(13) 153.65 308.95 T +(11) 153.65 294.95 T +(14) 153.65 280.95 T +( 6) 153.65 266.95 T +(15) 153.65 252.95 T +(16) 153.65 238.95 T +1 16 Q +(See Also) 117.65 216.29 T +2 12 Q +(select) 135.65 198.95 T +FMENDPAGE +%%EndPage: "36" 37 +%%Page: "37" 37 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-37) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(r) 63.65 732.95 T +(ep) 71.31 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Matrix replication.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(MatOut = rep\050MatIn, REPN\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +1.03 (rep) 135.65 588.95 P +3 F +0.43 ( is a low-level replication function. Not normally used directly) 157.24 588.95 P +0.43 (,) 460.13 588.95 P +2 F +1.03 (rep) 466.56 588.95 P +3 F +0.43 ( is called) 488.15 588.95 P +(by a number of functions in the GA-T) 135.65 574.95 T +(oolbox.) 317.01 574.95 T +2 F +1.3 (rep) 135.65 548.95 P +3 F +0.54 ( performs replication of a matrix,) 157.24 548.95 P +2 F +1.3 (MatIn) 322.71 548.95 P +3 F +0.54 (, speci\336ed by the numbers in) 358.69 548.95 P +2 F +1.3 (REPN) 502.86 548.95 P +3 F +(and returns the replicated matrix,) 135.65 534.95 T +2 F +(MatOut) 297.52 534.95 T +3 F +(.) 340.7 534.95 T +2 F +1.62 (REPN) 135.65 508.95 P +3 F +0.67 ( contains the number of replications in every direction.) 164.43 508.95 P +2 F +1.62 (REPN\0501\051) 436.3 508.95 P +3 F +0.67 ( speci\336es) 486.67 508.95 P +5.83 (the number of vertical replications,) 135.65 494.95 P +2 F +14 (REPN\0502\051) 336.02 494.95 P +3 F +5.83 ( the number of horizontal) 386.4 494.95 P +(replications.) 135.65 480.95 T +1 16 Q +(Example) 117.65 452.29 T +3 12 Q +( Consider the following matrix) 135.65 434.95 T +2 F +(MatIn) 286.56 434.95 T +3 F +(:) 322.54 434.95 T +2 F +(MatIn = [) 135.65 414.95 T +(1 2 3 4;) 153.65 400.95 T +(5 6 7 8]) 153.65 386.95 T +3 F +(T) 135.65 366.95 T +(o perform matrix replication:) 142.14 366.95 T +2 F +(MatOut = rep\050MatIn, [1 2]\051) 135.65 346.95 T +(MatOut =) 135.65 326.95 T +(1 2 3 4 1 2 3 4) 153.65 312.95 T +(5 6 7 8 5 6 7 8) 153.65 298.95 T +(MatOut = rep\050MatIn, [2 1]\051) 135.65 278.95 T +(MatOut =) 135.65 258.95 T +(1 2 3 4) 153.65 244.95 T +(5 6 7 8) 153.65 230.95 T +(1 2 3 4) 153.65 216.95 T +(5 6 7 8) 153.65 202.95 T +(MatOut = rep\050MatIn, [2 3]\051) 135.65 182.95 T +(MatOut =) 135.65 162.95 T +(1 2 3 4 1 2 3 4 1 2 3 4) 153.65 148.95 T +(5 6 7 8 5 6 7 8 5 6 7 8) 153.65 134.95 T +(1 2 3 4 1 2 3 4 1 2 3 4) 153.65 120.95 T +(5 6 7 8 5 6 7 8 5 6 7 8) 153.65 106.95 T +FMENDPAGE +%%EndPage: "37" 38 +%%Page: "38" 38 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-38) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(rws) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Roulette wheel selection) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrIx = rws\050FitnV, Nsel\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.41 (rws) 135.65 588.95 P +3 F +0.17 ( probabilistically selects) 157.24 588.95 P +2 F +0.41 (Nsel) 276.67 588.95 P +3 F +0.17 ( individuals for reproduction according to their) 305.45 588.95 P +(\336tness,) 135.65 574.95 T +2 F +(FitnV) 172.3 574.95 T +3 F +(, in the current population.) 206.73 574.95 T +2 F +8.66 (NewChrIx = rws\050FitnV, Nsel\051) 135.65 548.95 P +3 F +3.61 ( selects) 355.91 548.95 P +2 F +8.66 (Nsel) 401.1 548.95 P +3 F +3.61 ( individuals from a) 429.88 548.95 P +0.33 (population using roulette wheel selection.) 135.65 534.95 P +2 F +0.78 (FitnV) 340.48 534.95 P +3 F +0.33 ( is a column vector containing a) 376.46 534.95 P +0.69 (performance measure for each individual in the population. This can be achieved) 135.65 520.95 P +1.83 (by using the function) 135.65 506.95 P +2 F +4.39 (ranking) 247.57 506.95 P +3 F +1.83 ( or) 297.94 506.95 P +2 F +4.39 (scaling) 317.58 506.95 P +3 F +1.83 ( to assign a \336tness level to each) 367.95 506.95 P +0.79 (individual. The return value,) 135.65 492.95 P +2 F +1.89 (NewChrIx) 278.7 492.95 P +3 F +0.79 (, is the index of the individuals selected) 336.26 492.95 P +0.51 (for breeding, in the order that they were selected. The selected individuals can be) 135.65 478.95 P +(recovered by evaluating) 135.65 464.95 T +2 F +(Chrom\050NewChrIx,:\051) 253.88 464.95 T +3 F +(.) 376.21 464.95 T +2 F +(rws) 135.65 438.95 T +3 F +( is a low-level selection function normally called by) 157.24 438.95 T +2 F +(select) 409.4 438.95 T +3 F +(.) 452.57 438.95 T +1 16 Q +(Example) 117.65 410.29 T +3 12 Q +(Consider a population of 8 individuals with the assigned \336tness values,) 135.65 392.95 T +2 F +(FitnV) 479.45 392.95 T +3 F +(:) 514.54 392.95 T +2 F +(FitnV = [1.50; 1.35; 1.21; 1.07; 0.92; 0.78; 0.64; 0.5]) 135.65 372.95 T +3 F +(Select the indices of 6 individuals:) 135.65 352.95 T +2 F +(NewChrIx = rws\050FitnV, 6\051) 135.65 332.95 T +3 F +(Thus,) 135.65 312.95 T +2 F +(NewChrIx) 165.63 312.95 T +3 F +( can become:) 223.2 312.95 T +2 F +(NewChrIx =) 135.65 292.95 T +(2) 153.65 278.95 T +(5) 153.65 264.95 T +(1) 153.65 250.95 T +(1) 153.65 236.95 T +(3) 153.65 222.95 T +(7) 153.65 208.95 T +1 16 Q +(Algorithm) 117.65 186.29 T +3 12 Q +0.3 (A form of roulette wheel selection is implemented by obtaining a cumulative sum) 135.65 168.95 P +5.08 (of the \336tness vector) 135.65 154.95 P +5.08 (,) 244.67 154.95 P +2 F +12.19 (FitnV) 255.75 154.95 P +3 F +5.08 (, and generating) 290.18 154.95 P +2 F +12.19 (Nsel) 385.36 154.95 P +3 F +5.08 ( uniformly at random) 414.14 154.95 P +1.07 (distributed numbers between) 135.65 140.95 P +2 F +2.57 (0) 280.43 140.95 P +3 F +1.07 ( and) 287.63 140.95 P +2 F +2.57 (sum\050FitnV\051) 313.08 140.95 P +3 F +1.07 (. The index of the individuals) 385.05 140.95 P +1.03 (selected is determined by comparing the generated numbers with the cumulative) 135.65 126.95 P +(sum vector) 135.65 112.95 T +(. The probability of an individual being selected is then given by:) 187.95 112.95 T +FMENDPAGE +%%EndPage: "38" 39 +%%Page: "39" 39 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-39) 513.33 61.29 T +3 12 Q +(,) 380.93 725.53 T +2.94 (where) 135.65 664.71 P +0 F +2.94 (f\050x) 170.89 664.71 P +0 10 Q +2.45 (i) 183.54 661.71 P +0 12 Q +2.94 (\051) 186.32 664.71 P +3 F +2.94 ( is the \336tness of individual) 190.32 664.71 P +0 F +2.94 (x) 337.92 664.71 P +0 10 Q +2.45 (i) 343.25 661.71 P +3 12 Q +2.94 ( and) 346.03 664.71 P +0 F +2.94 (F\050x) 375.23 664.71 P +0 10 Q +2.45 (i) 391.88 661.71 P +0 12 Q +2.94 (\051) 394.66 664.71 P +3 F +2.94 ( is the probability of that) 398.65 664.71 P +(individual being selected.) 135.65 650.71 T +1 16 Q +(See Also) 117.65 622.04 T +2 12 Q +(select) 135.65 604.71 T +3 F +(,) 178.82 604.71 T +2 F +(sus) 184.82 604.71 T +3 F +(,) 206.41 604.71 T +2 F +(reins) 212.41 604.71 T +3 F +(,) 248.39 604.71 T +2 F +(ranking) 254.38 604.71 T +3 F +(,) 304.76 604.71 T +2 F +(scaling) 310.75 604.71 T +1 16 Q +(Refer) 117.65 582.04 T +(ence) 155.53 582.04 T +3 12 Q +0.67 ([1] J. E. Baker) 135.65 564.71 P +0.67 (, \322Reducing bias and inef) 206.8 564.71 P +0.67 (\336ciency in the selection algorithm\323,) 330.86 564.71 P +0 F +0.67 (Pr) 508.78 564.71 P +0.67 (oc) 520.33 564.71 P +(ICGA 2) 135.65 550.71 T +3 F +(, pp. 14-21, Lawrence Erlbaum Associates, Publishers, 1987.) 172.62 550.71 T +0.59 ([2] David E. Goldber) 135.65 524.71 P +0.59 (g,) 239.13 524.71 P +0 F +0.59 (Genetic Algorithms in Sear) 251.71 524.71 P +0.59 (ch, Optimization and Machine) 383.96 524.71 P +(Learning) 135.65 510.71 T +3 F +(, Addison W) 179.63 510.71 T +(esley) 239.63 510.71 T +(, 1989.) 263.5 510.71 T +283.37 686.71 380.93 744.95 C +0 12 Q +0 X +0 K +(F) 284.37 725.53 T +(x) 299.5 725.53 T +0 9 Q +(i) 305.29 721.74 T +4 12 Q +(\050) 294.4 725.53 T +(\051) 308.4 725.53 T +0 F +(f) 343.44 735.75 T +(x) 354.58 735.75 T +0 9 Q +(i) 360.36 731.97 T +4 12 Q +(\050) 349.48 735.75 T +(\051) 363.47 735.75 T +0 F +(f) 352.9 703.95 T +(x) 364.04 703.95 T +0 9 Q +(i) 369.83 700.17 T +4 12 Q +(\050) 358.94 703.95 T +(\051) 372.93 703.95 T +0 9 Q +(i) 333.98 689.66 T +3 F +(1) 347.41 689.66 T +4 F +(=) 339.47 689.66 T +0 F +(N) 335.47 720.47 T +0 6 Q +(i) 341.82 718.02 T +(n) 343.94 718.02 T +(d) 347.4 718.02 T +4 18 Q +(\345) 336.52 700.75 T +4 12 Q +(=) 320.39 725.53 T +333.98 728.12 378.68 728.12 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "39" 40 +%%Page: "40" 40 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-40) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(scaling) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Linear \336tness scaling) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(FitnV = scaling\050ObjV, Smul\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +6.16 (scaling) 135.65 588.95 P +3 F +2.57 ( converts the objective values,) 186.02 588.95 P +2 F +6.16 (ObjV) 346.75 588.95 P +3 F +2.57 (, of a population into a \336tness) 373.99 588.95 P +(measure with a known upper bound, determined by the value of) 135.65 574.95 T +2 F +(Smul) 444.75 574.95 T +3 F +(, such that,) 473.54 574.95 T +(,) 383.11 547.75 T +0.31 (where) 135.65 519.12 P +0 F +0.31 (f\050x) 168.26 519.12 P +0 10 Q +0.26 (i) 180.91 516.12 P +0 12 Q +0.31 (\051) 183.69 519.12 P +3 F +0.31 ( is the objective value of individual) 187.68 519.12 P +0 F +0.31 (x) 362.07 519.12 P +0 10 Q +0.26 (i) 367.39 516.12 P +3 12 Q +0.31 (,) 370.17 519.12 P +0 F +0.31 (a) 376.48 519.12 P +3 F +0.31 ( is a scaling coef) 382.47 519.12 P +0.31 (\336cient,) 463.43 519.12 P +0 F +0.31 (b) 499.71 519.12 P +3 F +0.31 ( is an) 505.71 519.12 P +0.47 (of) 135.65 505.12 P +0.47 (fset and) 145.42 505.12 P +0 F +0.47 (F\050x) 187 505.12 P +0 10 Q +0.39 (i) 203.64 502.12 P +0 12 Q +0.47 (\051) 206.42 505.12 P +3 F +0.47 ( is the resulting \336tness value of individual) 210.42 505.12 P +0 F +0.47 (x) 418.07 505.12 P +0 10 Q +0.39 (i) 423.39 502.12 P +3 12 Q +0.47 (. If) 426.17 505.12 P +0 F +0.47 (f) 444.09 505.12 P +0 10 Q +0.39 (ave) 447.43 502.12 P +3 12 Q +0.47 ( is the average) 461.3 505.12 P +0.77 (objective value in the current generation, then the maximum \336tness of the scaled) 135.65 491.12 P +0.5 (population is upper bounded at) 135.65 477.12 P +0 F +0.5 (f) 289.7 477.12 P +0 10 Q +0.41 (ave) 293.03 474.12 P +4 12 Q +0.5 ( \264) 306.91 477.12 P +2 F +1.19 ( Smul) 316.98 477.12 P +3 F +0.5 (. If) 354.15 477.12 P +2 F +1.19 (Smul) 372.13 477.12 P +3 F +0.5 ( is omitted then the default) 400.91 477.12 P +0.38 (value of) 135.65 463.12 P +2 F +0.92 (Smult = 2) 178.38 463.12 P +3 F +0.38 ( is assumed. The average \336tness of the scaled population is) 244.99 463.12 P +(also set to) 135.65 449.12 T +0 F +(f) 186.62 449.12 T +0 10 Q +(ave) 189.95 446.12 T +3 12 Q +(.) 203.83 449.12 T +1.76 (In the case of some of the objective values being negative, scaling attempts to) 135.65 423.12 P +(provide an of) 135.65 409.12 T +(fset,) 199.38 409.12 T +0 F +(b) 222.7 409.12 T +3 F +(, such that the scaled \336tness values are greater than zero.) 228.69 409.12 T +1 16 Q +(Algorithm) 117.65 380.45 T +2 12 Q +(scaling) 135.65 363.12 T +3 F +( uses the linear scaling method described by Goldber) 186.02 363.12 T +(g [1].) 439.62 363.12 T +1 F +1.97 (Note:) 135.65 337.12 P +3 F +1.97 ( linear scaling is not suitable for use with objective functions that return) 163.62 337.12 P +(negative \336tness values and is included here only for completeness.) 135.65 323.12 T +1 16 Q +(See Also) 117.65 294.45 T +2 12 Q +(ranking) 135.65 277.12 T +3 F +(,) 186.02 277.12 T +2 F +(reins) 192.02 277.12 T +3 F +(,) 228 277.12 T +2 F +(rws) 233.99 277.12 T +3 F +(,) 255.58 277.12 T +2 F +(select) 261.58 277.12 T +3 F +(,) 304.76 277.12 T +2 F +(sus) 310.75 277.12 T +1 16 Q +(Refer) 117.65 254.45 T +(ence) 155.53 254.45 T +3 12 Q +2.36 ([1] D. E. Goldber) 135.65 237.12 P +2.36 (g,) 226.77 237.12 P +0 F +2.36 (Genetic Algorithms in Sear) 241.12 237.12 P +2.36 (ch, Optimization and Machine) 378.67 237.12 P +(Learning) 135.65 223.12 T +3 F +(, Addison W) 179.63 223.12 T +(esley Publishing Company) 239.63 223.12 T +(, January 1989.) 367.46 223.12 T +281.19 541.12 383.11 556.95 C +0 12 Q +0 X +0 K +(F) 282.19 547.75 T +(x) 297.33 547.75 T +0 9 Q +(i) 303.11 543.97 T +4 12 Q +(\050) 292.23 547.75 T +(\051) 306.22 547.75 T +0 F +(a) 330.8 547.75 T +(f) 337.5 547.75 T +(x) 348.64 547.75 T +0 9 Q +(i) 354.43 543.97 T +4 12 Q +(\050) 343.54 547.75 T +(\051) 357.53 547.75 T +0 F +(b) 376.11 547.75 T +4 F +(+) 366.53 547.75 T +(=) 318.21 547.75 T +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "40" 41 +%%Page: "41" 41 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-41) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(select) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Selection of individuals from population \050high-level function\051.) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(SelCh = select\050SEL_F, Chrom, FitnV\051) 135.65 628.95 T +(SelCh = select\050SEL_F, Chrom, FitnV, GGAP\051) 135.65 608.95 T +(SelCh = select\050SEL_F, Chrom, FitnV, GGAP, SUBPOP\051) 135.65 588.95 T +1 16 Q +(Description) 117.65 566.29 T +2 12 Q +0.25 (select) 135.65 548.95 P +3 F +0.11 ( performs selection of individuals from a population,) 178.82 548.95 P +2 F +0.25 (Chrom) 435.84 548.95 P +3 F +0.11 (, and returns) 471.82 548.95 P +1.63 (the selected individuals in a new population,) 135.65 534.95 P +2 F +3.92 (SelCh) 363.6 534.95 P +3 F +1.63 (. Each row of) 399.58 534.95 P +2 F +3.92 (Chrom) 473.72 534.95 P +3 F +1.63 ( and) 509.7 534.95 P +2 F +(SelCh) 135.65 520.95 T +3 F +( corresponds to one individual.) 171.63 520.95 T +2 F +2.39 (SEL_F) 135.65 494.95 P +3 F +1 ( is a string and contains the name of the low-level selection function, for) 171.63 494.95 P +(example) 135.65 480.95 T +2 F +(rws) 179.28 480.95 T +3 F +( or) 200.87 480.95 T +2 F +(sus) 216.85 480.95 T +3 F +(.) 238.44 480.95 T +2 F +6.18 (FitnV) 135.65 454.95 P +3 F +2.57 ( is a column vector containing the \336tness values of the individuals in) 171.63 454.95 P +2 F +2.53 (Chrom) 135.65 440.95 P +3 F +1.06 (. The \336tness value indicates the expected probability of selection of each) 171.63 440.95 P +(individual.) 135.65 426.95 T +2 F +2.5 (GGAP) 135.65 400.95 P +3 F +1.04 ( is an optional parameter specifying the generation gap, the fraction of the) 164.43 400.95 P +-0.3 (population to be reproduced. If) 135.65 386.95 P +2 F +-0.72 (GGAP) 286.04 386.95 P +3 F +-0.3 ( is omitted or) 314.83 386.95 P +2 F +-0.72 (NaN,) 380.27 386.95 P +-0.72 (GGAP = 1.0) 411.75 386.95 P +3 F +-0.3 ( \050100%\051 is) 482.28 386.95 P +3.47 (assumed.) 135.65 372.95 P +2 F +8.33 (GGAP) 186.42 372.95 P +3 F +3.47 ( may also be greater than 1, allowing more of) 215.21 372.95 P +3.47 (fspring to be) 464.08 372.95 P +3.44 (produced then the number of parents. If) 135.65 358.95 P +2 F +8.25 (Chrom) 352.89 358.95 P +3 F +3.44 ( consists of more than one) 388.87 358.95 P +3.58 (subpopulation,) 135.65 344.95 P +2 F +8.58 (GGAP) 213.19 344.95 P +3 F +3.58 ( speci\336es the number of individuals to be selected per) 241.97 344.95 P +(subpopulation relative to the size of the subpopulation.) 135.65 330.95 T +2 F +0.01 (SUBPOP) 135.65 304.95 P +3 F +0.01 ( is an optional parameter and determines the number of subpopulations in) 178.82 304.95 P +2 F +8.57 (Chrom) 135.65 290.95 P +3 F +3.57 (. If) 171.63 290.95 P +2 F +8.57 (SUBPOP) 195.75 290.95 P +3 F +3.57 ( is omitted or) 238.93 290.95 P +2 F +8.57 (NaN,) 319.85 290.95 P +8.57 (SUBPOP = 1) 355.2 290.95 P +3 F +3.57 ( is assumed. All) 444.31 290.95 P +(subpopulations in) 135.65 276.95 T +2 F +(Chrom) 223.61 276.95 T +3 F +( must have the same size.) 259.59 276.95 T +1 16 Q +(Example) 117.65 248.29 T +3 12 Q +0.93 (Consider a population of 8 individuals,) 135.65 230.95 P +2 F +2.23 (Chrom) 331.45 230.95 P +3 F +0.93 (, with the assigned \336tness values,) 367.43 230.95 P +2 F +(FitnV) 135.65 216.95 T +3 F +(:) 170.74 216.95 T +FMENDPAGE +%%EndPage: "41" 42 +%%Page: "42" 42 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-42) 513.33 61.29 T +2 12 Q +(Chrom = [) 135.65 736.95 T +(1 11 21;) 153.65 722.95 T +(2 12 22;) 153.65 708.95 T +(3 13 23;) 153.65 694.95 T +(4 14 24;) 153.65 680.95 T +(5 15 25;) 153.65 666.95 T +(6 16 26;) 153.65 652.95 T +(7 17 27;) 153.65 638.95 T +(8 18 28]) 153.65 624.95 T +(FitnV = [1.50; 1.35; 1.21; 1.07; 0.92; 0.78; 0.64; 0.5]) 135.65 604.95 T +3 F +(Select 8 individuals by stochastic universal sampling,) 135.65 584.95 T +2 F +(sus) 395.5 584.95 T +3 F +(:) 417.08 584.95 T +2 F +(SelCh = select\050\324sus\325, Chrom, FitnV\051) 135.65 564.95 T +3 F +(Thus,) 135.65 544.95 T +2 F +(SelCh) 165.63 544.95 T +3 F +( can become:) 201.61 544.95 T +2 F +(SelCh =) 135.65 524.95 T +(7 17 27) 153.65 510.95 T +(1 11 21) 153.65 496.95 T +(6 16 26) 153.65 482.95 T +(1 11 21) 153.65 468.95 T +(5 15 25) 153.65 454.95 T +(2 12 22) 153.65 440.95 T +(3 13 23) 153.65 426.95 T +(4 14 24) 153.65 412.95 T +3 F +3.8 (Consider) 135.65 392.95 P +2 F +9.12 (Chrom) 185.76 392.95 P +3 F +3.8 ( consists of 2 subpopulations. Select 150% individuals per) 221.74 392.95 P +(subpopulation by roulette wheel selection,) 135.65 378.95 T +2 F +(rws) 341.52 378.95 T +3 F +(:) 363.1 378.95 T +2 F +(FitnV = [1.50; 1.16; 0.83; 0.50; 1.50; 1.16; 0.83; 0.5]) 135.65 358.95 T +(SelCh = select\050\324sus\325, Chrom, FitnV, 1.5, 2\051) 135.65 338.95 T +3 F +(Thus,) 135.65 318.95 T +2 F +(SelCh) 165.63 318.95 T +3 F +( can become:) 201.61 318.95 T +2 F +(SelCh =) 135.65 298.95 T +(3 13 23) 153.65 284.95 T +(2 12 22) 153.65 270.95 T +(1 11 21) 153.65 256.95 T +(2 12 22) 153.65 242.95 T +(2 12 22) 153.65 228.95 T +(1 11 21) 153.65 214.95 T +(6 16 26) 153.65 200.95 T +(7 17 27) 153.65 186.95 T +(7 17 27) 153.65 172.95 T +(6 16 26) 153.65 158.95 T +(7 17 27) 153.65 144.95 T +(5 15 25) 153.65 130.95 T +FMENDPAGE +%%EndPage: "42" 43 +%%Page: "43" 43 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-43) 513.33 61.29 T +1 16 Q +(Algorithm) 117.65 734.29 T +2 12 Q +4.38 (select) 135.65 716.95 P +3 F +1.83 ( checks the consistency of the input parameter and calls the low-level) 178.82 716.95 P +-0.05 (selection function. If) 135.65 702.95 P +2 F +-0.12 (select) 238.09 702.95 P +3 F +-0.05 ( is called with more than one subpopulation then the) 281.26 702.95 P +(low-level selection function is called separately for each subpopulation.) 135.65 688.95 T +1 16 Q +(See Also) 117.65 666.29 T +2 12 Q +(rws) 135.65 648.95 T +3 F +(,) 157.24 648.95 T +2 F +(sus) 163.23 648.95 T +3 F +(,) 184.82 648.95 T +2 F +(ranking) 190.82 648.95 T +3 F +(,) 241.19 648.95 T +2 F +(scaling) 247.19 648.95 T +3 F +(,) 297.56 648.95 T +2 F +(recombin) 303.56 648.95 T +3 F +(,) 361.12 648.95 T +2 F +(mutate) 367.12 648.95 T +FMENDPAGE +%%EndPage: "43" 44 +%%Page: "44" 44 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-44) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(sus) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Stochastic universal sampling) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrIx = sus\050FitnV, Nsel\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.41 (sus) 135.65 588.95 P +3 F +0.17 ( probabilistically selects) 157.24 588.95 P +2 F +0.41 (Nsel) 276.67 588.95 P +3 F +0.17 ( individuals for reproduction according to their) 305.45 588.95 P +(\336tness,) 135.65 574.95 T +2 F +(FitnV) 172.3 574.95 T +3 F +(, in the current population.) 206.73 574.95 T +2 F +8.66 (NewChrIx = rws\050FitnV, Nsel\051) 135.65 548.95 P +3 F +3.61 ( selects) 355.91 548.95 P +2 F +8.66 (Nsel) 401.1 548.95 P +3 F +3.61 ( individuals from a) 429.88 548.95 P +2.12 (population using stochastic universal sampling [1].) 135.65 534.95 P +2 F +5.09 (FitnV) 395.91 534.95 P +3 F +2.12 ( is a column vector) 431.89 534.95 P +0.51 (containing a performance measure for each individual in the population. This can) 135.65 520.95 P +0.09 (be achieved by using the function) 135.65 506.95 P +2 F +0.21 (ranking) 300.71 506.95 P +3 F +0.09 ( or) 351.08 506.95 P +2 F +0.21 (scaling) 367.24 506.95 P +3 F +0.09 ( to assign a \336tness level) 417.62 506.95 P +1.08 (to each individual. The return value,) 135.65 492.95 P +2 F +2.6 (NewChrIx) 319.34 492.95 P +3 F +1.08 (, is the index of the individuals) 376.91 492.95 P +-0.09 (selected for breeding, in the order that they were selected. The selected individuals) 135.65 478.95 P +(can be recovered by evaluating) 135.65 464.95 T +2 F +(Chrom\050NewChrIx,:\051) 287.84 464.95 T +3 F +(.) 410.18 464.95 T +2 F +(sus) 135.65 438.95 T +3 F +( is a low-level selection function normally called by) 157.24 438.95 T +2 F +(select) 409.4 438.95 T +3 F +(.) 452.57 438.95 T +1 16 Q +(Example) 117.65 410.29 T +3 12 Q +(Consider a population of 8 individuals with the assigned \336tness values,) 135.65 392.95 T +2 F +(FitnV) 479.45 392.95 T +3 F +(:) 514.54 392.95 T +2 F +(FitnV = [1.50; 1.35; 1.21; 1.07; 0.92; 0.78; 0.64; 0.5]) 135.65 372.95 T +3 F +(Select the indices of 6 individuals:) 135.65 352.95 T +2 F +(NewChrIx = sus\050FitnV, 6\051) 135.65 332.95 T +3 F +(Thus,) 135.65 312.95 T +2 F +(NewChrIx) 165.63 312.95 T +3 F +( can become:) 223.2 312.95 T +2 F +(NewChrIx =) 135.65 292.95 T +(5) 153.65 278.95 T +(6) 153.65 264.95 T +(3) 153.65 250.95 T +(1) 153.65 236.95 T +(1) 153.65 222.95 T +(2) 153.65 208.95 T +1 16 Q +(Algorithm) 117.65 186.29 T +3 12 Q +-0.07 (A form of stochastic universal sampling is implemented by obtaining a cumulative) 135.65 168.95 P +1.08 (sum of the \336tness vector) 135.65 154.95 P +1.08 (,) 256.73 154.95 P +2 F +2.58 (FitnV) 263.8 154.95 P +3 F +1.08 (, and generating) 298.23 154.95 P +2 F +2.58 (Nsel) 381.39 154.95 P +3 F +1.08 ( equally spaced numbers) 410.18 154.95 P +-0.22 (between) 135.65 140.95 P +2 F +-0.52 (0) 178.39 140.95 P +3 F +-0.22 ( and) 185.59 140.95 P +2 F +-0.52 (sum\050FitnV\051) 208.47 140.95 P +3 F +-0.22 (. Thus, only one random number is generated, all the) 280.43 140.95 P +1.83 (others used being equally spaced from that point. The index of the individuals) 135.65 126.95 P +FMENDPAGE +%%EndPage: "44" 45 +%%Page: "45" 45 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-45) 513.33 61.29 T +3 12 Q +1.03 (selected is determined by comparing the generated numbers with the cumulative) 135.65 736.95 P +(sum vector) 135.65 722.95 T +(. The probability of an individual being selected is then given by) 187.95 722.95 T +(\325) 380.43 685.53 T +2.94 (where) 135.65 624.71 P +0 F +2.94 (f\050x) 170.89 624.71 P +0 10 Q +2.45 (i) 183.54 621.71 P +0 12 Q +2.94 (\051) 186.32 624.71 P +3 F +2.94 ( is the \336tness of individual) 190.32 624.71 P +0 F +2.94 (x) 337.92 624.71 P +0 10 Q +2.45 (i) 343.25 621.71 P +3 12 Q +2.94 ( and) 346.03 624.71 P +0 F +2.94 (F\050x) 375.23 624.71 P +0 10 Q +2.45 (i) 391.88 621.71 P +0 12 Q +2.94 (\051) 394.66 624.71 P +3 F +2.94 ( is the probability of that) 398.65 624.71 P +(individual being selected.) 135.65 610.71 T +1 16 Q +(See Also) 117.65 582.04 T +2 12 Q +(select) 135.65 564.71 T +3 F +(,) 178.82 564.71 T +2 F +(rws) 184.82 564.71 T +3 F +(,) 206.41 564.71 T +2 F +(reins) 212.41 564.71 T +3 F +(,) 248.39 564.71 T +2 F +(ranking) 254.38 564.71 T +3 F +(,) 304.76 564.71 T +2 F +(scaling) 310.75 564.71 T +1 16 Q +(Refer) 117.65 542.04 T +(ence) 155.53 542.04 T +3 12 Q +0.42 ([1] J. E. Baker) 135.65 524.71 P +0.42 (, \322Reducing bias and inef) 206.05 524.71 P +0.42 (\336ciency in the selection algorithm\323,) 329.11 524.71 P +0 F +0.42 (Pr) 505.78 524.71 P +0.42 (oc.) 517.33 524.71 P +(ICGA 2) 135.65 510.71 T +3 F +(, pp. 14-21, Lawrence Erlbaum Associates, Publishers, 1987.) 172.62 510.71 T +282.87 646.71 380.43 704.95 C +0 12 Q +0 X +0 K +(F) 283.87 685.53 T +(x) 299.01 685.53 T +0 9 Q +(i) 304.79 681.74 T +4 12 Q +(\050) 293.91 685.53 T +(\051) 307.9 685.53 T +0 F +(f) 342.94 695.75 T +(x) 354.08 695.75 T +0 9 Q +(i) 359.87 691.97 T +4 12 Q +(\050) 348.98 695.75 T +(\051) 362.97 695.75 T +0 F +(f) 352.4 663.95 T +(x) 363.54 663.95 T +0 9 Q +(i) 369.33 660.17 T +4 12 Q +(\050) 358.44 663.95 T +(\051) 372.44 663.95 T +0 9 Q +(i) 333.48 649.66 T +3 F +(1) 346.91 649.66 T +4 F +(=) 338.98 649.66 T +0 F +(N) 334.98 680.47 T +0 6 Q +(i) 341.32 678.02 T +(n) 343.45 678.02 T +(d) 346.91 678.02 T +4 18 Q +(\345) 336.03 660.75 T +4 12 Q +(=) 319.89 685.53 T +333.48 688.12 378.18 688.12 2 L +0.33 H +0 Z +N +-8.35 24.95 603.65 816.95 C +FMENDPAGE +%%EndPage: "45" 46 +%%Page: "46" 46 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-46) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovdp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Double-point crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovdp\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +0.62 (xov) 135.65 588.95 P +3 F +0.26 (dp performs double-point crossover between pairs of individuals contained in) 157.24 588.95 P +0.18 (the current population,) 135.65 574.95 P +2 F +0.44 (OldChrom) 248.12 574.95 P +3 F +0.18 (, according to the crossover probability) 305.69 574.95 P +0.18 (,) 493.69 574.95 P +2 F +0.44 (XOVR) 499.86 574.95 P +3 F +0.18 (,) 528.65 574.95 P +0.61 (and returns a new population after mating,) 135.65 560.95 P +2 F +1.47 (NewChrom) 346.45 560.95 P +3 F +0.61 (. Each row of) 404.02 560.95 P +2 F +1.47 (OldChrom) 474.08 560.95 P +3 F +4.74 (and) 135.65 546.95 P +2 F +11.37 (NewChrom) 160.7 546.95 P +3 F +4.74 ( corresponds to one individual. For the chromosomes any) 218.27 546.95 P +(representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xovdp) 135.65 370.95 T +3 F +( is a low-level crossover function normally called by) 171.63 370.95 T +2 F +(recombin) 427.11 370.95 T +3 F +(.) 484.68 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +(Consider the following two binary strings of the same length:) 135.65 324.95 T +2 F +(A1 = [1 1 0 1 0 1]) 135.65 304.95 T +(A2 = [1 0 1 0 1 0]) 135.65 290.95 T +3 F +3.91 (Double point crossover involves selecting uniformly at random two integer) 135.65 270.95 P +0.16 (positions,) 135.65 256.95 P +0 F +0.16 (k1) 185.13 256.95 P +3 F +0.16 (and) 199.61 256.95 P +0 F +0.16 ( k2) 216.93 256.95 P +3 F +0.16 (, between 1 and) 231.41 256.95 P +2 F +0.39 (length\050A1\051) 310.32 256.95 P +3 F +0.16 (, and swapping the variables in) 382.28 256.95 P +0.88 (positions) 135.65 242.95 P +0 F +0.88 (k1+1) 182.85 242.95 P +3 F +0.88 ( to) 208.26 242.95 P +0 F +0.88 (k2) 225.36 242.95 P +3 F +0.88 ( between) 236.68 242.95 P +2 F +2.12 (A1) 284.4 242.95 P +3 F +0.88 ( and) 298.8 242.95 P +2 F +2.12 (A2) 323.88 242.95 P +3 F +0.88 (. Thus if the crossover positions) 338.27 242.95 P +0 F +0.88 (k1) 499.8 242.95 P +3 F +0.88 ( = 3) 511.12 242.95 P +(and) 135.65 228.95 T +0 F +(k2) 155.96 228.95 T +3 F +( = 5, then) 167.29 228.95 T +2 F +(A1) 215.69 228.95 T +3 F +( and) 230.08 228.95 T +2 F +(A2) 253.4 228.95 T +3 F +( would become:) 267.79 228.95 T +2 F +(A1\325 = [1 1 0 0 1 1]) 135.65 208.95 T +(A2\325 = [1 0 1 1 0 0]) 135.65 194.95 T +(xovdp) 135.65 174.95 T +3 F +( calls) 171.63 174.95 T +2 F +(xovmp) 199.61 174.95 T +3 F +( with the appropriate parameters.) 235.59 174.95 T +1 16 Q +(See Also) 117.65 152.29 T +2 12 Q +(xovdprs) 135.65 134.95 T +3 F +(,) 186.02 134.95 T +2 F +(xovsp) 192.02 134.95 T +3 F +(,) 228 134.95 T +2 F +(xovsh) 233.99 134.95 T +3 F +(,) 269.97 134.95 T +2 F +(xovmp) 275.97 134.95 T +3 F +(,) 311.95 134.95 T +2 F +(recombin) 317.95 134.95 T +3 F +(,) 375.52 134.95 T +2 F +(select) 381.51 134.95 T +FMENDPAGE +%%EndPage: "46" 47 +%%Page: "47" 47 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-47) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovdprs) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Double-point reduced surrogate crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovdprs\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +7.01 (xov) 135.65 588.95 P +3 F +2.92 (dprs performs double-point reduced surrogate crossover between pairs of) 157.24 588.95 P +2.78 (individuals contained in the current population,) 135.65 574.95 P +2 F +6.66 (OldChrom) 382.48 574.95 P +3 F +2.78 (, according to the) 440.05 574.95 P +5.65 (crossover probability) 135.65 560.95 P +5.65 (,) 242.12 560.95 P +2 F +13.57 (XOVR) 253.77 560.95 P +3 F +5.65 (, and returns a new population after mating,) 282.55 560.95 P +2 F +10.34 (NewChrom) 135.65 546.95 P +3 F +4.31 (. Each row of) 193.22 546.95 P +2 F +10.34 (OldChrom) 278.06 546.95 P +3 F +4.31 ( and) 335.62 546.95 P +2 F +10.34 (NewChrom) 367.56 546.95 P +3 F +4.31 ( corresponds to one) 425.13 546.95 P +(individual. For the chromosomes any representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xovdp) 135.65 370.95 T +3 F +(rs is a low-level crossover function normally called by) 171.63 370.95 T +2 F +(recombin) 435.77 370.95 T +3 F +(.) 493.34 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +(For double point crossover see) 135.65 324.95 T +2 F +(xovdp) 285.88 324.95 T +3 F +(.) 321.86 324.95 T +3.35 (The) 135.65 298.95 P +0 F +3.35 (r) 160.65 298.95 P +3.35 (educed surr) 164.87 298.95 P +3.35 (ogate) 224.74 298.95 P +3 F +3.35 ( operator constrains crossover to always produce new) 251.39 298.95 P +0.99 (individuals wherever possible. This is implemented by restricting the location of) 135.65 284.95 P +1.41 (crossover points such that crossover points only occur where gene values dif) 135.65 270.95 P +1.41 (fer) 518.34 270.95 P +([1].) 135.65 256.95 T +2 F +(xovdprs) 135.65 230.95 T +3 F +( calls) 186.02 230.95 T +2 F +(xovmp) 214 230.95 T +3 F +( with the appropriate parameters.) 249.98 230.95 T +1 16 Q +(See Also) 117.65 208.29 T +2 12 Q +(xovdp) 135.65 190.95 T +3 F +(,) 171.63 190.95 T +2 F +(xovsprs) 177.62 190.95 T +3 F +(,) 228 190.95 T +2 F +(xovshrs) 233.99 190.95 T +3 F +(,) 284.37 190.95 T +2 F +(xovmp) 290.36 190.95 T +3 F +(,) 326.34 190.95 T +2 F +(recombin) 332.34 190.95 T +3 F +(,) 389.91 190.95 T +2 F +(select) 395.9 190.95 T +1 16 Q +(Refer) 117.65 168.29 T +(ence) 155.53 168.29 T +3 12 Q +1.31 ([1] L. Booker) 135.65 150.95 P +1.31 (, \322Improving search in genetic algorithms,\323 In) 203.4 150.95 P +0 F +1.31 ( Genetic Algorithms) 432.42 150.95 P +5.64 (and Simulated Annealing) 135.65 136.95 P +3 F +5.64 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 268.2 136.95 P +5.64 (gan Kaufmann) 455.06 136.95 P +(Publishers, 1987) 135.65 122.95 T +2 F +(.) 215.61 122.95 T +FMENDPAGE +%%EndPage: "47" 48 +%%Page: "48" 48 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-48) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovmp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Multi-point crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovmp\050OldChrom, XOVR, Npt, Rs\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +1.93 (xovmp) 135.65 588.95 P +3 F +0.81 ( performs multi-point crossover between pairs of individuals contained in) 171.63 588.95 P +1.7 (the current population,) 135.65 574.95 P +2 F +4.08 (OldChrom) 252.67 574.95 P +3 F +1.7 (, and returns a new population after mating,) 310.24 574.95 P +2 F +10.34 (NewChrom) 135.65 560.95 P +3 F +4.31 (. Each row of) 193.22 560.95 P +2 F +10.34 (OldChrom) 278.06 560.95 P +3 F +4.31 ( and) 335.62 560.95 P +2 F +10.34 (NewChrom) 367.56 560.95 P +3 F +4.31 ( corresponds to one) 425.13 560.95 P +(individual. For the chromosomes any representation can be used.) 135.65 546.95 T +2 F +1.74 (XOVR) 135.65 526.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 526.95 P +2 F +1.74 (XOVR) 447.77 526.95 P +3 F +0.72 ( is omitted,) 476.56 526.95 P +(empty or) 135.65 512.95 T +2 F +(NaN,) 181.62 512.95 T +(XOVR = 0.7) 213.4 512.95 T +3 F +( is assumed.) 285.36 512.95 T +2 F +(Npt) 135.65 492.95 T +3 F +( is an optional parameter specifying the number of crosspoints:) 157.24 492.95 T +(0 - shuf) 171.65 478.95 T +(\337e crossover) 208.07 478.95 T +(.) 268.36 478.95 T +(1 - single point crossover) 171.65 464.95 T +(.) 292.24 464.95 T +(2 - double point crossover) 171.65 450.95 T +(.) 296.24 450.95 T +(If) 171.65 436.95 T +2 F +(Npt) 182.63 436.95 T +3 F +( is omitted, empty or) 204.22 436.95 T +2 F +(NaN,) 306.84 436.95 T +(Npt = 0) 338.62 436.95 T +3 F +( is assumed.) 388.99 436.95 T +2 F +(Rs) 135.65 416.95 T +3 F +( is an optional parameter specifying the use of reduced surrogate:) 150.04 416.95 T +(0 - no reduced surrogate.) 171.65 402.95 T +(1 - use reduced surrogate.) 171.65 388.95 T +(If) 171.65 374.95 T +2 F +(Rs) 182.63 374.95 T +3 F +( is omitted, empty or) 197.03 374.95 T +2 F +(NaN,) 299.64 374.95 T +(Rs = 0) 331.42 374.95 T +3 F +( is assumed.) 374.6 374.95 T +1.18 (The pairs are mated in order) 135.65 354.95 P +1.18 (, odd row with the next even row) 276.62 354.95 P +1.18 (. If the number of) 442.66 354.95 P +3.35 (rows in the matrix) 135.65 340.95 P +2 F +8.05 (OldChrom) 239.67 340.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 340.95 P +-0.12 (population should therefore be or) 135.65 326.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 326.95 P +0.8 (This can be achieved by using the function) 135.65 312.95 P +2 F +1.92 (ranking) 350.55 312.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 312.95 P +2.71 (each chromosome and a selection function \050) 135.65 298.95 P +2 F +6.52 (select) 363.11 298.95 P +3 F +2.71 (,) 406.28 298.95 P +2 F +6.52 (sus) 414.99 298.95 P +3 F +2.71 ( or) 436.58 298.95 P +2 F +6.52 (rws) 458 298.95 P +3 F +2.71 (\051 to select) 479.59 298.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 284.95 T +2 F +-0.06 (xov) 135.65 264.95 P +3 F +-0.03 (mp is a low-level crossover function called by all other crossover functions. If) 157.24 264.95 P +4.29 (called by) 135.65 250.95 P +2 F +10.3 (recombine) 190.86 250.95 P +10.3 (xovmp) 262.92 250.95 P +3 F +4.29 ( performs shuf) 298.9 250.95 P +4.29 (\337e crossover without reduced) 377.21 250.95 P +(surrogate identical to) 135.65 236.95 T +2 F +(xovsh) 239.91 236.95 T +3 F +(.) 275.89 236.95 T +1 16 Q +(Algorithm) 117.65 214.29 T +3 12 Q +3.98 (The algorithms used in single-point, double-point and shuf) 135.65 196.95 P +3.98 (\337e crossover are) 445.1 196.95 P +0.69 (described in the) 135.65 182.95 P +2 F +1.66 (xovsp) 216.66 182.95 P +3 F +0.69 (,) 252.64 182.95 P +2 F +1.66 (xovdp) 259.33 182.95 P +1.66 (and xovsh) 299 182.95 P +0 F +0.69 (Refer) 374.28 182.95 P +0.69 (ence) 399.82 182.95 P +3 F +0.69 (entries) 430.65 182.95 P +0.69 (respectively) 471.48 182.95 P +0.69 (.) 528.65 182.95 P +3.23 (The algorithms used in single-point, double-point and shuf) 135.65 168.95 P +3.23 (\337e crossover with) 439.91 168.95 P +1.66 (reduced surrogates are described in the) 135.65 154.95 P +2 F +3.99 (xovsprs) 335.44 154.95 P +3 F +1.66 (,) 385.82 154.95 P +2 F +3.99 (xovdprs) 393.47 154.95 P +3.99 (and xovshrs) 448.51 154.95 P +0 F +(Refer) 135.65 140.95 T +(ence) 161.18 140.95 T +3 F +( entries respectively) 183.15 140.95 T +(.) 278.3 140.95 T +1 16 Q +(See Also) 117.65 118.29 T +2 12 Q +(xovsp) 135.65 100.95 T +3 F +(,) 171.63 100.95 T +2 F +(xovdp) 177.62 100.95 T +3 F +(,) 213.6 100.95 T +2 F +(xovsh) 219.6 100.95 T +3 F +(,) 255.58 100.95 T +2 F +(xovsprs) 261.58 100.95 T +3 F +(,) 311.95 100.95 T +2 F +(xovdprs) 317.95 100.95 T +3 F +(,) 368.32 100.95 T +2 F +(xovshrs) 374.32 100.95 T +3 F +(,) 424.69 100.95 T +2 F +(recombin) 430.69 100.95 T +FMENDPAGE +%%EndPage: "48" 49 +%%Page: "49" 49 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-49) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovsh) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Shuf) 135.65 674.95 T +(\337e crossover) 158.09 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovsh\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +2.68 (xovsh) 135.65 588.95 P +3 F +1.12 ( performs shuf) 171.63 588.95 P +1.12 (\337e crossover between pairs of individuals contained in the) 243.59 588.95 P +-0.11 (current population,) 135.65 574.95 P +2 F +-0.27 (OldChrom) 229.69 574.95 P +3 F +-0.11 (, according to the crossover probability) 287.26 574.95 P +-0.11 (,) 473.78 574.95 P +2 F +-0.27 (XOVR) 479.66 574.95 P +3 F +-0.11 (, and) 508.45 574.95 P +0.61 (returns a new population after mating,) 135.65 560.95 P +2 F +1.47 (NewChrom) 325.52 560.95 P +3 F +0.61 (. Each row of) 383.09 560.95 P +2 F +1.47 (OldChrom) 453.15 560.95 P +3 F +0.61 ( and) 510.72 560.95 P +2 F +18.88 (NewChrom) 135.65 546.95 P +3 F +7.87 ( corresponds to one individual. For the chromosomes any) 193.22 546.95 P +(representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xov) 135.65 370.95 T +3 F +(sh is a low-level crossover function normally called by) 157.24 370.95 T +2 F +(recombin) 423.38 370.95 T +3 F +(.) 480.95 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +1.5 (Shuf) 135.65 324.95 P +1.5 (\337e crossover is single-point crossover \050see) 158.09 324.95 P +2 F +3.6 (xovsp) 373.6 324.95 P +3 F +1.5 (\051, but before the bits are) 409.58 324.95 P +1.15 (exchanged, they are randomly shuf) 135.65 310.95 P +1.15 (\337ed in both parents. After recombination, the) 308.23 310.95 P +1.44 (bits in the of) 135.65 296.95 P +1.44 (fspring are unshuf) 200.04 296.95 P +1.44 (\337ed. This removes positional bias as the bits are) 289.97 296.95 P +(randomly reassigned each time crossover is performed [1].) 135.65 282.95 T +2 F +(xov) 135.65 256.95 T +3 F +(sh calls) 157.24 256.95 T +2 F +(xovmp) 195.88 256.95 T +3 F +( with the appropriate parameters.) 231.86 256.95 T +1 16 Q +(See Also) 117.65 234.29 T +2 12 Q +(xovshrs) 135.65 216.95 T +3 F +(,) 186.02 216.95 T +2 F +(xovsp) 192.02 216.95 T +3 F +(,) 228 216.95 T +2 F +(xovdp) 233.99 216.95 T +3 F +(,) 269.97 216.95 T +2 F +(xovmp) 275.97 216.95 T +3 F +(,) 311.95 216.95 T +2 F +(recombin) 317.95 216.95 T +3 F +(,) 375.52 216.95 T +2 F +(select) 381.51 216.95 T +1 16 Q +(Refer) 117.65 194.29 T +(ence) 155.53 194.29 T +3 12 Q +-0.28 ([1] R. A. Caruana, L. A. Eshelman, J. D. Schaf) 135.65 176.95 P +-0.28 (fer) 358.39 176.95 P +-0.28 (, \322Representation and hidden bias) 371.23 176.95 P +1.86 (II: Eliminating de\336ning length bias in genetic search via shuf) 135.65 162.95 P +1.86 (\337e crossover\323, In) 445.66 162.95 P +0 F +0.3 (Eleventh International Joint Confer) 135.65 148.95 P +0.3 (ence on Arti\336cial Intelligence) 307.67 148.95 P +3 F +0.3 (, N. S. Sridharan) 450.8 148.95 P +(\050Ed.\051, V) 135.65 134.95 T +(ol. 1, pp. 750-755, Mor) 173.07 134.95 T +(gan Kaufmann Publishers, 1989.) 284.79 134.95 T +FMENDPAGE +%%EndPage: "49" 50 +%%Page: "50" 50 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-50) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovshrs) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Shuf) 135.65 674.95 T +(\337e crossover with reduced surrogate) 158.09 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovshrs\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +6.55 (xov) 135.65 588.95 P +3 F +2.73 (shrs performs shuf) 157.24 588.95 P +2.73 (\337e crossover with reduced surrogates between pairs of) 251.75 588.95 P +2.78 (individuals contained in the current population,) 135.65 574.95 P +2 F +6.66 (OldChrom) 382.48 574.95 P +3 F +2.78 (, according to the) 440.05 574.95 P +5.65 (crossover probability) 135.65 560.95 P +5.65 (,) 242.12 560.95 P +2 F +13.57 (XOVR) 253.77 560.95 P +3 F +5.65 (, and returns a new population after mating,) 282.55 560.95 P +2 F +10.34 (NewChrom) 135.65 546.95 P +3 F +4.31 (. Each row of) 193.22 546.95 P +2 F +10.34 (OldChrom) 278.06 546.95 P +3 F +4.31 ( and) 335.62 546.95 P +2 F +10.34 (NewChrom) 367.56 546.95 P +3 F +4.31 ( corresponds to one) 425.13 546.95 P +(individual. For the chromosomes any representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xov) 135.65 370.95 T +3 F +(shrs is a low-level crossover function normally called by) 157.24 370.95 T +2 F +(recombin) 432.04 370.95 T +3 F +(.) 489.61 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +(For shuf) 135.65 324.95 T +(\337e crossover algorithm see) 175.74 324.95 T +2 F +(xovsh) 307.64 324.95 T +3 F +(.) 343.63 324.95 T +3.35 (The) 135.65 298.95 P +0 F +3.35 (r) 160.65 298.95 P +3.35 (educed surr) 164.87 298.95 P +3.35 (ogate) 224.74 298.95 P +3 F +3.35 ( operator constrains crossover to always produce new) 251.39 298.95 P +0.99 (individuals wherever possible. This is implemented by restricting the location of) 135.65 284.95 P +1.41 (crossover points such that crossover points only occur where gene values dif) 135.65 270.95 P +1.41 (fer) 518.34 270.95 P +([1].) 135.65 256.95 T +2 F +(xovshrs) 135.65 230.95 T +3 F +( calls) 186.02 230.95 T +2 F +(xovmp) 214 230.95 T +3 F +( with the appropriate parameters.) 249.98 230.95 T +1 16 Q +(See Also) 117.65 208.29 T +2 12 Q +(xovsh) 135.65 190.95 T +3 F +(,) 171.63 190.95 T +2 F +(xovsprs) 177.62 190.95 T +3 F +(,) 228 190.95 T +2 F +(xovdprs) 233.99 190.95 T +3 F +(,) 284.37 190.95 T +2 F +(xovmp) 290.36 190.95 T +3 F +(,) 326.34 190.95 T +2 F +(recombin) 332.34 190.95 T +3 F +(,) 389.91 190.95 T +2 F +(select) 395.9 190.95 T +1 16 Q +(Refer) 117.65 168.29 T +(ence) 155.53 168.29 T +3 12 Q +1.31 ([1] L. Booker) 135.65 150.95 P +1.31 (, \322Improving search in genetic algorithms,\323 In) 203.4 150.95 P +0 F +1.31 ( Genetic Algorithms) 432.42 150.95 P +5.64 (and Simulated Annealing) 135.65 136.95 P +3 F +5.64 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 268.2 136.95 P +5.64 (gan Kaufmann) 455.06 136.95 P +(Publishers, 1987.) 135.65 122.95 T +FMENDPAGE +%%EndPage: "50" 51 +%%Page: "51" 51 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-51) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovsp) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Single-point crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovsp\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +2.04 (xov) 135.65 588.95 P +3 F +0.85 (sp performs single-point crossover between pairs of individuals contained in) 157.24 588.95 P +0.18 (the current population,) 135.65 574.95 P +2 F +0.44 (OldChrom) 248.12 574.95 P +3 F +0.18 (, according to the crossover probability) 305.69 574.95 P +0.18 (,) 493.69 574.95 P +2 F +0.44 (XOVR) 499.86 574.95 P +3 F +0.18 (,) 528.65 574.95 P +0.77 (and returns a new population after mating,) 135.65 560.95 P +2 F +1.85 (NewChrom) 347.57 560.95 P +3 F +0.77 (.) 405.14 560.95 P +2 F +1.85 (OldChrom) 411.91 560.95 P +3 F +0.77 ( contains the) 469.48 560.95 P +0.96 (chromosomes of the current population, each row corresponds to one individual.) 135.65 546.95 P +(For the chromosomes any representation can be used.) 135.65 532.95 T +2 F +1.74 (XOVR) 135.65 506.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 506.95 P +2 F +1.74 (XOVR) 447.77 506.95 P +3 F +0.72 ( is omitted,) 476.56 506.95 P +(empty or) 135.65 492.95 T +2 F +(NaN,) 181.62 492.95 T +(XOVR = 0.7) 213.4 492.95 T +3 F +( is assumed.) 285.36 492.95 T +1.18 (The pairs are mated in order) 135.65 466.95 P +1.18 (, odd row with the next even row) 276.62 466.95 P +1.18 (. If the number of) 442.66 466.95 P +3.35 (rows in the matrix) 135.65 452.95 P +2 F +8.05 (OldChrom) 239.67 452.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 452.95 P +-0.12 (population should therefore be or) 135.65 438.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 438.95 P +0.8 (This can be achieved by using the function) 135.65 424.95 P +2 F +1.92 (ranking) 350.55 424.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 424.95 P +2.71 (each chromosome and a selection function \050) 135.65 410.95 P +2 F +6.52 (select) 363.11 410.95 P +3 F +2.71 (,) 406.28 410.95 P +2 F +6.52 (sus) 414.99 410.95 P +3 F +2.71 ( or) 436.58 410.95 P +2 F +6.52 (rws) 458 410.95 P +3 F +2.71 (\051 to select) 479.59 410.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 396.95 T +2 F +(xovsp) 135.65 370.95 T +3 F +( is a low-level crossover function normally called by) 171.63 370.95 T +2 F +(recombin) 427.11 370.95 T +3 F +(.) 484.68 370.95 T +1 16 Q +(Algorithm) 117.65 342.29 T +3 12 Q +(Consider the following two binary strings of the same length:) 135.65 324.95 T +2 F +(A1 = [1 1 0 1 0 1]) 135.65 304.95 T +(A2 = [1 0 1 0 1 0]) 135.65 290.95 T +3 F +0.1 (Single-point crossover involves selecting uniformly at random an integer position,) 135.65 270.95 P +0 F +1.68 (k) 135.65 256.95 P +3 F +1.68 (, between 1 and) 140.97 256.95 P +2 F +4.03 (\050length\050A1\051-1\051) 225.95 256.95 P +3 F +1.68 (, and swapping the variables in positions) 326.7 256.95 P +0 F +0.9 (k+1) 135.65 242.95 P +3 F +0.9 ( to) 155.07 242.95 P +2 F +2.16 (length\050A1\051) 172.19 242.95 P +3 F +0.9 ( between) 244.15 242.95 P +2 F +2.16 (A1) 291.91 242.95 P +3 F +0.9 ( and) 306.3 242.95 P +2 F +2.16 (A2) 331.41 242.95 P +3 F +0.9 (. Thus if the crossover position) 345.8 242.95 P +0 F +0.9 (k) 502.77 242.95 P +3 F +0.9 ( = 3,) 508.09 242.95 P +(then) 135.65 228.95 T +2 F +(A1) 159.3 228.95 T +3 F +( and) 173.69 228.95 T +2 F +(A2) 197.01 228.95 T +3 F +( would become:) 211.4 228.95 T +2 F +(A1\325 = [1 1 0 0 1 0]) 135.65 208.95 T +(A2\325 = [1 0 1 1 0 1]) 135.65 194.95 T +(xovsp) 135.65 174.95 T +3 F +( calls) 171.63 174.95 T +2 F +(xovmp) 199.61 174.95 T +3 F +( with the appropriate parameters.) 235.59 174.95 T +1 16 Q +(See Also) 117.65 152.29 T +2 12 Q +(xovsprs) 135.65 134.95 T +3 F +(,) 186.02 134.95 T +2 F +(xovdp) 192.02 134.95 T +3 F +(,) 228 134.95 T +2 F +(xovsh) 233.99 134.95 T +3 F +(,) 269.97 134.95 T +2 F +(xovmp) 275.97 134.95 T +3 F +(,) 311.95 134.95 T +2 F +(recombin) 317.95 134.95 T +3 F +(,) 375.52 134.95 T +2 F +(select) 381.51 134.95 T +FMENDPAGE +%%EndPage: "51" 52 +%%Page: "52" 52 +595.3 841.9 0 FMBEGINPAGE +0 10 Q +0 X +0 K +(Genetic Algorithm Toolbox User\325s Guide) 63.65 61.61 T +(2-52) 513.33 61.29 T +63.65 716.95 531.65 726.95 C +63.65 725.95 531.65 725.95 2 L +1 H +2 Z +0 X +0 K +N +-8.35 24.95 603.65 816.95 C +1 18 Q +0 X +0 K +(xovsprs) 63.65 732.95 T +1 16 Q +(Purpose) 117.65 692.29 T +3 12 Q +(Single-point reduced surrogate crossover) 135.65 674.95 T +1 16 Q +(Synopsis) 117.65 646.29 T +2 12 Q +(NewChrom = xovsprs\050OldChrom, XOVR\051) 135.65 628.95 T +1 16 Q +(Description) 117.65 606.29 T +2 12 Q +8.61 (xov) 135.65 588.95 P +3 F +3.59 (sprs performs single-point reduced surrogate crossover between pairs of) 157.24 588.95 P +2.78 (individuals contained in the current population,) 135.65 574.95 P +2 F +6.66 (OldChrom) 382.48 574.95 P +3 F +2.78 (, according to the) 440.05 574.95 P +5.65 (crossover probability) 135.65 560.95 P +5.65 (,) 242.12 560.95 P +2 F +13.57 (XOVR) 253.77 560.95 P +3 F +5.65 (, and returns a new population after mating,) 282.55 560.95 P +2 F +5.91 (NewChrom) 135.65 546.95 P +3 F +2.46 (.) 193.22 546.95 P +2 F +5.91 (OldChrom) 201.68 546.95 P +3 F +2.46 ( contains the chromosomes of the current population,) 259.24 546.95 P +0.6 (each row corresponds to one individual. For the chromosomes any representation) 135.65 532.95 P +(can be used.) 135.65 518.95 T +2 F +1.74 (XOVR) 135.65 492.95 P +3 F +0.72 ( is an optional parameter specifying the crossover rate. If) 164.43 492.95 P +2 F +1.74 (XOVR) 447.77 492.95 P +3 F +0.72 ( is omitted,) 476.56 492.95 P +(empty or) 135.65 478.95 T +2 F +(NaN,) 181.62 478.95 T +(XOVR = 0.7) 213.4 478.95 T +3 F +( is assumed.) 285.36 478.95 T +1.18 (The pairs are mated in order) 135.65 452.95 P +1.18 (, odd row with the next even row) 276.62 452.95 P +1.18 (. If the number of) 442.66 452.95 P +3.35 (rows in the matrix) 135.65 438.95 P +2 F +8.05 (OldChrom) 239.67 438.95 P +3 F +3.35 ( is odd then the last row is not mated. The) 297.24 438.95 P +-0.12 (population should therefore be or) 135.65 424.95 P +-0.12 (ganised into contiguous pairs that require mating.) 294.84 424.95 P +0.8 (This can be achieved by using the function) 135.65 410.95 P +2 F +1.92 (ranking) 350.55 410.95 P +3 F +0.8 ( to assign a \336tness level to) 400.93 410.95 P +2.71 (each chromosome and a selection function \050) 135.65 396.95 P +2 F +6.52 (select) 363.11 396.95 P +3 F +2.71 (,) 406.28 396.95 P +2 F +6.52 (sus) 414.99 396.95 P +3 F +2.71 ( or) 436.58 396.95 P +2 F +6.52 (rws) 458 396.95 P +3 F +2.71 (\051 to select) 479.59 396.95 P +(individuals with a probability related to their \336tness in the current population.) 135.65 382.95 T +2 F +(xovsp) 135.65 356.95 T +3 F +(rs is a low-level crossover function normally called by) 171.63 356.95 T +2 F +(recombin) 435.77 356.95 T +3 F +(.) 493.34 356.95 T +1 16 Q +(Algorithm) 117.65 328.29 T +3 12 Q +(For single-point crossover see) 135.65 310.95 T +2 F +(xovsp) 282.88 310.95 T +3 F +(.) 318.86 310.95 T +3.35 (The) 135.65 290.95 P +0 F +3.35 (r) 160.65 290.95 P +3.35 (educed surr) 164.87 290.95 P +3.35 (ogate) 224.74 290.95 P +3 F +3.35 ( operator constrains crossover to always produce new) 251.39 290.95 P +0.99 (individuals wherever possible. This is implemented by restricting the location of) 135.65 276.95 P +1.41 (crossover points such that crossover points only occur where gene values dif) 135.65 262.95 P +1.41 (fer) 518.34 262.95 P +([1].) 135.65 248.95 T +2 F +(xovsprs) 135.65 228.95 T +3 F +( calls) 186.02 228.95 T +2 F +(xovmp) 214 228.95 T +3 F +( with the appropriate parameters.) 249.98 228.95 T +1 16 Q +(See Also) 117.65 206.29 T +2 12 Q +(xovsp) 135.65 188.95 T +3 F +(,) 171.63 188.95 T +2 F +(xovdp) 177.62 188.95 T +3 F +(,) 213.6 188.95 T +2 F +(xovdprs) 219.6 188.95 T +3 F +(,) 269.97 188.95 T +2 F +(xovsh) 275.97 188.95 T +3 F +(,) 311.95 188.95 T +2 F +(xovshrs) 317.95 188.95 T +3 F +(,) 368.32 188.95 T +2 F +(xovmp) 374.32 188.95 T +3 F +(,) 410.3 188.95 T +2 F +(recombin) 416.29 188.95 T +3 F +(,) 473.86 188.95 T +2 F +(select) 479.86 188.95 T +1 16 Q +(Refer) 117.65 166.29 T +(ence) 155.53 166.29 T +3 12 Q +1.31 ([1] L. Booker) 135.65 148.95 P +1.31 (, \322Improving search in genetic algorithms,\323 In) 203.4 148.95 P +0 F +1.31 (Genetic Algorithms) 436.73 148.95 P +5.64 (and Simulated Annealing) 135.65 134.95 P +3 F +5.64 (, L. Davis \050Ed.\051, pp. 61-73, Mor) 268.2 134.95 P +5.64 (gan Kaufmann) 455.06 134.95 P +(Publishers, 198) 135.65 120.95 T +2 F +(7.) 209.61 120.95 T +FMENDPAGE +%%EndPage: "52" 53 +%%Trailer +%%BoundingBox: 0 0 595.3 841.9 +%%Pages: 52 1 +%%DocumentFonts: Times-Italic +%%+ Times-Bold +%%+ Courier +%%+ Times-Roman +%%+ Symbol diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/The MathWorks - 1-18GTU Why do I get an error in MATLAB 6_0 (R12) where I got a warning in R11 with reference to uninitialized variables.mht" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/The MathWorks - 1-18GTU Why do I get an error in MATLAB 6_0 (R12) where I got a warning in R11 with reference to uninitialized variables.mht" index c660a637b42d77b4c892cff84bea9337a0f1a573..527623a5b6f54ee9ad27784b5874fe4a82903aad 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/The MathWorks - 1-18GTU Why do I get an error in MATLAB 6_0 (R12) where I got a warning in R11 with reference to uninitialized variables.mht" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/The MathWorks - 1-18GTU Why do I get an error in MATLAB 6_0 (R12) where I got a warning in R11 with reference to uninitialized variables.mht" @@ -1,3 +1,2628 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d87de481a3a91a069ddfdcd4c1f5d6d355e370de0410fa16ccfed84e6019e47d -size 98687 +From: <ÓÉ Microsoft Internet Explorer 5 ±£´æ> +Subject: The MathWorks - 1-18GTU: Why do I get an error in MATLAB 6.0 (R12) where I got a warning in R11 with reference to uninitialized variables? +Date: Mon, 28 Nov 2005 16:18:16 +0800 +MIME-Version: 1.0 +Content-Type: multipart/related; + boundary="----=_NextPart_000_000D_01C5F437.56C58110"; + type="text/html" +X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 + +This is a multi-part message in MIME format. + +------=_NextPart_000_000D_01C5F437.56C58110 +Content-Type: text/html; + charset="iso-8859-1" +Content-Transfer-Encoding: quoted-printable +Content-Location: http://www.mathworks.com/support/solutions/data/1-18GTU.html + + +The MathWorks - 1-18GTU: Why do I get an = +error in MATLAB 6.0 (R12) where I got a warning in R11 with reference to = +uninitialized variables? + + + + + + + + + + + + + =20 +
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Technical Solutions

+

Solution Number: 1-18GTU


Date Last Modified: 16 Aug = +2005=20 + + + + + + + + + + + + + + + + + + + + + +
Product: MATLAB=AE
Reported in Release: R12
Fixed in Release: 
Platform: All Platforms
Operating System: All OS
  +

+

Subject:

+

Why do I get an error in MATLAB 6.0 (R12) where I got a warning = +in R11=20 + with reference to uninitialized variables? = +

+

Problem Description:

+

Why do I get an error in MATLAB 6.0 (R12) = +where I=20 + got a warning in R11 with reference to uninitialized=20 + variables?

a =3D [a,3];

In MATLAB 5.3 = +(R11) I=20 + received the following warning:

Warning:=20 + Reference to uninitialized variable a.

In MATLAB 6.0 = +(R12) I=20 + get:

??? Undefined function or variable = + + 'a'.

+

+ + + +
+
+

Solution:

+

There are actually three cases to be considered with = +reference to=20 + uninitialized variables in MATLAB.

The first case is = +the one=20 + listed above where is a variable is used on the right hand = +side=20 + before being initialized.

function before1
a = +=3D=20 + [a,3];


MATLAB 5.3 (R11)

+

>> before1
Warning: Reference=20 + to uninitialized variable a in before1 at line 2.
> In = + + d:\temp\before1.m at line 2


MATLAB =
+6.x (R12.x)

+

>> before1
??? Undefined=20 + function or variable 'a'.

Error in =3D=3D>=20 + d:\temp\before1.m
On line 2 =3D=3D> a =3D = +[a,3];


MATLAB 6.5 (R13)

+

>> before1
??? Undefined=20 + function or variable 'a'.

Error in =3D=3D>=20 + d:\temp\before1.m
On line 2 =3D=3D> a =3D = +[a,3];

The=20 + second case is where a variable is used on the right hand = +side after=20 + it first appeared on the left hand side of an assignment = +which was=20 + not executed. For example:

function = +before2
if=20 + 0
a =3D 1;
end
a =3D = +[a,3];


MATLAB 5.3 (R11)

+

>> before2
Warning: Reference=20 + to uninitialized variable a in before2 at line 5.
> In = + + d:\temp\before2.m at line 5


MATLAB =
+6.x (R12.x)

+

>> before2
Warning: Reference=20 + to uninitialized variable a in before2 at line 5.
> In = + + d:\temp\before2.m at line 5


MATLAB =
+6.5 (R13)

+

>> before2
??? Undefined=20 + function or variable 'a'.

Error in =3D=3D>=20 + d:\temp\before2.m
On line 5 =3D=3D> a =3D = +[a,3];

The=20 + third case is called undefined. It occurs when a variable = +first=20 + appears on the right-hand side of an assignment which was = +not yet=20 + executed. For example,

function before3
if = +0
z =3D=20 + a;
end
a =3D [a,3];


MATLAB 5.3 =
+(R11)

+

>> before3
??? Undefined=20 + function or variable 'a'.

Error in =3D=3D>=20 + d:\temp\before3.m
On line 5 =3D=3D> a =3D = +[a,3];


MATLAB 6.x (R12.x)

+

>> before3
??? Undefined=20 + function or variable 'a'.

Error in =3D=3D>=20 + d:\temp\before3.m
On line 5 =3D=3D> a =3D = +[a,3];


MATLAB 6.5 (R13)

+

>> before3
??? Undefined=20 + function or variable 'a'.

Error in =3D=3D>=20 + d:\temp\before3.m
On line 5 =3D=3D> a =3D = +[a,3];

The=20 + finalized behavior for this issue is that using an = +uninitialized=20 + variable is always an error.

There are various ways = +to deal=20 + with this new behavior. One alternative is to set the = +variable in=20 + question to empty at the beginning of the M-file. Since=20 + uninitialized variables were implicitly treated as empty = +matrices,=20 + this will preserve the semantics of the program. However, a = +better=20 + second-order fix would be to determine why the variable is = +being=20 + used before being assigned and correct the = +discrepancy.

An=20 + example:

function out =3D before(in)
% x = +and out are=20 + undefined if in >=3D 0
if (in < 0)
x =3D -in; = +
out =3D x;=20 +
end
y =3D ones(x);

Another fix would=20 + be:

function out =3D before(in)
if (in < = +0)
x =3D=20 + -in;
out =3D x;
else
x =3D in;
if nargout >=20 + 0
error('Too many outputs requested for positive value of = + + IN');
end
end
y =3D ones(x);
 +

+ + + +
  Prov= +ide=20 + feedback to help us improve this solution!=20 +

+ + + +
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PADDING-LEFT: 10px; BORDER-LEFT: #7384a5 1px solid; PADDING-TOP: 8px; = +BACKGROUND-COLOR: #e6edf7 +} +#rightcol .us { + FONT-STYLE: italic +} +#wedgetp { + PADDING-LEFT: 10px; BORDER-LEFT: #7384a5 1px solid; BORDER-BOTTOM: = +#7384a5 1px solid; BACKGROUND-COLOR: #e6edf7 +} +.spotlight { + PADDING-RIGHT: 5px; PADDING-LEFT: 8px; PADDING-BOTTOM: 14px; = +PADDING-TOP: 10px; BORDER-BOTTOM: #dcdcdc 1px solid; BACKGROUND-COLOR: = +#f4f4f4 +} +.spotlight DIV.action { + MARGIN-TOP: 10px +} +DIV.attr { + COLOR: #800000; TEXT-ALIGN: right +} +DIV.divider { + MARGIN: 5px +} +.callout { + BORDER-RIGHT: gray 1px solid; PADDING-RIGHT: 10px; BORDER-TOP: gray 1px = +solid; PADDING-LEFT: 10px; PADDING-BOTTOM: 10px; BORDER-LEFT: gray 1px = +solid; PADDING-TOP: 10px; BORDER-BOTTOM: gray 1px solid; = +BACKGROUND-COLOR: #f7f7f7 +} +.pleft { + PADDING-LEFT: 10px +} +.pright { + PADDING-RIGHT: 10px +} +UL.cboxlist { + LIST-STYLE-IMAGE: none; LIST-STYLE-TYPE: none +} +UL.cboxlist LI { + TEXT-INDENT: -20px +} +UL.cboxlist INPUT { + MARGIN-BOTTOM: 1px +} +DIV.twocol { +=09 +} +DIV.twocol DIV.col { + WIDTH: 49% +} +DIV.threecol { +=09 +} +DIV.threecol DIV.col { + WIDTH: 32% +} +DIV.onecol:unknown { + CLEAR: both; DISPLAY: block; VISIBILITY: hidden; HEIGHT: 0px; content: = +"." +} +DIV.twocol:unknown { + CLEAR: both; DISPLAY: block; VISIBILITY: hidden; HEIGHT: 0px; content: = +"." +} +DIV.threecol:unknown { + CLEAR: both; DISPLAY: block; VISIBILITY: hidden; HEIGHT: 0px; content: = +"." +} +DIV.col { + FLOAT: left +} +DIV.spacer { + FLOAT: left; WIDTH: 2%; HEIGHT: 10px +} +UL.pagenav LI { + LIST-STYLE-IMAGE: url(/images/common/pagenav/page_nav_inactive.gif) +} +UL.pagenav LI.active { + FONT-WEIGHT: bold; LIST-STYLE-IMAGE: = +url(/images/common/pagenav/arrow_orange.gif) +} +.datatable1 { + BORDER-RIGHT: #d3d3d3 1px solid; BORDER-TOP: #d3d3d3 1px solid; = +BORDER-LEFT: #d3d3d3 1px solid; BORDER-BOTTOM: #d3d3d3 1px solid +} +.datatable1 TD { + PADDING-RIGHT: 6px; PADDING-LEFT: 6px; PADDING-BOTTOM: 6px; = +VERTICAL-ALIGN: top; PADDING-TOP: 6px +} +.datatable1 TH { + PADDING-RIGHT: 5px; PADDING-LEFT: 5px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 4px; COLOR: #ffffff; PADDING-TOP: 4px; BACKGROUND-COLOR: = +#004a9d; TEXT-ALIGN: left +} +.datatable1 .level2 TD { + BACKGROUND-COLOR: #5a7cc3 +} +#bodycol .datatable1 TD.level2 A:link { + FONT-WEIGHT: bold; COLOR: white +} +#bodycol .datatable1 TD.level2 A:visited { + FONT-WEIGHT: bold; COLOR: white +} +.datatable2 { + BORDER-RIGHT: #d3d3d3 1px solid; BORDER-TOP: #d3d3d3 1px solid; = +BORDER-LEFT: #d3d3d3 1px solid; BORDER-BOTTOM: #d3d3d3 1px solid +} +.datatable2 TD { + PADDING-RIGHT: 2px; PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; = +VERTICAL-ALIGN: top; PADDING-TOP: 2px +} +.datatable2 TH { + PADDING-RIGHT: 2px; PADDING-LEFT: 2px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 2px; COLOR: #ffffff; PADDING-TOP: 2px; BACKGROUND-COLOR: = +#004a9d; TEXT-ALIGN: center +} +.datatable3 { + BORDER-RIGHT: #d3d3d3 1px solid; BORDER-TOP: #d3d3d3 1px solid; = +BORDER-LEFT: #d3d3d3 1px solid; BORDER-BOTTOM: #d3d3d3 1px solid +} +.datatable4 { + BORDER-RIGHT: #d3d3d3 1px solid; BORDER-TOP: #d3d3d3 1px solid; = +BORDER-LEFT: #d3d3d3 1px solid; BORDER-BOTTOM: #d3d3d3 1px solid +} +.datatable3 TD { + PADDING-RIGHT: 8px; PADDING-LEFT: 8px; PADDING-BOTTOM: 8px; = +VERTICAL-ALIGN: top; PADDING-TOP: 8px; BACKGROUND-COLOR: #ffffff +} +.datatable4 TD { + PADDING-RIGHT: 8px; PADDING-LEFT: 8px; PADDING-BOTTOM: 8px; = +VERTICAL-ALIGN: top; PADDING-TOP: 8px; BACKGROUND-COLOR: #ffffff +} +.datatable3 TH { + PADDING-RIGHT: 5px; PADDING-LEFT: 8px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 4px; COLOR: #000000; PADDING-TOP: 4px; BACKGROUND-COLOR: = +#e4e9ef; TEXT-ALIGN: left +} +.datatable4 TH { + PADDING-RIGHT: 5px; PADDING-LEFT: 8px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 4px; COLOR: #000000; PADDING-TOP: 4px; BACKGROUND-COLOR: = +#e4e9ef; TEXT-ALIGN: left +} +#bodycol .datatable3 .level2 A:link { + FONT-WEIGHT: bold; COLOR: #0d2b98 +} +#bodycol .datatable4 .level2 A:link { + FONT-WEIGHT: bold; COLOR: #0d2b98 +} +#bodycol .datatable3 .level2 A:visited { + FONT-WEIGHT: bold; COLOR: #405c9c +} +#bodycol .datatable4 .level2 A:visited { + FONT-WEIGHT: bold; COLOR: #405c9c +} +TABLE.datatable3 TR.level2 TD { + PADDING-RIGHT: 5px; PADDING-LEFT: 8px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 4px; COLOR: #000000; PADDING-TOP: 4px; BACKGROUND-COLOR: = +#ffffff; TEXT-ALIGN: left +} +TABLE.datatable4 TR.level2 TD { + PADDING-RIGHT: 5px; PADDING-LEFT: 8px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 4px; COLOR: #000000; PADDING-TOP: 4px; BACKGROUND-COLOR: = +#ffffff; TEXT-ALIGN: left +} +TABLE.datatable3 TR TD { + PADDING-LEFT: 8px +} +TABLE.datatable4 TR TD { + PADDING-LEFT: 8px +} +TABLE.datatable3 TD { + BORDER-TOP: #d3d3d3 1px solid +} +#bodycol .datatable1 TH A:visited { + COLOR: #ffffff +} +#bodycol .datatable1 TH A:link { + COLOR: #ffffff +} +#bodycol .datatable1 TH A:hover { + COLOR: #ffffff +} +.datatable5 TH { + PADDING-RIGHT: 0px; PADDING-LEFT: 10px; FONT-WEIGHT: bold; FONT-SIZE: = +11px; PADDING-BOTTOM: 2px; MARGIN: 10px 0px 0px; COLOR: #000000; = +PADDING-TOP: 2px; BORDER-BOTTOM: #d3d3d3 1px solid; BACKGROUND-COLOR: = +#e4e9ef; TEXT-ALIGN: left +} +.datatable5 { + BORDER-RIGHT: #d3d3d3 1px solid; BORDER-TOP: #d3d3d3 1px solid; = +BORDER-LEFT: #d3d3d3 1px solid; BORDER-BOTTOM: #d3d3d3 1px solid +} +.datatable5 TD { + PADDING-RIGHT: 10px; PADDING-LEFT: 10px; PADDING-BOTTOM: 10px; = +VERTICAL-ALIGN: top; PADDING-TOP: 10px; TEXT-ALIGN: left +} +.datatable5 UL { + MARGIN-BOTTOM: 0px +} +.datatable5 .nested TD { + PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: 0px; = +PADDING-TOP: 0px +} +.datatable5 .feature { + BACKGROUND-COLOR: #f6f6f6 +} +.inputbody { + PADDING-RIGHT: 10px; PADDING-LEFT: 15px; PADDING-BOTTOM: 10px; = +PADDING-TOP: 10px; BACKGROUND-COLOR: #eeeeee +} +TABLE.inputtable1 { + BORDER-RIGHT: #546e8f 1px solid; BORDER-TOP: #546e8f 1px solid; = +BORDER-LEFT: #546e8f 1px solid; BORDER-BOTTOM: #546e8f 1px solid +} +.inputtable1 TH { + PADDING-RIGHT: 5px; PADDING-LEFT: 5px; PADDING-BOTTOM: 2px; = +PADDING-TOP: 2px; BACKGROUND-COLOR: #e4e9ef; TEXT-ALIGN: left +} +.level2 { + PADDING-RIGHT: 5px; PADDING-LEFT: 5px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 2px; COLOR: white; PADDING-TOP: 2px; BACKGROUND-COLOR: = +#6377a9; TEXT-ALIGN: left +} +.level2 A:link { + COLOR: #ffffff; TEXT-DECORATION: underline +} +.level2 TD A:visited { + COLOR: #ffffff; TEXT-DECORATION: underline +} +.level2 A:hover { + COLOR: #ffffff; TEXT-DECORATION: none +} +.inputtable1 INPUT { + MARGIN-BOTTOM: 5px +} +.inputtable1 SELECT { + MARGIN-BOTTOM: 5px +} +.inputtable1 INPUT.toggle { + MARGIN-BOTTOM: 0px +} +.inputtable1 TEXTAREA { + BORDER-TOP-WIDTH: 0px; BORDER-LEFT-WIDTH: 0px; BORDER-BOTTOM-WIDTH: = +0px; MARGIN-BOTTOM: 10px; BORDER-RIGHT-WIDTH: 0px +} +.inputtable1 .cboxtbl { + BORDER-TOP-WIDTH: 0px; BORDER-LEFT-WIDTH: 0px; BORDER-BOTTOM-WIDTH: = +0px; MARGIN-BOTTOM: 10px; BORDER-RIGHT-WIDTH: 0px +} +.inputtable1 FIELDSET { + BORDER-TOP-WIDTH: 0px; BORDER-LEFT-WIDTH: 0px; BORDER-BOTTOM-WIDTH: = +0px; MARGIN-BOTTOM: 10px; BORDER-RIGHT-WIDTH: 0px +} +FIELDSET { + FONT-WEIGHT: bold; COLOR: #000000 +} +.demotable TD { + PADDING-BOTTOM: 20px +} +.intabletop1 TH { + PADDING-RIGHT: 0px; PADDING-LEFT: 5px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 3px; COLOR: #ffffff; PADDING-TOP: 0px; BACKGROUND-COLOR: = +#004a9d; TEXT-ALIGN: left +} +.intabletop1 TH.corner { + VERTICAL-ALIGN: top; TEXT-ALIGN: right +} +TD.intabletop2 { + PADDING-RIGHT: 0px; PADDING-LEFT: 5px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 2px; COLOR: #ffffff; PADDING-TOP: 0px; WHITE-SPACE: = +nowrap; BACKGROUND-COLOR: #004a9d +} +.oddrow { + BACKGROUND-COLOR: #eeeeee +} +TH.decimal { + TEXT-ALIGN: center +} +TH.integer { + TEXT-ALIGN: center +} +.integer { + TEXT-ALIGN: center +} +.decimal { + TEXT-ALIGN: right +} +.date { + WHITE-SPACE: nowrap +} +LABEL { + DISPLAY: block; FONT-WEIGHT: bold; COLOR: #525252 +} +LABEL.toggle { + DISPLAY: inline; FONT-WEIGHT: normal; COLOR: #000000 +} +LABEL.question { + FONT-SIZE: 11px; COLOR: #800000 +} +CAPTION { + PADDING-RIGHT: 5px; FONT-SIZE: smaller; FONT-STYLE: italic; TEXT-ALIGN: = +right +} +.req { + COLOR: #ff0000 +} +.inputbody { + PADDING-RIGHT: 10px; PADDING-LEFT: 15px; PADDING-BOTTOM: 10px; = +PADDING-TOP: 10px; BACKGROUND-COLOR: #f9f7f3 +} +.shadedcell1 { + PADDING-RIGHT: 5px; PADDING-LEFT: 5px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 1px; COLOR: #ffffff; PADDING-TOP: 1px; BACKGROUND-COLOR: = +#edf7fc +} +.shadedcell2 { + PADDING-RIGHT: 5px; PADDING-LEFT: 5px; FONT-WEIGHT: bold; = +PADDING-BOTTOM: 1px; COLOR: #ffffff; PADDING-TOP: 1px; BACKGROUND-COLOR: = +#004a9d; TEXT-ALIGN: center +} +.alertbox { + BORDER-RIGHT: #000000 1px solid; BORDER-TOP: #000000 1px solid; = +BORDER-LEFT: #000000 1px solid; BORDER-BOTTOM: #000000 1px solid; = +BACKGROUND-COLOR: #e6ebf8 +} +.alertbox TD { + PADDING-RIGHT: 7px; PADDING-LEFT: 7px; PADDING-BOTTOM: 7px; = +PADDING-TOP: 7px +} +H1 SUP.prod { + FONT-SIZE: 70% +} +SUP.prod { + FONT-SIZE: 80% +} +A SUP.prod { + TEXT-DECORATION: none +} +A:link SUP.prod { + TEXT-DECORATION: none +} +A:visited SUP.prod { + TEXT-DECORATION: none +} + +------=_NextPart_000_000D_01C5F437.56C58110 +Content-Type: text/css; + charset="gb2312" +Content-Transfer-Encoding: quoted-printable +Content-Location: http://www.mathworks.com/includes/css/print.css + +BODY { + BACKGROUND-COLOR: white +} +A:link { + FONT-WEIGHT: bold; BACKGROUND: none transparent scroll repeat 0% 0%; = +COLOR: #003366; TEXT-DECORATION: underline +} +A:visited { + FONT-WEIGHT: bold; BACKGROUND: none transparent scroll repeat 0% 0%; = +COLOR: #003366; TEXT-DECORATION: underline +} +#leftnavcol { + DISPLAY: none +} +#banner { + DISPLAY: none +} +#rightcol { + DISPLAY: none +} +#globaltop2 { + WIDTH: 669px; align: left +} +#bodycol { + WIDTH: 669px; align: left +} +#topnav { + WIDTH: 669px; align: left +} +#globaltop2 { + BACKGROUND-IMAGE: none; BACKGROUND-COLOR: white +} +#site_search { + DISPLAY: none +} +#search_button { + DISPLAY: none +} +#ptools2 { + DISPLAY: none +} +#access2 { + DISPLAY: none +} +#pixelfade { + DISPLAY: none +} +#topstrip { + DISPLAY: none +} +#language_pref { + DISPLAY: none +} +#mainbody { + MARGIN-BOTTOM: 20px; MARGIN-LEFT: 0px +} +#print_logo { + DISPLAY: block +} + +------=_NextPart_000_000D_01C5F437.56C58110 +Content-Type: application/octet-stream +Content-Transfer-Encoding: quoted-printable +Content-Location: http://www.mathworks.com/includes_content/jscript/popup_menus/popup_menus.js + +/*Killer OO JS Menu Script by Pete Smith Version 1.1*/=0A= +=0A= +var menu_script_loaded =3D true;=0A= +=0A= +function Menu(label){=0A= + this.items =3D new Array();=0A= + this.actions =3D new Array();=0A= +=0A= +//Now, make the container of menus=0A= +//Automatically add it to the array of menus=0A= + this.label =3D label;=0A= +=0A= +//methods for this object=0A= + this.html =3D Html;=0A= + this.showMenu =3D showMenu;=0A= + this.hideMenu =3D hideMenu;=0A= +}=0A= +=0A= +=0A= +Menu.prototype.addMenuItem =3D function addMenuItem(label, action) {=0A= + this.items[this.items.length] =3D label;=0A= + this.actions[this.actions.length] =3D action;=0A= +=0A= +}=0A= +=0A= +function Html(){=0A= + var output =3D new String();=0A= + output +=3D '
';=0A= + //output +=3D this.label;=0A= + for (var a in this.actions){=0A= + if (this.actions[a]){=0A= + output +=3D '\n
';=0A= + output +=3D ' ';=0A= + output +=3D this.items[a]+ ' '=0A= + output +=3D '
\n';=0A= + } else {=0A= + output +=3D '\n
'+this.items[a]+'
';=0A= + }=0A= + }=0A= + output +=3D '
\n\n';=0A= +return output;=0A= +}=0A= +=0A= +=0A= +=0A= +=0A= +function fireMenu( menu_id, thisLink, orient ) {=0A= + thisMenu =3D window.menus[menu_id];=0A= + thisLink.onmouseout =3D function(){ = +thisLink.style.backgroundColor=3D''; thisMenu.hideMenu();}=0A= + hideAllMenus();=0A= +=0A= + thisMenu.showMenu();=0A= + positionMenu(thisLink,orient);=0A= +=0A= + =0A= +=0A= + //=0A= +=0A= + //DD detection Section=0A= + //Now we get the rendered position coords, and attach to the object.=0A= + thisMenu.coords =3D = +getMyCoords(document.getElementById(thisMenu.label));=0A= + //Now we loop over all, attaching coords only if IE=0A= + if (document.all) {=0A= + for (var i in document.all){=0A= + if (document.all[i].type =3D=3D "select-one" || = +document.all[i].type =3D=3D "select-multiple") {=0A= + document.all[i].coords =3D getMyCoords(document.all[i]);=0A= + if ( doICollide (thisMenu , document.all[i]) ) {=0A= + hideObject(document.all[i]);=0A= + }=0A= + }=0A= + }=0A= + }=0A= +}=0A= +=0A= +function showHiddenDD(){=0A= + if (document.all){=0A= + for (var i in document.all){=0A= + if (document.all[i].type =3D=3D "select-one" || = +document.all[i].type =3D=3D "select-multiple" && = +document.all[i].style.visibility =3D=3D "hidden") {=0A= + showObject(document.all[i]);=0A= + }=0A= + }=0A= + }=0A= +}=0A= +=0A= +function hideObject(hideObject){=0A= + hideObject.style.visibility =3D "hidden";=0A= +}=0A= +=0A= +function showObject(showObject){=0A= + showObject.style.visibility =3D "visible";=0A= +}=0A= +=0A= +=0A= +function getMyCoords(getObject){=0A= + coords =3D new Object();=0A= + coords.width =3D getObject.offsetWidth;=0A= + coords.height =3D getObject.offsetHeight;=0A= + coords.oLeft =3D getPageOffsetLeft(getObject);=0A= + coords.oTop =3D getPageOffsetTop(getObject);=0A= + return coords;=0A= +}=0A= +=0A= +function doICollide(object1 , object2) {=0A= + //First we find out if the A coord is within the object2.=0A= + if (object1.coords.oLeft < object2.coords.oLeft + = +object2.coords.width && object2.coords.oLeft < object1.coords.oLeft + = +object1.coords.width ) {=0A= + if (object1.coords.oTop < object2.coords.oTop + = +object2.coords.height && object2.coords.oTop < object1.coords.oTop + = +object1.coords.height ) {=0A= + return true;=0A= + }=0A= + }=0A= +}=0A= +=0A= +function positionMenu(thisObject,orient){=0A= +//Get x and y position of the link=0A= + coords =3D getMyCoords(thisObject);=0A= +//Now calculate the Height and Width=0A= + linkHeight =3D thisObject.offsetHeight;=0A= + linkWidth =3D thisObject.offsetWidth;=0A= + switch(orient) {=0A= + case "r":=0A= + oLeft =3D coords.oLeft + linkWidth;=0A= + oTop =3D coords.oTop;=0A= + break;=0A= + default:=0A= + oLeft =3D coords.oLeft;=0A= + oTop =3D coords.oTop + linkHeight;=0A= + break;=0A= + }=0A= + //Now we position the menu=0A= + document.getElementById(thisMenu.label).style.left =3D oLeft + "px";=0A= + document.getElementById(thisMenu.label).style.top =3D oTop + "px";=0A= + //We only want to position to left edge of block level elements, and = +only handles the shorties.=0A= + if ( thisObject.tagName !=3D "A" && = +document.getElementById(thisMenu.label).offsetWidth < = +thisObject.offsetWidth ) {=0A= + document.getElementById(thisMenu.label).style.width =3D = +thisObject.offsetWidth + 15;=0A= + }=0A= +=0A= +}=0A= +=0A= +function hideAllMenus(){=0A= + for (var a in window.menus) {=0A= + document.getElementById(window.menus[a].label).style.display =3D = +"none";=0A= + }=0A= + showHiddenDD();=0A= +}=0A= +=0A= +function showMenu(){=0A= + if (window.hideMenuTimer) window.clearTimeout(hideMenuTimer);=0A= + document.getElementById(thisMenu.label).style.display =3D "block";=0A= +}=0A= +=0A= +function hideMenu(){=0A= + hideMenuTimer =3D = +setTimeout("document.getElementById('"+thisMenu.label+"').style.display = +=3D 'none'; showHiddenDD();",850);=0A= +}=0A= +=0A= +=0A= +function onMenuItemOver(thisMenuItem){=0A= + thisMenuItem.className =3D "menuitem_hover";=0A= +}=0A= +=0A= +function onMenuItemOut(thisMenuItem){=0A= + thisMenuItem.className =3D "menuitem";=0A= +}=0A= +=0A= +function addMenu(menu){=0A= + //The array that holds the menu objects is menus=0A= + if (!window.menus) window.menus =3D new Array();=0A= + window.menus[menu.label] =3D menu;=0A= + //window.menus[window.menus.length] =3D menu;=0A= +}=0A= +=0A= +function makeMenus(){=0A= + if (!document.getElementById("menuContainer")){=0A= + container =3D document.createElement("DIV");=0A= + container.id =3D "menuContainer"=0A= + }=0A= +document.body.appendChild(container) ;=0A= +//Now, put our nice html in da laya playa.=0A= + container.innerHTML =3D complete_html;=0A= +=0A= +}=0A= +=0A= +function printMenus(){=0A= +var h =3D new String();=0A= + for (var c in window.menus) {=0A= + h +=3D menus[c].html();=0A= + }=0A= +return h;=0A= +}=0A= +=0A= + +------=_NextPart_000_000D_01C5F437.56C58110 +Content-Type: application/octet-stream +Content-Transfer-Encoding: quoted-printable +Content-Location: http://www.mathworks.com/includes_content/jscript/global_nav/global_nav_en.js + + var myMenu =3D new Menu("WorldwideGlobal");=0A= + myMenu.addMenuItem("US/Canada", host_pre + ".mathworks.com");=0A= + myMenu.addMenuItem("Belgium", host_pre + ".mathworks.nl");=0A= + myMenu.addMenuItem("Denmark", host_pre + ".se.mathworks.com");=0A= + myMenu.addMenuItem("Finland", host_pre + ".se.mathworks.com");=0A= + myMenu.addMenuItem("France", host_pre + ".mathworks.fr");=0A= + myMenu.addMenuItem("Germany", host_pre + ".mathworks.de");=0A= + myMenu.addMenuItem("Ireland", host_pre + ".mathworks.co.uk");=0A= + myMenu.addMenuItem("Italy" , host_pre + ".mathworks.it");=0A= + myMenu.addMenuItem("Korea" , host_pre + ".mathworks.co.kr");=0A= + myMenu.addMenuItem("Luxembourg", host_pre + ".mathworks.nl");=0A= + myMenu.addMenuItem("Netherlands" , host_pre + ".mathworks.nl");=0A= + myMenu.addMenuItem("Norway", host_pre + ".se.mathworks.com");=0A= + myMenu.addMenuItem("Portugal", host_pre + ".mathworks.es");=0A= + myMenu.addMenuItem("Spain", host_pre + ".mathworks.es");=0A= + myMenu.addMenuItem("Sweden", host_pre + ".se.mathworks.com");=0A= + myMenu.addMenuItem("Switzerland", host_pre + ".mathworks.ch");=0A= + myMenu.addMenuItem("United Kingdom", host_pre + ".mathworks.co.uk");=0A= + myMenu.addMenuItem("All Other Countries","/company/worldwide/");=0A= + addMenu(myMenu);=0A= +=0A= +=0A= +=0A= + +------=_NextPart_000_000D_01C5F437.56C58110 +Content-Type: application/octet-stream +Content-Transfer-Encoding: quoted-printable +Content-Location: http://www.mathworks.com/includes/jscript/local_nav.js + +/* Local Navigation Menu Script */=0A= +/* By Peter Smith Version 1 */=0A= +=0A= +/* ShowMe toggles the currently selected menu, image */=0A= +function showMe (index) {=0A= + // if IE 5.X, IE 6.X , Moz, DOM=0A= + if (document.getElementById) {=0A= + var menutrs =3D = +document.getElementById("leftnav").getElementsByTagName("tr");=0A= + //First, we toggle the one we selected=0A= + for (a=3D0; a < menutrs.length; a++) {=0A= + br =3D new RegExp(index + "-");=0A= + if ( menutrs[a].id.match(br) ) {=0A= + menutrs[a].className =3D ( menutrs[a].className !=3D "hid") ? = +"hid" : "";=0A= + } // end if=0A= + } // end for=0A= + //Now, we toggle the image and titles=0A= + img =3D document.getElementById("limg-" + index);=0A= + img.src =3D ( img.src.match("collapse.gif") ) ? = +"/includes/images/local_nav/expand.gif" : = +"/includes/images/local_nav/collapse.gif" ;=0A= + img.alt =3D ( img.alt !=3D "Hide Section" ) ? "Hide Section" : "Show = +Section";=0A= + link =3D img.parentNode;=0A= + link.title =3D ( link.title !=3D "Hide Section") ? "Hide Section" : = +"Show Section";=0A= + } // end if=0A= +} // end function showMe +------=_NextPart_000_000D_01C5F437.56C58110 +Content-Type: application/octet-stream +Content-Transfer-Encoding: quoted-printable +Content-Location: http://www.mathworks.com/includes/jscript/common.js + +function printWindow () {=0A= + bV =3D parseInt(navigator.appVersion)=0A= + if (bV >=3D 4) window.print()=0A= +} // end function printWindow=0A= +=0A= +function openWindow ( url, width, height, options, name ) {=0A= + if ( ! width ) width =3D 640;=0A= + if ( ! height ) height =3D 420;=0A= + if ( ! options ) options =3D = +"scrollbars=3Dyes,menubar=3Dyes,toolbar=3Dyes,location=3Dyes,status=3Dyes= +,resizable=3Dyes";=0A= + if ( ! name ) name =3D "outsideSiteWindow";=0A= + var newWin =3D window.open( url, name, "width=3D" + width + = +",height=3D" + height + "," + options );=0A= +} // end function openWindow=0A= +=0A= +function jumpMenu (targ,selObj,restore) { //v3.0=0A= + = +eval(targ+".location=3D'"+selObj.options[selObj.selectedIndex].value+"'")= +;=0A= + if (restore) selObj.selectedIndex=3D0;=0A= +} // end function jumpMenu=0A= +=0A= +/* Get X-coordinate of an object */=0A= +function getPageOffsetLeft (el) {=0A= + var ol=3Del.offsetLeft;=0A= + while ((el=3Del.offsetParent) !=3D null) { ol +=3D el.offsetLeft; }=0A= + return ol;=0A= +} // end function getPageOffsetLeft=0A= +=0A= +/* Get Y-coordinate of an object */=0A= +function getPageOffsetTop (el) {=0A= + var ot=3Del.offsetTop;=0A= + while((el=3Del.offsetParent) !=3D null) { ot +=3D el.offsetTop; }=0A= + return ot;=0A= +} // end function getPageOffsetTop=0A= +=0A= +/*Functions for TopNav Hovering*/=0A= +function topNavHover(topnav) {=0A= + topnav =3D document.getElementById(topnav);=0A= + topnav.style.backgroundColor =3D "#DBE4F5" ;=0A= +}=0A= +=0A= +function topNavHoverOff(topnav) {=0A= + topnav =3D document.getElementById(topnav);=0A= + topnav.style.backgroundColor =3D "" ;=0A= +}=0A= +=0A= +function mouseover(thisEl, thisImg, thisRollOver) {=0A= + var prevSrc =3D thisImg.src;=0A= + thisImg.src =3D thisRollOver;=0A= + thisEl.onmouseout =3D function () {thisImg.src =3D prevSrc;}=0A= +}=0A= +=0A= +function compMatch() {=0A= +=0A= + // not all documents have the response form we detect Salutation=0A= + if (document.getElementById("Salutation") =3D=3D null) {=0A= + return true;=0A= + }=0A= +=0A= + // not all response forms have the Company_or_University field=0A= + if (document.getElementById("Company_or_University") =3D=3D null) {=0A= + return true;=0A= + }=0A= +=0A= + var compValue =3D = +document.getElementById("Company_or_University").value;=0A= +=0A= + // not all response forms have the nr_Department field=0A= + if (document.getElementById("Department") !=3D null) {=0A= + if (document.getElementById("Department").value =3D=3D "") {=0A= + var subjects =3D ["college" , "univ" ];=0A= + for (var i in subjects) {=0A= + var pattern =3D new RegExp(subjects[i], "i");=0A= + if (pattern.test(compValue)) {=0A= + if (confirm (=0A= + "Please provide your department name. "+=0A= + "You have submitted a company/university address = +that typically requires "+=0A= + "a department name in order for the post office = +and your organization's mail room "+=0A= + "to deliver the materials you are requesting. "+=0A= + "Click 'OK' to go back and specify a department = +or "+=0A= + "click 'cancel' to submit the form without a = +department.")) {=0A= + document.getElementById("Department").focus();=0A= + return false;=0A= + }=0A= + }=0A= + }=0A= + }=0A= + }=0A= + // not all response forms have the Mail_stop field=0A= + if (document.getElementById("Mail_stop") !=3D null) {=0A= + if (document.getElementById("Mail_stop").value =3D=3D "") {=0A= + var subjects =3D ["air force", "bae", "boeing", = +"daimlerchrysler", "delphi", "ford", "general motors", "gm", "honeywell",=0A= + "ibm", "jet propulsion", "lockheed", "mit lincoln", = +"nasa", "navair", "naval air", "naval research", "raytheon", = +"Richardson", "sun micro", "visteon" ];=0A= + for (var i in subjects) {=0A= + var pattern =3D new RegExp(subjects[i], "i");=0A= + if (pattern.test(compValue)) {=0A= + if (confirm (=0A= + "Please provide your mail stop. "+=0A= + "You have submitted an address for a company = +that typically requires "+=0A= + "a mail stop in order for the post office and = +your organization's mail room "+=0A= + "to deliver the materials you are requesting. "+=0A= + "Click 'OK' to go back and specify a mail stop = +or "+=0A= + "click 'Cancel' to submit the form without a = +mail stop.")){=0A= + document.getElementById("Mail_stop").focus();=0A= + return false;=0A= + }=0A= + }=0A= + }=0A= + }=0A= + }=0A= + return true;=0A= +} // end function compMatch=0A= +=0A= +function sizeTables () {=0A= + var bodyTables =3D = +document.getElementById("mainbody").getElementsByTagName("table");=0A= + var rightCol =3D document.getElementById("rightcol");=0A= + var rightColHeight =3D rightCol.offsetHeight;=0A= + var rcolY =3D getPageOffsetTop(rightCol);=0A= + var rcolTotal =3D (rcolY + rightColHeight);=0A= + for (i=3D0; i 420 && = +getPageOffsetTop(bodyTables[i]) < rcolTotal && = +document.getElementById("leftnavcol")) {=0A= + bodyTables[i].width =3D 420 ;=0A= + }// end if=0A= + } // end for=0A= +} // end function sizeTables=0A= +=0A= +/* OnLoad Firing */=0A= +onload =3D function () {=0A= + if (navigator.appName =3D=3D "Microsoft Internet Explorer") {=0A= + if ( document.getElementById("mainbody") && = +document.getElementById("rightcol") ) {=0A= + sizeTables();=0A= + } // end if=0A= + } // end if=0A= +} // end anonymous function=0A= + +------=_NextPart_000_000D_01C5F437.56C58110 +Content-Type: application/octet-stream +Content-Transfer-Encoding: quoted-printable +Content-Location: http://www.mathworks.com/includes_content/jscript/omniture/s_code_remote.js + +/************************ ADDITIONAL FEATURES ************************ + Dynamic Account Selection + Plugins +*/ +/************************** CONFIG SECTION **************************/ +/* You may add or alter any code config here. */ +/* Specify the Report Suite ID(s) to track here */ +var s_account=3D"mathmain" +var s_dynamicAccountSelection=3Dtrue +var = +s_dynamicAccountList=3D"mathdev=3Dwww-external-dev.;mathIntranet=3Dwww-in= +ternal.;mathExtra=3Ddistribs/;mathGlobal,mathUK=3D.co.uk;mathGlobal,mathC= +H=3D.ch;mathGlobal,mathES=3D.es;mathGlobal,mathNordic=3Dse.;mathGlobal,ma= 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+ /* Add calls to plugins here */ +} + +/************************** PLUGINS SECTION *************************/ +/* You may insert any plugins you wish to use here. */ + +/* + * Utility Function: Split a string (compatible with Javascript 1.0) + */ +function s_split(s,p) + {var i=3D0,a=3Dnew Array(),j;if(s&&p){while((s.length>0)&&(p.length + >0)){j=3Ds.indexOf(p);if((!j)&&(p!=3Ds.substring(0,p.length)))break; + if(j=3D=3D-1){a[i++] =3D = +s;break;}a[i++]=3Ds.substring(0,j);s=3Ds.substring + (j+p.length,s.length)}}return a} +/* + * Plugin: Get Plugin Modified Value + */ +function s_vp_getValue(vs) + {var k=3Dvs.substring(0,2)=3D=3D's_'?vs.substring(2):vs;return s_wd[ + 's_vpm_'+k]?s_wd['s_vpv_'+k]:s_gg(k)} +/* + * Plugin: Get Query String CGI Variable Value + */ +function s_vp_getCGI(vs,k) + {var v=3D'';if(k&&s_wd.location.search){var q=3Ds_wd.location.search, + qq=3Dq.indexOf('?');q=3Dqq<0?q:q.substring(qq+1);v=3Ds_pt(q,'&',s_cgif, + k)}s_vpr(vs,v)}function s_cgif(t,k){if(t){var te=3Dt.indexOf('=3D'), + sk=3Dte<0?t:t.substring(0,te),sv=3Dte<0?'True':t.substring(te+1);if( + sk=3D=3Dk)return s_epa(sv)}return ''} +/* + * Plugin: Get Value From Cookie + */ +function s_vp_getCookie(vs,k) + {s_vpr(vs,s_c_r(k))} +/* + * Plugin Utilities v2.0 (Required For All Plugins) + */ +function s_vpr(vs,v){if(s_wd[vs])s_wd[vs]=3Ds_wd[vs];else s_wd[vs]=3D'' +if(vs.substring(0,2) =3D=3D = +'s_')vs=3Dvs.substring(2);s_wd['s_vpv_'+vs]=3Dv +s_wd['s_vpm_'+vs]=3D1}function s_dt(tz,t){var d=3Dnew = +Date;if(t)d.setTime( +t);d=3Dnew Date(d.getTime()+(d.getTimezoneOffset()*60*1000)) +return new Date(Math.floor(d.getTime()+(tz*60*60*1000)))} +function s_vh_gt(k,v){var = +vh=3D'|'+s_c_r('s_vh_'+k),vi=3Dvh.indexOf('|'+v ++'=3D'),ti=3Dvi<0?vi:vi+2+v.length,pi=3Dvh.indexOf('|',ti),t=3Dti<0?'': +vh.substring(ti,pi<0?vh.length:pi);return t}function s_vh_gl(k){var +vh=3Ds_c_r('s_vh_'+k),e=3Dvh?vh.indexOf('=3D'):0;return = +vh?(vh.substring(0, +e?e:vh.length)):''}function s_vh_s(k,v){if(k&&v){var 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+m]?s_wd['s_vpv_'+t]:s_gg(t);if(s_lnk||s_eo){v=3Dv?v+',pageName,pageURL,' ++'referrer,charSet,cookieDomainPeriods,cookieLifetime,currencyCode,pu' ++'rchaseID':'';if(v&&!s_pt(v,',',s_isf,t))s_wd[k]=3D'';if(t=3D=3D'events'= +&&e +)s_wd[k]=3Ds_fs(s_wd[k],e)}s_wd[m]=3D0;if(t=3D=3D'pageURL')q=3D'g';else = +if(t=3D=3D +'referrer')q=3D'r';else if(t=3D=3D'charSet')q=3D'ce';else if(t=3D=3D +'cookieDomainPeriods')q=3D'cdp';else if(t=3D=3D'cookieLifetime')q=3D'cl' +else if(t=3D=3D'currencyCode')q=3D'cc';else = +if(t=3D=3D'channel')q=3D'ch';else if( +t=3D=3D'campaign')q=3D'v0';else = +if(s_num(s)){if(b=3D=3D'prop')q=3D'c'+n;else if( +b=3D=3D'eVar')q=3D'v'+n;else = +if(b=3D=3D'hier')q=3D'h'+n}if(s_wd[k]&&t!=3D +'linkName'&&t!=3D'linkType')s_qav+=3D'&'+q+'=3D'+s_ape(s_wd[k]);return = +''} +function s_hav(){var n,av=3D'charSet,cookieDomainPeriods,cookieLifetime' ++',pageName,pageURL,referrer,channel,server,pageType,campaign,state,z' ++'ip,events,products,currencyCode,purchaseID,linkName,linkType' +for(n=3D1;n<26;n++)av+=3D',prop'+n+',eVar'+n+',hier'+n;s_qav=3D'';s_pt(av= +, +',',s_havf,0);return s_qav}function s_lnf(t,h){t=3Dt?t.toLowerCase():'' +h=3Dh?h.toLowerCase():'';var = +te=3Dt.indexOf('=3D');if(t&&te>0&&h.indexOf( +t.substring(te+1))>=3D0)return t.substring(0,te);return ''} +function s_ln(h){if(s_gg('linkNames'))return s_pt(s_gg('linkNames'), +',',s_lnf,h);return ''}function = +s_ltdf(t,h){t=3Dt?t.toLowerCase():'';h=3D +h?h.toLowerCase():'';var = +qi=3Dh.indexOf('?');h=3Dqi>=3D0?h.substring(0,qi):h +if(t&&h.substring(h.length-(t.length+1))=3D=3D'.'+t)return 1;return 0} +function = +s_ltef(t,h){t=3Dt?t.toLowerCase():'';h=3Dh?h.toLowerCase():'';if( +t&&h.indexOf(t)>=3D0)return 1;return 0}function s_lt(h){var lft=3Ds_gg( +'linkDownloadFileTypes'),lef=3Ds_gg('linkExternalFilters'),lif=3Ds_gg( +'linkInternalFilters')?s_gg('linkInternalFilters'): +s_wd.location.hostname;h=3Dh.toLowerCase();if(s_gg('trackDownloadLinks' +)&&lft&&s_pt(lft,',',s_ltdf,h))return 'd';if(s_gg('trackExternalLinks' +)&&(lef||lif)&&(!lef||s_pt(lef,',',s_ltef,h))&&(!lif||!s_pt(lif,',', +s_ltef,h)))return 'e';return ''}function s_lc(e){s_lnk=3Ds_co(this) +s_gs('');s_lnk=3D'';if(this.s_oc)return this.s_oc(e);return true} +function s_ls(){var l,ln,oc;for(ln=3D0;ln=3D0?','+t.substring(0,e) ++',':'';return u&&u.indexOf(','+un+',')>=3D0?s_epa(t.substring(e+1)):''} +function s_rq(un){var = +c=3Dun.indexOf(','),v=3Ds_c_r('s_sq'),q=3D'';if(c<0) +return s_pt(v,'&',s_rqf,un);return s_pt(un,',',s_rq,0)}var s_sqq,s_squ +function s_sqp(t,a){var = +e=3Dt.indexOf('=3D'),q=3De<0?'':s_epa(t.substring(e ++1));s_sqq[q]=3D'';if(e>=3D0)s_pt(t.substring(0,e),',',s_sqs,q);return = +0} +function s_sqs(un,q){s_squ[un]=3Dq;return 0}function s_sq(un,q){s_sqq=3D +new Object;s_squ=3Dnew Object;s_sqq[q]=3D'';var = +k=3D's_sq',v=3Ds_c_r(k),x,c=3D0 +s_pt(v,'&',s_sqp,0);s_pt(un,',',s_sqs,q);v=3D'';for(x in s_squ)s_sqq[ +s_squ[x]]+=3D(s_sqq[s_squ[x]]?',':'')+x;for(x in s_sqq)if(x&&s_sqq[x]&&( +x=3D=3Dq||c<2)){v+=3D(v?'&':'')+s_sqq[x]+'=3D'+s_ape(x);c++}return = +s_c_w(k,v,0 +)}function s_wdl(e){s_wd.s_wd_l=3D1;var = +r=3Dtrue;if(s_wd.s_ol)r=3Ds_wd.s_ol( +e);if(s_wd.s_ls)s_wd.s_ls();return r}function s_wds(un){un=3D +un.toLowerCase();s_wd.s_wd_l=3D1;if(s_apv>3&&(!s_isie||!s_ismac||s_apv>=3D= + +5)){s_wd.s_wd_l=3D0;if(!s_wd.s_unl)s_wd.s_unl=3Dnew Array;s_wd.s_unl[ +s_wd.s_unl.length]=3Dun;if(s_d.body&&s_d.body.attachEvent){if( +!s_wd.s_bcr&&s_d.body.attachEvent('onclick',s_bc))s_wd.s_bcr=3D1} +else if(s_d.body&&s_d.body.addEventListener){if(!s_wd.s_bcr&& +s_d.body.addEventListener('click',s_bc,false))s_wd.s_bcr=3D1}else{var +ol=3Ds_wd.onload?s_wd.onload.toString():'';if(ol.indexOf("s_wdl(")<0){ +s_wd.s_ol=3Ds_wd.onload;s_wd.onload=3Ds_wdl}}}}function s_iepf(i,a){if( +i.substring(0,1)!=3D'{')i=3D'{'+i+'}';if(s_d.body.isComponentInstalled(i,= + +'ComponentID')){var n=3Ds_pl.length;s_pl[n]=3Dnew = +Object;s_pl[n].name=3Di ++':'+s_d.body.getComponentVersion(i,'ComponentID')}return 0} +function s_vs(un,x){var s=3Ds_gg('visitorSampling'),g=3Ds_gg( +'visitorSamplingGroup'),k=3D's_vsn_'+un+(g?'_'+g:''),n=3Ds_c_r(k),e=3D +new Date,y=3De.getYear();e.setYear(y+10+(y<1900?1900:0));if(s){s*=3D100 +if(!n){if(!s_c_w(k,x,e))return 0;n=3Dx}if(n%10000>s)return 0}return 1} +function s_dyasmf(t,m){if(t&&m&&m.indexOf(t)>=3D0)return 1;return 0} +function s_dyasf(t,m){var = +i=3Dt?t.indexOf('=3D'):-1,un,s;if(i>=3D0&&m){var +un=3Dt.substring(0,i),s=3Dt.substring(i+1);if(s_pt(s,',',s_dyasmf,m)) +return un}return 0}function s_dyas(un,l,m){if(!m)m=3Ds_wd.location.host +if(!m.toLowerCase)m=3Dm.toString();l=3Dl.toLowerCase();m=3Dm.toLowerCase(= +) +var nun=3Ds_pt(l,';',s_dyasf,m);if(nun)return nun;return un} +function s_gs(un){un=3Dun.toLowerCase() +var dyas=3Ds_gg('dynamicAccountSelection'),dyal=3Ds_gg( +'dynamicAccountList'),dyam=3Ds_gg('dynamicAccountMatch');if(dyas&&dyal) +un=3Ds_dyas(un,dyal,dyam); +s_un=3Dun;var trk=3D1,tm=3Dnew Date,sed=3DMath&&Math.random?Math.floor( +Math.random()*10000000000000):tm.getTime(),sess=3D's'+Math.floor( +tm.getTime()/10800000)%10+sed,yr=3Dtm.getYear(),tfs=3Ds_gtfs(),t,ta=3D'',= +q=3D +'',qs=3D'';yr=3Dyr<1900?yr+1900:yr;t=3Dtm.getDate()+'/'+tm.getMonth()+'/'= ++yr ++' '+tm.getHours()+':'+tm.getMinutes()+':'+tm.getSeconds()+' ' ++tm.getDay()+' '+tm.getTimezoneOffset();if(!s_q){var tl=3Dtfs.location, +s=3D'',c=3D'',v=3D'',p=3D'',bw=3D'',bh=3D'',j=3D'1.0',k=3Ds_c_w('s_cc','t= +rue',0)?'Y': +'N',hp=3D'',ct=3D'',iepl=3Ds_gg('iePlugins'),pn=3D0,ps;if(s_apv>=3D4)s=3D= + +screen.width+'x'+screen.height;if(s_isns||s_isopera){if(s_apv>=3D3){j=3D +'1.1';v=3Ds_n.javaEnabled()?'Y':'N';if(s_apv>=3D4){j=3D'1.2';c=3D +screen.pixelDepth;bw=3Ds_wd.innerWidth;bh=3Ds_wd.innerHeight;if(s_apv>=3D= + +4.06)j=3D'1.3'}}s_pl=3Ds_n.plugins}else if(s_isie){if(s_apv>=3D4){v=3D +s_n.javaEnabled()?'Y':'N';j=3D'1.2';c=3Dscreen.colorDepth;if(s_apv>=3D5){= +bw=3D +s_d.documentElement.offsetWidth;bh=3Ds_d.documentElement.offsetHeight;j=3D= + +'1.3';if(!s_ismac&&s_d.body){s_d.body.addBehavior("#default#homePage") +hp=3Ds_d.body.isHomePage(tl)?"Y":"N";s_d.body.addBehavior( +"#default#clientCaps");ct=3Ds_d.body.connectionType;if(iepl){s_pl=3D +new Array;s_pt(iepl,',',s_iepf,'');}}}}else = +r=3D'';if(!s_pl&&iepl)s_pl=3D +s_n.plugins}if(s_pl)while(pn=3D= + +0)return = +''}ta=3Do.target;h=3Do.href?o.href:'';i=3Dh.indexOf('?');h=3Ds_gg( +'linkLeaveQueryString')||i<0?h:h.substring(0,i);l=3Ds_gg('linkName')? +s_gg('linkName'):s_ln(h);t=3Ds_gg('linkType')?s_gg('linkType' +).toLowerCase():s_lt(h);if(t&&(h||l))q+=3D'&pe=3Dlnk_'+(t=3D=3D'd'||t=3D=3D= +'e'? +s_ape(t):'o')+(h?'&pev1=3D'+s_ape(h):'')+(l?'&pev2=3D'+s_ape(l):'');else +trk=3D0;if(s_gg('trackInlineStats')){if(!p){p=3Ds_wd.s_g_pageURL;w=3D0}t=3D= + +s_ot(o);i=3Do.sourceIndex;if(s_gg('objectID')){n=3Ds_gg('objectID');x=3D1= +;i=3D +1}if(p&&n&&t)qs=3D'&pid=3D'+s_ape(s_fl(p,255))+(w?'&pidt=3D'+w:'')+'&oid=3D= +' ++s_ape(s_fl(n,100))+(x?'&oidt=3D'+x:'')+'&ot=3D'+s_ape(t)+(i?'&oi=3D'+i:'= +')} +s_wd.s_linkName=3Ds_wd.s_linkType=3Ds_wd.s_objectID=3Ds_lnk=3Ds_eo=3D'';i= +f( +!s_wd.s_disableLegacyVars)s_wd.linkName=3Ds_wd.linkType=3Ds_wd.objectID=3D= +'' +}if(!trk&&!qs)return '';var = +code=3D'';if(un){if(trk&&s_vs(un,sed))code+=3D +s_mr(un,sess,q+(qs?qs:s_rq(un)),ta);s_sq(un,trk?'':qs)}else if( +s_wd.s_unl)for(var unn=3D0;unn + Copyright (C) + + This program is free software; you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation; either version 2 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program; if not, write to the Free Software + Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + + +Also add information on how to contact you by electronic and paper mail. + +If the program is interactive, make it output a short notice like this +when it starts in an interactive mode: + + Gnomovision version 69, Copyright (C) year name of author + Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, the commands you use may +be called something other than `show w' and `show c'; they could even be +mouse-clicks or menu items--whatever suits your program. + +You should also get your employer (if you work as a programmer) or your +school, if any, to sign a "copyright disclaimer" for the program, if +necessary. Here is a sample; alter the names: + + Yoyodyne, Inc., hereby disclaims all copyright interest in the program + `Gnomovision' (which makes passes at compilers) written by James Hacker. + + , 1 April 1989 + Ty Coon, President of Vice + +This General Public License does not permit incorporating your program into +proprietary programs. If your program is a subroutine library, you may +consider it more useful to permit linking proprietary applications with the +library. If this is what you want to do, use the GNU Library General +Public License instead of this License. + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/readme.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/readme.txt" index 4cf475aba666e83f03fd1360abee8845ebfd3ee6..1fc14934cb83aad48e7010257f0237ad5f96d01d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/readme.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/DOC/readme.txt" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:11dc2df89b57204a887774ba1d899fa66f9bd107145882ff875ed825cec11a8b -size 1525 +---------------------------------------------------------------------- + +Genetic Algorithm Toolbox for MATLAB, v1.2 +========================================== + +Thank you for requesting a copy of the Genetic Algorithm Toolbox. + +The Genetic Algorithm Toolbox for MATLAB was developed at the +Department of Automatic Control and Systems Engineering of The +University of Sheffield, UK, in order to make GA's accessible to the +control engineer within the framework of a existing computer-aided +control system design package. The toolbox was written with the +support of a UK SERC grant, and the final version (v1.2) was +completed in 1994. + +The Toolbox was originally developed for MATLAB v4.2. It has also +been successfully used with subsequent versions up to and including +MATLAB 7. + +For a more detailed introduction to the capabilities and use of the +GA Toolbox, please refer to the two introductory papers and the +Toolbox User's Guide, all of which are available at the GA Toolbox +homepage at http://www.shef.ac.uk/acse/research/ecrg/gat.html. + +The GA Toolbox is copyright the original authors and The University +of Sheffield, and is published here under the GNU General Public +License. (See http://www.fsf.org/licenses/licenses.html) + +We would be interested to hear of your experiences with, criticisms +of, and enhancements to, the GA Toolbox. Please direct all such +correspondence to ga-toolbox@acse.sheffield.ac.uk. + +---------------------------------------------------------------------- + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MIGRATE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MIGRATE.M" index 3aba7a1a0b52f47c0362456fbab46ce78ae5af9f..d5d122be6acc1030714d00d400456363c00a060d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MIGRATE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MIGRATE.M" @@ -1,3 +1,149 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8294ef22c9e4017f0b8f14ca16d39e04ff6a922b813b78f5bb7c3034d2efeeb3 -size 7205 +% MIGRATE.M (MIGRATion of individuals between subpopulations) +% +% This function performs migration of individuals. +% +% Syntax: [Chrom, ObjV] = migrate(Chrom, SUBPOP, MigOpt, ObjV) +% +% Input parameters: +% Chrom - Matrix containing the individuals of the current +% population. Each row corresponds to one individual. +% SUBPOP - Number of subpopulations +% MigOpt - (optional) Vector containing migration parameters +% MigOpt(1): MIGR - Rate of individuals to be migrated per +% subpopulation (% of subpopulation) +% if omitted or NaN, 0.2 (20%) is assumed +% MigOpt(2): Select - number indicating the selection method +% of replacing individuals +% 0 - uniform selection +% 1 - fitness-based selection (replace worst +% individuals) +% if omitted or NaN, 0 is assumed +% MigOpt(3): Structure - number indicating the structure +% of the subpopulations for migration +% 0 - net structure (unconstrained migration) +% 1 - neighbourhood structure +% 2 - ring structure +% if omitted or NaN, 0 is assumed +% ObjV - (optional) Column vector containing the objective values +% of the individuals in the current population, needed for +% fitness-based migration, this saves the +% recalculation of objective values for population. +% +% Output parameters: +% Chrom - Matrix containing the individuals of the current +% population after migration. +% ObjV - if ObjV is input parameter, than column vector containing +% the objective values of the individuals of the current +% generation after migration. + +% Author: Hartmut Pohlheim +% History: 16.02.94 file created +% 18.02.94 comments at the beginning added +% exchange of ObjV too +% 25.02.94 clean up +% 26.02.94 ObjV optional input parameter +% Select and Structure added, parameter reordered +% 17.03.94 renamed to migrate.m, more parameter checks + +function [Chrom, ObjV] = migrate(Chrom, SUBPOP, MigOpt, ObjV); + + +% Check parameter consistency + if nargin < 2, error('Input parameter SUBPOP missing'); end + if (nargout == 2 & nargin < 4), error('Input parameter ObjV missing'); end + + [Nind, Nvar] = size(Chrom); + if length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + if SUBPOP == 1, return; end + if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('Chrom and SUBPOP disagree'); end + NIND = Nind/SUBPOP; % Compute number of individuals per subpopulation + + if nargin > 3, + [mO, nO] = size(ObjV); + if nO ~= 1, error('ObjV must be a column vector'); end + if Nind ~= mO, error('Chrom and ObjV disagree'); end + IsObjV = 1; + else IsObjV = 0; ObjV = []; + end + + if nargin < 3, MIGR = 0.2; Select = 0; Structure = 0; end + if nargin > 2, + if isempty(MigOpt), MIGR = 0.2; Select = 0; Structure = 0; + elseif isnan(MigOpt), MIGR = 0.2; Select = 0; Structure = 0; + else + MIGR = NaN; Select = NaN; Structure = NaN; + if length(MigOpt) > 3, error('Parameter MigOpt is too long'); end + if length(MigOpt) >= 1, MIGR = MigOpt(1); end + if length(MigOpt) >= 2, Select = MigOpt(2); end + if length(MigOpt) >= 3, Structure = MigOpt(3); end + if isnan(MIGR), MIGR =0.2; end + if isnan(Select), Select = 0; end + if isnan(Structure), Structure = 0; end + end + end + + if (MIGR < 0 | MIGR > 1), error('Parameter for migration rate must be a scalar in [0 1]'); end + if (Select ~= 0 & Select ~= 1), error('Parameter for selection method must be 0 or 1'); end + if (Structure < 0 | Structure > 2), error ('Parameter for structure must be 0, 1 or 2'); end + if (Select == 1 & IsObjV == 0), error('ObjV for fitness-based migration needed');end + + if MIGR == 0, return; end + MigTeil = max(floor(NIND * MIGR), 1); % Number of individuals to migrate + +% Perform migration between subpopulations --> create a matrix for migration +% in every subpopulation from best individuals of the other subpopulations + + % Clear storing matrices + ChromMigAll = []; + if IsObjV == 1, ObjVAll = []; end + + % Create matrix with best/uniform individuals of all subpopulations + for irun = 1:SUBPOP + % sort ObjV of actual subpopulation + if Select == 1, % fitness-based selection + [Dummy, IndMigSo]=sort(ObjV((irun-1)*NIND+1:irun*NIND)); + else % if Select == 0 % uniform selection + [Dummy, IndMigSo]=sort(rand(NIND, 1)); + end + % take MigTeil (best) individuals, copy individuals and objective values + IndMigTeil=IndMigSo(1:MigTeil)+(irun-1)*NIND; + ChromMigAll = [ChromMigAll; Chrom(IndMigTeil,:)]; + if IsObjV == 1, ObjVAll = [ObjVAll; ObjV(IndMigTeil,:)]; end + end + + % perform migration + for irun = 1:SUBPOP + ChromMig = ChromMigAll; + if IsObjV == 1, ObjVMig = ObjVAll; end + if Structure == 1, % neighbourhood + % select individuals of neighbourhood subpopulations for ChromMig and ObjVMig + popnum = [SUBPOP 1:SUBPOP 1]; + ins1 = popnum(irun); ins2 = popnum(irun + 2); + InsRows = [(ins1-1)*MigTeil+1:ins1*MigTeil (ins2-1)*MigTeil+1:ins2*MigTeil]; + ChromMig = ChromMig(InsRows,:); + if IsObjV == 1, ObjVMig = ObjVMig(InsRows,:); end + elseif Structure == 2, % ring + % select individuals of actual-1 subpopulation for ChromMig and ObjVMig + popnum = [SUBPOP 1:SUBPOP 1]; + ins1 = popnum(irun); + InsRows = (ins1-1)*MigTeil+1:ins1*MigTeil; + ChromMig = ChromMig(InsRows,:); + if IsObjV == 1, ObjVMig = ObjVMig(InsRows,:); end + else % if Structure == 0, % complete net + % delete individuals of actual subpopulation from ChromMig and ObjVMig + DelRows = (irun-1)*MigTeil+1:irun*MigTeil; + ChromMig(DelRows,:) = []; + if IsObjV == 1, ObjVMig(DelRows,:) = []; end + end + % Create an index from a sorted vector with random numbers + [Dummy,IndMigRa]=sort(rand(size(ChromMig,1),1)); + % Take MigTeil numbers from the random vector + IndMigN=IndMigRa((1:MigTeil)'); + % copy MigTeil individuals into Chrom and ObjV + Chrom((1:MigTeil)+(irun-1)*NIND,:) = ChromMig(IndMigN,:); + if IsObjV == 1, ObjV((1:MigTeil)+(irun-1)*NIND,:) = ObjVMig(IndMigN,:); end + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MPGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MPGA.M" index 153850ca22ef86f5213b076f928a242deebe4615..47dc198b9e94f9974b5571ba40f963522f8fd54b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MPGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MPGA.M" @@ -1,3 +1,119 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3be3ef407462f6d47ada9326340791bb891df5a4e5cecd7e783b01e9b693b195 -size 4019 +% mpga multi population genetic algorithm +% +% This script implements the Multi Population Genetic Algorithm. +% A real-valued representation of the individuals is used. +% + +% Author: Andrew Chipperfield +% History: 30-Mar-94 file created + +NVAR = 20; % No. of decision variables (control steps) +RANGE = [0;200]; % Bounds on decision variables + +% Set field descriptor + FieldD = rep(RANGE,[1,NVAR]); + +% Define GA Parameters + GGAP = .8; % Generation gap, how many new individuals are created + XOVR = 1; % Crossover rate + MUTR = 1/NVAR; % Mutation rate depending on NVAR + MAXGEN = 1200; % Maximum number of generations + TERMEXACT = 1e-4; % Value for termination if minimum reached + INSR = .9; % Insertion rate, how many of the offspring are inserted + SUBPOP = 8; % Number of subpopulations + MIGR = 0.2; % Migration rate between subpopulations + MIGGEN = 20; % Number of generations between migration + NIND = 20; % Number of individuals per subpopulation + +% Specify other routines as strings + SEL_F = 'sus'; % Name of selection function + XOV_F = 'recdis'; % Name of recombination function for individuals + MUT_F = 'mutbga'; % Name of mutation function + OBJ_F = 'objharv'; % Name of function for objective values + + +% Get value of minimum, defined in objective function + GlobalMin = feval(OBJ_F,[],3); + +% Get title of objective function, defined in objective function + FigTitle = [feval(OBJ_F,[],2) ' (' int2str(SUBPOP) ':' int2str(MAXGEN) ') ']; + +% Clear Best and storing matrix + % Initialise Matrix for storing best results + Best = NaN * ones(MAXGEN,3); + Best(:,3) = zeros(size(Best,1),1); + % Matrix for storing best individuals + IndAll = []; + +% Create real population + Chrom = crtrp(SUBPOP*NIND,FieldD); + +% reset count variables + gen = 0; + +% Calculate objective function for population + ObjV = feval(OBJ_F,Chrom); + % count number of objective function evaluations + Best(gen+1,3) = Best(gen+1,3) + NIND; + +% Generational loop + while gen < MAXGEN, + + % Save the best and average objective values and the best individual + [Best(gen+1,1),ix] = min(ObjV); + Best(gen+1,2) = mean(ObjV); + IndAll = [IndAll; Chrom(ix,:)]; + + % Fitness assignment to whole population + FitnV = ranking(ObjV,2 ,SUBPOP); + + % Select individuals from population + SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); + + % Recombine selected individuals + SelCh=recombin(XOV_F, SelCh, XOVR, SUBPOP); + + % Mutate offspring + SelCh=mutate(MUT_F, SelCh, FieldD, [MUTR], SUBPOP); + + % Calculate objective function for offsprings + ObjVOff = feval(OBJ_F,SelCh); + Best(gen+1,3) = Best(gen+1,3) + size(SelCh,1); + + % Insert best offspring in population replacing worst parents + [Chrom, ObjV] = reins(Chrom, SelCh, SUBPOP, [1 INSR], ObjV, ObjVOff); + + gen=gen+1; + + % Plot some results, rename title of figure for graphic output + if ((rem(gen,20) == 1) | (rem(gen,MAXGEN) == 0)), + set(gcf,'Name',[FigTitle ' in ' int2str(gen)]); + resplot(Chrom(1:2:size(Chrom,1),:),... + IndAll(max(1,gen-39):size(IndAll,1),:),... + [ObjV; GlobalMin], Best(max(1,gen-19):gen,[1 2]), gen); + end + + + % migrate individuals between subpopulations + if (rem(gen,MIGGEN) == 0) + [Chrom, ObjV] = migrate(Chrom, SUBPOP, [MIGR, 1, 0], ObjV); + end + + end + + +% Results + % add number of objective function evaluations + Results = cumsum(Best(1:gen,3)); + % number of function evaluation, mean and best results + Results = [Results Best(1:gen,2) Best(1:gen,1)]; + +% Plot Results and show best individuals => optimum + figure('Name',['Results of ' FigTitle]); + subplot(2,1,1), plot(Results(:,1),Results(:,2),'-',Results(:,1),Results(:,3),':'); + subplot(2,1,2), plot(IndAll(gen-4:gen,:)'); + + +% End of script + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MUT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MUT.M" index 97670ab6d17e49a1cfc8ba383a6a22e2feebff1b..07e58149d6e75735021811ebf20a833c50bc081e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MUT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MUT.M" @@ -1,3 +1,54 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f5deb82096f3db334fb30159caacc236ae351eeb99cac69a4b214ed2f88d4d80 -size 1609 +% MUT.m +% +% This function takes the representation of the current population, +% mutates each element with given probability and returns the resulting +% population. +% +% Syntax: NewChrom = mut(OldChrom,Pm,BaseV) +% +% Input parameters: +% +% OldChrom - A matrix containing the chromosomes of the +% current population. Each row corresponds to +% an individuals string representation. +% +% Pm - Mutation probability (scalar). Default value +% of Pm = 0.7/Lind, where Lind is the chromosome +% length is assumed if omitted. +% +% BaseV - Optional row vector of the same length as the +% chromosome structure defining the base of the +% individual elements of the chromosome. Binary +% representation is assumed if omitted. +% +% Output parameter: +% +% NewChrom - A Matrix containing a mutated version of +% OldChrom. +% + +% Author: Andrew Chipperfield +% Date: 25-Jan-94 + +function NewChrom = mut(OldChrom,Pm,BaseV) + +% get population size (Nind) and chromosome length (Lind) +[Nind, Lind] = size(OldChrom) ; + +% check input parameters +if nargin < 2, Pm = 0.7/Lind ; end +if isnan(Pm), Pm = 0.7/Lind; end + +if (nargin < 3), BaseV = crtbase(Lind); end +if (isnan(BaseV)), BaseV = crtbase(Lind); end +if (isempty(BaseV)), BaseV = crtbase(Lind); end + +if (nargin == 3) & (Lind ~= length(BaseV)) + error('OldChrom and BaseV are incompatible'), end + +% create mutation mask matrix +BaseM = BaseV(ones(Nind,1),:) ; + +% perform mutation on chromosome structure +NewChrom = rem(OldChrom+(rand(Nind,Lind) 4, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('OldChrom and SUBPOP disagree'); end + Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation + +% Select individuals of one subpopulation and call low level function + NewChrom = []; + for irun = 1:SUBPOP, + ChromSub = OldChrom((irun-1)*Nind+1:irun*Nind,:); + if IsDiscret == 1, NewChromSub = feval(MUT_F, ChromSub, MutOpt, FieldDR); + elseif IsDiscret == 0, NewChromSub = feval(MUT_F, ChromSub, FieldDR, MutOpt); end + NewChrom=[NewChrom; NewChromSub]; + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MUTBGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MUTBGA.M" index e3bf6ec246c1647f5beb2c6df4510a94d17c8062..bf50a83f63d79bbcc154faf9d29b30d0e5e425c9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MUTBGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/MUTBGA.M" @@ -1,3 +1,113 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b9fe17257bc5a3c5ee901553861c8a13ca51711984d5e24a9dc8d76b391ddf53 -size 4943 +% MUTBGA.M (real-value MUTation like Breeder Genetic Algorithm) +% +% This function takes a matrix OldChrom containing the real +% representation of the individuals in the current population, +% mutates the individuals with probability MutR and returns +% the resulting population. +% +% This function implements the mutation operator of the Breeder Genetic +% Algorithm. (Muehlenbein et. al.) +% +% Syntax: NewChrom = mutbga(OldChrom, FieldDR, MutOpt) +% +% Input parameter: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual. +% FieldDR - Matrix describing the boundaries of each variable. +% MutOpt - (optional) Vector containing mutation rate and shrink value +% MutOpt(1): MutR - number containing the mutation rate - +% probability for mutation of a variable +% if omitted or NaN, MutR = 1/variables per individual +% is assumed +% MutOpt(2): MutShrink - (optional) number for shrinking the +% mutation range in the range [0 1], possibility to +% shrink the range of the mutation depending on, +% for instance actual generation. +% if omitted or NaN, MutShrink = 1 is assumed +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mutation in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 23.11.93 file created +% 24.11.93 function optimised (for,for-loop to for-loop) +% mutation rate included +% style improved +% 06.12.93 change of function name +% check of boundaries after mutation out of loop +% 16.12.93 NewMutMat and OldMutMat included for compability +% 16.02.94 preparation for multi-subpopulations at once +% 25.02.94 NewMutMat and OldMutMat removed (now in mutran10.m) +% clean up +% change of function name in mutbga.m +% 03.03.94 Lower and Upper directly used (less memory) +% 19.03.94 multipopulation support removed +% more parameter checks +% 27.03.94 Delta exact calculated, for loop saved + + +function NewChrom = mutbga(OldChrom, FieldDR, MutOpt); + +% Check parameter consistency + if nargin < 2, error('Not enough input parameter'); end + + % Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + + [mF, nF] = size(FieldDR); + if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end + if Nvar ~= nF, error('FieldDR and OldChrom disagree'); end + + if nargin < 3, MutR = 1/Nvar; MutShrink = 1; + elseif isempty(MutOpt), MutR = 1/Nvar; MutShrink = 1; + elseif isnan(MutOpt), MutR = 1/Nvar; MutShrink = 1; + else + if length(MutOpt) == 1, MutR = MutOpt; MutShrink = 1; + elseif length(MutOpt) == 2, MutR = MutOpt(1); MutShrink = MutOpt(2); + else, error(' Too many parameter in MutOpt'); end + end + + if isempty(MutR), MutR = 1/Nvar; + elseif isnan(MutR), MutR = 1/Nvar; + elseif length(MutR) ~= 1, error('Parameter for mutation rate must be a scalar'); + elseif (MutR < 0 | MutR > 1), error('Parameter for mutation rate must be a scalar in [0, 1]'); end + + if isempty(MutShrink), MutShrink = 1; + elseif isnan(MutShrink), MutShrink = 1; + elseif length(MutShrink) ~= 1, error('Parameter for shrinking mutation range must be a scalar'); + elseif (MutShrink < 0 | MutShrink > 1), + error('Parameter for shrinking mutation range must be a scalar in [0, 1]'); + end + +% the variables are mutated with probability MutR +% NewChrom = OldChrom (+ or -) * Range * MutShrink * Delta +% Range = 0.5 * (upperbound - lowerbound) +% Delta = Sum(Alpha_i * 2^-i) from 0 to ACCUR; Alpha_i = rand(ACCUR,1) < 1/ACCUR + +% Matrix with range values for every variable + Range = rep(0.5 * MutShrink *(FieldDR(2,:)-FieldDR(1,:)),[Nind 1]); + +% zeros and ones for mutate or not this variable, together with Range + Range = Range .* (rand(Nind,Nvar) < MutR); + +% compute, if + or - sign + Range = Range .* (1 - 2 * (rand(Nind,Nvar) < 0.5)); + +% used for later computing, here only ones computed + ACCUR = 20; + Vect = 2 .^ (-(0:(ACCUR-1))'); + Delta = (rand(Nind,ACCUR) < 1/ACCUR) * Vect; + Delta = rep(Delta, [1 Nvar]); + +% perform mutation + NewChrom = OldChrom + Range .* Delta; + +% Ensure variables boundaries, compare with lower and upper boundaries + NewChrom = max(rep(FieldDR(1,:),[Nind 1]), NewChrom); + NewChrom = min(rep(FieldDR(2,:),[Nind 1]), NewChrom); + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/OBJFUN1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/OBJFUN1.M" index da49989d1cd5d7f0468836d7b6aea9481f11973d..73dc9b465d7290d94ef8252f96fd1694bda1cc0f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/OBJFUN1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/OBJFUN1.M" @@ -1,3 +1,71 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:95863e65c0113af3f1400e6d4fbb0c3d376e840e9330202a38bf19551bb6ea9e -size 2629 +% OBJFUN1.M (OBJective function for De Jong's FUNction 1) +% +% This function implements the De Jong function 1. +% +% Syntax: ObjVal = objfun1(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 26.11.93 file created +% 27.11.93 text of title and switch added +% 30.11.93 show Dim in figure title +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objfun1(Chrom,switch); + +% Dimension of objective function + Dim = 20; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['DE JONG function 1-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = 100*[-5.12; 5.12]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 1, sum of xi^2 for i = 1:Dim (Dim=30) + % n = Dim, -5.12 <= xi <= 5.12 + % global minimum at (xi)=(0) ; fmin=0 + ObjVal = sum((Chrom .* Chrom)')'; + % ObjVal = diag(Chrom * Chrom'); % both lines produce the same + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/OBJHARV.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/OBJHARV.M" index 0a06fbddb9b0e6fca015f108a6138388f066a0c5..d056d7b3f9e7aa0e74085dfa58d2070ec0d9ccbd 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/OBJHARV.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/OBJHARV.M" @@ -1,3 +1,78 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a6208b888f3af5f91cd4717815f2702f3eba5edc0e9ef1fd36a98ae33d1ea36f -size 2559 +% OBJHARV.M (OBJective function for HARVest problem) +% +% This function implements the HARVEST PROBLEM. +% +% Syntax: ObjVal = objharv(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 18.02.94 file created (copy of vallinq.m) +% 01.03.94 name changed in obj* + +function ObjVal = objharv(Chrom,switch); + +% global gen; + +% Dimension of objective function + Dim = 20; + +% values from MICHALEWICZ + a = 1.1; + x0 = 100; + xend = x0; + XENDWEIGHT = 0.4/(Dim^0.6); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['HARVEST PROBLEM-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = -sqrt(x0*(a^Dim-1)^2/(a^(Dim-1)*(a-1))); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal1 = [0; 10*Dim]; + ObjVal = rep(ObjVal1,[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + ObjVal = zeros(Nind,1); + X = rep(x0,[Nind 1]); + for irun = 1:Nvar, + X = a*X - Chrom(:,irun); + end + X; + ObjVal = -(sum(sqrt(Chrom)')' - XENDWEIGHT * abs(X-x0)); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RANKING.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RANKING.M" index f816ea7d86d2051fb07ab800e0903630ded9bb70..af9127e20152816091ae4a8e88188e14a42bef1b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RANKING.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RANKING.M" @@ -1,3 +1,125 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:90523e59f9863d00812e95c0952b04e2064d7e08ca14dfa3830770cf580bb0bb -size 4709 +% RANKING.M (RANK-based fitness assignment) +% +% This function performs ranking of individuals. +% +% Syntax: FitnV = ranking(ObjV, RFun, SUBPOP) +% +% This function ranks individuals represented by their associated +% cost, to be *minimized*, and returns a column vector FitnV +% containing the corresponding individual fitnesses. For multiple +% subpopulations the ranking is performed separately for each +% subpopulation. +% +% Input parameters: +% ObjV - Column vector containing the objective values of the +% individuals in the current population (cost values). +% RFun - (optional) If RFun is a scalar in [1, 2] linear ranking is +% assumed and the scalar indicates the selective pressure. +% If RFun is a 2 element vector: +% RFun(1): SP - scalar indicating the selective pressure +% RFun(2): RM - ranking method +% RM = 0: linear ranking +% RM = 1: non-linear ranking +% If RFun is a vector with length(Rfun) > 2 it contains +% the fitness to be assigned to each rank. It should have +% the same length as ObjV. Usually RFun is monotonously +% increasing. +% If RFun is omitted or NaN, linear ranking +% and a selective pressure of 2 are assumed. +% SUBPOP - (optional) Number of subpopulations +% if omitted or NaN, 1 subpopulation is assumed +% +% Output parameters: +% FitnV - Column vector containing the fitness values of the +% individuals in the current population. +% + +% Author: Hartmut Pohlheim (Carlos Fonseca) +% History: 01.03.94 non-linear ranking +% 10.03.94 multiple populations + +function FitnV = ranking(ObjV, RFun, SUBPOP); + +% Identify the vector size (Nind) + [Nind,ans] = size(ObjV); + + if nargin < 2, RFun = []; end + if nargin > 1, if isnan(RFun), RFun = []; end, end + if prod(size(RFun)) == 2, + if RFun(2) == 1, NonLin = 1; + elseif RFun(2) == 0, NonLin = 0; + else error('Parameter for ranking method must be 0 or 1'); end + RFun = RFun(1); + if isnan(RFun), RFun = 2; end + elseif prod(size(RFun)) > 2, + if prod(size(RFun)) ~= Nind, error('ObjV and RFun disagree'); end + end + + if nargin < 3, SUBPOP = 1; end + if nargin > 2, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('ObjV and SUBPOP disagree'); end + Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation + +% Check ranking function and use default values if necessary + if isempty(RFun), + % linear ranking with selective pressure 2 + RFun = 2*[0:Nind-1]'/(Nind-1); + elseif prod(size(RFun)) == 1 + if NonLin == 1, + % non-linear ranking + if RFun(1) < 1, error('Selective pressure must be greater than 1'); + elseif RFun(1) > Nind-2, error('Selective pressure too big'); end + Root1 = roots([RFun(1)-Nind [RFun(1)*ones(1,Nind-1)]]); + RFun = (abs(Root1(1)) * ones(Nind,1)) .^ [(0:Nind-1)']; + RFun = RFun / sum(RFun) * Nind; + else + % linear ranking with SP between 1 and 2 + if (RFun(1) < 1 | RFun(1) > 2), + error('Selective pressure for linear ranking must be between 1 and 2'); + end + RFun = 2-RFun + 2*(RFun-1)*[0:Nind-1]'/(Nind-1); + end + end; + + FitnV = []; + +% loop over all subpopulations +for irun = 1:SUBPOP, + % Copy objective values of actual subpopulation + ObjVSub = ObjV((irun-1)*Nind+1:irun*Nind); + % Sort does not handle NaN values as required. So, find those... + NaNix = isnan(ObjVSub); + Validix = find(~NaNix); + % ... and sort only numeric values (smaller is better). + [ans,ix] = sort(-ObjVSub(Validix)); + + % Now build indexing vector assuming NaN are worse than numbers, + % (including Inf!)... + ix = [find(NaNix) ; Validix(ix)]; + % ... and obtain a sorted version of ObjV + Sorted = ObjVSub(ix); + + % Assign fitness according to RFun. + i = 1; + FitnVSub = zeros(Nind,1); + for j = [find(Sorted(1:Nind-1) ~= Sorted(2:Nind)); Nind]', + FitnVSub(i:j) = sum(RFun(i:j)) * ones(j-i+1,1) / (j-i+1); + i =j+1; + end + + % Finally, return unsorted vector. + [ans,uix] = sort(ix); + FitnVSub = FitnVSub(uix); + + % Add FitnVSub to FitnV + FitnV = [FitnV; FitnVSub]; +end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECDIS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECDIS.M" index 06de83a8ed1662c5b1bbdb70d2676354f073e28b..0c6ed8a67af00986661aa95b81d94f9a04ead856 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECDIS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECDIS.M" @@ -1,3 +1,52 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3509a126379548e879abb7f9eec4abb67786958f23516a46bc0ea71a44354d0d -size 1825 +% RECDIS.M (RECombination DIScrete) +% +% This function performs discret recombination between pairs of individuals +% and returns the new individuals after mating. +% +% Syntax: NewChrom = recdis(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real-values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. (not used, only for compatibility) +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 23.11.93 file created +% 24.11.93 style improved +% 06.12.93 change of name of function +% 25.02.94 clean up +% 19.03.94 multipopulation support removed + +function NewChrom = recdis(OldChrom, XOVR); + +% Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + +% Identify the number of matings + Xops = floor(Nind/2); + +% which parent gives the value + Mask1 = (rand(Xops,Nvar)<0.5); + Mask2 = (rand(Xops,Nvar)<0.5); + +% Performs crossover + odd = 1:2:Nind-1; + even= 2:2:Nind; + NewChrom(odd,:) = (OldChrom(odd,:).* Mask1) + (OldChrom(even,:).*(~Mask1)); + NewChrom(even,:) = (OldChrom(odd,:).* Mask2) + (OldChrom(even,:).*(~Mask2)); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population + if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECINT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECINT.M" index 7d9aafbbf73a550417eb34b56486dbe19edacb92..cac6d76a3d5f4a48ca82601e2b13d4d1e2bf3e0e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECINT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECINT.M" @@ -1,3 +1,55 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f28039ff4addb00e9527bb5c81eb6c73fdf542b9ebe15a9b929cca771cf5cd0b -size 1895 +% RECINT.M (RECombination extended INTermediate) +% +% This function performs extended intermediate recombination between +% pairs of individuals and returns the new individuals after mating. +% +% Syntax: NewChrom = recint(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one +% individual +% XOVR - Probability of crossover occurring between pairs +% of individuals. (not used, only for compatibility) +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 06.12.93 change of name of function +% 25.02.94 clean up +% 19.03.94 multipopulation support removed + +function NewChrom = recint(OldChrom, XOVR); + +% Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + +% Identify the number of matings + Xops = floor(Nind/2); + +% Performs recombination + odd = 1:2:Nind-1; + even= 2:2:Nind; + + % position of value of offspring compared to parents + Alpha = -0.25 + 1.5 * rand(Xops,Nvar); + + % recombination + NewChrom(odd,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); + + % the same ones more for second half of offspring + Alpha = -0.25 + 1.5 * rand(Xops,Nvar); + NewChrom(even,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population + if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECLIN.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECLIN.M" index 721f62b4d5ded537ccf9c9369e09975bc92db245..d76084444d778b795004e0f8042442dd8a5e8654 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECLIN.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECLIN.M" @@ -1,3 +1,57 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:34f0a46f19e514e77b173b8841a91e686cef0a5f864c3dff6725cb4ab59ff861 -size 1953 +% RECLIN.M (RECombination extended LINe) +% +% This function performs extended line recombination between +% pairs of individuals and returns the new individuals after mating. +% +% Syntax: NewChrom = reclin(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one +% individual +% XOVR - Probability of crossover occurring between pairs +% of individuals. (not used, only for compatibility) +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 26.11.93 file created +% 06.12.93 change of name of function +% 25.02.94 clean up +% 19.03.94 multipopulation support removed + +function NewChrom = reclin(OldChrom, XOVR); + +% Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + +% Identify the number of matings + Xops = floor(Nind/2); + +% Performs recombination + odd = 1:2:Nind-1; + even= 2:2:Nind; + + % position of value of offspring compared to parents + Alpha = -0.25 + 1.5 * rand(Xops,1); + Alpha = Alpha(1:Xops,ones(Nvar,1)); + + % recombination + NewChrom(odd,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); + + % the same ones more for second half of offspring + Alpha = -0.25 + 1.5 * rand(Xops,1); + Alpha = Alpha(1:Xops,ones(Nvar,1)); + NewChrom(even,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population + if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECMUT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECMUT.M" index a2447ff5122359772a59db31f3b7cce1c1f6d574..12642cb9125aafaa9729e24def4504d0ace42335 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECMUT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECMUT.M" @@ -1,3 +1,118 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1dba80855d9d825d038f939d30b7cddb249dc460ae0b449d0cf6cb9f6a4bc738 -size 4852 +% RECLIN.M (line RECombination with MUTation features) +% +% This function performs line recombination with mutation features between +% pairs of individuals and returns the new individuals after mating. +% +% Syntax: NewChrom = recmut(OldChrom, FieldDR, MutOpt) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% FieldDR - Matrix describing the boundaries of each variable. +% MutOpt - (optional) Vector containing recombination rate and shrink value +% MutOpt(1): MutR - number containing the recombination rate - +% probability for recombine a pair of parents +% if omitted or NaN, MutOpt(1) = 1 is assumed +% MutOpt(2): MutShrink - (optional) number for shrinking the +% recombination range in the range [0 1], possibility to +% shrink the range of the recombination depending on, +% for instance actual generation. +% if omitted or NaN, MutOpt(2) = 1 is assumed +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 27.03.94 file created + +function NewChrom = recmut(OldChrom, FieldDR, MutOpt); + +% Check parameter consistency + if nargin < 2, error('Not enough input parameter'); end + + % Identify the population size (Nind) and the number of variables (Nvar) + [Nind,Nvar] = size(OldChrom); + + [mF, nF] = size(FieldDR); + if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end + if Nvar ~= nF, error('FieldDR and OldChrom disagree'); end + + if nargin < 3, MutR = 1; MutShrink = 1; + elseif isempty(MutOpt), MutR = 1; MutShrink = 1; + elseif isnan(MutOpt), MutR = 1; MutShrink = 1; + else + if length(MutOpt) == 1, MutR = MutOpt; MutShrink = 1; + elseif length(MutOpt) == 2, MutR = MutOpt(1); MutShrink = MutOpt(2); + else, error(' Too many parameter in MutOpt'); end + end + + if isempty(MutR), MutR = 1; + elseif isnan(MutR), MutR = 1; + elseif length(MutR) ~= 1, error('Parameter for recombination rate must be a scalar'); + elseif (MutR < 0 | MutR > 1), error('Parameter for recombination rate must be a scalar in [0, 1]'); end + + if isempty(MutShrink), MutShrink = 1; + elseif isnan(MutShrink), MutShrink = 1; + elseif length(MutShrink) ~= 1, error('Parameter for shrinking recombination range must be a scalar'); + elseif (MutShrink < 0 | MutShrink > 1), + error('Parameter for shrinking recombination range must be a scalar in [0, 1]'); + end + +% Identify the number of matings + Xops = floor(Nind/2); + +% NewChrom = OldChrom (+ or -) * Range * MutShrink * Delta * ChromDiff +% - with probability 0.9, + with probability 0.1 +% Range = 0.5 * (upperbound - lowerbound), given by FieldDR +% Delta = Sum(Alpha_i * 2^-i) from 0 to ACCUR; Alpha_i = rand(ACCUR,1) < 1/ACCUR +% ChromDiff = (individual1 - individual2) / Distance between individuals + +% Matrix with range values for every variable + Range = rep(0.5 * MutShrink *(FieldDR(2,:)-FieldDR(1,:)),[Xops 1]); + +% zeros and ones for recombine or not this variable, together with Range + if MutR < 1, Range = Range .* rep((rand(Xops,1) < MutR), [1 Nvar]); end + +% compute, if + or - sign + Range = Range .* (1 - 2 * (rand(Xops,Nvar) < 0.9)); + +% compute distance between mating pairs + NormO = zeros(Xops,1); + for irun = 1:Xops, + NormO(irun) = max(realmin,abs(norm(OldChrom(2*irun,:)) - norm(OldChrom(2*irun-1,:)))); + end + +% compute difference between variables divided by distance + ChromDiff = zeros(Xops,Nvar); + for irun = 1:Xops + ChromDiff(irun,:) = diff([OldChrom(2*irun-1,:); OldChrom(2*irun,:)]) / NormO(irun); + end + +% compute delta value for all individuals + ACCUR = 20; + Vect = 2 .^ (-(0:(ACCUR-1))'); + Delta = (rand(Xops,ACCUR) < 1/ACCUR) * Vect; + Delta = rep(Delta, [1 Nvar]); + +% Performs recombination + odd = 1:2:Nind-1; + even= 2:2:Nind; + + % recombination + NewChrom(odd,:) = OldChrom(odd,:) + Range .* Delta .* (ChromDiff); + NewChrom(even,:) = OldChrom(even,:) + Range .* Delta .* (-ChromDiff); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population + if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end + +% Ensure variables boundaries, compare with lower and upper boundaries + NewChrom = max(rep(FieldDR(1,:),[Nind 1]), NewChrom); + NewChrom = min(rep(FieldDR(2,:),[Nind 1]), NewChrom); + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECOMBIN.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECOMBIN.M" index 760a482ee729bee15d30775766209361a64cdb54..9c47af9e83f9ddb26eb58828fef7ac404ac25760 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECOMBIN.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RECOMBIN.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1beb08befa03089753f61e6daa8117587823cc59d2e0949e5f78fc4cfa2db767 -size 2438 +% RECOMBIN.M (RECOMBINation high-level function) +% +% This function performs recombination between pairs of individuals +% and returns the new individuals after mating. The function handles +% multiple populations and calls the low-level recombination function +% for the actual recombination process. +% +% Syntax: NewChrom = recombin(REC_F, OldChrom, RecOpt, SUBPOP) +% +% Input parameters: +% REC_F - String containing the name of the recombination or +% crossover function +% Chrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% RecOpt - (optional) Scalar containing the probability of +% recombination/crossover occurring between pairs +% of individuals. +% if omitted or NaN, 1 is assumed +% SUBPOP - (optional) Number of subpopulations +% if omitted or NaN, 1 subpopulation is assumed +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after recombination in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 18.03.94 file created + + +function NewChrom = recombin(REC_F, Chrom, RecOpt, SUBPOP); + + +% Check parameter consistency + if nargin < 2, error('Not enough input parameter'); end + + % Identify the population size (Nind) + [Nind,Nvar] = size(Chrom); + + if nargin < 4, SUBPOP = 1; end + if nargin > 3, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('Chrom and SUBPOP disagree'); end + Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation + + if nargin < 3, RecOpt = 0.7; end + if nargin > 2, + if isempty(RecOpt), RecOpt = 0.7; + elseif isnan(RecOpt), RecOpt = 0.7; + elseif length(RecOpt) ~= 1, error('RecOpt must be a scalar'); + elseif (RecOpt < 0 | RecOpt > 1), error('RecOpt must be a scalar in [0, 1]'); end + end + + +% Select individuals of one subpopulation and call low level function + NewChrom = []; + for irun = 1:SUBPOP, + ChromSub = Chrom((irun-1)*Nind+1:irun*Nind,:); + NewChromSub = feval(REC_F, ChromSub, RecOpt); + NewChrom=[NewChrom; NewChromSub]; + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/REINS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/REINS.M" index fc150a058d9411f715e8b425ec400e966f0836c8..87074fbe810db520bc05b7978065adcac19f7af9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/REINS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/REINS.M" @@ -1,3 +1,123 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3f260e5b26029fd5b658901251e50c7c6c66ec858682f07c14ad986a44fda98d -size 5574 +% REINS.M (RE-INSertion of offspring in population replacing parents) +% +% This function reinserts offspring in the population. +% +% Syntax: [Chrom, ObjVCh] = reins(Chrom, SelCh, SUBPOP, InsOpt, ObjVCh, ObjVSel) +% +% Input parameters: +% Chrom - Matrix containing the individuals (parents) of the current +% population. Each row corresponds to one individual. +% SelCh - Matrix containing the offspring of the current +% population. Each row corresponds to one individual. +% SUBPOP - (optional) Number of subpopulations +% if omitted or NaN, 1 subpopulation is assumed +% InsOpt - (optional) Vector containing the insertion method parameters +% ExOpt(1): Select - number indicating kind of insertion +% 0 - uniform insertion +% 1 - fitness-based insertion +% if omitted or NaN, 0 is assumed +% ExOpt(2): INSR - Rate of offspring to be inserted per +% subpopulation (% of subpopulation) +% if omitted or NaN, 1.0 (100%) is assumed +% ObjVCh - (optional) Column vector containing the objective values +% of the individuals (parents - Chrom) in the current +% population, needed for fitness-based insertion +% saves recalculation of objective values for population +% ObjVSel - (optional) Column vector containing the objective values +% of the offspring (SelCh) in the current population, needed for +% partial insertion of offspring, +% saves recalculation of objective values for population +% +% Output parameters: +% Chrom - Matrix containing the individuals of the current +% population after reinsertion. +% ObjVCh - if ObjVCh and ObjVSel are input parameter, than column +% vector containing the objective values of the individuals +% of the current generation after reinsertion. + +% Author: Hartmut Pohlheim +% History: 10.03.94 file created +% 19.03.94 parameter checking improved + +function [Chrom, ObjVCh] = reins(Chrom, SelCh, SUBPOP, InsOpt, ObjVCh, ObjVSel); + + +% Check parameter consistency + if nargin < 2, error('Not enough input parameter'); end + if (nargout == 2 & nargin < 6), error('Input parameter missing: ObjVCh and/or ObjVSel'); end + + [NindP, NvarP] = size(Chrom); + [NindO, NvarO] = size(SelCh); + + if nargin == 2, SUBPOP = 1; end + if nargin > 2, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (NindP/SUBPOP) ~= fix(NindP/SUBPOP), error('Chrom and SUBPOP disagree'); end + if (NindO/SUBPOP) ~= fix(NindO/SUBPOP), error('SelCh and SUBPOP disagree'); end + NIND = NindP/SUBPOP; % Compute number of individuals per subpopulation + NSEL = NindO/SUBPOP; % Compute number of offspring per subpopulation + + IsObjVCh = 0; IsObjVSel = 0; + if nargin > 4, + [mO, nO] = size(ObjVCh); + if nO ~= 1, error('ObjVCh must be a column vector'); end + if NindP ~= mO, error('Chrom and ObjVCh disagree'); end + IsObjVCh = 1; + end + if nargin > 5, + [mO, nO] = size(ObjVSel); + if nO ~= 1, error('ObjVSel must be a column vector'); end + if NindO ~= mO, error('SelCh and ObjVSel disagree'); end + IsObjVSel = 1; + end + + if nargin < 4, INSR = 1.0; Select = 0; end + if nargin >= 4, + if isempty(InsOpt), INSR = 1.0; Select = 0; + elseif isnan(InsOpt), INSR = 1.0; Select = 0; + else + INSR = NaN; Select = NaN; + if (length(InsOpt) > 2), error('Parameter InsOpt too long'); end + if (length(InsOpt) >= 1), Select = InsOpt(1); end + if (length(InsOpt) >= 2), INSR = InsOpt(2); end + if isnan(Select), Select = 0; end + if isnan(INSR), INSR =1.0; end + end + end + + if (INSR < 0 | INSR > 1), error('Parameter for insertion rate must be a scalar in [0, 1]'); end + if (INSR < 1 & IsObjVSel ~= 1), error('For selection of offspring ObjVSel is needed'); end + if (Select ~= 0 & Select ~= 1), error('Parameter for selection method must be 0 or 1'); end + if (Select == 1 & IsObjVCh == 0), error('ObjVCh for fitness-based exchange needed'); end + + if INSR == 0, return; end + NIns = min(max(floor(INSR*NSEL+.5),1),NIND); % Number of offspring to insert + +% perform insertion for each subpopulation + for irun = 1:SUBPOP, + % Calculate positions in old subpopulation, where offspring are inserted + if Select == 1, % fitness-based reinsertion + [Dummy, ChIx] = sort(-ObjVCh((irun-1)*NIND+1:irun*NIND)); + else % uniform reinsertion + [Dummy, ChIx] = sort(rand(NIND,1)); + end + PopIx = ChIx((1:NIns)')+ (irun-1)*NIND; + % Calculate position of Nins-% best offspring + if (NIns < NSEL), % select best offspring + [Dummy,OffIx] = sort(ObjVSel((irun-1)*NSEL+1:irun*NSEL)); + else + OffIx = (1:NIns)'; + end + SelIx = OffIx((1:NIns)')+(irun-1)*NSEL; + % Insert offspring in subpopulation -> new subpopulation + Chrom(PopIx,:) = SelCh(SelIx,:); + if (IsObjVCh == 1 & IsObjVSel == 1), ObjVCh(PopIx) = ObjVSel(SelIx); end + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/REP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/REP.M" index ba187d520acfadd5aa12492f6861b2f74094cff6..9255c007f35ec19293b0a3abbeed12f5e6829db1 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/REP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/REP.M" @@ -1,3 +1,46 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:78ec47d1d557452415eae600d8b8bfb01621fc1a319e1f8c8e62d45b887ef7c7 -size 1208 +% REP.m Replicate a matrix +% +% This function replicates a matrix in both dimensions. +% +% Syntax: MatOut = rep(MatIn,REPN); +% +% Input parameters: +% MatIn - Input Matrix (before replicating) +% +% REPN - Vector of 2 numbers, how many replications in each dimension +% REPN(1): replicate vertically +% REPN(2): replicate horizontally +% +% Example: +% +% MatIn = [1 2 3] +% REPN = [1 2]: MatOut = [1 2 3 1 2 3] +% REPN = [2 1]: MatOut = [1 2 3; +% 1 2 3] +% REPN = [3 2]: MatOut = [1 2 3 1 2 3; +% 1 2 3 1 2 3; +% 1 2 3 1 2 3] +% +% Output parameter: +% MatOut - Output Matrix (after replicating) +% + +% Author: Carlos Fonseca & Hartmut Pohlheim +% History: 14.02.94 file created + + +function MatOut = rep(MatIn,REPN) + +% Get size of input matrix + [N_D,N_L] = size(MatIn); + +% Calculate + Ind_D = rem(0:REPN(1)*N_D-1,N_D) + 1; + Ind_L = rem(0:REPN(2)*N_L-1,N_L) + 1; + +% Create output matrix + MatOut = MatIn(Ind_D,Ind_L); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RESPLOT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RESPLOT.M" index dd669edea0aa1ce64db0c9e5e2ad3c1feb6fc9a1..f7ee499f07fed7997d04dc353d0e5662081c9a3b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RESPLOT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RESPLOT.M" @@ -1,3 +1,56 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f1c65ba1bd79521d9bd0ce65a2a5381bed89e3e767071ca11c95dd781c637622 -size 2080 +% RESPLOT.M (RESult PLOTing) +% +% This function plots some results during computation. +% +% Syntax: resplot(Chrom,IndAll,ObjV,Best,gen) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each line corresponds to one individual. +% IndAll - Matrix containing the best individual (variables) of each +% generation. Each line corresponds to one individual. +% ObjV - Vector containing objective values of the current +% generation +% Best - Matrix containing the best and average Objective values of +% each generation, [best value per generation,average value +% per generation] +% gen - Scalar containing the number of the current generation +% +% Output parameter: +% no output parameter + +% Author: Hartmut Pohlheim +% History: 27.11.93 file created +% 29.11.93 decision, if plot or not deleted +% yscale not log +% 15.12.93 MutMatrix as parameter and plot added +% 16.03.94 function cleaned, MutMatrix removed, IndAll added + +function resplot(Chrom,IndAll,ObjV,Best,gen); + + % plot of best and mean value per generation + subplot(2,2,1), plot(Best); + title('Best and mean objective value'); + xlabel('generation'), ylabel('objective value'); + + % plot of best individuals in all generations + subplot(2,2,2), plot(IndAll); + title(['Best individuals']); + xlabel('generation'), ylabel('value of variable'); + + % plot of variables of all individuals in current generation + subplot(2,2,3), plot(Chrom'); + title(['All individuals in gen ',num2str(gen)]); + xlabel('number of variable'), ylabel('value of variable'); + + % plot of all objective values in current generation + subplot(2,2,4), plot(ObjV,'y.'); + title(['All objective values']); + xlabel('number of individual'), ylabel('objective value'); + + drawnow; + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RWS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RWS.M" index cf4492cf5a6688a9b9ec9c0c9480172a101cdd56..f6d5c146d5cea92cee0d560fac2cfadb4397d9c4 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RWS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/RWS.M" @@ -1,3 +1,31 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1b6fe643ae24bb2a32e135ec0f2d88a2b0b62fa7261b19b427315020161ce7e2 -size 1090 +% RWS.m - Roulette Wheel Selection +% +% Syntax: +% NewChrIx = rws(FitnV, Nsel) +% +% This function selects a given number of individuals Nsel from a +% population. FitnV is a column vector containing the fitness +% values of the individuals in the population. +% +% The function returns another column vector containing the +% indexes of the new generation of chromosomes relative to the +% original population matrix, shuffled. The new population, ready +% for mating, can be obtained by calculating +% OldChrom(NewChrIx, :). + +% Author: Carlos Fonseca, Updated: Andrew Chipperfield +% Date: 04/10/93, Date: 27-Jan-94 + +function NewChrIx = rws(FitnV,Nsel); + +% Identify the population size (Nind) +[Nind,ans] = size(FitnV); + +% Perform Stochastic Sampling with Replacement +cumfit = cumsum(FitnV); +trials = cumfit(Nind) .* rand(Nsel, 1); +Mf = cumfit(:, ones(1, Nsel)); +Mt = trials(:, ones(1, Nind))'; +[NewChrIx, ans] = find(Mt < Mf & ... + [ zeros(1, Nsel); Mf(1:Nind-1, :) ] <= Mt); + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SCALING.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SCALING.M" index 63238cf32b4aa039a9d27dbcc84843a125aea408..fe854dacc550cd57add8e1c9d7ce5d752c347a69 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SCALING.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SCALING.M" @@ -1,3 +1,52 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9f95050c5b2cedddd9606d27edcf0515f83f9b2fec85a1090d30180e24b0a09b -size 1270 +% SCALING.m - linear fitness scaling +% +% This function implements a linear fitness scaling algorithm as described +% by Goldberg in "Genetic Algorithms in Search, Optimization and Machine +% Learning", Addison Wesley, 1989. It use is not recommended when fitness +% functions produce negative results as the scaling will become unreliable. +% It is included in this version of the GA Toolbox only for the sake of +% completeness. +% +% Syntax: FitnV = scaling(ObjV, Smul) +% +% Input parameters: +% +% Objv - A vector containing the values of individuals +% fitness. +% +% Smul - Optional scaling parameter (default 2). +% +% Output parameters: +% +% FitnV - A vector containing the individual fitnesses +% for the current population. +% +% + +% Author: Andrew Chipperfield +% Date: 24-Feb-94 + + +function FitnV = scaling( ObjV, Smul ) + +if nargin == 1 + Smul = 2 ; +end + +[Nind, Nobj] = size( ObjV ) ; +Oave = sum( ObjV ) / Nind ; +Omin = min( ObjV ) ; +Omax = max( ObjV ) ; + +if (Omin > ( Smul * Oave - Omax ) / ( Smul - 1.0 )) + delta = Omax - Oave + a = ( Smul - 1.0 ) * Oave / delta + b = Oave * ( Omax - Smul * Oave ) / delta +else + delta = Oave - Omin ; + a = Oave / delta ; + b = -Omin * Oave / delta ; +end + +FitnV = ObjV.*a + b ; + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SELECT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SELECT.M" index 0c07bdf5a26a41687e8ba64a5b74b82505c28917..627fb50670a6f88d991badf5802655b60849f39a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SELECT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SELECT.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:93e9c1b839da6ecb637ea9004d21115ecb1084036ee1372172393ad8da6588be -size 2401 +% SELECT.M (universal SELECTion) +% +% This function performs universal selection. The function handles +% multiple populations and calls the low level selection function +% for the actual selection process. + +% +% Syntax: SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP) +% +% Input parameters: +% SEL_F - Name of the selection function +% Chrom - Matrix containing the individuals (parents) of the current +% population. Each row corresponds to one individual. +% FitnV - Column vector containing the fitness values of the +% individuals in the population. +% GGAP - (optional) Rate of individuals to be selected +% if omitted 1.0 is assumed +% SUBPOP - (optional) Number of subpopulations +% if omitted 1 subpopulation is assumed +% +% Output parameters: +% SelCh - Matrix containing the selected individuals. + +% Author: Hartmut Pohlheim +% History: 10.03.94 file created + +function SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); + +% Check parameter consistency + if nargin < 3, error('Not enough input parameter'); end + + % Identify the population size (Nind) + [NindCh,Nvar] = size(Chrom); + [NindF,VarF] = size(FitnV); + if NindCh ~= NindF, error('Chrom and FitnV disagree'); end + if VarF ~= 1, error('FitnV must be a column vector'); end + + if nargin < 5, SUBPOP = 1; end + if nargin > 4, + if isempty(SUBPOP), SUBPOP = 1; + elseif isnan(SUBPOP), SUBPOP = 1; + elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end + end + + if (NindCh/SUBPOP) ~= fix(NindCh/SUBPOP), error('Chrom and SUBPOP disagree'); end + Nind = NindCh/SUBPOP; % Compute number of individuals per subpopulation + + if nargin < 4, GGAP = 1; end + if nargin > 3, + if isempty(GGAP), GGAP = 1; + elseif isnan(GGAP), GGAP = 1; + elseif length(GGAP) ~= 1, error('GGAP must be a scalar'); + elseif (GGAP < 0), error('GGAP must be a scalar bigger than 0'); end + end + +% Compute number of new individuals (to select) + NSel=max(floor(Nind*GGAP+.5),2); + +% Select individuals from population + SelCh = []; + for irun = 1:SUBPOP, + FitnVSub = FitnV((irun-1)*Nind+1:irun*Nind); + ChrIx=feval(SEL_F, FitnVSub, NSel)+(irun-1)*Nind; + SelCh=[SelCh; Chrom(ChrIx,:)]; + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SGA.M" index a4af7ee703999c688081450150f035bb8c700c88..f01cd948dda399b04bca0504e66130f036e4f77a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SGA.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ed469760636b72242f946ec8e3a852688c48ba5f6059ae2835a4fff3bda61b56 -size 2143 +% sga +% +% This script implements the Simple Genetic Algorithm described +% in the examples section of the GA Toolbox manual. +% + +% Author: Andrew Chipperfield +% History: 23-Mar-94 file created + + +NIND = 40; % Number of individuals per subpopulations +MAXGEN = 300; % maximum Number of generations +GGAP = .9; % Generation gap, how many new individuals are created +NVAR = 20; % Generation gap, how many new individuals are created +PRECI = 20; % Precision of binary representation + +% Build field descriptor + FieldD = [rep([PRECI],[1, NVAR]); rep([-512;512],[1, NVAR]);... + rep([1; 0; 1 ;1], [1, NVAR])]; + +% Initialise population + Chrom = crtbp(NIND, NVAR*PRECI); + +% Reset counters + Best = NaN*ones(MAXGEN,1); % best in current population + gen = 0; % generational counter + +% Evaluate initial population + ObjV = objfun1(bs2rv(Chrom,FieldD)); + +% Track best individual and display convergence + Best(gen+1) = min(ObjV); + plot(log10(Best),'ro');xlabel('generation'); ylabel('log10(f(x))'); + text(0.5,0.95,['Best = ', num2str(Best(gen+1))],'Units','normalized'); + drawnow; + + +% Generational loop + while gen < MAXGEN, + + % Assign fitness-value to entire population + FitnV = ranking(ObjV); + + % Select individuals for breeding + SelCh = select('sus', Chrom, FitnV, GGAP); + + % Recombine selected individuals (crossover) + SelCh = recombin('xovsp',SelCh,0.7); + + % Perform mutation on offspring + SelCh = mut(SelCh); + + % Evaluate offspring, call objective function + ObjVSel = objfun1(bs2rv(SelCh,FieldD)); + + % Reinsert offspring into current population + [Chrom ObjV]=reins(Chrom,SelCh,1,1,ObjV,ObjVSel); + + % Increment generational counter + gen = gen+1; + + % Update display and record current best individual + Best(gen+1) = min(ObjV); + plot(log10(Best),'ro'); xlabel('generation'); ylabel('log10(f(x))'); + text(0.5,0.95,['Best = ', num2str(Best(gen+1))],'Units','normalized'); + drawnow; + end +% End of GA + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SUS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SUS.M" index c2c69374c32708ede202103d0a783a53d3c7d5f2..89f38577421926d597bc7ed205077935033220ad 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SUS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/SUS.M" @@ -1,3 +1,41 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2b10ad5906524d4e218787b0fb5d1f3c52c24cc66dc847d05fd714d0f0b01d9a -size 1319 +% SUS.M (Stochastic Universal Sampling) +% +% This function performs selection with STOCHASTIC UNIVERSAL SAMPLING. +% +% Syntax: NewChrIx = sus(FitnV, Nsel) +% +% Input parameters: +% FitnV - Column vector containing the fitness values of the +% individuals in the population. +% Nsel - number of individuals to be selected +% +% Output parameters: +% NewChrIx - column vector containing the indexes of the selected +% individuals relative to the original population, shuffled. +% The new population, ready for mating, can be obtained +% by calculating OldChrom(NewChrIx,:). + +% Author: Hartmut Pohlheim (Carlos Fonseca) +% History: 12.12.93 file created +% 22.02.94 clean up, comments + + +function NewChrIx = sus(FitnV,Nsel); + +% Identify the population size (Nind) + [Nind,ans] = size(FitnV); + +% Perform stochastic universal sampling + cumfit = cumsum(FitnV); + trials = cumfit(Nind) / Nsel * (rand + (0:Nsel-1)'); + Mf = cumfit(:, ones(1, Nsel)); + Mt = trials(:, ones(1, Nind))'; + [NewChrIx, ans] = find(Mt < Mf & [ zeros(1, Nsel); Mf(1:Nind-1, :) ] <= Mt); + +% Shuffle new population + [ans, shuf] = sort(rand(Nsel, 1)); + NewChrIx = NewChrIx(shuf); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/DEMOGA1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/DEMOGA1.M" index 24fe9f60580009447a287314da5bcb113ae8820f..84cdcafa128f15fc5ddadf499aa5e8f7165e0168 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/DEMOGA1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/DEMOGA1.M" @@ -1,3 +1,118 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8c93f0a6c891265b64430b43ee597e54872267bde5189c2200cec9397548cb01 -size 5035 +% DEMOGA1.M (DEMO of Genetic Algorithms 1) +% +% This function displays a number of figures. Select a number of these +% figures with the mouse by click in the area of the shape. These +% figure are the parents for the next generation. The offspring are +% created by recombination and mutation. The user is the selector. +% +% The shape of the figures is defined by Points X- and Y-values each. +% These points are ploted by patch(), each figure in a rectangle. +% The X- and Y-values are the variables of a individual. +% +% Aim of this demo is, to "construct" a special figure, e.g. a square +% or a star or ..., imagine, what you want and select appropriate. +% +% Parameters inside function for changing: +% Num - Number of figures (4, 9, 16, 25, ...) +% Points - Number of Points per figure (3, 4, 5...), 5 recommended +% MAXGEN - Number of generations (more than 30 recommended) +% +% Syntax: demoga1(); +% +% Input parameters: +% no input parameter +% Output parameter: +% no output parameter + +% Author: Hartmut Pohlheim +% History: 24.03.94 file created + + +function demoga1(); + +Num = 16; % Number of figures +Points = 6; % Number of points per figure +MAXGEN = 30; % Number of generations +FieldDR = rep([0; 1], [1 Points]); % Fielddescription for mutation + +% Function needs as many rows as columns, every place has to be filled +if sqrt(Num) ~= ceil(sqrt(Num)), + error('sqrt(Num) must be an integer'); +end + +ColRowNum = ceil(sqrt(Num)); % Number of columns and rows +Shrink=Num/ColRowNum; % Value for shrinking of area +SelectNumber = ColRowNum; % Number of parents by selection + +Cols = 1:1:ColRowNum; % Index of individuals in first columns +Rows = 1:ColRowNum:Num; % Index of individuals in first row + +h = figure; % Open a new figure for output +axes('Position',[0 0 1 1]); % Set axes to whole figure +set(gca, 'xcolor',[0 0 0]); % Make X-Axis invisible +set(gca, 'ycolor',[0 0 0]); % Make Y-Axis invisible +axis('ij'); % Position start in left-upper corner +axis(axis); % Freeze axes + +XStart = (Cols(1:ColRowNum-1)/Shrink); % Calculate X-start- and Y-endvalues of lines +XLine1 = [XStart; XStart]; % between figures +YLine1 = [zeros(1,ColRowNum-1); ones(1,ColRowNum-1)]; % X-end- and Y-startvalues +XLine = [XLine1 YLine1]; YLine = [YLine1 XLine1]; % Assemble line vectors + +MatX=rand(Points,Num); % Create X-values of figures at random +MatY=rand(Points,Num); % Create Y-values of figures at random + +for igen = 1:MAXGEN, % Loop over all generations + + % Recombine individuals + MatXYOff = recombin('recint', [MatX MatY]',NaN, 2); + + % Mutate individuals + MatXYOff = mutbga(MatXYOff, FieldDR, 1/Points); + + MatXYOff = MatXYOff'; % Invert matrix of individuals + MatX = MatXYOff(:,1:Num); % Select X- and Y-values + MatY = MatXYOff(:,size(MatXYOff,2)/2+1:size(MatXYOff,2)/2+Num); + + PolyMatX = MatX / Shrink; % Shrink X-values for fitting in small area + PolyMatY = MatY / Shrink; % Shrink Y-values for fitting in small area + + % Add a value to the X-value for placing individual in the appropriate column + for irun = 1:ColRowNum-1, + PolyMatX(:,Rows+irun)=PolyMatX(:,Rows+irun)+(irun)/Shrink; + end + + % Add a value to the Y-value for placing individual in the appropriate row + for irun = 1:ColRowNum-1, + PolyMatY(:,Cols+(irun*ColRowNum))= ... + PolyMatY(:,Cols+(irun*ColRowNum))+(irun)/Shrink; + end + + cla; % Clear axes, removes all earlier figures + patch(PolyMatX,PolyMatY,'b'); % Plot shape of figures + lh = line(XLine, YLine); % Plot lines between figures + set(lh,'Color',[.6 .6 .6]); % Set linecolor to grey + + xclick = []; yclick = []; % Reset vectors for storing click points + for isel = 1:SelectNumber, % Loop for as many points as individuals to select + set(gcf,'Name',[ ' Select ' int2str(isel) '. figure (of ' ... + int2str(SelectNumber) ') with mouseclick (Generation ' ... + int2str(igen) ' of ' int2str(MAXGEN) ')']); + [xclick1 yclick1] = ginput(1); % get position of mouse click + xclick = [xclick; xclick1]; yclick = [yclick; yclick1]; % add position to vectors + end + + xpos = ceil(xclick * Shrink); % Calculate column of mouse click + ypos = ceil(yclick * Shrink); % Calculate row of mouse click + + SelNumber = xpos + ColRowNum * (ypos-1); % Calculate numbers of selected figures + + % select X- and Y-values of individuals and repeat them + MatX = rep(MatX(:,SelNumber),[1 ceil(Num/SelectNumber)]); + MatY = rep(MatY(:,SelNumber),[1 ceil(Num/SelectNumber)]); + +end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/MPGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/MPGA.M" index 2a177f22c771a9962e156f4b3330f936527005ea..b3ebdaeaa4d52bea2d5cec4b7857437189ceee6e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/MPGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/MPGA.M" @@ -1,3 +1,127 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c2f727ca711d45d9d3092595193ceb9f562b7dac9a509abb74694ecb1b8a31aa -size 4726 +% MPGA.M (Multi Population Genetic Algorithm) +% +% This script implements the Multi Population Genetic Algorithm. +% Real valued representation for the individuals is used. +% +% Author: Hartmut Pohlheim +% History: 23.03.94 file created + +GGAP = .8; % Generation gap, how many new individuals are created +INSR = .9; % Insertion rate, how many of the offspring are inserted +XOVR = 1; % Crossover rate +SP = 2; % Selective Pressure +MUTR = 1; % Mutation rate; only a factor; +MIGR = 0.2; % Migration rate between subpopulations +MIGGEN = 20; % Number of generations between migration (isolation time) + +TERMEXACT = 1e-4; % Value for termination if minimum reached + +SEL_F = 'sus'; % Name of selection function +XOV_F = 'recdis'; % Name of recombination function for individuals +MUT_F = 'mutbga'; % Name of mutation function + +OBJ_F = 'objharv'; % Name of function for objective values + +% Get boundaries of objective function + FieldDR = feval(OBJ_F,[],1); + +% compute SUBPOP, NIND depending on number of variables (defined in objective function) + NVAR = size(FieldDR,2); % Get number of variables from objective function + SUBPOP = 2 * floor(sqrt(NVAR)); % Number of subpopulations + NIND = 20 + 5 * floor(NVAR/50); % Number of individuals per subpopulations + MAXGEN = 300 * floor(sqrt(NVAR)); % Maximal number of generations + MUTR = MUTR / NVAR; % Mutation rate depending on NVAR + +% Get value of minimum, defined in objective function + GlobalMin = feval(OBJ_F,[],3); + +% Get title of objective function, defined in objective function + FigTitle = [feval(OBJ_F,[],2) ' (' int2str(SUBPOP) ':' int2str(MAXGEN) ') ']; + +% Clear Best and storing matrix + % Initialise Matrix for storing best results + Best = NaN * ones(MAXGEN,3); + Best(:,3) = zeros(size(Best,1),1); + % Matrix for storing best individuals + IndAll = []; + +% Create real population + Chrom = crtrp(SUBPOP*NIND,FieldDR); + +% reset count variables + gen = 0; + termopt = 0; + +% Calculate objective function for population + ObjV = feval(OBJ_F,Chrom); + % count number of objective function evaluations + Best(gen+1,3) = Best(gen+1,3) + NIND; + +% Iterate subpopulation till termination or MAXGEN + while ((gen < MAXGEN) & (termopt == 0)), + + % Save the best and average objective values and the best individual + [Best(gen+1,1),ix] = min(ObjV); + Best(gen+1,2) = mean(ObjV); + IndAll = [IndAll; Chrom(ix,:)]; + + % Fitness assignement to whole population + FitnV = ranking(ObjV,[2 0],SUBPOP); + + % Select individuals from population + SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); + + % Recombine selected individuals + SelCh=recombin(XOV_F, SelCh, XOVR, SUBPOP); + + % Mutate offspring + SelCh=mutate(MUT_F, SelCh, FieldDR, [MUTR], SUBPOP); + + % Calculate objective function for offsprings + ObjVOff = feval(OBJ_F,SelCh); + Best(gen+1,3) = Best(gen+1,3) + size(SelCh,1); + + % Insert best offspring in population replacing worst parents + [Chrom, ObjV] = reins(Chrom, SelCh, SUBPOP, [1 INSR], ObjV, ObjVOff); + + gen=gen+1; + + % Plot some results, rename title of figure for graphic output + if ((rem(gen,20) == 1) | (rem(gen,MAXGEN) == 0) | (termopt == 1)), + set(gcf,'Name',[FigTitle ' in ' int2str(gen)]); + resplot(Chrom(1:2:size(Chrom,1),:),... + IndAll(max(1,gen-39):size(IndAll,1),:),... + [ObjV; GlobalMin], Best(max(1,gen-19):gen,[1 2]), gen); + end + + % Check, if best objective value near GlobalMin -> termination criterion + % compute differenz between GlobalMin and best objective value + ActualMin = abs(min(ObjV) - GlobalMin); + % if ActualMin smaller than TERMEXACT --> termination + if ((ActualMin < (TERMEXACT * abs(GlobalMin))) | (ActualMin < TERMEXACT)) + termopt = 1; + end + + % migrate individuals between subpopulations + if ((termopt ~= 1) & (rem(gen,MIGGEN) == 0)) + [Chrom, ObjV] = migrate(Chrom, SUBPOP, [MIGR, 1, 0], ObjV); + end + + end + + +% Results + % add number of objective function evaluations + Results = cumsum(Best(1:gen,3)); + % number of function evaluation, mean and best results + Results = [Results Best(1:gen,2) Best(1:gen,1)]; + +% Plot Results and show best individuals => optimum + figure('Name',['Results of ' FigTitle]); + subplot(2,1,1), plot(Results(:,1),Results(:,2),'-',Results(:,1),Results(:,3),':'); + subplot(2,1,2), plot(IndAll(gen-4:gen,:)'); + + +% End of script + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJBRAN.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJBRAN.M" index e1584434e51a3abe3c95cedcd4daab0651090282..6a5ddff67b3363e96657402d9689ef40729d44ee 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJBRAN.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJBRAN.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8cff116c0c77ce82edb0fe38de3c3b5d53b1862a196c4cec016126fba51dd19d -size 2529 +% OBJBRAN.M (OBJective function for BRANin RCOS function) +% +% This function implements the BRANIN RCOS function. +% +% Syntax: ObjVal = objbran(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 27.11.93 text of title and switch added +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objbran(Chrom,switch); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [] + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = 'BRANINs RCOS function'; + % return value of global minimum + elseif switch == 3 + ObjVal = 0.397887; + % define size of boundary-matrix and values + else + % x1 x2 + ObjVal = [-5 0; % lower bounds + 10 15]; % upper bounds + end + % if two variables, compute values of function + elseif Nvar == 2 + % BRANIN's RCOS function + % -5 <= x1 <= 10 ; 0 <= x2 <= 15 + % global minimum at (x1,x2)=(-pi,12.275), (pi,2.275), and + % (9.42478,2.475) ; fmin=0.397887 + x1 = Chrom(:,1); + x2 = Chrom(:,2); + ObjVal = 1*(x2-(5.1/(4*pi^2))*x1.^2+(5/pi)*x1-6).^2+10*(1-(1/(8*pi))).*cos(x1)+10; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJDOPI.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJDOPI.M" index 6a5f5bf34ff44d4dc42aa07450bc7de00c798b8e..26acff5e574808777876dbce4c1d9b80d00f4574 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJDOPI.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJDOPI.M" @@ -1,3 +1,107 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:12d7bdb0c861db2fc742355bc7873e2f6036ac90c685f502a99a056e20de58cf -size 4077 +% OBJDOPI.M (OBJective function for DOuble Integrator) +% +% This function implements the Double Integrator. +% +% Syntax: ObjVal = objdopi(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 17.12.93 file created (copy of valfun7.m) +% 19.12.93 Dim reintroduced +% Dim and STEPSIMU independend from each other, rk23 +% can compute control between times +% 01.03.94 name changed in obj* +% 05.04.94 trapz used + +function [ObjVal,t,x] = objdopi(Chrom,switch1); + +% Define used method + method = 1; % 1 - sim: simulink model + % 2 - ode: ordinary differential equations + % 3 - con: transfer function to state space + +% Dimension of objective function + Dim = 20; + TSTART = 0; + TEND = 1; + STEPSIMU = min(0.1,abs((TEND-TSTART)/(Dim-1))); + TIMEVEC = linspace(TSTART,TEND,Dim)'; + +% initial conditions + XINIT = [ 0; -1]; + +% end conditions + XEND = [ 0; 0]; + +% weights for control and end + XENDWEIGHT = 12 * [1; 1]; % XEND(1); XEND(2) + UWEIGHT = [0.5]; % Control vector + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then + if Nind == 0 + % return text of title for graphic output + if switch1 == 2 + if method == 2, ObjVal = ['Double Integrator (ode)-' int2str(Dim)]; + elseif method == 3, ObjVal = ['Double Integrator (con)-' int2str(Dim)]; + else ObjVal = ['Double Integrator (sim)-' int2str(Dim)]; + end + % return value of global minimum + elseif switch1 == 3 + ObjVal = 2; % UWEIGHT * 3 * (TEND - TSTART); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal1 = [-15; 15]; + ObjVal = rep(ObjVal1,[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + if method == 3, % Convert transfer function to state space system + [Ai2 Bi2 Ci2 Di2] = tf2ss(1, [1 0 0]); + t = TIMEVEC; + end + ObjVal = zeros(Nind,1); + for indrun = 1:Nind + steuerung = [TIMEVEC [Chrom(indrun,:)]']; + if method == 2, + [t x] = rk23('simdopi2',[TSTART TEND],XINIT,[1e-3;STEPSIMU;STEPSIMU],steuerung); + elseif method == 3, + [y x] = lsim(Ai2, Bi2, Ci2, Di2, Chrom(indrun,:),TIMEVEC, XINIT); + else + [t x] = rk23('simdopi1',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); + end + % Calculate objective function, endvalues, trapez-integration for control vector + ObjVal(indrun) = sum(XENDWEIGHT .* abs( x(size(x,1),:)' - XEND )) + ... + (UWEIGHT / (Dim-1) * trapz(Chrom(indrun,:).^2)); + end + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJEASO.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJEASO.M" index d5cf20f38293d617f40e57f10c40ea9132f52d13..ca51b7f221a7003afee3c76865509141792df7dd 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJEASO.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJEASO.M" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:038c5bb2a6c7567435818ba7da42a9f0f4a39c648cd1e7f061a84f952582938e -size 2427 +% OBJEASO.M (OBJective function for EASom function) +% +% This function implements the EASOM function. +% +% Syntax: ObjVal = objeaso(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 27.11.93 text of title and switch added +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + + +function ObjVal = objeaso(Chrom,switch); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [] + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = 'EASOMs function'; + % return value of global minimum + elseif switch == 3 + ObjVal = -1; + % define size of boundary-matrix and values + else + % x1 x2 + ObjVal = [-100 -100; % lower bounds + 100 100]; % upper bounds + end + % if two variables, compute values of function + elseif Nvar == 2 + % EASOM's function + % -100(-5) <= x1 <= 100(5) ; -100(-5) <= x2 <= 100(5) + % global minimum at (x1,x2)=(pi,pi) ; fmin=-1 + x1 = Chrom(:,1); + x2 = Chrom(:,2); + ObjVal = -cos(x1).*cos(x2).*exp(-((x1-pi).^2+(x2-pi).^2)); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1.M" index c82d90eb2884a47986207d1b3590df3a3ff9f6b5..05934f8cf7d8e372aadee7c1aacff10aa59a71a3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1.M" @@ -1,3 +1,71 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:70cd1dad619ec59d82150e5357de52a5410d02dafc8bfc43642d3ace77cd4ca7 -size 2632 +% OBJFUN1.M (OBJective function for de jong's FUNction 1) +% +% This function implements the DE JONG function 1. +% +% Syntax: ObjVal = objfun1(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 26.11.93 file created +% 27.11.93 text of title and switch added +% 30.11.93 show Dim in figure titel +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objfun1(Chrom,switch1); + +% Dimension of objective function + Dim = 20; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch1 == 2 + ObjVal = ['DE JONG function 1-' int2str(Dim)]; + % return value of global minimum + elseif switch1 == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = 100*[-5.12; 5.12]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 1, sum of xi^2 for i = 1:Dim (Dim=30) + % n = Dim, -5.12 <= xi <= 5.12 + % global minimum at (xi)=(0) ; fmin=0 + ObjVal = sum((Chrom .* Chrom)')'; + % ObjVal = diag(Chrom * Chrom'); % both lines produce the same + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1A.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1A.M" index 92911f849cc4a3ae8cf1515e2c15e42a9de4f7f9..7ecf1528deceac63936915fc669afad80baa0b57 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1A.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1A.M" @@ -1,3 +1,68 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:335e74ac50e7b5fa5eeb6732ab08d3c7258a88ba8615e4b9b75655fed29b20eb -size 2501 +% OBJFUN1A.M (OBJective function for axis parallel hyper-ellipsoid) +% +% This function implements the axis parallel hyper-ellipsoid. +% +% Syntax: ObjVal = objfun1a(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 07.04.94 file created + +function ObjVal = objfun1a(Chrom,switch); + +% Dimension of objective function + Dim = 10; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['Axis Parallel Hyper-Ellipsoid 1a-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = 100*[-5.12; 5.12]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 1a, sum of i * xi^2 for i = 1:Dim (Dim=30) + % n = Dim, -5.12 <= xi <= 5.12 + % global minimum at (xi)=(0) ; fmin=0 + nummer = rep(1:Dim,[Nind 1]); + ObjVal = sum((nummer .* (Chrom .* Chrom))')'; + % ObjVal = diag((nummer .* (Chrom * Chrom))'); % both lines produce the same + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1B.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1B.M" index c02207ca72b8faa14ed2e348db5ff32f3d2f6f5e..eba7140333b8d5d9a6f1349bb1ab678af4b17329 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1B.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN1B.M" @@ -1,3 +1,66 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9ec112b6d95a471539bfeaa4614e10c249dd5e200240eb1d8fd094e572d5a0c6 -size 2360 +% OBJFUN1B.M (OBJective function for rotated hyper-ellipsoid) +% +% This function implements the rotated hyper-ellipsoid. +% +% Syntax: ObjVal = objfun1b(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 07.04.94 file created + +function ObjVal = objfun1b(Chrom,switch); + +% Dimension of objective function + Dim = 10; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['Rotated Hyper-Ellipsoid 1b-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-65; 65]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 1b, sum over i of ( sum of xj )^2 for i = 1:Dim, j = 1:i (Dim=30) + % n = Dim, -65 <= xj <= 65 + % global minimum at (xi)=(0) ; fmin=0 + ObjVal = sum(cumsum(Chrom').^2)'; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN2.M" index b2462f4af9a069e3720c222426ae483fd27010c1..fab9da9cd44282815f8debaf8637fd24a3a4a225 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN2.M" @@ -1,3 +1,72 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9c23916aaee358f3bff7e371882a0278ee1b6e002d613b9436b65f0e9fc4946d -size 2522 +% OBJFUN2.M (OBJective function for rosenbrock's FUNction) +% +% This function implements the ROSENBROCK valley (DE JONG's Function 2). +% +% Syntax: ObjVal = objfun2(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one +% individual's string representation. +% if called with Chrom == [], then boundaries of +% the function or title for figure will be returned +% switch - if Chrom == [] and switch == 1 (or []) then return +% boundaries, if switch == 2 return title +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% the matrix with the boundaries of the function or +% the Text for the title of the graphic output +% + +% Author: Hartmut Pohlheim +% History: 26.01.94 file created +% 01.03.94 name changed in obj* + + +function ObjVal = objfun2(Chrom,switch); + +% Dimension of objective function + Dim = 2; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['ROSENBROCKs function 2-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-2; 2]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 11, sum of 100* (x(i+1) -xi^2)^2+(1-xi)^2 for i = 1:Dim (Dim=10) + % n = Dim, -10 <= xi <= 10 + % global minimum at (xi)=(1) ; fmin=0 + Mat1 = Chrom(:,1:Nvar-1); + Mat2 = Chrom(:,2:Nvar); + if Dim == 2 + ObjVal = 100*(Mat2-Mat1.^2).^2+(1-Mat1).^2; + else + ObjVal = sum((100*(Mat2-Mat1.^2).^2+(1-Mat1).^2)')'; + end + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN6.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN6.M" index ed9f13b8b8cbdca7d3bf43c1dcda0306ecece6ba..f03c49ceba5258fbe72ddde19001721144f50600 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN6.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN6.M" @@ -1,3 +1,73 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9e9b9d03f1ad19c8e5b5492ff7a1e6289d6e8564d07235fa7beafc1b51c5ca5a -size 2735 +% OBJFUN6.M (OBJective function for rastrigins FUNction 6) +% +% This function implements the RASTRIGIN function 6. +% +% Syntax: ObjVal = objfun6(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 26.11.93 file created +% 27.11.93 text of title and switch added +% 30.11.93 show Dim in figure titel +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objfun6(Chrom,switch); + +% Dimension of objective function + Dim = 20; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['RASTRIGINs function 6-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-5.12; 5.12]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 6, Dim*A + sum of (xi^2 - A*cos(Omega*xi)) for i = 1:Dim (Dim=20) + % n = Dim, -5.12 <= xi <= 5.12 + % global minimum at (xi)=(0) ; fmin=0 + A = 10; + Omega = 2 * pi; + ObjVal = Dim * A + sum(((Chrom .* Chrom) - A * cos(Omega * Chrom))')'; + % ObjVal = diag(Chrom * Chrom'); % both lines produce the same + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN7.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN7.M" index cc34ec0fb8b59a72bbb07e84781e946b355833c6..c1651dfd78c5c99810a4acd6a1b66cc8aebd1979 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN7.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN7.M" @@ -1,3 +1,68 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c2d8e97be04a95910b9ef6ee144e39d018a0a8e902ffc6bc0d8dae7f9d50a3bc -size 2449 +% OBJFUN7.M (OBJective function for schwefel's FUNction) +% +% This function implements the SCHWEFEL function 7. +% +% Syntax: ObjVal = objfun7(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one +% individual's string representation. +% if called with Chrom == [], then boundaries of +% the function or title for figure will be returned +% switch - if Chrom == [] and switch == 1 (or []) then return +% boundaries, if switch == 2 return title +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% the matrix with the boundaries of the function or +% the Text for the title of the graphic output +% + +% Author: Hartmut Pohlheim +% History: 27.11.93 file created +% 30.11.93 show Dim in figure titel +% 01.03.94 name changed in obj* + + +function ObjVal = objfun7(Chrom,switch); + +% Dimension of objective function + Dim = 20; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['SCHWEFELs function 7-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + xmin = 420.9687; + ObjVal = Dim * (-xmin * sin(sqrt(abs(xmin)))); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-500; 500]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 7, sum of -xi*sin(sqrt(abs(xi))) for i = 1:Dim (Dim=10) + % n = Dim, -500 <= xi <= 500 + % global minimum at (xi)=(420.9687) ; fmin=? + ObjVal = sum((-Chrom .* sin(sqrt(abs(Chrom))))')'; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN8.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN8.M" index bba085560b0eba3b404448883add6a502f2a9939..388454c280eb7bae4b17db561a46ebcdefa42f11 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN8.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN8.M" @@ -1,3 +1,72 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:48d08e996e74eee124e3e7cd224bdf1ef1fe12dd78410276efaab2af1245f7b5 -size 2664 +% OBJFUN8.M (OBJective function for griewangk's FUNction) +% +% This function implements the GRIEWANGK function 8. +% +% Syntax: ObjVal = objfun8(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 12.12.93 file created (copy of valfun7.m) +% 16.12.93 switch == 3, return value of global minimum +% 27.01.94 20* in formula, correction ?? +% 01.03.94 name changed in obj* + + +function ObjVal = objfun8(Chrom,switch); + +% Dimension of objective function + Dim = 10; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['GRIEWANGKs function 8-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-600; 600]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 8, sum(xi^2/4000) - 20*prod(cos(xi/sqrt(i))) + 1 for i = 1:Dim (Dim=10) + % n = Dim, -600 <= xi <= 600 + % global minimum at (xi)=(0) ; fmin=0 + % nummer = 1:Dim; + nummer = rep(1:Dim,[Nind 1]); + ObjVal = sum(((Chrom.^2) / 4000)')' - prod(cos(Chrom ./ sqrt(nummer))')' + 1; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN9.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN9.M" index 4c6849502eecabec838cf9dd6387f336ba55755a..13864aeeb9d215e83f25598a2415e30d66272df1 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN9.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJFUN9.M" @@ -1,3 +1,67 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:bf0e7e8d9a68317c34ca930b133d0d156e6655425f6397d6ebad000dc4927574 -size 2386 +% OBJFUN9.M (OBJective function for sum of different power FUNction 9) +% +% This function implements the sum of different power. +% +% Syntax: ObjVal = objfun9(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 07.04.94 file created + +function ObjVal = objfun9(Chrom,switch); + +% Dimension of objective function + Dim = 10; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = ['Sum of different Power 9-' int2str(Dim)]; + % return value of global minimum + elseif switch == 3 + ObjVal = 0; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [-1; 1]; + ObjVal = ObjVal(1:2,ones(Dim,1)); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + % function 9, sum of abs(xi)^(i+1) for i = 1:Dim (Dim=30) + % n = Dim, -1 <= xi <= 1 + % global minimum at (xi)=(0) ; fmin=0 + nummer = rep(1:Dim,[Nind 1]); + ObjVal = sum((abs(Chrom).^(nummer+1))')'; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJGOLD.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJGOLD.M" index 4388b3c5b4b8ec21bedc1bc0b24a96f3ac965707..1be67cc00cb1becaee2be41c4ee2db07fcffb433 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJGOLD.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJGOLD.M" @@ -1,3 +1,71 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:683ff891777d96ffa9aa34b86b508f6a819deaf524e463c0f0b3e00a6d5745f7 -size 2615 +% OBJGOLD.M (OBJective function for GOLDstein-price function) +% +% This function implements the GOLDSTEIN-PRICE function. +% +% Syntax: ObjVal = objgold(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 27.11.93 text of title and switch added +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + + +function ObjVal = objgold(Chrom,switch); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = 'GOLDSTEIN-PRICE function'; + % return value of global minimum + elseif switch == 3 + ObjVal = 3; + % define size of boundary-matrix and values + else + brd = 3; + % x1 x2 + ObjVal = [-brd -brd; % lower bounds + brd brd]; % upper bounds + end + % if two variables, compute values of function + elseif Nvar == 2 + % GOLDSTEIN-PRICE function + % -2 <= x1 <= 2 ; -2 <= x2 <= 2 (or -10 <= xi <= 10) + % global minimum at (x1,x2)=(0,-1) ; fmin=3 + x1 = Chrom(:,1); + x2 = Chrom(:,2); + ObjVal = ((1+(x1+x2+1).^2.*(19-14*x1+3*x1.^2-14*x2+6*x1.*x2+3*x2.^2))... + .*(30+(2*x1-3*x2).^2.*(18-32*x1+12*x1.^2+48*x2-36*x1.*x2+27*x2.^2))); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJHARV.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJHARV.M" index 5ee88caa8818bf455edbc5a30ea653fdc90f7f31..c6cbd4c731e9bff1d5a5f5e9d1f4282140100214 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJHARV.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJHARV.M" @@ -1,3 +1,78 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:93c23f4d35adb4f6efa7a5e04bbd05ab30361c22d7365af23c9e997d05b7c260 -size 2563 +% OBJHARV.M (OBJective function for HARVest problem) +% +% This function implements the HARVEST PROBLEM. +% +% Syntax: ObjVal = objharv(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 18.02.94 file created (copy of vallinq.m) +% 01.03.94 name changed in obj* + +function ObjVal = objharv(Chrom,switch1); + +% global gen; + +% Dimension of objective function + Dim = 20; + +% values from MICHALEWICZ + a = 1.1; + x0 = 100; + xend = x0; + XENDWEIGHT = 0.4/(Dim^0.6); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch1 == 2 + ObjVal = ['HARVEST PROBLEM-' int2str(Dim)]; + % return value of global minimum + elseif switch1 == 3 + ObjVal = -sqrt(x0*(a^Dim-1)^2/(a^(Dim-1)*(a-1))); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal1 = [0; 10*Dim]; + ObjVal = rep(ObjVal1,[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + ObjVal = zeros(Nind,1); + X = rep(x0,[Nind 1]); + for irun = 1:Nvar, + X = a*X - Chrom(:,irun); + end + X; + ObjVal = -(sum(sqrt(Chrom)')' - XENDWEIGHT * abs(X-x0)); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJLINQ.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJLINQ.M" index 0ee9d46f9795710c4ad5ebbefd81e33cb8c8f34c..8863b1f50de2394a8b0433afe261316d2859a7f3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJLINQ.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJLINQ.M" @@ -1,3 +1,86 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:571bf5682a930e75a01cb02c7cd5be3488aec06f57c764fad16f5709dbeb2b8d -size 3300 +% OBJLINQ.M (OBJective function for LINear Quadratic problem) +% +% This function implements the discret LINEAR-QUADRATIC PROBLEM. +% +% Syntax: ObjVal = objlinq(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 18.02.94 file created (copy of valfun7.m) +% 01.03.94 name changed in obj* + +function ObjVal = objlinq(Chrom,switch1); + +% Dimension of objective function + Dim = 45; + +% values from MICHALEWICZ + x0 = 100; % start of X + var = 1; % 1 - 10 possible + Para = [ 1 1 1 1 1 16180.3399; + 10 1 1 1 1 109160.7978; + 1000 1 1 1 1 10009990.0200; + 1 10 1 1 1 37015.6212; + 1 1000 1 1 1 287569.3725; + 1 1 0 1 1 16180.3399; + 1 1 1000 1 1 16180.3399; + 1 1 1 0.01 1 10000.5000; + 1 1 1 1 0.01 431004.0987; + 1 1 1 1 100 10000.9999]; + s = Para(var,1); r = Para(var,2); q = Para(var,3); + a = Para(var,4); b = Para(var,5); GlobalMinimum = Para(var,6); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch1 == 2 + ObjVal = ['Linear-quadratic problem (dis)-' int2str(Dim)]; + % return value of global minimum + elseif switch1 == 3 + ObjVal = GlobalMinimum; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal1 = [-100 -70 -50; 20 20 20]; + ObjVal = [ObjVal1 rep([-30;20],[1 Dim-3])]; + end + % if Dim variables, compute values of function + elseif Nvar == Dim + ObjVal = zeros(Nind,1); + X = zeros(Nind,Nvar+1); + X(:,1) = rep(x0,[Nind 1]); + for irun = 1:Nvar, + X(:,irun+1) = a*X(:,irun) + b*Chrom(:,irun); + end + ObjVal = q * X(:,Nvar+1).^2 + sum((s * X(:,1:Nvar).^2 + r * Chrom.^2)')'; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJLINQ2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJLINQ2.M" index 87f94a842656df799ba059c46308f5d49b45faec..50f7f218f6b89b87f3758e816110825be1a20b8e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJLINQ2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJLINQ2.M" @@ -1,3 +1,105 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:73e21e33e6f035caad2f6e5ece899eae4fdcfd478e906fe407259566f77e5562 -size 3952 +% OBJLINQ2.M (OBJective function for LINear Quadratic problem) +% +% This function implements the continuous LINear Quadratic problem. +% +% Syntax: ObjVal = objlinq2(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then special values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 03.03.94 file created +% 06.04.94 all linq (sim, ode, con) in 1 file + +function [ObjVal,t,x] = objlinq2(Chrom,switch); + +% Define used method + method = 1; % 1 - sim: simulink model + % 2 - ode: ordinary differential equations + % 3 - con: transfer function to state space + +% Dimension of objective function + Dim = 50; + TSTART = 0; + TEND = 1; + STEPSIMU = min(0.1,abs((TEND-TSTART)/(Dim-1))); + TIMEVEC = linspace(TSTART,TEND,Dim)'; + +% initial conditions + XINIT = [100]; + +% end conditions + XEND = [0]; + +% weights for control and end + XENDWEIGHT = [20]; % XEND + XWEIGHT = [2]; % State vector + UWEIGHT = [1]; % Control vector + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then + if Nind == 0 + % return text of title for graphic output + if switch == 2 + if method == 2, ObjVal = ['Linear-quadratic problem (ode)-' int2str(Dim)]; + elseif method == 3, ObjVal = ['Linear-quadratic problem (con)-' int2str(Dim)]; + else ObjVal = ['Linear-quadratic problem (sim)-' int2str(Dim)]; + end + % return value of global minimum + elseif switch == 3 + ObjVal = 16180.3399; + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = rep([-600; 0],[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + if method == 3, % Convert transfer function to state space system + [NC DC]=cloop(1, [1 0], +1); + [Ai2 Bi2 Ci2 Di2] = tf2ss(NC, DC); + t = TIMEVEC; + end + ObjVal = zeros(Nind,1); + for indrun = 1:Nind + steuerung = [TIMEVEC Chrom(indrun,:)']; + if method == 2, + [t x] = linsim('simlinq2',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); + elseif method == 3, + [y x] = lsim(Ai2, Bi2, Ci2, Di2, Chrom(indrun,:),TIMEVEC, XINIT); + else + [t x] = linsim('simlinq1',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); + end + % Calculate objective function, endvalues, trapez-integration for control vector + ObjVal(indrun) = (XENDWEIGHT * ( x(size(x,1),:)^2 )) + ... + (UWEIGHT / (Dim-1) * trapz(Chrom(indrun,:).^2)) + ... + (XWEIGHT / size(x,1) * sum(x.^2)); + end + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJPUSH.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJPUSH.M" index c48ea470538f825fa159a3dbaa02b4d74ecc60fd..4065fc9e09dc0dd7ee14e1560e36b0c4032b7ba7 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJPUSH.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJPUSH.M" @@ -1,3 +1,75 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:59a6e95f4fb7e87fd11d02a1d9de92e71d637f3fe2d6524b9b45c235c967780b -size 2598 +% OBJPUSH.M (OBJective function for PUSH-cart problem) +% +% This function implements the PUSH-CART PROBLEM. +% +% Syntax: ObjVal = objpush(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 19.02.94 file created (copy of valharv.m) +% 01.03.94 name changed in obj* + +function ObjVal = objpush(Chrom,switch1); + +% Dimension of objective function + Dim = 20; + +% values from MICHALEWICZ + x0 = [0 0]; + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch1 == 2 + ObjVal = ['PUSH-CART PROBLEM-' int2str(Dim)]; + % return value of global minimum + elseif switch1 == 3 + ObjVal = -(1/3 - ((3*Dim-1)/(6*Dim^2)) - (1/(2*Dim^3))*sum((1:Dim-1).^2)); + % define size of boundary-matrix and values + else + % lower and upper bound, identical for all n variables + ObjVal = [0; 5]; + ObjVal = rep(ObjVal,[1 Dim]); + end + % if Dim variables, compute values of function + elseif Nvar == Dim + ObjVal = zeros(Nind,1); + X = rep(x0,[Nind 1]); + for irun = 1:Nvar, + Xsave = X; + X(:,1) = Xsave(:,2); + X(:,2) = 2 * X(:,2) - Xsave(:,1) + (1/Dim^2) * Chrom(:,irun); + end + X; + ObjVal = -(X(:,1) - (1/(2*Dim)) * sum((Chrom.^2)')'); + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJSIXH.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJSIXH.M" index c96ff94530b49a5a92f6a1efc6c43bad9818c264..5824ce29d4cefb34f64bdf625513ff255c3f40f9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJSIXH.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/OBJSIXH.M" @@ -1,3 +1,68 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:61da893b40bb39e526de184ec3e52e610b1b8af6bfae65d782fe38550d399394 -size 2525 +% OBJSIXH.M (OBJective function for SIX Hump camelback function) +% +% This function implements the six hump camelback function. +% +% Syntax: ObjVal = objsixh(Chrom,switch) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each row corresponds to one individual's +% string representation. +% if Chrom == [], then speziell values will be returned +% switch - if Chrom == [] and +% switch == 1 (or []) return boundaries +% switch == 2 return title +% switch == 3 return value of global minimum +% +% Output parameters: +% ObjVal - Column vector containing the objective values of the +% individuals in the current population. +% if called with Chrom == [], then ObjVal contains +% switch == 1, matrix with the boundaries of the function +% switch == 2, text for the title of the graphic output +% switch == 3, value of global minimum +% + +% Author: Hartmut Pohlheim +% History: 25.11.93 file created +% 27.11.93 text of title and switch added +% 16.12.93 switch == 3, return value of global minimum +% 01.03.94 name changed in obj* + +function ObjVal = objsixh(Chrom,switch); + +% Compute population parameters + [Nind,Nvar] = size(Chrom); + +% Check size of Chrom and do the appropriate thing + % if Chrom is [], then define size of boundary-matrix and values + if Nind == 0 + % return text of title for graphic output + if switch == 2 + ObjVal = 'six-hump camelback function'; + % return value of global minimum + elseif switch == 3 + ObjVal = -1.0316; + % define size of boundary-matrix and values + else + % x1 x2 + ObjVal = [-3 -2; % lower bounds + 3 2]; % upper bounds + end + % if two variables, compute values of function + elseif Nvar == 2 + % six-hump camelback function + % -3 <= x1 <= 3 ; -2 <= x2 <= 2 + % global minimum at (x1,x2)=(-0.0898,0.7126),(0.0898,-0.7126) ; fmin=-1.0316 + x1 = Chrom(:,1); + x2 = Chrom(:,2); + ObjVal = (4-2.1*x1.^2+1/3*x1.^4).*x1.^2+x1.*x2+(-4+4*x2.^2).*x2.^2; + % otherwise error, wrong format of Chrom + else + error('size of matrix Chrom is not correct for function evaluation'); + end + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/RESPLOT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/RESPLOT.M" index b1632ce6f6c27142c7189ddc8fbe61d547733ddc..be2c3eba8bfdded9d64fb89addadbc451aa522f2 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/RESPLOT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/RESPLOT.M" @@ -1,3 +1,55 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:15424c52c7db18fd673d1d7d2004f7177a6ef38a34607db94dd1d37b3856bd37 -size 2067 +% RESPLOT.M (RESult PLOTing) +% +% This function plots some of the results during computation. +% +% Syntax: resplot(Chrom,IndAll,ObjV,Best,gen) +% +% Input parameters: +% Chrom - Matrix containing the chromosomes of the current +% population. Each line corresponds to one individual. +% IndAll - Matrix containing the best individual (variables) of each +% generation. Each line corresponds to one individual. +% ObjV - Vector containing objective values of the current +% generation +% Best - Matrix containing the best and average Objective values of each +% generation, [best value per generation,average value per generation] +% gen - Scalar containing the number of the current generation +% +% Output parameter: +% no output parameter + +% Author: Hartmut Pohlheim +% History: 27.11.93 file created +% 29.11.93 decision, if plot or not deleted +% yscale not log +% 15.12.93 MutMatrix as parameter and plot added +% 16.03.94 function cleaned, MutMatrix removed, IndAll added + +function resplot(Chrom,IndAll,ObjV,Best,gen); + + % plot of best and mean value per generation + subplot(2,2,1), plot(Best); + title('Best and mean objective value'); + xlabel('generation'), ylabel('objective value'); + + % plot of best individuals in all generations + subplot(2,2,2), plot(IndAll); + title(['Best individuals']); + xlabel('generation'), ylabel('value of variable'); + + % plot of variables of all individuals in current generation + subplot(2,2,3), plot(Chrom'); + title(['All individuals in gen ',num2str(gen)]); + xlabel('number of variable'), ylabel('value of variable'); + + % plot of all objective values in current generation + subplot(2,2,4), plot(ObjV,'y.'); + title(['All objective values']); + xlabel('number of individual'), ylabel('objective value'); + + drawnow; + + +% End of function + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SGA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SGA.M" index 2136fd475839e3d8c51ffff26b4a12dd35bff651..e7abb4f4ebc44e217f6c6aecde82a421936f34aa 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SGA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SGA.M" @@ -1,3 +1,67 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:e65330edf6404154493ef42c844dbcc005548383ac20ea3e5b5436237289736c -size 1911 +% SGA.M (Simple Genetic Algorithm) +% +% This script implements the Simple Genetic Algorithm. +% Binary representation for the individuals is used. +% +% Author: Hartmut Pohlheim +% History: 23.03.94 file created + +NIND = 20; % Number of individuals per subpopulations +MAXGEN = 300; % maximal Number of generations +GGAP = .8; % Generation gap, how many new individuals are created + +SEL_F = 'sus'; % Name of selection function +XOV_F = 'xovsp'; % Name of recombination function for individuals +MUT_F = 'mut'; % Name of mutation function for individuals +OBJ_F = 'objfun1'; % Name of function for objective values + +% Get boundaries of objective function + FieldDR = feval(OBJ_F,[],1); + +% Number of variables of objective function, in OBJ_F defined + NVAR = size(FieldDR,2); + +% Build fielddescription matrix + PRECI = 20; % Precisicion of binary representation + FieldDD = [rep([PRECI],[1, NVAR]);... + FieldDR;... + rep([1; 0; 1 ;1], [1, NVAR])]; + +% Create population + Chrom = crtbp(NIND, NVAR*PRECI); + +% reset count variables + gen = 0; + Best = NaN*ones(MAXGEN,1); + +% Iterate population + while gen < MAXGEN, + + % Calculate objective function for population + ObjV = feval(OBJ_F,bs2rv(Chrom, FieldDD)); + Best(gen+1) = min(ObjV); + plot(log10(Best),'ro'); + drawnow; + + % Fitness assignement to whole population + FitnV = ranking(ObjV); + + % Select individuals from population + SelCh = select(SEL_F, Chrom, FitnV, GGAP); + + % Recombine selected individuals (crossover) + SelCh=recombin(XOV_F, SelCh); + + % Mutate offspring + SelCh=mutate(MUT_F, SelCh); + + % Insert offspring in population replacing parents + Chrom = reins(Chrom, SelCh); + + gen=gen+1; + + end + +% End of script + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMDOPI1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMDOPI1.M" index c10d64b65c8f4b675a287bdaf5048e766310a504..ae4f9981a671506d108f7e26c279a18a06459ab0 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMDOPI1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMDOPI1.M" @@ -1,3 +1,80 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:72e18d256066390606b71890a08513834396f3adf51dadd1b53013a60b79b6dd -size 2690 +function [ret,x0,str]=simdopi1(t,x,u,flag); +%SIMDOPI1 is the M-file description of the SIMULINK system named SIMDOPI1. +% The block-diagram can be displayed by typing: SIMDOPI1. +% +% SYS=SIMDOPI1(T,X,U,FLAG) returns depending on FLAG certain +% system values given time point, T, current state vector, X, +% and input vector, U. +% FLAG is used to indicate the type of output to be returned in SYS. +% +% Setting FLAG=1 causes SIMDOPI1 to return state derivatives, FLAG=2 +% discrete states, FLAG=3 system outputs and FLAG=4 next sample +% time. For more information and other options see SFUNC. +% +% Calling SIMDOPI1 with a FLAG of zero: +% [SIZES]=SIMDOPI1([],[],[],0), returns a vector, SIZES, which +% contains the sizes of the state vector and other parameters. +% SIZES(1) number of states +% SIZES(2) number of discrete states +% SIZES(3) number of outputs +% SIZES(4) number of inputs. +% For the definition of other parameters in SIZES, see SFUNC. +% See also, TRIM, LINMOD, LINSIM, EULER, RK23, RK45, ADAMS, GEAR. + +% Note: This M-file is only used for saving graphical information; +% after the model is loaded into memory an internal model +% representation is used. + +% the system will take on the name of this mfile: +sys = mfilename; +new_system(sys) +simver(1.2) +if(0 == (nargin + nargout)) + set_param(sys,'Location',[100,100,600,400]) + open_system(sys) +end; +set_param(sys,'algorithm', 'RK-45') +set_param(sys,'Start time', '0.0') +set_param(sys,'Stop time', '1') +set_param(sys,'Min step size', '0.001') +set_param(sys,'Max step size', '0.01') +set_param(sys,'Relative error','1e-3') +set_param(sys,'Return vars', '') + +add_block('built-in/Inport',[sys,'/','Inport']) +set_param([sys,'/','Inport'],... + 'position',[65,95,85,115]) + +add_block('built-in/Note',[sys,'/','Doppelintegrator']) +set_param([sys,'/','Doppelintegrator'],... + 'position',[225,10,230,15]) + +add_block('built-in/Note',[sys,'/','Steuerung']) +set_param([sys,'/','Steuerung'],... + 'position',[75,65,80,70]) + +add_block('built-in/Integrator',[sys,'/','Integrator1']) +set_param([sys,'/','Integrator1'],... + 'position',[175,95,195,115]) + +add_block('built-in/Integrator',[sys,'/','Integrator2']) +set_param([sys,'/','Integrator2'],... + 'Initial','-1',... + 'position',[280,95,300,115]) +add_line(sys,[90,105;165,105]) +add_line(sys,[200,105;270,105]) + +% Return any arguments. +if (nargin | nargout) + % Must use feval here to access system in memory + if (nargin > 3) + if (flag == 0) + eval(['[ret,x0,str]=',sys,'(t,x,u,flag);']) + else + eval(['ret =', sys,'(t,x,u,flag);']) + end + else + [ret,x0,str] = feval(sys); + end +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMDOPI2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMDOPI2.M" index 5a7bb989ad6ab8b90bafd59c08fe70361cefe552..5b9b359ae753d7c5ca6bc3fbbf2aca187b4846ef 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMDOPI2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMDOPI2.M" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:255cafd990073ce958dc1325fd285885e3c58af02c8cfedfed68658f9a27cc9c -size 873 +% SIMDOPI2.M (Modell of DOPpelINTegrator, s-function) +% +% This function implements the modell of the DOPPELINTEGRATOR. +% +% Syntax: [sys, x0] = simdopi2(t, x, u, flag) +% +% Input parameters: +% t - given time point +% x - current state vector +% u - input vector +% flag - flags +% +% Output parameters: +% sys - Vector containing the new state derivatives +% x0 - initial value + +% Author: Hartmut Pohlheim +% History: 17.12.93 file created + +function [sys, x0] = simdopi2(t, x, u, flag); + +% Linear Systems Description + + if abs(flag) == 1 + sys(1) = u(1); % Derivatives + sys(2) = x(1); % Derivatives + elseif abs(flag) == 0 + sys=[2,0,0,1,0,0]; x0 = [0; -1]; + else + sys = []; % Real time update (ignored). + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMLINQ1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMLINQ1.M" index 9c2fa4244f94aa096a39308a26a00775fce6b44a..43d905fd47f68409dc52cffbdca46f14f0f897b2 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMLINQ1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMLINQ1.M" @@ -1,3 +1,73 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2afe43a7503bbfb0053683720878eb62368da4a7462acf99cf8dbf196ad5cabb -size 2445 +function [ret,x0,str]=simlinq1(t,x,u,flag); +%SIMLINQ1 is the M-file description of the SIMULINK system named SIMLINQ1. +% The block-diagram can be displayed by typing: SIMLINQ1. +% +% SYS=SIMLINQ1(T,X,U,FLAG) returns depending on FLAG certain +% system values given time point, T, current state vector, X, +% and input vector, U. +% FLAG is used to indicate the type of output to be returned in SYS. +% +% Setting FLAG=1 causes SIMLINQ1 to return state derivatives, FLAG=2 +% discrete states, FLAG=3 system outputs and FLAG=4 next sample +% time. For more information and other options see SFUNC. +% +% Calling SIMLINQ1 with a FLAG of zero: +% [SIZES]=SIMLINQ1([],[],[],0), returns a vector, SIZES, which +% contains the sizes of the state vector and other parameters. +% SIZES(1) number of states +% SIZES(2) number of discrete states +% SIZES(3) number of outputs +% SIZES(4) number of inputs. +% For the definition of other parameters in SIZES, see SFUNC. +% See also, TRIM, LINMOD, LINSIM, EULER, RK23, RK45, ADAMS, GEAR. + +% Note: This M-file is only used for saving graphical information; +% after the model is loaded into memory an internal model +% representation is used. + +% the system will take on the name of this mfile: +sys = mfilename; +new_system(sys) +simver(1.2) +if(0 == (nargin + nargout)) + set_param(sys,'Location',[208,245,596,426]) + open_system(sys) +end; +set_param(sys,'algorithm', 'RK-45') +set_param(sys,'Start time', '0.0') +set_param(sys,'Stop time', '1') +set_param(sys,'Min step size', '0.05') +set_param(sys,'Max step size', '0.05') +set_param(sys,'Relative error','1e-3') +set_param(sys,'Return vars', '') + +add_block('built-in/Sum',[sys,'/','Sum']) +set_param([sys,'/','Sum'],... + 'position',[110,65,130,85]) + +add_block('built-in/Integrator',[sys,'/','Integrator']) +set_param([sys,'/','Integrator'],... + 'Initial','100',... + 'position',[180,65,200,85]) + +add_block('built-in/Inport',[sys,'/','Inport']) +set_param([sys,'/','Inport'],... + 'position',[25,70,45,90]) +add_line(sys,[135,75;170,75]) +add_line(sys,[205,75;205,40;90,40;90,70;100,70]) +add_line(sys,[50,80;100,80]) + +% Return any arguments. +if (nargin | nargout) + % Must use feval here to access system in memory + if (nargin > 3) + if (flag == 0) + eval(['[ret,x0,str]=',sys,'(t,x,u,flag);']) + else + eval(['ret =', sys,'(t,x,u,flag);']) + end + else + [ret,x0,str] = feval(sys); + end +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMLINQ2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMLINQ2.M" index ef70654c63fda68e2f4dd25ae3eeda8aef5d00a8..80dab36b37f5282486a703e7332405092c526d84 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMLINQ2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMLINQ2.M" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a4740cd7ba9cba0f82b2830778204d2f3c1d08f588fd7a3df4d08066150fea35 -size 854 +% SIMLINQ2.M (Modell of Linear Quadratic Problem, s-function) +% +% This function implements the modell of the Linear Quadratic Problem. +% +% Syntax: [sys, x0] = simlinq2(t, x, u, flag) +% +% Input parameters: +% t - given time point +% x - current state vector +% u - input vector +% flag - flags +% +% Output parameters: +% sys - Vector containing the new state derivatives +% x0 - initial value + +% Author: Hartmut Pohlheim +% History: 23.03.94 file created + +function [sys, x0] = simlinq2(t, x, u, flag); + +% Linear Systems Description + + if abs(flag) == 1 + sys(1) = u(1) + x(1); % Derivatives + elseif abs(flag) == 0 + sys=[1,0,0,1,0,0]; x0 = [100]; + else + sys = []; % Real time update (ignored). + end + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMOBJP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMOBJP.M" index 0e7c78dc1a22c19413e8510ad3a074b7557f1f05..772ec2096b440e33a55c79a947c0ab50f0d37332 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMOBJP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/SIMOBJP.M" @@ -1,3 +1,22 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:4ae538fcd5128e0492210f325e63d2f7b5ebf41d4f02ff1bb0e3ad71d1c9448f -size 535 +% SIMOBJP.M (Plot SIMulation results of OBJective function) +% +% This function takes the name of a simulation objective +% function and the matrix of the best individuals and +% plots the states of the system over time for the +% last best individual. + +% Author: Hartmut Pohlheim +% History: 25.03.94 file created + +function [val, t, x] = simobjp(OBJ_F, IndAll); + +BestInd1=IndAll(size(IndAll,1),:); + +[val t x] = feval(OBJ_F, BestInd1); + +set(gcf,'Name',feval(OBJ_F,[],2)); +plot(t, x); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/TEST_FNS.PS" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/TEST_FNS.PS" index cbfa1ca1b5f7a7e1491c57d625d33e21443ed9fb..5bc62a5fa61cb23f3e21f82d1b9e1c8ccc51d93b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/TEST_FNS.PS" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/TEST_FNS/TEST_FNS.PS" @@ -1,3 +1,6239 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d31867c6f030b7a43c5154fed1ceed2a59756a9742678e00cfd41d33cb177d84 -size 140988 +%!PS-Adobe-3.0 +%%Creator: Windows PSCRIPT +%%Title: Microsoft Word - TEST_FCN.DOC +%%BoundingBox: 18 23 577 819 +%%DocumentNeededResources: (atend) +%%DocumentSuppliedResources: (atend) +%%Pages: (atend) +%%BeginResource: procset Win35Dict 3 1 +/Win35Dict 290 dict def Win35Dict begin/bd{bind def}bind def/in{72 +mul}bd/ed{exch def}bd/ld{load def}bd/tr/translate ld/gs/gsave ld/gr +/grestore ld/M/moveto ld/L/lineto ld/rmt/rmoveto ld/rlt/rlineto ld +/rct/rcurveto ld/st/stroke ld/n/newpath ld/sm/setmatrix ld/cm/currentmatrix +ld/cp/closepath ld/ARC/arcn ld/TR{65536 div}bd/lj/setlinejoin ld/lc +/setlinecap ld/ml/setmiterlimit ld/sl/setlinewidth ld/scignore false +def/sc{scignore{pop pop pop}{0 index 2 index eq 2 index 4 index eq +and{pop pop 255 div setgray}{3{255 div 3 1 roll}repeat setrgbcolor}ifelse}ifelse}bd +/FC{bR bG bB sc}bd/fC{/bB ed/bG ed/bR ed}bd/HC{hR hG hB sc}bd/hC{ +/hB ed/hG ed/hR ed}bd/PC{pR pG pB sc}bd/pC{/pB ed/pG ed/pR ed}bd/sM +matrix def/PenW 1 def/iPen 5 def/mxF matrix def/mxE matrix def/mxUE +matrix def/mxUF matrix def/fBE false def/iDevRes 72 0 matrix defaultmatrix +dtransform dup mul exch dup mul add sqrt def/fPP false def/SS{fPP{ +/SV save def}{gs}ifelse}bd/RS{fPP{SV restore}{gr}ifelse}bd/EJ{gsave +showpage grestore}bd/#C{userdict begin/#copies ed end}bd/FEbuf 2 string +def/FEglyph(G )def/FE{1 exch{dup 16 FEbuf cvrs FEglyph exch 1 exch +putinterval 1 index exch FEglyph cvn put}for}bd/SM{/iRes ed/cyP ed +/cxPg ed/cyM ed/cxM ed 72 100 div dup scale dup 0 ne{90 eq{cyM exch +0 eq{cxM exch tr -90 rotate -1 1 scale}{cxM cxPg add exch tr +90 rotate}ifelse}{cyP +cyM sub exch 0 ne{cxM exch tr -90 rotate}{cxM cxPg add exch tr -90 +rotate 1 -1 scale}ifelse}ifelse}{pop cyP cyM sub exch 0 ne{cxM cxPg +add exch tr 180 rotate}{cxM exch tr 1 -1 scale}ifelse}ifelse 100 iRes +div dup scale 0 0 transform .25 add round .25 sub exch .25 add round +.25 sub exch itransform translate}bd/SJ{1 index 0 eq{pop pop/fBE false +def}{1 index/Break ed div/dxBreak ed/fBE true def}ifelse}bd/ANSIVec[ +16#0/grave 16#1/acute 16#2/circumflex 16#3/tilde 16#4/macron 16#5/breve +16#6/dotaccent 16#7/dieresis 16#8/ring 16#9/cedilla 16#A/hungarumlaut +16#B/ogonek 16#C/caron 16#D/dotlessi 16#27/quotesingle 16#60/grave +16#7C/bar 16#82/quotesinglbase 16#83/florin 16#84/quotedblbase 16#85 +/ellipsis 16#86/dagger 16#87/daggerdbl 16#88/circumflex 16#89/perthousand +16#8A/Scaron 16#8B/guilsinglleft 16#8C/OE 16#91/quoteleft 16#92/quoteright +16#93/quotedblleft 16#94/quotedblright 16#95/bullet 16#96/endash 16#97 +/emdash 16#98/tilde 16#99/trademark 16#9A/scaron 16#9B/guilsinglright +16#9C/oe 16#9F/Ydieresis 16#A0/space 16#A1/exclamdown 16#A4/currency +16#A5/yen 16#A6/brokenbar 16#A7/section 16#A8/dieresis 16#A9/copyright +16#AA/ordfeminine 16#AB/guillemotleft 16#AC/logicalnot 16#AD/hyphen +16#AE/registered 16#AF/macron 16#B0/degree 16#B1/plusminus 16#B2/twosuperior +16#B3/threesuperior 16#B4/acute 16#B5/mu 16#B6/paragraph 16#B7/periodcentered +16#B8/cedilla 16#B9/onesuperior 16#BA/ordmasculine 16#BB/guillemotright +16#BC/onequarter 16#BD/onehalf 16#BE/threequarters 16#BF/questiondown +16#C0/Agrave 16#C1/Aacute 16#C2/Acircumflex 16#C3/Atilde 16#C4/Adieresis +16#C5/Aring 16#C6/AE 16#C7/Ccedilla 16#C8/Egrave 16#C9/Eacute 16#CA +/Ecircumflex 16#CB/Edieresis 16#CC/Igrave 16#CD/Iacute 16#CE/Icircumflex +16#CF/Idieresis 16#D0/Eth 16#D1/Ntilde 16#D2/Ograve 16#D3/Oacute 16#D4 +/Ocircumflex 16#D5/Otilde 16#D6/Odieresis 16#D7/multiply 16#D8/Oslash +16#D9/Ugrave 16#DA/Uacute 16#DB/Ucircumflex 16#DC/Udieresis 16#DD/Yacute +16#DE/Thorn 16#DF/germandbls 16#E0/agrave 16#E1/aacute 16#E2/acircumflex +16#E3/atilde 16#E4/adieresis 16#E5/aring 16#E6/ae 16#E7/ccedilla 16#E8 +/egrave 16#E9/eacute 16#EA/ecircumflex 16#EB/edieresis 16#EC/igrave +16#ED/iacute 16#EE/icircumflex 16#EF/idieresis 16#F0/eth 16#F1/ntilde +16#F2/ograve 16#F3/oacute 16#F4/ocircumflex 16#F5/otilde 16#F6/odieresis +16#F7/divide 16#F8/oslash 16#F9/ugrave 16#FA/uacute 16#FB/ucircumflex +16#FC/udieresis 16#FD/yacute 16#FE/thorn 16#FF/ydieresis ] def/reencdict +12 dict def/IsChar{basefontdict/CharStrings get exch known}bd/MapCh{dup +IsChar not{pop/bullet}if newfont/Encoding get 3 1 roll put}bd/MapDegree{16#b0 +/degree IsChar{/degree}{/ring}ifelse MapCh}bd/MapBB{16#a6/brokenbar +IsChar{/brokenbar}{/bar}ifelse MapCh}bd/ANSIFont{reencdict begin/newfontname +ed/basefontname ed FontDirectory newfontname known not{/basefontdict +basefontname findfont def/newfont basefontdict maxlength dict def basefontdict{exch +dup/FID ne{dup/Encoding eq{exch dup length array copy newfont 3 1 roll +put}{exch newfont 3 1 roll put}ifelse}{pop pop}ifelse}forall newfont +/FontName newfontname put 127 1 159{newfont/Encoding get exch/bullet +put}for ANSIVec aload pop ANSIVec length 2 idiv{MapCh}repeat MapDegree +MapBB newfontname newfont definefont pop}if newfontname end}bd/SB{FC +/ULlen ed/str ed str length fBE not{dup 1 gt{1 sub}if}if/cbStr ed +/dxGdi ed/y0 ed/x0 ed str stringwidth dup 0 ne{/y1 ed/x1 ed y1 y1 +mul x1 x1 mul add sqrt dxGdi exch div 1 sub dup x1 mul cbStr div exch +y1 mul cbStr div}{exch abs neg dxGdi add cbStr div exch}ifelse/dyExtra +ed/dxExtra ed x0 y0 M fBE{dxBreak 0 BCh dxExtra dyExtra str awidthshow}{dxExtra +dyExtra str ashow}ifelse fUL{x0 y0 M dxUL dyUL rmt ULlen fBE{Break +add}if 0 mxUE transform gs rlt cyUL sl [] 0 setdash st gr}if fSO{x0 +y0 M dxSO dySO rmt ULlen fBE{Break add}if 0 mxUE transform gs rlt cyUL +sl [] 0 setdash st gr}if n/fBE false def}bd/font{/name ed/Ascent ed +0 ne/fT3 ed 0 ne/fSO ed 0 ne/fUL ed/Sy ed/Sx ed 10.0 div/ori ed -10.0 +div/esc ed/BCh ed name findfont/xAscent 0 def/yAscent Ascent def/ULesc +esc def ULesc mxUE rotate pop fT3{/esc 0 def xAscent yAscent mxUE transform +/yAscent ed/xAscent ed}if [Sx 0 0 Sy neg xAscent yAscent] esc mxE +rotate mxF concatmatrix makefont setfont [Sx 0 0 Sy neg 0 Ascent] mxUE +mxUF concatmatrix pop fUL{currentfont dup/FontInfo get/UnderlinePosition +known not{pop/Courier findfont}if/FontInfo get/UnderlinePosition get +1000 div 0 exch mxUF transform/dyUL ed/dxUL ed}if fSO{0 .3 mxUF transform +/dySO ed/dxSO ed}if fUL fSO or{currentfont dup/FontInfo get/UnderlineThickness +known not{pop/Courier findfont}if/FontInfo get/UnderlineThickness get +1000 div Sy mul/cyUL ed}if}bd/min{2 copy gt{exch}if pop}bd/max{2 copy +lt{exch}if pop}bd/CP{/ft ed{{ft 0 eq{clip}{eoclip}ifelse}stopped{currentflat +1 add setflat}{exit}ifelse}loop}bd/patfont 10 dict def patfont begin +/FontType 3 def/FontMatrix [1 0 0 -1 0 0] def/FontBBox [0 0 16 16] +def/Encoding StandardEncoding def/BuildChar{pop pop 16 0 0 0 16 16 +setcachedevice 16 16 false [1 0 0 1 .25 .25]{pat}imagemask}bd end/p{ +/pat 32 string def{}forall 0 1 7{dup 2 mul pat exch 3 index put dup +2 mul 1 add pat exch 3 index put dup 2 mul 16 add pat exch 3 index +put 2 mul 17 add pat exch 2 index put pop}for}bd/pfill{/PatFont patfont +definefont setfont/ch(AAAA)def X0 64 X1{Y1 -16 Y0{1 index exch M ch +show}for pop}for}bd/vert{X0 w X1{dup Y0 M Y1 L st}for}bd/horz{Y0 w +Y1{dup X0 exch M X1 exch L st}for}bd/fdiag{X0 w X1{Y0 M X1 X0 sub dup +rlt st}for Y0 w Y1{X0 exch M Y1 Y0 sub dup rlt st}for}bd/bdiag{X0 w +X1{Y1 M X1 X0 sub dup neg rlt st}for Y0 w Y1{X0 exch M Y1 Y0 sub dup +neg rlt st}for}bd/AU{1 add cvi 15 or}bd/AD{1 sub cvi -16 and}bd/SHR{pathbbox +AU/Y1 ed AU/X1 ed AD/Y0 ed AD/X0 ed}bd/hfill{/w iRes 37.5 div round +def 0.1 sl [] 0 setdash n dup 0 eq{horz}if dup 1 eq{vert}if dup 2 eq{fdiag}if +dup 3 eq{bdiag}if dup 4 eq{horz vert}if 5 eq{fdiag bdiag}if}bd/F{/ft +ed fm 256 and 0 ne{gs FC ft 0 eq{fill}{eofill}ifelse gr}if fm 1536 +and 0 ne{SHR gs HC ft CP fm 1024 and 0 ne{/Tmp save def pfill Tmp restore}{fm +15 and hfill}ifelse gr}if}bd/S{PenW sl PC st}bd/m matrix def/GW{iRes +12 div PenW add cvi}bd/DoW{iRes 50 div PenW add cvi}bd/DW{iRes 8 div +PenW add cvi}bd/SP{/PenW ed/iPen ed iPen 0 eq iPen 6 eq or{[] 0 setdash}if +iPen 1 eq{[DW GW] 0 setdash}if iPen 2 eq{[DoW GW] 0 setdash}if iPen +3 eq{[DW GW DoW GW] 0 setdash}if iPen 4 eq{[DW GW DoW GW DoW GW] 0 +setdash}if}bd/E{m cm pop tr scale 1 0 moveto 0 0 1 0 360 arc cp m sm}bd +/AG{/sy ed/sx ed sx div 4 1 roll sy div 4 1 roll sx div 4 1 roll sy +div 4 1 roll atan/a2 ed atan/a1 ed sx sy scale a1 a2 ARC}def/A{m cm +pop tr AG m sm}def/P{m cm pop tr 0 0 M AG cp m sm}def/RRect{n 4 copy +M 3 1 roll exch L 4 2 roll L L cp}bd/RRCC{/r ed/y1 ed/x1 ed/y0 ed/x0 +ed x0 x1 add 2 div y0 M x1 y0 x1 y1 r arcto 4{pop}repeat x1 y1 x0 y1 +r arcto 4{pop}repeat x0 y1 x0 y0 r arcto 4{pop}repeat x0 y0 x1 y0 r +arcto 4{pop}repeat cp}bd/RR{2 copy 0 eq exch 0 eq or{pop pop RRect}{2 +copy eq{pop RRCC}{m cm pop/y2 ed/x2 ed/ys y2 x2 div 1 max def/xs x2 +y2 div 1 max def/y1 exch ys div def/x1 exch xs div def/y0 exch ys div +def/x0 exch xs div def/r2 x2 y2 min def xs ys scale x0 x1 add 2 div +y0 M x1 y0 x1 y1 r2 arcto 4{pop}repeat x1 y1 x0 y1 r2 arcto 4{pop}repeat +x0 y1 x0 y0 r2 arcto 4{pop}repeat x0 y0 x1 y0 r2 arcto 4{pop}repeat +m sm cp}ifelse}ifelse}bd/PP{{rlt}repeat}bd/OB{gs 0 ne{7 3 roll/y ed +/x ed x y translate ULesc rotate x neg y neg translate x y 7 -3 roll}if +sc B fill gr}bd/B{M/dy ed/dx ed dx 0 rlt 0 dy rlt dx neg 0 rlt cp}bd +/CB{B clip n}bd/ErrHandler{errordict dup maxlength exch length gt +dup{errordict begin}if/errhelpdict 12 dict def errhelpdict begin/stackunderflow(operand stack underflow)def +/undefined(this name is not defined in a dictionary)def/VMerror(you have used up all the printer's memory)def +/typecheck(operator was expecting a different type of operand)def +/ioerror(input/output error occured)def end{end}if errordict begin +/handleerror{$error begin newerror{/newerror false def showpage 72 +72 scale/x .25 def/y 9.6 def/Helvetica findfont .2 scalefont setfont +x y moveto(Offending Command = )show/command load{dup type/stringtype +ne{(max err string)cvs}if show}exec/y y .2 sub def x y moveto(Error = )show +errorname{dup type dup( max err string )cvs show( : )show/stringtype +ne{( max err string )cvs}if show}exec errordict begin errhelpdict errorname +known{x 1 add y .2 sub moveto errhelpdict errorname get show}if end +/y y .4 sub def x y moveto(Stack =)show ostack{/y y .2 sub def x 1 +add y moveto dup type/stringtype ne{( max err string )cvs}if show}forall +showpage}if end}def end}bd end +%%EndResource +/SVDoc save def +%%EndProlog +%%BeginSetup +Win35Dict begin +ErrHandler +statusdict begin 0 setjobtimeout end +statusdict begin statusdict /jobname (Microsoft Word - TEST_FCN.DOC) put end +/oldDictCnt countdictstack def {}stopped +{ countdictstack oldDictCnt lt { Win35Dict begin } +{1 1 countdictstack oldDictCnt sub {pop end } for } ifelse } if +/oldDictCnt countdictstack def {a4 +}stopped +{ countdictstack oldDictCnt lt { Win35Dict begin } +{1 1 countdictstack oldDictCnt sub {pop end } for } ifelse } if +[ +{mark 1.0 1.0 .98 .9 .82 .68 .56 .48 .28 .1 .06 .0 counttomark dup 3 add -1 roll exch 2 sub mul dup floor cvi dup 3 1 roll sub exch dup 3 add index exch 2 add index dup 4 1 roll sub mul add counttomark 1 add 1 roll cleartomark } bind +/exec load currenttransfer /exec load] cvx settransfer +%%EndSetup +%%Page: 1 1 +%%PageResources: (atend) +SS +0 0 25 31 776 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Rotated hyper-ellipsoid) 553 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +962 1849 416 (................................) 416 SB +1378 1849 416 (................................) 416 SB +1794 1849 221 (.................) 221 SB +2026 1849 25 (4) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +397 1924 935 (2.4. Rosenbrock's valley \(De Jong's function 2\)) 935 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1339 1924 416 (................................) 416 SB +1755 1924 260 (....................) 260 SB +2026 1924 25 (4) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +397 1999 509 (2.5. 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74 454 1171 B +1 F +n +2 74 927 1171 B +1 F +n +5 74 2048 1171 B +1 F +n +gs 196 78 258 1246 CB +372 1267 25 (3) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1246 CB +480 1271 240 (objfun1b) 240 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1246 CB +952 1267 448 (rotated hyper-ellipsoid) 448 SB +gr +5 2 252 1246 B +1 F +n +195 2 258 1246 B +1 F +n +2 2 454 1246 B +1 F +n +469 2 457 1246 B +1 F +n +2 2 927 1246 B +1 F +n +1117 2 930 1246 B +1 F +n +5 2 2048 1246 B +1 F +n +5 74 252 1249 B +1 F +n +2 74 454 1249 B +1 F +n +2 74 927 1249 B +1 F +n +5 74 2048 1249 B +1 F +n +gs 196 78 258 1324 CB +372 1345 25 (4) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1324 CB +480 1349 210 (objfun2) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1324 CB +952 1345 754 (Rosenbrock's valley \(banana function\)) 754 SB +gr +5 2 252 1324 B +1 F +n +195 2 258 1324 B +1 F +n +2 2 454 1324 B +1 F +n +469 2 457 1324 B +1 F +n +2 2 927 1324 B +1 F +n +1117 2 930 1324 B +1 F +n +5 2 2048 1324 B +1 F +n +5 74 252 1327 B +1 F +n +2 74 454 1327 B +1 F +n +2 74 927 1327 B +1 F +n +5 74 2048 1327 B +1 F +n +gs 196 78 258 1402 CB +372 1423 25 (5) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1402 CB +480 1427 210 (objfun6) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1402 CB +952 1423 401 (Rastrigins's function) 401 SB +gr +5 2 252 1402 B +1 F +n +195 2 258 1402 B +1 F +n +2 2 454 1402 B +1 F +n +469 2 457 1402 B +1 F +n +2 2 927 1402 B +1 F +n +1117 2 930 1402 B +1 F +n +5 2 2048 1402 B +1 F +n +5 74 252 1405 B +1 F +n +2 74 454 1405 B +1 F +n +2 74 927 1405 B +1 F +n +5 74 2048 1405 B +1 F +n +gs 196 78 258 1480 CB +372 1501 25 (6) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1480 CB +480 1505 210 (objfun7) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman 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50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1636 CB +480 1661 210 (objfun9) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1636 CB +952 1657 454 (sum of different power) 454 SB +gr +5 2 252 1636 B +1 F +n +195 2 258 1636 B +1 F +n +2 2 454 1636 B +1 F +n +469 2 457 1636 B +1 F +n +2 2 927 1636 B +1 F +n +1117 2 930 1636 B +1 F +n +5 2 2048 1636 B +1 F +n +5 74 252 1639 B +1 F +n +2 74 454 1639 B +1 F +n +2 74 927 1639 B +1 F +n +5 74 2048 1639 B +1 F +n +gs 196 81 258 1714 CB +372 1738 25 (9) 25 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 81 457 1714 CB +480 1742 210 (objdopi) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 81 930 1714 CB +952 1738 342 (double integrator) 342 SB +gr +5 5 252 1714 B +1 F +n +195 5 258 1714 B +1 F +n +5 5 454 1714 B +1 F +n +466 5 460 1714 B +1 F +n +5 5 927 1714 B +1 F +n +1114 5 933 1714 B +1 F +n +5 5 2048 1714 B +1 F +n +5 74 252 1720 B +1 F +n +2 74 454 1720 B +1 F +n +2 74 927 1720 B +1 F +n +5 74 2048 1720 B +1 F +n +gs 196 78 258 1795 CB +347 1816 50 (10) 50 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1795 CB +480 1820 210 (objharv) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1795 CB +952 1816 319 (harvest problem) 319 SB +gr +5 2 252 1795 B +1 F +n +195 2 258 1795 B +1 F +n +2 2 454 1795 B +1 F +n +469 2 457 1795 B +1 F +n +2 2 927 1795 B +1 F +n +1117 2 930 1795 B +1 F +n +5 2 2048 1795 B +1 F +n +5 74 252 1798 B +1 F +n +2 74 454 1798 B +1 F +n +2 74 927 1798 B +1 F +n +5 74 2048 1798 B +1 F +n +gs 196 78 258 1873 CB +347 1894 50 (11) 50 SB +gr +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +gs 470 78 457 1873 CB +480 1898 210 (objlinq) 210 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 1118 78 930 1873 CB +952 1894 842 (linear-quadratic problem \(discret function\)) 842 SB +gr +5 2 252 1873 B +1 F +n +195 2 258 1873 B +1 F 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(100) 75 SB +991 736 25 (1) 25 SB +1320 736 25 (2) 25 SB +1364 736 75 (048) 75 SB +1577 736 25 (2) 25 SB +1620 736 75 (048) 75 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +443 696 17 (a) 17 SB +490 696 17 (f) 17 SB + +%%BeginResource: font MSTT31c2af +/G63 [17.0 0.0 2.0 -15.0 14.0 50.0] +/G63 { + 12 65 true [1 0 0 -1 -2.0 50.0] {<00100030006000c001c0018003800300070006000e000e001c001c001c003c003800380078007800 +780078007000f000f000f000f000f000f000f000f000f000f000f000f000f000f000f000f000f000 +f000f00070007800780078007800380038003c001c001c001c000e000e0006000600030003000180 +01c000c0006000300010>} imagemask + } + 99 /G63 MSTT31c2af AddChar +%%EndResource + +711 696 17 (c) 17 SB + +%%BeginResource: font MSTT31c2af +/G68 [17.0 0.0 0.0 -15.0 13.0 50.0] +/G68 { + 13 65 true [1 0 0 -1 0.0 50.0] {<400060007000300018000c000c000600070003000380038001c001c001c001e000e000e000f000f0 +00f000f0007000700078007800780078007800780078007800780078007800780078007800780078 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MSTT31c2af AddChar +%%EndResource + +1098 696 17 (g) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +517 730 27 (=) 27 SB +694 730 13 (\327) 13 SB +808 730 27 (-) 27 SB +941 730 27 (+) 27 SB +1021 730 27 (-) 27 SB +1284 730 27 (-) 27 SB +1448 730 27 (\243) 27 SB +1538 730 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +765 764 16 (+) 16 SB +575 800 16 (=) 16 SB +578 700 16 (-) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +557 716 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1346 736 13 (,) 13 SB +1602 736 13 (,) 13 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 869 333 (global minimum) 333 SB +732 869 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 867 22 (x) 22 SB +1004 867 14 (f) 14 SB +1048 867 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 900 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +842 863 27 (=) 27 SB +1101 863 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +877 869 25 (1) 25 SB +1141 869 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1027 828 17 (a) 17 SB +1074 828 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1001 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 1007 270 (objfun2.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 1001 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 1168 634 (2.5. Rastrigin's function 6) 634 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1353 99 (This ) 103 SB +382 1353 176 (function ) 180 SB +562 1353 44 (is ) 48 SB +610 1353 125 (based ) 129 SB +739 1353 63 (on ) 67 SB +806 1353 176 (function ) 180 SB +986 1353 38 (1 ) 42 SB +1028 1353 100 (with ) 104 SB +1132 1353 74 (the ) 78 SB +1210 1353 174 (addition ) 178 SB +1388 1353 54 (of ) 58 SB +1446 1353 138 (cosine ) 142 SB +1588 1353 237 (modulation ) 242 SB +1830 1353 54 (to ) 59 SB +1889 1353 162 (produce) 162 SB +279 1428 119 (many ) 123 SB +402 1428 107 (local ) 111 SB +513 1428 170 (minima. ) 174 SB +687 1428 125 (Thus, ) 129 SB +816 1428 74 (the ) 78 SB +894 1428 84 (test ) 88 SB +982 1428 176 (function ) 180 SB +1162 1428 44 (is ) 48 SB +1210 1428 133 (highly ) 137 SB +1347 1428 249 (multimodal. ) 253 SB +1600 1428 209 (However, ) 213 SB +1813 1428 74 (the ) 79 SB +1892 1428 159 (location) 159 SB +279 1503 771 (of the minima are regularly distributed.) 771 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 1617 14 (f) 14 SB +464 1617 22 (x) 22 SB +627 1617 25 (n) 25 SB +777 1617 22 (x) 22 SB +1128 1617 22 (x) 22 SB +1523 1617 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +800 1649 8 (i) 8 SB +1151 1649 8 (i) 8 SB +705 1685 8 (i) 8 SB +717 1585 15 (n) 15 SB +1546 1649 8 (i) 8 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +422 1650 15 (6) 15 SB +803 1616 15 (2) 15 SB +731 1686 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +552 1619 50 (10) 50 SB +865 1619 50 (10) 50 SB +1023 1619 25 (2) 25 SB +1383 1619 25 (5) 25 SB +1420 1619 50 (12) 50 SB +1610 1619 25 (5) 25 SB +1647 1619 50 (12) 50 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +443 1579 17 (a) 17 SB +489 1579 17 (f) 17 SB +1005 1579 17 (b) 17 SB +1167 1579 17 (g) 17 SB +756 1579 17 (c) 17 SB +1184 1579 17 (h) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +517 1613 27 (=) 27 SB +608 1613 13 (\327) 13 SB +661 1613 27 (+) 27 SB +832 1613 27 (-) 27 SB +921 1613 13 (\327) 13 SB +1055 1613 13 (\327) 13 SB +1107 1613 13 (\327) 13 SB +1347 1613 27 (-) 27 SB +1482 1613 27 (\243) 27 SB +1571 1613 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +715 1683 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +697 1599 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +939 1619 66 (cos) 66 SB +1407 1619 13 (,) 13 SB +1633 1619 13 (,) 13 SB +32 0 0 50 50 0 0 0 51 /Symbol font +1073 1613 27 (p) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 1752 333 (global minimum) 333 SB +731 1752 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 1750 22 (x) 22 SB +1012 1750 14 (f) 14 SB +1056 1750 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 1783 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +841 1746 27 (=) 27 SB +1109 1746 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +881 1752 25 (0) 25 SB +1149 1752 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1035 1711 17 (a) 17 SB +1082 1711 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1884 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 1890 270 (objfun6.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 1884 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 2051 621 (2.6. Schwefel's function 7) 621 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2236 221 (Schwefel's ) 223 SB +502 2236 176 (function ) 178 SB +680 2236 44 (is ) 46 SB +726 2236 202 (deceptive ) 204 SB +930 2236 49 (in ) 51 SB +981 2236 89 (that ) 91 SB +1072 2236 74 (the ) 76 SB +1148 2236 134 (global ) 136 SB +1284 2236 197 (minimum ) 199 SB +1483 2236 44 (is ) 47 SB +1530 2236 268 (geometricaly ) 271 SB +1801 2236 158 (distant, ) 161 SB +1962 2236 89 (over) 89 SB +279 2311 74 (the ) 78 SB +357 2311 212 (parameter ) 216 SB +573 2311 136 (space, ) 140 SB +713 2311 108 (from ) 112 SB +825 2311 74 (the ) 79 SB +904 2311 98 (next ) 103 SB +1007 2311 93 (best ) 98 SB +1105 2311 107 (local ) 112 SB +1217 2311 170 (minima. ) 175 SB +1392 2311 222 (Therefore, ) 227 SB +1619 2311 74 (the ) 79 SB +1698 2311 139 (search ) 144 SB +1842 2311 209 (algorithms) 209 SB +279 2386 1191 (are potentially prone to convergence in the wrong direction.) 1191 SB +1 lc +1 lj +0 0 0 pC +0 2 SP +831 2504 M 0 60 1 PP +S +n +880 2504 M 0 60 1 PP +S +n +797 2543 M 6 -3 1 PP +S +n +0 4 SP +803 2541 M 10 25 1 PP +S +n +0 2 SP +814 2566 M 12 -71 1 PP +S +n +826 2495 M 61 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 2500 14 (f) 14 SB +464 2500 22 (x) 22 SB +650 2500 22 (x) 22 SB +839 2500 22 (x) 22 SB +1217 2500 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +673 2532 8 (i) 8 SB +862 2532 8 (i) 8 SB +564 2568 8 (i) 8 SB +576 2468 15 (n) 15 SB +1240 2532 8 (i) 8 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +423 2533 15 (7) 15 SB +590 2569 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1089 2502 75 (500) 75 SB +1304 2502 75 (500) 75 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +442 2462 17 (a) 17 SB +489 2462 17 (f) 17 SB + +%%BeginResource: font MSTT31c2af +/G65 [17.0 0.0 2.0 -18.0 14.0 61.0] +/G65 { + 12 79 true [1 0 0 -1 -2.0 61.0] {<001000300060006000c000c00180038003000300060006000e000e000c001c001c001c003c003800 +38003800780078007800780070007000f000f000f000f000f000f000f000f000f000f000f000f000 +f000f000f000f000f000f000f000f000f000f000f000700078007800780078007800380038003800 +3c001c001c001c000c000e000e0006000600030003000300018001c000c00060006000300010>} imagemask + } + 101 /G65 MSTT31c2af AddChar +%%EndResource + +776 2462 17 (e) 17 SB + +%%BeginResource: font MSTT31c2af +/G6a [17.0 0.0 0.0 -18.0 13.0 61.0] +/G6a { + 13 79 true [1 0 0 -1 0.0 61.0] {<4000600060003000380018000c000c00060006000700030003800380038001c001c001c001e000e0 +00e000e000f000f000f000f000700070007000780078007800780078007800780078007800780078 +007800780078007800780078007800780078007800700070007000f000f000f000f000e000e000e0 +01e001c001c001c003800380038003000700060006000c000c00180038003000600060004000>} imagemask + } + 106 /G6a MSTT31c2af AddChar +%%EndResource + +890 2462 17 (j) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +517 2496 27 (=) 27 SB +617 2496 27 (-) 27 SB +699 2496 13 (\327) 13 SB +1053 2496 27 (-) 27 SB +1176 2496 27 (\243) 27 SB +1265 2496 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +574 2566 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +556 2482 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +716 2502 58 (sin) 58 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 2635 333 (global minimum) 333 SB +732 2635 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 2633 22 (x) 22 SB +1180 2633 14 (f) 14 SB +1224 2633 22 (x) 22 SB +1317 2633 25 (n) 25 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 2666 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +842 2629 27 (=) 27 SB +1277 2629 27 (=) 27 SB +1348 2629 13 (\327) 13 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +882 2635 75 (420) 75 SB +975 2635 100 (9687) 100 SB +1367 2635 75 (418) 75 SB +1458 2635 100 (9829) 100 SB +957 2635 13 (,) 13 SB +1440 2635 13 (,) 13 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1203 2594 17 (a) 17 SB +1250 2594 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2767 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 2773 270 (objfun7.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 2767 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 5 5 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 414 (2. Parametric Optimization) 414 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (5) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 210 677 (2.7. Griewangk's function 8) 677 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 395 259 (Griewangk's ) 269 SB +548 395 176 (function ) 186 SB +734 395 44 (is ) 54 SB +788 395 144 (similar ) 154 SB +942 395 54 (to ) 64 SB +1006 395 219 (Rastrigin's ) 229 SB +1235 395 189 (function. ) 199 SB +1434 395 45 (It ) 55 SB +1489 395 78 (has ) 89 SB +1578 395 119 (many ) 130 SB +1708 395 238 (widespread ) 249 SB +1957 395 94 (local) 94 SB +279 470 1396 (minima. However, the location of the minima are regularly distributed.) 1396 SB +1 lc +1 lj +0 0 0 pC +0 2 SP +617 618 M 106 0 1 PP +S +n +937 660 M 6 -4 1 PP +S +n +0 4 SP +943 657 M 9 15 1 PP +S +n +0 2 SP +953 672 M 13 -46 1 PP +S +n +966 626 M 19 0 1 PP +S +n +932 618 M 57 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 584 14 (f) 14 SB +463 584 22 (x) 22 SB +649 552 22 (x) 22 SB +943 552 22 (x) 22 SB +968 623 14 (i) 14 SB +1390 584 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +672 585 8 (i) 8 SB +563 652 8 (i) 8 SB +575 552 15 (n) 15 SB +966 585 8 (i) 8 SB +781 652 8 (i) 8 SB +794 552 15 (n) 15 SB +1413 616 8 (i) 8 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +422 617 15 (8) 15 SB +675 551 15 (2) 15 SB +589 653 15 (1) 15 SB +808 653 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +621 625 100 (4000) 100 SB +1056 586 25 (1) 25 SB +1262 586 75 (600) 75 SB +1476 586 75 (600) 75 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +441 546 17 (a) 17 SB +488 546 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +516 580 27 (=) 27 SB +734 580 27 (-) 27 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +905 520 19 (F) 19 SB +905 580 19 (H) 19 SB +905 551 19 (G) 19 SB +991 520 19 (I) 19 SB +991 580 19 (K) 19 SB +991 551 19 (J) 19 SB +32 0 0 50 50 0 0 0 51 /Symbol font +1024 580 27 (+) 27 SB +1226 580 27 (-) 27 SB +1348 580 27 (\243) 27 SB +1438 580 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +573 650 16 (=) 16 SB +792 650 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +555 566 53 (\345) 53 SB +770 566 62 (\325) 62 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +838 586 66 (cos) 66 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 719 333 (global minimum) 333 SB +731 719 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 717 22 (x) 22 SB +1012 717 14 (f) 14 SB +1056 717 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 750 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +841 713 27 (=) 27 SB +1109 713 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +881 719 25 (0) 25 SB +1149 719 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1035 678 17 (a) 17 SB +1082 678 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 851 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 857 270 (objfun8.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 851 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 1018 1002 (2.8. Sum of different Powers \(function 9\)) 1002 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1203 1435 (The sum of different powers is a commonly used unimodal test function.) 1435 SB +619 1321 M 0 60 1 PP +S +n +668 1321 M 0 60 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 1317 14 (f) 14 SB +464 1317 22 (x) 22 SB +627 1317 22 (x) 22 SB +992 1317 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +650 1349 8 (i) 8 SB +684 1307 8 (i) 8 SB +564 1385 8 (i) 8 SB +576 1285 15 (n) 15 SB +1015 1349 8 (i) 8 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +422 1350 15 (9) 15 SB +710 1308 15 (1) 15 SB +590 1386 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +918 1319 25 (1) 25 SB +1075 1319 25 (1) 25 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +443 1279 17 (a) 17 SB +489 1279 17 (f) 17 SB + +%%BeginResource: font MSTT31c2d2 +/MSTT31c2d2 [58.0 0 0 0 0 0] 17 -136 [-58.0 -58.0 58.0 58.0] [1 58 div 0 0 1 58 div 0 0] /MSTT31c2d2 GreNewFont +%%EndResource + +32 0 0 58 58 0 0 1 49 /MSTT31c2d2 font + +%%BeginResource: font MSTT31c2d2 +/G61 [10.0 0.0 1.0 -6.0 8.0 23.0] +/G61 { + 7 29 true [1 0 0 -1 -1.0 23.0] {<020408103020606060c0c0c0c0c0c0c0c0c0c0c0606060203010080402>} imagemask + } + 97 /G61 MSTT31c2d2 AddChar +%%EndResource + +673 1284 10 (a) 10 SB + +%%BeginResource: font MSTT31c2d2 +/G66 [10.0 0.0 1.0 -6.0 8.0 23.0] +/G66 { + 7 29 true [1 0 0 -1 -1.0 23.0] {<804020101008080c0c04060606060606060606040c0c08081010204080>} imagemask + } + 102 /G66 MSTT31c2d2 AddChar +%%EndResource + +724 1284 10 (f) 10 SB +32 0 0 50 50 0 0 0 51 /Symbol font +517 1313 27 (=) 27 SB +886 1313 27 (-) 27 SB +951 1313 27 (\243) 27 SB +1040 1313 27 (\243) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +695 1305 16 (+) 16 SB +574 1383 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +556 1299 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 1452 333 (global minimum) 333 SB +731 1452 14 (:) 14 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +793 1450 22 (x) 22 SB +1012 1450 14 (f) 14 SB +1056 1450 22 (x) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +816 1483 8 (i) 8 SB +32 0 0 50 50 0 0 0 51 /Symbol font +841 1446 27 (=) 27 SB +1109 1446 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +881 1452 25 (0) 25 SB +1149 1452 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1035 1411 17 (a) 17 SB +1082 1411 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1584 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 1590 270 (objfun9.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 1584 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font MSTT31c2d2 +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 6 6 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 376 (3. Dynamic optimization) 376 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (6) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 67 67 0 0 0 61 /Times-Bold /font29 ANSIFont font +279 305 702 (3. Dynamic optimization) 702 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 499 189 (Dynamic ) 200 SB +479 499 155 (control ) 166 SB +645 499 195 (problems ) 206 SB +851 499 74 (are ) 85 SB +936 499 181 (complex ) 193 SB +1129 499 84 (and ) 96 SB +1225 499 166 (difficult ) 178 SB +1403 499 54 (to ) 66 SB +1469 499 129 (solve. ) 141 SB +1610 499 90 (The ) 102 SB +1712 499 79 (use ) 91 SB +1803 499 54 (of ) 66 SB +1869 499 182 (dynamic-) 182 SB +279 574 261 (optimization ) 262 SB +541 574 162 (specific ) 163 SB +704 574 194 (methods, ) 195 SB +899 574 103 (such ) 104 SB +1003 574 54 (as ) 55 SB +1058 574 268 (Hamiltonian, ) 269 SB +1327 574 44 (is ) 45 SB +1372 574 253 (complicated ) 254 SB +1626 574 84 (and ) 86 SB +1712 574 260 (problematic. ) 262 SB +1974 574 77 (The) 77 SB +279 649 799 (application of specific methods requires ) 800 SB +1079 649 35 (a ) 36 SB +1115 649 111 (large ) 112 SB +1227 649 162 (amount ) 163 SB +1390 649 54 (of ) 55 SB +1445 649 275 (mathematical ) 276 SB +1721 649 165 (support ) 166 SB +1887 649 105 (even ) 106 SB +1993 649 58 (for) 58 SB +279 724 1696 (systems of moderate size, and only the most trivial systems can be solved analytically.) 1696 SB +279 849 54 (In ) 71 SB +350 849 74 (the ) 91 SB +441 849 201 (following ) 218 SB +659 849 177 (example ) 194 SB +853 849 208 (problems, ) 225 SB +1078 849 103 (each ) 121 SB +1199 849 206 (individual ) 224 SB +1423 849 49 (in ) 67 SB +1490 849 74 (the ) 92 SB +1582 849 261 (evolutionary ) 279 SB +1861 849 190 (algorithm) 190 SB +279 924 255 (corresponds ) 261 SB +540 924 54 (to ) 60 SB +600 924 35 (a ) 41 SB +641 924 201 (\(discrete\) ) 207 SB +848 924 155 (control ) 161 SB +1009 924 152 (vector. ) 158 SB +1167 924 112 (Each ) 119 SB +1286 924 168 (variable ) 175 SB +1461 924 49 (in ) 56 SB +1517 924 59 (an ) 66 SB +1583 924 206 (individual ) 213 SB +1796 924 44 (is ) 51 SB +1847 924 204 (associated) 204 SB +279 999 1027 (with the control input at a time step of the dynamic ) 1028 SB +1307 999 261 (optimization ) 262 SB +1569 999 189 (problem. ) 190 SB +1759 999 54 (In ) 55 SB +1814 999 83 (this ) 84 SB +1898 999 153 (section,) 153 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +279 1074 22 (x) 22 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +301 1074 460 ( is the state vector and ) 460 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +761 1074 25 (u) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +786 1074 618 ( the control vector of a system.) 618 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 1239 542 (3.1. Double integrator) 542 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1424 1510 (The double integrator problem is described by the following state equations.) 1510 SB + +%%BeginResource: font MSTT31c2ea +/MSTT31c2ea [50.0 0 0 0 0 0] 20 -140 [-50.0 -50.0 50.0 50.0] [1 50 div 0 0 1 50 div 0 0] /MSTT31c2ea GreNewFont +%%EndResource + +32 0 0 50 50 0 0 1 40 /MSTT31c2ea font + +%%BeginResource: font MSTT31c2ea +/G26 [17.0 0.0 6.0 27.0 12.0 32.0] +/G26 { + 6 5 true [1 0 0 -1 -6.0 32.0] {<78fcfcfc78>} imagemask + } + 38 /G26 MSTT31c2ea AddChar +%%EndResource + +412 1504 17 (&) 17 SB +408 1580 17 (&) 17 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +407 1499 22 (x) 22 SB +497 1499 25 (u) 25 SB +403 1576 22 (x) 22 SB +501 1576 22 (x) 22 SB +424 1653 22 (y) 22 SB +501 1653 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +428 1533 15 (1) 15 SB +426 1609 15 (2) 15 SB +522 1609 15 (1) 15 SB +524 1686 15 (2) 15 SB +32 0 0 50 50 0 0 0 51 /Symbol font +458 1495 27 (=) 27 SB +458 1572 27 (=) 27 SB +458 1649 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1782 90 (The ) 95 SB +374 1782 118 (value ) 123 SB +497 1782 54 (of ) 59 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +562 1780 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +585 1814 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +606 1782 13 ( ) 18 SB +624 1782 78 (has ) 83 SB +707 1782 54 (to ) 59 SB +766 1782 59 (be ) 64 SB +830 1782 177 (changed ) 182 SB +1012 1782 141 (during ) 146 SB +1158 1782 35 (a ) 40 SB +1198 1782 99 (time ) 104 SB +1302 1782 140 (period ) 145 SB +1447 1782 100 (with ) 106 SB +1553 1782 54 (as ) 60 SB +1613 1782 101 (little ) 107 SB +1720 1782 155 (control ) 161 SB +1881 1782 123 (effort ) 129 SB +2010 1782 41 (as) 41 SB +279 1862 172 (possible ) 185 SB +464 1862 84 (and ) 97 SB +561 1862 74 (the ) 87 SB +648 1862 98 (final ) 111 SB +759 1862 218 (conditions ) 232 SB +991 1862 109 (must ) 123 SB +1114 1862 59 (be ) 73 SB +1187 1862 100 (met, ) 114 SB +1301 1862 103 (such ) 117 SB +1418 1862 89 (that ) 103 SB +1521 1862 74 (the ) 88 SB +1609 1862 201 (following ) 215 SB +1824 1862 152 (criteria ) 166 SB +1990 1862 61 (are) 61 SB +279 1937 174 (satisfied.) 174 SB +321 2037 17 (-) 17 SB +397 2037 100 (time:) 100 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +578 2037 25 (0) 25 SB +715 2037 25 (1) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +614 2031 27 (\243) 27 SB +680 2031 27 (\243) 27 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +653 2035 14 (t) 14 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +321 2132 17 (-) 17 SB +397 2132 341 (initial conditions:) 341 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +877 2130 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +898 2164 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +935 2132 25 (0) 25 SB +1029 2132 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +916 2091 17 (a) 17 SB +962 2091 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +989 2126 27 (=) 27 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +1321 2130 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +1344 2164 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1383 2132 25 (0) 25 SB +1506 2132 25 (1) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1365 2091 17 (a) 17 SB +1410 2091 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +1438 2126 27 (=) 27 SB +1478 2126 27 (-) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +321 2232 17 (-) 17 SB +397 2232 317 (final conditions:) 317 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +877 2230 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +898 2264 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +930 2232 25 (1) 25 SB +1020 2232 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +916 2191 17 (a) 17 SB +953 2191 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +980 2226 27 (=) 27 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +1321 2230 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +1344 2264 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1468 2232 25 (0) 25 SB +1379 2232 25 (1) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +1365 2191 17 (a) 17 SB +1402 2191 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +1429 2226 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2362 832 (The objective function to be minimized is:) 832 SB +321 2482 17 (-) 17 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 2481 14 (f) 14 SB +449 2481 25 (u) 25 SB +581 2481 25 (u) 25 SB +625 2481 14 (t) 14 SB +683 2481 39 (dt) 39 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +542 2555 8 (t) 8 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +431 2443 17 (a) 17 SB +476 2443 17 (f) 17 SB +607 2443 17 (a) 17 SB +642 2443 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +502 2482 28 (=) 28 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +552 2556 16 (=) 16 SB +660 2476 15 (2) 15 SB +570 2556 15 (0) 15 SB +556 2443 15 (1) 15 SB +32 0 0 150 150 0 0 0 126 /MSTT31c2c7 font +%%BeginResource: font MSTT31c2c7 +currentfile eexec +9e67edc6b858a3e762244b628c0ab7daa0b706cbfc30718cf7399d83b4740f145229fb5ebdf788594b78bd5bf887825721eed2187e122621fabcc001faf87e69 +55872dd11bc9d0c6e3ec101e88b39d47077e52e02d7beecfd26e5d831e87d0280b97317bd99f4c0fcba055becc1f50cdc54bcd98e175c7aae256ab25b2c1f3f7 +780254f44e71c247e618c37736f3bc442d257fc46894d8bf47dc3306e73d59d1fd0bb04a6d2131749f481f3c9cf0496abd9bf2305eaa45f704f1da62443b86ac +87f1afa4dc4b1c11ff429d5e9109b5e1ad76301fcf7dd3c688b11bc52d9fb47ac50b5503e0ebe4054414cb2ec04a1dd50e6c625aa0164854e7db634a16393dff +45764f66ebea31f889dc747ef85310dd41e5dbbc8beff08726609f26871a7a177fc24d4fb038f1b5fd1d127deb25874e05c3871265ae26967e5c6d53852da61f +0ad3c982c70edbb404e8caf1616c6776810160a11655 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 + +cleartomark +%%EndResource +552 2419 21 (z) 21 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +730 2482 13 (.) 13 SB +279 2658 1132 (For these conditions an analytical solution is found to be:) 1132 SB +321 2753 17 (-) 17 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +399 2751 25 (u) 25 SB +635 2751 14 (t) 14 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +435 2754 28 (=) 28 SB +502 2754 13 ( ) 13 SB +524 2754 17 (-) 17 SB +549 2754 13 ( ) 13 SB +810 2754 200 (Minimum) 200 SB +1022 2754 28 (=) 28 SB +1057 2754 50 (12) 50 SB +474 2754 25 (6) 25 SB +561 2754 50 (12) 50 SB +32 0 0 50 50 0 0 0 51 /Symbol font +617 2748 13 (\327) 13 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +650 2754 13 (,) 13 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1110 2753 13 (.) 13 SB +279 2883 141 (Figure ) 141 SB +420 2883 25 (1) 25 SB +445 2883 1414 ( shows the optimal control vector and states for the continuous system:) 1414 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font MSTT31c2ea +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 7 7 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 376 (3. Dynamic optimization) 376 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (7) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +1 lc +1 lj +0 0 0 pC +0 4 SP +361 841 M 0 -568 1 PP +S +n +353 841 M 8 0 1 PP +S +n +353 747 M 8 0 1 PP +S +n +353 652 M 8 0 1 PP +S +n +353 557 M 8 0 1 PP +S +n +353 462 M 8 0 1 PP +S +n +353 368 M 8 0 1 PP +S +n +353 273 M 8 0 1 PP +S +n +361 841 M 1136 0 1 PP +S +n +361 849 M 0 -16 1 PP +S +n +475 849 M 0 -16 1 PP +S +n +588 849 M 0 -16 1 PP +S +n +702 849 M 0 -16 1 PP +S +n +815 849 M 0 -16 1 PP +S +n +929 849 M 0 -16 1 PP +S +n +1043 849 M 0 -16 1 PP +S +n +1156 849 M 0 -16 1 PP +S +n +1270 849 M 0 -16 1 PP +S +n +1384 849 M 0 -16 1 PP +S +n +1497 849 M 0 -16 1 PP +S +n +1 1 SP +gs 115 58 361 273 CB +361 273 M 114 57 1 PP +S +n +gr +gs 114 58 475 330 CB +475 330 M 113 57 1 PP +S +n +gr +gs 115 57 588 387 CB +588 387 M 114 56 1 PP +S +n +gr +gs 114 58 702 443 CB +702 443 M 113 57 1 PP +S +n +gr +gs 115 58 815 500 CB +815 500 M 114 57 1 PP +S +n +gr +gs 115 58 929 557 CB +929 557 M 114 57 1 PP +S +n +gr +gs 114 58 1043 614 CB +1043 614 M 113 57 1 PP +S +n +gr +gs 115 58 1156 671 CB +1156 671 M 114 57 1 PP +S +n +gr +gs 115 58 1270 728 CB +1270 728 M 114 57 1 PP +S +n +gr +gs 114 57 1384 785 CB +1384 785 M 113 56 1 PP +S +n +gr +2 1 SP +gs 115 2 361 603 CB +361 604 M 114 -1 1 PP +S +n +gr +gs 114 4 475 600 CB +475 603 M 113 -3 1 PP +S +n +gr +gs 115 7 588 594 CB +588 600 M 114 -6 1 PP +S +n +gr +gs 114 7 702 588 CB +702 594 M 113 -6 1 PP +S +n +gr +gs 115 8 815 581 CB +815 588 M 114 -7 1 PP +S +n +gr +gs 115 8 929 574 CB +929 581 M 114 -7 1 PP +S +n +gr +gs 114 8 1043 567 CB +1043 574 M 113 -7 1 PP +S +n +gr +gs 115 6 1156 562 CB +1156 567 M 114 -5 1 PP +S +n +gr +gs 115 5 1270 558 CB +1270 562 M 114 -4 1 PP +S +n +gr +gs 114 2 1384 557 CB +1384 558 M 113 -1 1 PP +S +n +gr +0 1 SP +gs 115 26 361 532 CB +361 557 M 114 -25 1 PP +S +n +gr +gs 114 21 475 512 CB +475 532 M 113 -20 1 PP +S +n +gr +gs 115 16 588 497 CB +588 512 M 114 -15 1 PP +S +n +gr +gs 114 9 702 489 CB +702 497 M 113 -8 1 PP +S +n +gr +gs 115 4 815 486 CB +815 489 M 114 -3 1 PP +S +n +gr +gs 115 4 929 486 CB +929 486 M 114 3 1 PP +S +n +gr +gs 114 9 1043 489 CB +1043 489 M 113 8 1 PP +S +n +gr +gs 115 16 1156 497 CB +1156 497 M 114 15 1 PP +S +n +gr +gs 115 21 1270 512 CB +1270 512 M 114 20 1 PP +S +n +gr +gs 114 26 1384 532 CB +1384 532 M 113 25 1 PP +S +n +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 1287 749 278 201 CB +299 817 35 (-6) 35 SB +gr +gs 1287 749 278 201 CB +299 722 35 (-4) 35 SB +gr +gs 1287 749 278 201 CB +299 627 35 (-2) 35 SB +gr +gs 1287 749 278 201 CB +313 533 21 (0) 21 SB +gr +gs 1287 749 278 201 CB +313 438 21 (2) 21 SB +gr +gs 1287 749 278 201 CB +313 343 21 (4) 21 SB +gr +gs 1287 749 278 201 CB +313 248 21 (6) 21 SB +gr +gs 1287 749 278 201 CB +351 874 21 (0) 21 SB +gr +gs 1287 749 278 201 CB +562 874 53 (0.2) 53 SB +gr +gs 1287 749 278 201 CB +789 874 53 (0.4) 53 SB +gr +gs 1287 749 278 201 CB +1016 874 53 (0.6) 53 SB +gr +gs 1287 749 278 201 CB +1244 874 53 (0.8) 53 SB +gr +gs 1287 749 278 201 CB +1487 874 21 (1) 21 SB +gr +gs 57 75 1019 418 CB +1026 431 42 (x1) 42 SB +gr +gs 57 75 529 589 CB +537 602 42 (x2) 42 SB +gr +gs 36 75 549 305 CB +557 318 21 (u) 21 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 976 78 (Fig. ) 78 SB +357 976 21 (1) 21 SB +378 976 12 (:) 12 SB +456 976 956 (Input and states of double integrator for optimal solution) 956 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1090 90 (The ) 101 SB +380 1090 147 (double ) 159 SB +539 1090 208 (integrator ) 220 SB +759 1090 44 (is ) 56 SB +815 1090 266 (implemented ) 278 SB +1093 1090 49 (in ) 61 SB +1154 1090 74 (the ) 86 SB +1240 1090 128 (m-file ) 140 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1380 1096 270 (objdopi.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1650 1090 13 ( ) 25 SB +1675 1090 118 (using ) 130 SB +1805 1090 35 (a ) 47 SB +1852 1090 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +1880 1099 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1167 148 (model, ) 150 SB +429 1167 59 (an ) 61 SB +490 1167 212 (s-function ) 214 SB +704 1167 84 (and ) 86 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +790 1167 168 (Control ) 170 SB +960 1167 151 (System ) 154 SB +1114 1167 164 (Toolbox) 164 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1278 1167 13 ( ) 16 SB +1294 1167 186 (routines. ) 189 SB +1483 1167 90 (The ) 93 SB +1576 1167 318 (implementation ) 321 SB +1897 1167 104 (used ) 107 SB +2004 1167 47 (by) 47 SB +279 1242 74 (the ) 79 SB +358 1242 192 (objective ) 197 SB +555 1242 176 (function ) 182 SB +737 1242 44 (is ) 50 SB +787 1242 150 (chosen ) 156 SB +943 1242 169 (through ) 175 SB +1118 1242 59 (an ) 65 SB +1183 1242 175 (optional ) 181 SB +1364 1242 212 (parameter ) 218 SB +1582 1242 127 (inside ) 133 SB +1715 1242 74 (the ) 80 SB +1795 1242 189 (function, ) 195 SB +1990 1242 61 (the) 61 SB +279 1317 267 (default is the ) 267 SB +546 1317 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +574 1326 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +745 1317 148 ( model.) 148 SB +0 lc +0 lj +6 4 SP +255 255 255 fC +149 124 633 1403 B +1 F +S +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +0 0 0 fC +683 1433 58 (1/s) 58 SB +255 255 255 fC +149 124 983 1403 B +1 F +S +n +0 0 0 fC +1033 1433 58 (1/s) 58 SB +255 255 255 fC +149 124 283 1403 B +1 F +S +n +0 0 0 fC +333 1433 25 (1) 25 SB +1 lc +1 lj +433 1478 M 200 0 1 PP +S +n +633 1478 M -25 -25 1 PP +S +n +608 1503 M 25 -25 1 PP +S +n +783 1478 M 200 0 1 PP +S +n +983 1478 M -25 -25 1 PP +S +n +958 1503 M 25 -25 1 PP +S +n +1133 1478 M 200 0 1 PP +S +n +1333 1478 M -25 -25 1 PP +S +n +1308 1503 M 25 -25 1 PP +S +n +808 1408 131 (state 1) 131 SB +1158 1408 131 (state 2) 131 SB +308 1534 119 (inport) 119 SB +608 1534 233 (integrator 1) 233 SB +958 1534 233 (integrator 2) 233 SB +0 lc +0 lj +255 255 255 fC +149 124 1333 1403 B +1 F +S +n +0 0 0 fC +1383 1433 25 (1) 25 SB +1333 1534 149 (outport) 149 SB +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 1618 78 (Fig. ) 78 SB +357 1618 21 (2) 21 SB +378 1618 12 (:) 12 SB +456 1618 593 (Block diagram of double integrator) 593 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1732 90 (The ) 90 SB +369 1732 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +397 1741 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +568 1732 660 ( method uses the model in figure ) 660 SB +1228 1732 25 (2) 25 SB +1253 1732 30 ( \() 30 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1283 1738 300 (simdopi1.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1583 1732 345 (\). The s-function ) 346 SB +1929 1732 122 (solves) 122 SB +279 1807 74 (the ) 76 SB +355 1807 122 (linear ) 124 SB +479 1807 203 (equations ) 205 SB +684 1807 17 (\() 17 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +701 1813 300 (simdopi2.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1001 1807 30 (\) ) 32 SB +1033 1807 120 (given ) 122 SB +1155 1807 131 (above ) 133 SB +1288 1807 84 (and ) 86 SB +1374 1807 74 (the ) 77 SB +1451 1807 106 (third ) 109 SB +1560 1807 162 (method ) 165 SB +1725 1807 17 (\() 17 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +1742 1807 168 (Control ) 171 SB +1913 1807 138 (System) 138 SB +279 1884 164 (Toolbox) 164 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +443 1884 543 (\) uses the transfer function:) 543 SB +1 lc +1 lj +0 2 SP +545 2024 M 48 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +400 1990 36 (G) 36 SB +456 1990 19 (s) 19 SB +549 2029 19 (s) 19 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +437 1952 17 (a) 17 SB +477 1952 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +504 1986 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +557 1960 25 (1) 25 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +571 2028 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +601 1992 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 2191 712 (3.2. Linear-quadratic system) 712 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2376 944 (The linear-quadratic system is one-dimensional:) 944 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 2465 22 (x) 22 SB +446 2465 22 (k) 22 SB +602 2465 25 (a) 25 SB +654 2465 22 (x) 22 SB +697 2465 22 (k) 22 SB +785 2465 25 (b) 25 SB +833 2465 25 (u) 25 SB +878 2465 22 (k) 22 SB +1017 2465 22 (k) 22 SB +32 0 0 50 50 0 0 0 51 /Symbol font +479 2461 27 (+) 27 SB +562 2461 27 (=) 27 SB +633 2461 13 (\327) 13 SB +748 2461 27 (+) 27 SB +816 2461 13 (\327) 13 SB +1053 2461 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +512 2467 25 (1) 25 SB +1089 2467 25 (1) 25 SB +1128 2467 25 (2) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +427 2426 17 (a) 17 SB +535 2426 17 (f) 17 SB +679 2426 17 (a) 17 SB +724 2426 17 (f) 17 SB +859 2426 17 (a) 17 SB +904 2426 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1110 2467 13 (,) 13 SB +1153 2467 13 (,) 13 SB +1169 2467 13 (.) 13 SB +1184 2467 13 (.) 13 SB +1199 2467 13 (.) 13 SB +1215 2467 13 (,) 13 SB +1233 2467 36 (N) 36 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1276 2467 13 (.) 13 SB +279 2601 1054 (The objective function for minimization is defined as:) 1054 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 2715 14 (f) 14 SB +452 2715 22 (x) 22 SB +494 2715 25 (u) 25 SB +587 2715 25 (q) 25 SB +639 2715 22 (x) 22 SB +685 2715 33 (N) 33 SB +947 2715 19 (s) 19 SB +993 2715 22 (x) 22 SB +1037 2715 22 (k) 22 SB +1146 2715 19 (r) 19 SB +1190 2715 25 (u) 25 SB +1235 2715 22 (k) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +874 2783 13 (k) 13 SB +886 2683 19 (N) 19 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +476 2717 13 (,) 13 SB +547 2717 28 (=) 28 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +431 2677 17 (a) 17 SB +520 2677 17 (f) 17 SB +664 2677 17 (a) 17 SB +786 2677 17 (f) 17 SB +1018 2677 17 (a) 17 SB +1063 2677 17 (f) 17 SB +1216 2677 17 (a) 17 SB +1261 2677 17 (f) 17 SB + +%%BeginResource: font MSTT31c2af +/G64 [17.0 0.0 2.0 -16.0 14.0 56.0] +/G64 { + 12 72 true [1 0 0 -1 -2.0 56.0] {<00100030006000e000c00180018003000300060006000e000e001c001c001c003c003c0038003800 +780078007800780070007000f000f000f000f000f000f000f000f000f000f000f000f000f000f000 +f000f000f000f000f000f0007000780078007800780078003800380038003c001c001c001c000e00 +0e0006000600030003000180018000c000e0006000300010>} imagemask + } + 100 /G64 MSTT31c2af AddChar +%%EndResource + +928 2677 17 (d) 17 SB + +%%BeginResource: font MSTT31c2af +/G69 [17.0 0.0 0.0 -16.0 13.0 56.0] +/G69 { + 13 72 true [1 0 0 -1 0.0 56.0] {<400060007000300018001c000c000e0006000700030003800380018001c001c001c001e000e000e0 +00f000f000f000f00070007000780078007800780078007800780078007800780078007800780078 +007800780078007800780078007000f000f000f000f000f000e000e001e001c001c001c001800380 +03800300070006000e000c001c00180030007000e0004000>} imagemask + } + 105 /G69 MSTT31c2af AddChar +%%EndResource + +1301 2677 17 (i) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +618 2711 13 (\327) 13 SB +730 2711 27 (+) 27 SB +832 2711 27 (+) 27 SB +973 2711 13 (\327) 13 SB +1110 2711 27 (+) 27 SB +1173 2711 13 (\327) 13 SB +32 0 0 29 29 0 0 0 29 /Symbol font +890 2781 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +869 2697 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +763 2717 25 (1) 25 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +803 2710 15 (2) 15 SB +1080 2710 15 (2) 15 SB +1279 2710 15 (2) 15 SB +906 2784 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1322 2717 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 8 8 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 376 (3. Dynamic optimization) 376 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (8) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 231 81 270 202 CB +357 226 56 (set) 56 SB +gr +gs 162 81 504 202 CB +567 226 36 (N) 36 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 162 81 669 202 CB +706 221 25 (x) 25 SB +gr +gs 162 81 669 202 CB +751 221 25 (0) 25 SB +gr +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +gs 162 81 669 202 CB +732 180 17 (a) 17 SB +gr +gs 162 81 669 202 CB +778 180 17 (f) 17 SB +gr +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +gs 163 81 834 202 CB +906 226 19 (s) 19 SB +gr +gs 162 81 1000 202 CB +1073 226 17 (r) 17 SB +gr +gs 163 81 1165 202 CB +1234 226 25 (q) 25 SB +gr +gs 162 81 1331 202 CB +1401 226 22 (a) 22 SB +gr +gs 162 81 1496 202 CB +1566 226 24 (b) 24 SB +gr +gs 375 81 1661 202 CB +1711 226 277 (exact solution) 277 SB +gr +5 5 264 202 B +1 F +n +5 5 264 202 B +1 F +n +230 5 270 202 B +1 F +n +5 5 501 202 B +1 F +n +158 5 507 202 B +1 F +n +5 5 666 202 B +1 F +n +158 5 672 202 B +1 F +n +5 5 831 202 B +1 F +n +159 5 837 202 B +1 F +n +5 5 997 202 B +1 F +n +158 5 1003 202 B +1 F +n +5 5 1162 202 B +1 F +n +159 5 1168 202 B +1 F +n +5 5 1328 202 B +1 F +n +158 5 1334 202 B +1 F +n +5 5 1493 202 B +1 F +n +158 5 1499 202 B +1 F +n +5 5 1658 202 B +1 F +n +371 5 1664 202 B +1 F +n +5 5 2036 202 B +1 F +n +5 5 2036 202 B +1 F +n +5 74 264 208 B +1 F +n +2 74 501 208 B +1 F +n +2 74 666 208 B +1 F +n +2 74 831 208 B +1 F +n +2 74 997 208 B +1 F +n +2 74 1162 208 B +1 F +n +2 74 1328 208 B +1 F +n +2 74 1493 208 B +1 F +n +2 74 1658 208 B +1 F +n +5 74 2036 208 B +1 F +n +gs 231 81 270 283 CB +419 307 25 (1) 25 SB +gr +gs 162 81 504 283 CB +571 307 50 (45) 50 SB +gr +gs 162 81 669 283 CB +712 307 75 (100) 75 SB +gr +gs 163 81 834 283 CB +927 307 25 (1) 25 SB +gr +gs 162 81 1000 283 CB +1093 307 25 (1) 25 SB +gr +gs 163 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SB +1592 2328 212 (s-function ) 216 SB +1808 2328 84 (and ) 88 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +1896 2328 155 (Control) 155 SB +279 2401 151 (System ) 185 SB +464 2401 164 (Toolbox) 164 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +628 2401 13 ( ) 47 SB +675 2401 173 (routines ) 207 SB +882 2401 44 (is ) 78 SB +960 2401 266 (implemented ) 300 SB +1260 2401 49 (in ) 83 SB +1343 2401 74 (the ) 108 SB +1451 2401 128 (m-file ) 162 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1613 2407 300 (objlinq2.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1913 2401 26 (. ) 61 SB +1974 2401 77 (The) 77 SB +279 2478 318 (implementation ) 322 SB +601 2478 104 (used ) 108 SB +709 2478 60 (by ) 64 SB +773 2478 74 (the ) 79 SB +852 2478 192 (objective ) 197 SB +1049 2478 176 (function ) 181 SB +1230 2478 44 (is ) 49 SB +1279 2478 150 (chosen ) 155 SB +1434 2478 169 (through ) 174 SB +1608 2478 59 (an ) 64 SB +1672 2478 175 (optional ) 180 SB +1852 2478 199 (parameter) 199 SB +279 2553 731 (inside the function, the default is the ) 731 SB +1010 2553 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +1038 2562 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1209 2553 148 ( model.) 148 SB +0 lc +0 lj +6 4 SP +255 255 255 fC +149 124 983 2714 B +1 F +S +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +0 0 0 fC +1033 2744 58 (1/s) 58 SB +255 255 255 fC +149 124 283 2714 B +1 F +S +n +0 0 0 fC +333 2744 25 (1) 25 SB +1 lc +1 lj +433 2789 M 200 0 1 PP +S +n +633 2789 M -25 -25 1 PP +S +n +608 2814 M 25 -25 1 PP +S +n +1133 2789 M 225 0 1 PP +S +n +1358 2789 M -25 -25 1 PP +S +n +1333 2814 M 25 -25 1 PP +S +n +1158 2719 131 (state 1) 131 SB +308 2844 119 (inport) 119 SB +958 2844 233 (integrator 1) 233 SB +0 lc +0 lj +255 255 255 fC +149 124 1358 2714 B +1 F +S +n +0 0 0 fC +1408 2744 25 (1) 25 SB +1358 2844 149 (outport) 149 SB +1 lc +1 lj +1308 2639 M 0 150 1 PP +S +n +533 2639 M 775 0 1 PP +S +n +0 lc +0 lj +255 255 255 fC +149 124 633 2714 B +1 F +S +n +0 0 0 fC +658 2844 90 (Sum) 90 SB +1 lc +1 lj +533 2639 M 0 100 1 PP +S +n +533 2739 M 100 0 1 PP +S +n +633 2739 M -25 -25 1 PP +S +n +633 2739 M -25 25 1 PP +S +n +644 2713 28 (+) 28 SB +644 2763 28 (+) 28 SB +783 2789 M 200 0 1 PP +S +n +983 2789 M -25 -25 1 PP +S +n +958 2814 M 25 -25 1 PP +S +n +6 6 1308 2788 E +1 F +n +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 2928 78 (Fig. ) 78 SB +357 2928 21 (4) 21 SB +378 2928 12 (:) 12 SB +456 2928 699 (Block diagram of linear-quadratic system) 699 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2c7 +%%+ font 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Dynamic optimization) 376 SB +1949 116 83 (Page ) 83 SB +2032 116 19 (9) 19 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 218 90 (The ) 90 SB +369 218 28 (S) 28 SB +32 0 0 40 40 0 0 0 36 /Times-Roman /font32 ANSIFont font +397 227 171 (IMULINK) 171 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +568 218 660 ( method uses the model in figure ) 660 SB +1228 218 25 (4) 25 SB +1253 218 30 ( \() 30 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1283 224 300 (simlinq1.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1583 218 345 (\). The s-function ) 346 SB +1929 218 122 (solves) 122 SB +279 293 416 (the linear equations \() 416 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +695 299 300 (simlinq2.m) 300 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +995 293 31 (\):) 31 SB +32 0 0 50 50 0 0 1 40 /MSTT31c2ea font +408 373 17 (&) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +535 447 13 (.) 13 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 369 22 (x) 22 SB +496 369 22 (x) 22 SB +580 369 25 (u) 25 SB +419 445 22 (y) 22 SB +496 445 22 (x) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +424 402 15 (1) 15 SB +517 402 15 (1) 15 SB +517 478 15 (1) 15 SB +32 0 0 50 50 0 0 0 51 /Symbol font +454 365 27 (=) 27 SB +544 365 27 (+) 27 SB +454 441 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 578 443 (and the third method \() 443 SB +32 0 0 50 50 0 0 0 45 /Times-Italic /font31 ANSIFont font +722 578 483 (Control System Toolbox) 483 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1205 578 543 (\) uses the transfer function:) 543 SB +1 lc +1 lj +0 0 0 pC +0 2 SP +546 718 M 88 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +400 684 36 (G) 36 SB +456 684 19 (s) 19 SB +549 723 19 (s) 19 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +437 646 17 (a) 17 SB +477 646 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +505 680 27 (=) 27 SB +578 719 27 (-) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +577 654 25 (1) 25 SB +610 725 25 (1) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +639 686 13 (.) 13 SB +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 885 483 (3.3. Harvest system) 483 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 1070 1599 (The harvest system is a one-dimensional equation of growth with one constraint:) 1599 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 1159 22 (x) 22 SB +446 1159 22 (k) 22 SB +602 1159 25 (a) 25 SB +654 1159 22 (x) 22 SB +697 1159 22 (k) 22 SB +783 1159 25 (u) 25 SB +828 1159 22 (k) 22 SB +967 1159 22 (k) 22 SB +32 0 0 50 50 0 0 0 51 /Symbol font +479 1155 27 (+) 27 SB +562 1155 27 (=) 27 SB +633 1155 13 (\327) 13 SB +748 1155 27 (-) 27 SB +1004 1155 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +512 1161 25 (1) 25 SB +1039 1161 25 (1) 25 SB +1078 1161 25 (2) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +427 1120 17 (a) 17 SB +535 1120 17 (f) 17 SB +679 1120 17 (a) 17 SB +724 1120 17 (f) 17 SB +809 1120 17 (a) 17 SB +854 1120 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1060 1161 13 (,) 13 SB +1103 1161 13 (,) 13 SB +1119 1161 13 (.) 13 SB +1134 1161 13 (.) 13 SB +1150 1161 13 (.) 13 SB +1165 1161 13 (,) 13 SB +1184 1161 36 (N) 36 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1226 1161 13 (,) 13 SB +397 1265 192 (such that ) 192 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +595 1263 22 (x) 22 SB +734 1263 22 (x) 22 SB +780 1263 33 (N) 33 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +638 1265 25 (0) 25 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +619 1224 17 (a) 17 SB +665 1224 17 (f) 17 SB +759 1224 17 (a) 17 SB +818 1224 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +692 1259 27 (=) 27 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +839 1265 13 (.) 13 SB +279 1395 1247 (The objective function for minimization is therefore defined as:) 1247 SB +621 1552 M 7 -4 1 PP +S +n +0 4 SP +628 1549 M 9 22 1 PP +S +n +0 2 SP +638 1571 M 12 -63 1 PP +S +n +650 1508 M 91 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 1509 14 (f) 14 SB +449 1509 25 (u) 25 SB +652 1509 25 (u) 25 SB +697 1509 22 (k) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +563 1577 13 (k) 13 SB +576 1477 19 (N) 19 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +431 1471 17 (a) 17 SB +476 1471 17 (f) 17 SB +678 1471 17 (a) 17 SB +723 1471 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +502 1511 28 (=) 28 SB +541 1511 17 (-) 17 SB +32 0 0 29 29 0 0 0 29 /Symbol font +580 1575 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +559 1491 53 (\345) 53 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +595 1578 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +747 1511 13 (.) 13 SB +279 1678 943 (The exact solution can be analytically found by:) 943 SB +704 1856 M 293 0 1 PP +S +n +671 1866 M 6 -4 1 PP +S +n +0 4 SP +677 1863 M 9 59 1 PP +S +n +0 2 SP +687 1922 M 13 -156 1 PP +S +n +700 1766 M 301 0 1 PP +S +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 1823 200 (Minimum) 200 SB +612 1823 28 (=) 28 SB +651 1823 17 (-) 17 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +709 1782 22 (x) 22 SB +836 1782 25 (a) 25 SB +735 1860 25 (a) 25 SB +862 1860 25 (a) 25 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +866 1779 19 (N) 19 SB +764 1858 19 (N) 19 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +752 1784 25 (0) 25 SB +933 1784 25 (1) 25 SB +928 1862 25 (1) 25 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +974 1769 15 (2) 15 SB +803 1859 15 (1) 15 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +734 1744 17 (a) 17 SB +779 1744 17 (f) 17 SB +817 1744 17 (c) 17 SB +956 1744 17 (h) 17 SB +843 1822 17 (a) 17 SB +951 1822 17 (f) 17 SB +32 0 0 50 50 0 0 0 51 /Symbol font +801 1778 13 (\327) 13 SB +901 1778 27 (-) 27 SB +826 1856 13 (\327) 13 SB +896 1856 27 (-) 27 SB +32 0 0 29 29 0 0 0 29 /Symbol font +787 1856 16 (-) 16 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1005 1823 13 (.) 13 SB +279 1999 141 (Figure ) 141 SB +420 1999 25 (5) 25 SB +445 1999 1194 ( shows the control vector for the harvest system with N=20.) 1194 SB +0 4 SP +440 2573 M 0 -423 1 PP +S +n +434 2573 M 6 0 1 PP +S +n +434 2503 M 6 0 1 PP +S +n +434 2432 M 6 0 1 PP +S +n +434 2362 M 6 0 1 PP +S +n +434 2291 M 6 0 1 PP +S +n +434 2220 M 6 0 1 PP +S +n +434 2150 M 6 0 1 PP +S +n +440 2573 M 1061 0 1 PP +S +n +440 2579 M 0 -12 1 PP +S +n +496 2579 M 0 -12 1 PP +S +n +552 2579 M 0 -12 1 PP +S +n +608 2579 M 0 -12 1 PP +S +n +663 2579 M 0 -12 1 PP +S +n +719 2579 M 0 -12 1 PP +S +n +775 2579 M 0 -12 1 PP +S +n +831 2579 M 0 -12 1 PP +S +n +887 2579 M 0 -12 1 PP +S +n +943 2579 M 0 -12 1 PP +S +n +998 2579 M 0 -12 1 PP +S +n +1054 2579 M 0 -12 1 PP +S +n +1110 2579 M 0 -12 1 PP +S +n +1166 2579 M 0 -12 1 PP +S +n +1221 2579 M 0 -12 1 PP +S +n +1277 2579 M 0 -12 1 PP +S +n +1333 2579 M 0 -12 1 PP +S +n +1389 2579 M 0 -12 1 PP +S +n +1445 2579 M 0 -12 1 PP +S +n +1501 2579 M 0 -12 1 PP +S +n +0 1 SP +gs 57 3 440 2560 CB +440 2562 M 56 -2 1 PP +S +n +gr +gs 57 4 496 2557 CB +496 2560 M 56 -3 1 PP +S +n +gr +gs 57 5 552 2553 CB +552 2557 M 56 -4 1 PP +S +n +gr +gs 56 6 608 2548 CB +608 2553 M 55 -5 1 PP +S +n +gr +gs 57 5 663 2544 CB +663 2548 M 56 -4 1 PP +S +n +gr +gs 57 6 719 2539 CB +719 2544 M 56 -5 1 PP +S +n +gr +gs 57 11 775 2529 CB +775 2539 M 56 -10 1 PP +S +n +gr +gs 57 9 831 2521 CB +831 2529 M 56 -8 1 PP +S +n +gr +gs 57 10 887 2512 CB +887 2521 M 56 -9 1 PP +S +n +gr +gs 56 17 943 2496 CB +943 2512 M 55 -16 1 PP +S +n +gr +gs 57 22 998 2475 CB +998 2496 M 56 -21 1 PP +S +n +gr +gs 57 17 1054 2459 CB +1054 2475 M 56 -16 1 PP +S +n +gr +gs 57 23 1110 2437 CB +1110 2459 M 56 -22 1 PP +S +n +gr +gs 56 39 1166 2399 CB +1166 2437 M 55 -38 1 PP +S +n +gr +gs 57 29 1221 2371 CB +1221 2399 M 56 -28 1 PP +S +n +gr +gs 57 42 1277 2330 CB +1277 2371 M 56 -41 1 PP +S +n +gr +gs 57 55 1333 2276 CB +1333 2330 M 56 -54 1 PP +S +n +gr +gs 57 70 1389 2207 CB +1389 2276 M 56 -69 1 PP +S +n +gr +gs 57 51 1445 2157 CB +1445 2207 M 56 -50 1 PP +S +n +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 85 75 928 2664 CB +935 2677 70 (u\(k\)) 70 SB +gr +32 -2700 -2700 42 42 0 0 0 37 /Times-Roman /font32 ANSIFont font +gs 75 77 293 2323 CB +304 2393 62 (f\(u\)) 62 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 1283 674 278 2080 CB +394 2549 21 (0) 21 SB +gr +gs 1283 674 278 2080 CB +373 2478 42 (10) 42 SB +gr +gs 1283 674 278 2080 CB +373 2408 42 (20) 42 SB +gr +gs 1283 674 278 2080 CB +373 2337 42 (30) 42 SB +gr +gs 1283 674 278 2080 CB +373 2266 42 (40) 42 SB +gr +gs 1283 674 278 2080 CB +373 2196 42 (50) 42 SB +gr +gs 1283 674 278 2080 CB +373 2125 42 (60) 42 SB +gr +gs 1283 674 278 2080 CB +430 2604 21 (1) 21 SB +gr +gs 1283 674 278 2080 CB +541 2604 21 (3) 21 SB +gr +gs 1283 674 278 2080 CB +653 2604 21 (5) 21 SB +gr +gs 1283 674 278 2080 CB +765 2604 21 (7) 21 SB +gr +gs 1283 674 278 2080 CB +876 2604 21 (9) 21 SB +gr +gs 1283 674 278 2080 CB +977 2604 42 (11) 42 SB +gr +gs 1283 674 278 2080 CB +1089 2604 42 (13) 42 SB +gr +gs 1283 674 278 2080 CB +1200 2604 42 (15) 42 SB +gr +gs 1283 674 278 2080 CB +1312 2604 42 (17) 42 SB +gr +gs 1283 674 278 2080 CB +1424 2604 42 (19) 42 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 2780 78 (Fig. ) 78 SB +357 2780 21 (5) 21 SB +378 2780 12 (:) 12 SB +456 2780 956 (Optimal control vector for the harvest system with N=20) 956 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2894 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 2900 270 (objharv.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 2894 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font MSTT31c2ea +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 10 10 +%%PageResources: (atend) +SS +0 0 25 31 776 1169 300 SM +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +0 0 0 fC +279 116 376 (3. Dynamic optimization) 376 SB +1930 116 83 (Page ) 83 SB +2013 116 38 (10) 38 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 58 58 0 0 0 54 /Times-Bold /font29 ANSIFont font +279 210 526 (3.4. Push-cart system) 526 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 395 1746 (The push-cart system is a two-dimensional system described by the following equations:) 1746 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 484 22 (x) 22 SB +461 484 22 (k) 22 SB +619 484 22 (x) 22 SB +682 484 22 (k) 22 SB +921 484 22 (k) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +424 518 15 (1) 15 SB +642 518 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +527 486 25 (1) 25 SB +993 486 25 (1) 25 SB +1032 486 25 (2) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +494 480 27 (+) 27 SB +577 480 27 (=) 27 SB +957 480 27 (=) 27 SB +32 0 0 101 101 0 0 0 85 /MSTT31c2c7 font +442 445 17 (a) 17 SB +549 445 17 (f) 17 SB +663 445 17 (a) 17 SB +708 445 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1014 486 13 (,) 13 SB +1057 486 13 (,) 13 SB +1073 486 13 (.) 13 SB +1088 486 13 (.) 13 SB +1103 486 13 (.) 13 SB +1119 486 13 (,) 13 SB +1138 486 36 (N) 36 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1180 486 13 (,) 13 SB +1 lc +1 lj +0 0 0 pC +0 2 SP +972 635 M 67 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +403 601 22 (x) 22 SB +466 601 22 (k) 22 SB +673 601 22 (x) 22 SB +736 601 22 (k) 22 SB +825 601 22 (x) 22 SB +884 601 22 (k) 22 SB +978 640 33 (N) 33 SB +1047 601 25 (u) 25 SB +1091 601 22 (k) 22 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +426 635 15 (2) 15 SB +696 635 15 (2) 15 SB +847 635 15 (1) 15 SB +1017 639 15 (2) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +531 603 25 (1) 25 SB +621 603 25 (2) 25 SB +993 571 25 (1) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +499 597 27 (+) 27 SB +582 597 27 (=) 27 SB +652 597 13 (\327) 13 SB +786 597 27 (-) 27 SB +934 597 27 (+) 27 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +447 563 17 (a) 17 SB +554 563 17 (f) 17 SB +717 563 17 (a) 17 SB +762 563 17 (f) 17 SB +865 563 17 (a) 17 SB +910 563 17 (f) 17 SB +1072 563 17 (a) 17 SB +1117 563 17 (f) 17 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1139 603 13 (.) 13 SB +279 762 1247 (The objective function for minimization is therefore defined as:) 1247 SB +829 910 M 94 0 1 PP +S +n +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +408 876 14 (f) 14 SB +452 876 22 (x) 22 SB +494 876 25 (u) 25 SB +606 876 22 (x) 22 SB +667 876 33 (N) 33 SB +884 915 33 (N) 33 SB +991 876 25 (u) 25 SB +1058 876 22 (k) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +936 944 13 (k) 13 SB +948 844 19 (N) 19 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +476 878 13 (,) 13 SB +547 878 28 (=) 28 SB +585 878 17 (-) 17 SB +32 0 0 100 100 0 0 1 84 /MSTT31c2af font +431 838 17 (a) 17 SB +520 838 17 (f) 17 SB +645 838 17 (a) 17 SB +767 838 17 (f) 17 SB +1039 838 17 (a) 17 SB +1084 838 17 (f) 17 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +627 909 15 (1) 15 SB +1018 875 15 (2) 15 SB +968 945 15 (1) 15 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +744 878 25 (1) 25 SB +864 846 25 (1) 25 SB +832 917 25 (2) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +712 872 27 (+) 27 SB +791 872 27 (+) 27 SB +863 911 13 (\327) 13 SB +32 0 0 29 29 0 0 0 29 /Symbol font +952 942 16 (=) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +932 858 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1105 878 13 (.) 13 SB +279 1045 943 (The exact solution can be analytically found by:) 943 SB +688 1193 M 28 0 1 PP +S +n +765 1193 M 153 0 1 PP +S +n +966 1193 M 115 0 1 PP +S +n +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +400 1161 200 (Minimum) 200 SB +612 1161 28 (=) 28 SB +690 1129 25 (1) 25 SB +691 1200 25 (3) 25 SB +32 0 0 50 50 0 0 0 51 /Symbol font +652 1155 27 (-) 27 SB +727 1155 27 (+) 27 SB +796 1123 13 (\327) 13 SB +862 1123 27 (-) 27 SB +817 1194 13 (\327) 13 SB +928 1155 27 (+) 27 SB +1000 1194 13 (\327) 13 SB +32 0 0 29 29 0 0 0 29 /Symbol font +1110 1225 16 (=) 16 SB +1114 1125 16 (-) 16 SB +32 0 0 75 75 0 0 0 76 /Symbol font +1089 1141 53 (\345) 53 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +767 1129 25 (3) 25 SB +894 1129 25 (1) 25 SB +786 1200 25 (6) 25 SB +1011 1129 25 (1) 25 SB +969 1200 25 (2) 25 SB +32 0 0 29 29 0 0 0 26 /Times-Roman /font32 ANSIFont font +876 1196 15 (2) 15 SB +1059 1196 15 (3) 15 SB +1177 1158 15 (2) 15 SB +1126 1228 15 (1) 15 SB +1130 1128 15 (1) 15 SB +32 0 0 50 50 0 0 0 47 /Times-Italic /font31 ANSIFont font +817 1127 33 (N) 33 SB +838 1198 33 (N) 33 SB +1021 1198 33 (N) 33 SB +1150 1159 22 (k) 22 SB +32 0 0 29 29 0 0 0 27 /Times-Italic /font31 ANSIFont font +1094 1227 13 (k) 13 SB +1091 1127 19 (N) 19 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1201 1161 13 (.) 13 SB +279 1328 141 (Figure ) 141 SB +420 1328 25 (6) 25 SB +445 1328 1237 ( shows the control vector for the push-cart system with N=20.) 1237 SB +0 4 SP +451 1905 M 0 -426 1 PP +S +n +445 1905 M 6 0 1 PP +S +n +445 1820 M 6 0 1 PP +S +n +445 1735 M 6 0 1 PP +S +n +445 1650 M 6 0 1 PP +S +n +445 1564 M 6 0 1 PP +S +n +445 1479 M 6 0 1 PP +S +n +451 1905 M 1047 0 1 PP +S +n +451 1911 M 0 -12 1 PP +S +n +506 1911 M 0 -12 1 PP +S +n +561 1911 M 0 -12 1 PP +S +n +616 1911 M 0 -12 1 PP +S +n +671 1911 M 0 -12 1 PP +S +n +726 1911 M 0 -12 1 PP +S +n +782 1911 M 0 -12 1 PP +S +n +837 1911 M 0 -12 1 PP +S +n +892 1911 M 0 -12 1 PP +S +n +947 1911 M 0 -12 1 PP +S +n +1002 1911 M 0 -12 1 PP +S +n +1057 1911 M 0 -12 1 PP +S +n +1112 1911 M 0 -12 1 PP +S +n +1167 1911 M 0 -12 1 PP +S +n +1222 1911 M 0 -12 1 PP +S +n +1277 1911 M 0 -12 1 PP +S +n +1332 1911 M 0 -12 1 PP +S +n +1387 1911 M 0 -12 1 PP +S +n +1443 1911 M 0 -12 1 PP +S +n +1498 1911 M 0 -12 1 PP +S +n +0 1 SP +gs 56 22 451 1500 CB +451 1500 M 55 21 1 PP +S +n +gr +gs 56 23 506 1521 CB +506 1521 M 55 22 1 PP +S +n +gr +gs 56 22 561 1543 CB +561 1543 M 55 21 1 PP +S +n +gr +gs 56 23 616 1564 CB +616 1564 M 55 22 1 PP +S +n +gr +gs 56 22 671 1586 CB +671 1586 M 55 21 1 PP +S +n +gr +gs 57 22 726 1607 CB +726 1607 M 56 21 1 PP +S +n +gr +gs 56 22 782 1628 CB +782 1628 M 55 21 1 PP +S +n +gr +gs 56 23 837 1649 CB +837 1649 M 55 22 1 PP +S +n +gr +gs 56 22 892 1671 CB +892 1671 M 55 21 1 PP +S +n +gr +gs 56 23 947 1692 CB +947 1692 M 55 22 1 PP +S +n +gr +gs 56 22 1002 1714 CB +1002 1714 M 55 21 1 PP +S +n +gr +gs 56 22 1057 1735 CB +1057 1735 M 55 21 1 PP +S +n +gr +gs 56 23 1112 1756 CB +1112 1756 M 55 22 1 PP +S +n +gr +gs 56 22 1167 1778 CB +1167 1778 M 55 21 1 PP +S +n +gr +gs 56 22 1222 1799 CB +1222 1799 M 55 21 1 PP +S +n +gr +gs 56 22 1277 1820 CB +1277 1820 M 55 21 1 PP +S +n +gr +gs 56 23 1332 1841 CB +1332 1841 M 55 22 1 PP +S +n +gr +gs 57 22 1387 1863 CB +1387 1863 M 56 21 1 PP +S +n +gr +gs 56 22 1443 1884 CB +1443 1884 M 55 21 1 PP +S +n +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 85 75 932 1996 CB +939 2009 70 (u\(k\)) 70 SB +gr +32 -2700 -2700 42 42 0 0 0 37 /Times-Roman /font32 ANSIFont font +gs 75 108 293 1638 CB +304 1739 94 (f\(x,u\)) 94 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +gs 1280 677 278 1409 CB +405 1881 21 (0) 21 SB +gr +gs 1280 677 278 1409 CB +373 1796 53 (0.2) 53 SB +gr +gs 1280 677 278 1409 CB +373 1710 53 (0.4) 53 SB +gr +gs 1280 677 278 1409 CB +373 1625 53 (0.6) 53 SB +gr +gs 1280 677 278 1409 CB +373 1540 53 (0.8) 53 SB +gr +gs 1280 677 278 1409 CB +405 1454 21 (1) 21 SB +gr +gs 1280 677 278 1409 CB +440 1936 21 (1) 21 SB +gr +gs 1280 677 278 1409 CB +551 1936 21 (3) 21 SB +gr +gs 1280 677 278 1409 CB +661 1936 21 (5) 21 SB +gr +gs 1280 677 278 1409 CB +771 1936 21 (7) 21 SB +gr +gs 1280 677 278 1409 CB +881 1936 21 (9) 21 SB +gr +gs 1280 677 278 1409 CB +981 1936 42 (11) 42 SB +gr +gs 1280 677 278 1409 CB +1091 1936 42 (13) 42 SB +gr +gs 1280 677 278 1409 CB +1201 1936 42 (15) 42 SB +gr +gs 1280 677 278 1409 CB +1311 1936 42 (17) 42 SB +gr +gs 1280 677 278 1409 CB +1422 1936 42 (19) 42 SB +gr +32 0 0 42 42 0 0 0 38 /Times-Roman /font32 ANSIFont font +279 2112 78 (Fig. ) 78 SB +357 2112 21 (6) 21 SB +378 2112 12 (:) 12 SB +456 2112 992 (Optimal control vector for the push-cart system with N=20) 992 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 2226 836 (This function is implemented in the m-file ) 836 SB +32 0 0 50 50 0 0 0 39 /Courier /font0 ANSIFont font +1115 2232 270 (objpush.m) 270 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +1385 2226 13 (.) 13 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Courier +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman +%%Page: 11 11 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References) 207 SB +1930 116 83 (Page ) 83 SB +2013 116 38 (11) 38 SB +255 255 255 fC +/fm 256 def +1783 3 273 159 B +1 F +n +0 0 0 fC +1783 2 273 163 B +1 F +n +32 0 0 67 67 0 0 0 61 /Times-Bold /font29 ANSIFont font +279 305 382 (4. References) 382 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +279 499 162 ([Mic92]) 162 SB +515 499 1370 (Michalewicz, Z.: "Genetic Algorithms + Data Structures = Evolution) 1370 SB +515 574 1160 (Programs"; Berlin, Heidelberg, New York: Springer, 1992) 1160 SB +279 699 189 ([MSB91]) 189 SB +515 699 44 (M) 44 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +559 699 25 (\374) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +584 699 1456 (hlenbein, H., Schomisch, M. and Born, J.: "The parallel genetic algorithm) 1456 SB +515 774 1304 (as function optimizer"; Parallel Computing, 17, pp.619-632, 1991) 1304 SB +279 899 192 ([OGH93]) 192 SB +515 899 1526 (Ostermeier, A., Gawelczyk, A. and Hansen, N.: "A Derandomized Approach) 1526 SB +515 974 1474 (to Self Adaptation of Evolution Strategies"; Technical Report TR-93-003,) 1474 SB +515 1049 326 (TU Berlin, 1993) 326 SB +279 1174 161 ([Rec73]) 161 SB +515 1174 1534 (Rechenberg, I.: "Evolutionsstrategie - Optimierung technischer Systeme nach) 1534 SB +515 1249 1435 (Prinzipien der biologischen Evolution"; Stuttgart: Frommann-Holzboog,) 1435 SB +515 1324 100 (1973) 100 SB +279 1449 161 ([Rec94]) 161 SB +515 1449 1475 (Rechenberg, I.: "Evolutionsstrategie 94"; Stuttgart: Frommann-Holzboog,) 1475 SB +515 1524 100 (1994) 100 SB +279 1649 158 ([Sch81]) 158 SB +515 1649 1507 (Schwefel, H.-P.: "Numerical optimization of computer models"; Chichester:) 1507 SB +515 1724 402 (Wiley & Sons, 1981) 402 SB +279 1849 143 ([SE92]) 143 SB +515 1849 1418 (Stuckmann, B. E.; Easom, E. E.: "A Comparison of Bayesian/Sampling) 1418 SB +515 1924 1516 (Global Optimization Techniques"; IEEE Transactions on Systems, Man, and) 1516 SB +515 1999 980 (Cybernetics, Vol. 22, No. 5, pp.1024-1032, 1992) 980 SB +279 2124 175 ([SHF94]) 175 SB +515 2124 74 (Sch) 74 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +589 2124 25 (\366) 25 SB +32 0 0 50 50 0 0 0 45 /Times-Roman /font32 ANSIFont font +614 2124 1416 (neburg, E., Heinzmann, F. and Feddersen, S.: "Genetische Algorithmen) 1416 SB +515 2199 1470 (und Evolutionsstrategien"; Bonn, Paris, Reading, Mass.: Addison-Wesley,) 1470 SB +515 2274 100 (1994) 100 SB +279 2399 145 ([TZ89]) 145 SB +515 2399 1468 (T\366rn, A. and Zilinskas, A.: "Global Optimization"; volume 350 of Lecture) 1468 SB +515 2474 1494 (Notes in Computer Science, Berlin, Heidelberg, New York: Springer, 1989) 1494 SB +32 0 0 38 38 0 0 0 34 /Times-Roman /font32 ANSIFont font +279 3120 420 (Genetic Algorithm Toolbox) 420 SB +1826 3120 225 (Test Functions) 225 SB +255 255 255 fC +1783 3 273 3071 B +1 F +n +0 0 0 fC +1783 2 273 3068 B +1 F +n +1 #C +statusdict begin /manualfeed false store end +EJ RS +%%PageTrailer +%%PageResources: font Times-Bold +%%+ font Times-Roman +%%Trailer +SVDoc restore +end +%%Pages: 11 +% TrueType font name key: +% MSTT310000 = +% MSTT310000 = +% MSTT310000 = +% MSTT310000 = +% MSTT310000 = +% MSTT31c1c0 = 2aa7DTimes New RomanF00000000000001900000 +% MSTT31c1cd = 2aa7DTimes New RomanF00000032000001900000 +% MSTT31c26e = 2aa7DTimes New RomanF00000043000002bc0000 +% MSTT31c27b = 2aa7DTimes New RomanF00000028000001900000 +% MSTT31c288 = 2aa7DTimes New RomanF0000002a000001900000 +% MSTT31c295 = 2aa7DTimes New RomanF00000026000001900000 +% MSTT31c20e = 2aa7DCourier NewF00000032000001900000 +% MSTT31c2a2 = 2aa7DTimes New RomanF0000003a000002bc0000 +% MSTT31c2af = 2aa7DFencesF00000064000001900000 +% MSTT31c2ba = 2aa7DTimes New RomanF00000010000001900000 +% MSTT31c2c7 = 2aa7DFencesF00000000000001900000 +% MSTT31c2d2 = 2aa7DFencesF0000003a000001900000 +% MSTT31c2dd = 2aa7DTimes New RomanF00000032000001900001 +% MSTT31c2ea = 2aa7DMT ExtraF00000032000001900000 +% MSTT31c2f5 = 2aa7DArialF00000021000002bc0000 +% MSTT31c300 = 2aa7DTimes New RomanF0000000a000001900000 +% MSTT31c30d = 2aa7DTimes New RomanF0000001a000001900000 +% MSTT31c31a = 2aa7DTimes New RomanF0000002af57401900000 +%%DocumentSuppliedResources: procset Win35Dict 3 1 +%%+ font MSTT31c2af +%%+ font MSTT31c2c7 +%%+ font MSTT31c2d2 +%%+ font MSTT31c2ea + +%%DocumentNeededResources: font Courier +%%+ font Symbol +%%+ font Times-Bold +%%+ font Times-Italic +%%+ font Times-Roman + +%%EOF + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVDP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVDP.M" index edcbd786d18e2b455ea6fc29c9bd0e01c76e6848..76aab634fbcad1e9a5e57fc67037e00552782be3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVDP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVDP.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:36e7e1f37a0707c6785ec214489d551b56d157f8c2c1227e27f93a880df6c70b -size 1042 +% XOVDP.M (CROSSOVer Double Point) +% +% This function performs double point crossover between pairs of +% individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovdp(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovdp(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 2, 0); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVDPRS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVDPRS.M" index 902f4f6c09a3473197b746d4714c397960859a6b..e65331226383389f327e7b596f6db1aca13058dd 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVDPRS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVDPRS.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9e38f004605377c6c745681434ae98682be231ea910b71894507753f334c8e54 -size 1090 +% XOVDPRS.M (CROSSOVer Double-Point with Reduced Surrogate) +% +% This function performs double-point 'reduced surrogate' crossover between +% pairs of individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovdprs(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovdprs(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low-level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 2, 1); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVMP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVMP.M" index 0125c287895f7b43b938db33b4691ad377c536d9..1b49416566cdb5b2088b055891d1a34ac22609d3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVMP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVMP.M" @@ -1,3 +1,84 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:492c5255f6c08d5cd3a89d284b09cbbe072271fcb15b44833df2758df7dc7425 -size 2795 +% XOVMP.m Multi-point crossover +% +% Syntax: NewChrom = xovmp(OldChrom, Px, Npt, Rs) +% +% This function takes a matrix OldChrom containing the binary +% representation of the individuals in the current population, +% applies crossover to consecutive pairs of individuals with +% probability Px and returns the resulting population. +% +% Npt indicates how many crossover points to use (1 or 2, zero +% indicates shuffle crossover). +% Rs indicates whether or not to force the production of +% offspring different from their parents. +% + +% Author: Carlos Fonseca, Updated: Andrew Chipperfield +% Date: 28/09/93, Date: 27-Jan-94 + +function NewChrom = xovmp(OldChrom, Px, Npt, Rs); + +% Identify the population size (Nind) and the chromosome length (Lind) +[Nind,Lind] = size(OldChrom); + +if Lind < 2, NewChrom = OldChrom; return; end + +if nargin < 4, Rs = 0; end +if nargin < 3, Npt = 0; Rs = 0; end +if nargin < 2, Px = 0.7; Npt = 0; Rs = 0; end +if isnan(Px), Px = 0.7; end +if isnan(Npt), Npt = 0; end +if isnan(Rs), Rs = 0; end +if isempty(Px), Px = 0.7; end +if isempty(Npt), Npt = 0; end +if isempty(Rs), Rs = 0; end + +Xops = floor(Nind/2); +DoCross = rand(Xops,1) < Px; +odd = 1:2:Nind-1; +even = 2:2:Nind; + +% Compute the effective length of each chromosome pair +Mask = ~Rs | (OldChrom(odd, :) ~= OldChrom(even, :)); +Mask = cumsum(Mask')'; + +% Compute cross sites for each pair of individuals, according to their +% effective length and Px (two equal cross sites mean no crossover) +xsites(:, 1) = Mask(:, Lind); +if Npt >= 2, + xsites(:, 1) = ceil(xsites(:, 1) .* rand(Xops, 1)); +end +xsites(:,2) = rem(xsites + ceil((Mask(:, Lind)-1) .* rand(Xops, 1)) ... + .* DoCross - 1 , Mask(:, Lind) )+1; + +% Express cross sites in terms of a 0-1 mask +Mask = (xsites(:,ones(1,Lind)) < Mask) == ... + (xsites(:,2*ones(1,Lind)) < Mask); + +if ~Npt, + shuff = rand(Lind,Xops); + [ans,shuff] = sort(shuff); + for i=1:Xops + OldChrom(odd(i),:)=OldChrom(odd(i),shuff(:,i)); + OldChrom(even(i),:)=OldChrom(even(i),shuff(:,i)); + end +end + +% Perform crossover +NewChrom(odd,:) = (OldChrom(odd,:).* Mask) + (OldChrom(even,:).*(~Mask)); +NewChrom(even,:) = (OldChrom(odd,:).*(~Mask)) + (OldChrom(even,:).*Mask); + +% If the number of individuals is odd, the last individual cannot be mated +% but must be included in the new population +if rem(Nind,2), + NewChrom(Nind,:)=OldChrom(Nind,:); +end + +if ~Npt, + [ans,unshuff] = sort(shuff); + for i=1:Xops + NewChrom(odd(i),:)=NewChrom(odd(i),unshuff(:,i)); + NewChrom(even(i),:)=NewChrom(even(i),unshuff(:,i)); + end +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSH.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSH.M" index 738452b855b533b9c25c985217770a2aa05e8c2a..f44f5b6d039c6b0363c290e5db4d5c1936416ce8 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSH.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSH.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:fba081244535a69f8765c25d7dc572af5fdc23be033333c847981673ec02a2a4 -size 1032 +% XOVSH.M (CROSSOVer SHuffle) +% +% This function performs shuffle crossover between pairs of +% individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovsh(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovsh(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 0, 0); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSHRS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSHRS.M" index a9c8be0baeda8668ede638f71df18ef5db466e73..4ceea7550e2f8ccb2cd1c560cc31fcc130bd40ae 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSHRS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSHRS.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:05e39153994c1cd4415d9c9412e1f5a2d7298171fdf2501fbd053f3bd3749894 -size 1080 +% XOVSHRS.M (CROSSOVer SHuffle with Reduced Surrogate) +% +% This function performs shuffle 'reduced surrogate' crossover between +% pairs of individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovshrs(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovshrs(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 0, 1); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSP.M" index c4ae37ba22b78fec3557b99d4b8080ba05904a9f..b5f029eccfc239ae1d6a578552568dca6dc1687a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSP.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:83492d75f6a1da8f4624cff6a540a7844f89ccdd99d046251a2cf80cae2e2245 -size 1043 +% XOVSP.M (CROSSOVer Single-Point) +% +% This function performs single-point crossover between pairs of +% individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovsp(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovsp(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 1, 0); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSPRS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSPRS.M" index 7305f1eb57cfc9186cc2151720fe0e20251af26d..0809b4dc4cd913f9cd7b516869a85e74ee4d17a7 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSPRS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/gatbx/gatbx-toolbox/gatbx/XOVSPRS.M" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1fd4438f59f1e79d28ca7949a48dd466fc29300d0a969728af9657bea8809c26 -size 1090 +% XOVSPRS.M (CROSSOVer Single-Point with Reduced Surrogate) +% +% This function performs single-point 'reduced surrogate' crossover between +% pairs of individuals and returns the current generation after mating. +% +% Syntax: NewChrom = xovsprs(OldChrom, XOVR) +% +% Input parameters: +% OldChrom - Matrix containing the chromosomes of the old +% population. Each line corresponds to one individual +% (in any form, not necessarily real-values). +% XOVR - Probability of recombination occurring between pairs +% of individuals. +% +% Output parameter: +% NewChrom - Matrix containing the chromosomes of the population +% after mating, ready to be mutated and/or evaluated, +% in the same format as OldChrom. + +% Author: Hartmut Pohlheim +% History: 28.03.94 file created + +function NewChrom = xovsprs(OldChrom, XOVR); + +if nargin < 2, XOVR = NaN; end + +% call low-level function with appropriate parameters + NewChrom = xovmp(OldChrom, XOVR, 1, 1); + + +% End of function + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/\350\257\264\346\230\216.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/\350\257\264\346\230\216.txt" index c15316385bf2b657a47f1d0e7f554c79d2221b5b..029daa8d2f0856b329bf9ee19425f2df3931b859 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/\350\257\264\346\230\216.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\343\200\212Matlab\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261\345\217\212\345\272\224\347\224\250\343\200\213\346\272\220\347\240\201/\350\257\264\346\230\216.txt" @@ -1,3 +1,11 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1495561e594f04992870dbeeebd16eb5072cbdf9119f2084ed6181fc3c4ea6ee -size 927 +1.¸½¼þ½á¹¹: gatbx.rar: (1)gatbx-origin.zip; (2)gatbx-toolbox.rar; (3)gatbx-example.rar + +2.µ÷ÊÔËùÓÃMatlab°æ±¾ÊÇ6.5£¬gatbx-toolboxÊǵ÷ÊÔ¹ý³ÌÖÐʹÓõŤ¾ßÏ䣬ÓÐЩÈÈÐĵÄÑÐÓÑÒѾ­ÌṩÁ˸ù¤¾ßÏ䣬֮ËùÒÔÔÙÌùÒ»±é£¬ÊÇÒòΪ6.5°æ±¾Ïµ÷ÊԸù¤¾ßÏä»á³öÏÖһЩ´íÎóÌáʾ£¬Ôڸð汾ÖÐÒѾ­½øÐÐÁ˸ÄÕý£¬Ê¹Óøù¤¾ßÏäÖ»ÐèÒª½«Ñ¹Ëõ°üϵÄgatbxºÍgatbx\Test_fns¼ÓÈëµ½MatlabËÑË÷·¾¶¼´¿É£¬ÁíÍâgatbx-originÊÇSheffield´óѧÌṩµÄԭʼ°æ±¾µÄ¹¤¾ßÏ䣬δ×öÈκθĶ¯£¬Á½Õß¿É×ö±È½ÏÖ®Óà + +3.gatbx-exampleÊÇËãÀýµ÷ÊÔÔ´ÂëºÍ¸÷ËãÀýµÄµ÷ÊÔ˵Ã÷£¬´ó¼Ò¿ÉÒÔ¶ÔÕÕÔ­Êé½øÐÐ±È½Ï + +4.ÇÔÒÔΪgatbx¹¤¾ßÏä½ÏÖ®Matlab7аæϵÄgads¹¤¾ßÏä¸üÄÜÈÃÈËÊìϤºÍÁ˽âÒÅ´«Ëã·¨µÄÔ­ÀíºÍ¼ÆËã¹ý³Ì£¬ËäÈ»ÔÚ¿ÉÊÓ»¯·½Ãæ²»¼°gads + +5.ѧϰÒÅ´«Ëã·¨Èç¹ûÊ×ÏÈÓÃÊìÏà¹Ø¹¤¾ßÏäµÄ»°£¬Äܹ»ÏÈÅàÑøÐÅÐÄ£¬È»ºó¸üÓÐÐËȤȥרÑкÍÁ˽â¾ßÌåµÄËã·¨£¬Èç¹û¾ÍÓÃÏÖÓеŤ¾ßÏä¾ÍÄܽâ¾öÎÊÌâµÄ»°£¬²»Á˽âÆäÏêϸµÄË㷨Ҳδ³¢²»¿É£¬±Ï¾¹²»ÊÇÿ¸öÑÐÓѶ¼ÄÜÏòsee_moonlightÄÇÑù¿ª·¢×Ô¼ºµÄ¹¤¾ßÏä°É, + +×îºó¸Ðлsee_moonlight°ßÖñµÄ´óÁ¦Ö§³ÖºÍ¹ÄÀø£¬Ôڴ˽÷ÖÂлÒ⣡ diff --git 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"b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\205\263\344\272\216\351\201\227\344\274\240\347\256\227\346\263\225\345\272\224\347\224\250\347\232\204\344\270\200\344\272\233\345\217\202\350\200\203\346\226\207\347\214\256/\344\270\211\344\270\252\351\201\227\344\274\240\347\256\227\346\263\225matlab\347\250\213\345\272\217\345\256\236\344\276\213.docx" index a8ae9c3aaee59e647ae8eb46b02293f15ffbbda6..5fc0fa83f01dafc75fbb5695cb1f4033ce940e85 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\205\263\344\272\216\351\201\227\344\274\240\347\256\227\346\263\225\345\272\224\347\224\250\347\232\204\344\270\200\344\272\233\345\217\202\350\200\203\346\226\207\347\214\256/\344\270\211\344\270\252\351\201\227\344\274\240\347\256\227\346\263\225matlab\347\250\213\345\272\217\345\256\236\344\276\213.docx" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\205\263\344\272\216\351\201\227\344\274\240\347\256\227\346\263\225\345\272\224\347\224\250\347\232\204\344\270\200\344\272\233\345\217\202\350\200\203\346\226\207\347\214\256/\344\270\211\344\270\252\351\201\227\344\274\240\347\256\227\346\263\225matlab\347\250\213\345\272\217\345\256\236\344\276\213.docx" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/Contents.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/Contents.m" index 9c2b3246bd58b4288de45f7fac9ebf5dea026263..a41b2d59953a8508fe785b1750f71365f0ded45f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/Contents.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/Contents.m" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:11678efe112025b2703e2059dd1d9ff1f02b2d23c73cc6c7d18e149a7278616a -size 3021 +% Genetic Optimization Toolbox +% +% Main interface +% ga.m The Genetic Algorithm +% initialize.m Initialization function Used by ga.m +% +% Operators used during simulated evolution +% +% Crossover Operators +% heuristicXover.m Operator for the Algorithm Used by ga.m +% arithXover.m Operator for the Algorithm Used by ga.m +% simpleXover.m Operator for the Algorithm Used by ga.m +% +% Mutation Operators +% binaryMutation.m Operator for the Algorithm Used by ga.m +% boundaryMutation.m Operator for the Algorithm Used by ga.m +% multiNonUnifMutation.m Operator for the Algorithm Used by ga.m +% nonUnifMutation.m Operator for the Algorithm Used by ga.m +% unifMutation.m Operator for the Algorithm Used by ga.m +% +% Selection Functions +% normGeomSelect.m Selection function Used by ga.m +% roulette.m Selection function Used by ga.m +% tournSelect.m Selection function Used by ga.m +% +% Termination Functions +% maxGenTerm.m Termination function Used by ga.m +% optMaxGenTerm.m Termination function Used by ga.m +% +% Functions used for binary representation +% calcbits.m Binary precision function used by ga.m +% f2b.m Float to Binary conversion used by ga.m +% b2f.m Binary to Float conversion used by ga.m +% +% Utility functions +% parse.m Parse blank separated names used by ga.m +% delta.m Used by nonUnifMutation.m and mult...m +% +% Demonstrations +% gademo1.m Introductory demo of GAOT +% gademo2.m Multi-dimensional demo of GAOT +% gademo3.m Reference for GAOT +% +% Functions used in Demonstrations +% gademo1eval1.m Example eval function used by gademo1.m +% coranaEval.m Calculate Corana functions used by gademo2.m +% coranaMin.m Calculate negative of Corana used by gademo2.m +% gaEval.m Calculation of Corana used for testing +% gaGradEval.m Evaluation Used for Testing +% gaGradGrad.m Gradient used for SQP during Testing + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/README" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/README" index 9a308668a1087e12b42b82f6b784df999b1cb05e..3d85da627ab354060212897de7ca172b70a81cd4 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/README" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/README" @@ -1,3 +1,21 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:60a56c5a7a7fd04540480a74dea68e1f19126771813c1a28c68321525e9f74f6 -size 803 +This directory contains the Genetic Algorithm Optimization Toolbox for +Matlab. + +To use this, if you are local to NCSU and have AFS access to this +directory, simply extend the matlab path here. + +>>path(path,'/afs/eos/info/ie589k_info/GAOT'); + +Otherwise, install the .m files into a directory named GAOT and extend +the matlab path to that directory. The compressed tar archive and the +zip file should automatically create the GAOT directory for you. + +The companion paper describing this toolbox is included here as +gaot.ps. This and the three demo files, gademo1.m gademo2.m gademo3.m, +should be sufficient explanation of this toolbox. For any questions, +comments, suggestions send mail to jjoine@eos.ncsu.edu. + +For a list of the files in the tool box get help on GAOT. + +Thanks for trying the toolbox. + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/arithXover.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/arithXover.m" index bb9f1ccddf67cf466fa62066dbd059dbc7f47e76..c6b4ca600debff94bec57eeff50070937c49ba48 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/arithXover.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/arithXover.m" @@ -1,3 +1,36 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:fa289c849b880cde1e2b6bda6f1cfd9cecfb7d98b4c2754fb4c0680cbafbf90e -size 1490 +function [c1,c2] = arithXover(p1,p2,bounds,Ops) +% Arith crossover takes two parents P1,P2 and performs an interpolation +% along the line formed by the two parents. +% +% function [c1,c2] = arithXover(p1,p2,bounds,Ops) +% p1 - the first parent ( [solution string function value] ) +% p2 - the second parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options matrix for arith crossover [gen #ArithXovers] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +% Pick a random mix amount +a = rand; + +% Create the children +c1 = p1*a + p2*(1-a); +c2 = p1*(1-a) + p2*a; +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/b2f.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/b2f.m" index c7660a6d44ddfd1e95a2270591d4ab73f72df405..f712bf281fc3c26e160ba09ed6e2696adb905a8c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/b2f.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/b2f.m" @@ -1,3 +1,36 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:06b62dd9938e52d9911900f1a3aec805331dc31a0f57acbae7f35c36cf808dcd -size 1495 +function [fval] = b2f(bval,bounds,bits) +% function [fval] = b2f(bval,bounds,bits) +% +% Return the float number corresponing to the binary representation of bval. +% +% fval - the float representation of the number +% bval - the binary representation of the number +% bounds - the bounds on the variables +% bits - the number of bits to represent each variable + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables +numV=size(bounds,1); +cs=[0 cumsum(bits)]; +for i=1:numV + a=bval((cs(i)+1):cs(i+1)); + fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/binaryMutation.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/binaryMutation.m" index d1efee7ee568604dd411b1e01c61b6b83cd912e8..93a51bc638e3184b404727bd4d85f8f5d0c22b6e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/binaryMutation.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/binaryMutation.m" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:5eaf2ba477545018f14e5464ac1bb514388e3a7ad60cd37e2c2f737f0b6cae39 -size 1507 +function [parent] = binaryMutate(parent,bounds,Ops) +% Binary mutation changes each of the bits of the parent +% based on the probability of mutation +% +% function [newSol] = binaryMutate(parent,bounds,Ops) +% parent - the first parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options for binaryMutation [gen prob_of_mutation] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +pm=Ops(2); +numVar = size(parent,2)-1; % Get the number of variables +% Pick a variable to mutate randomly from 1-number of vars +rN=rand(1,numVar)1) + r=.99; + % disp(sprintf('max gen %d < current gen %d setting ratio = 1',mt,ct)); +end +change = y*(rand*(1-r))^b; + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/f2b.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/f2b.m" index 5eccf2562e2305c6059932d1b0097ec8697a9daf..495df74f52964fa7808aa4440f46d21f4d9c376a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/f2b.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/f2b.m" @@ -1,3 +1,36 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c9f42ca7cd8c605bbecd2900755b84c2040852f9c2f4c5659907d3487e6194f6 -size 1492 +function [bval] = function(fval,bounds,bits) +% function [bval] = f2b(fval,bounds,bits) +% +% Return the binary representation of the float number fval. +% +% fval - the float representation of the number +% bval - the binary representation of the number +% bounds - the bounds on the variables +% bits - the number of bits to represent each variable + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +scale=(2.^bits-1)./ (bounds(:,2)-bounds(:,1))'; %The range of the variables +numV=size(bounds,1); +cs=[0 cumsum(bits)]; +for i=1:numV + fval(i)=(fval(i)-bounds(i,1)) * scale(i); + bval=[bval rem(floor(fval(i)*pow2(1-bits(i):0)),2)]; +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/ga.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/ga.m" index 8f7be6fccb8b85f13698f699529dfdca13bf811c..fa54cb37114901c6a534c40a3be79fc1593743aa 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/ga.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/ga.m" @@ -1,3 +1,303 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3db58ee3ec1b4a262cd8021f12084b0430db596c4d0708b29a3be5da9fa44fe0 -size 10718 +function [x,endPop,bPop,traceInfo] = ga(bounds,evalFN,evalOps,startPop,opts,... +termFN,termOps,selectFN,selectOps,xOverFNs,xOverOps,mutFNs,mutOps) +% GA run a genetic algorithm +% function [x,endPop,bPop,traceInfo]=ga(bounds,evalFN,evalOps,startPop,opts, +% termFN,termOps,selectFN,selectOps, +% xOverFNs,xOverOps,mutFNs,mutOps) +% +% Output Arguments: +% x - the best solution found during the course of the run +% endPop - the final population +% bPop - a trace of the best population +% traceInfo - a matrix of best and means of the ga for each generation +% +% Input Arguments: +% bounds - a matrix of upper and lower bounds on the variables +% evalFN - the name of the evaluation .m function +% evalOps - options to pass to the evaluation function ([NULL]) +% startPop - a matrix of solutions that can be initialized +% from initialize.m +% opts - [epsilon prob_ops display] change required to consider two +% solutions different, prob_ops 0 if you want to apply the +% genetic operators probabilistly to each solution, 1 if +% you are supplying a deterministic number of operator +% applications and display is 1 to output progress 0 for +% quiet. ([1e-6 1 0]) +% termFN - name of the .m termination function (['maxGenTerm']) +% termOps - options string to be passed to the termination function +% ([100]). +% selectFN - name of the .m selection function (['normGeomSelect']) +% selectOpts - options string to be passed to select after +% select(pop,#,opts) ([0.08]) +% xOverFNS - a string containing blank seperated names of Xover.m +% files (['arithXover heuristicXover simpleXover']) +% xOverOps - A matrix of options to pass to Xover.m files with the +% first column being the number of that xOver to perform +% similiarly for mutation ([2 0;2 3;2 0]) +% mutFNs - a string containing blank seperated names of mutation.m +% files (['boundaryMutation multiNonUnifMutation ... +% nonUnifMutation unifMutation']) +% mutOps - A matrix of options to pass to Xover.m files with the +% first column being the number of that xOver to perform +% similiarly for mutation ([4 0 0;6 100 3;4 100 3;4 0 0]) + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +%%$Log: ga.m,v $ +%Revision 1.10 1996/02/02 15:03:00 jjoine +% Fixed the ordering of imput arguments in the comments to match +% the actual order in the ga function. +% +%Revision 1.9 1995/08/28 20:01:07 chouck +% Updated initialization parameters, updated mutation parameters to reflect +% b being the third option to the nonuniform mutations +% +%Revision 1.8 1995/08/10 12:59:49 jjoine +%Started Logfile to keep track of revisions +% + + +n=nargin; +if n<2 | n==6 | n==10 | n==12 + disp('Insufficient arguements') +end +if n<3 %Default evalation opts. + evalOps=[]; +end +if n<5 + opts = [1e-6 1 0]; +end +if opts==[] + opts = [1e-6 1 0]; +end + +if any(evalFN<48) %Not using a .m file + if opts(2)==1 %Float ga + e1str=['x=c1; c1(xZomeLength)=', evalFN ';']; + e2str=['x=c2; c2(xZomeLength)=', evalFN ';']; + else %Binary ga + e1str=['x=b2f(endPop(j,:),bounds,bits); endPop(j,xZomeLength)=',... + evalFN ';']; + end +else %Are using a .m file + if opts(2)==1 %Float ga + e1str=['[c1(xZomeLength) c1]=' evalFN '(c1,[gen evalOps]);']; + e2str=['[c2(xZomeLength) c2]=' evalFN '(c2,[gen evalOps]);']; + else %Binary ga + e1str=['x=b2f(endPop(j,:),bounds,bits);[v x]=' evalFN ... + '(x,[gen evalOps]); endPop(j,:)=[f2b(x,bounds,bits) v];']; + end +end + + +if n<6 %Default termination information + termOps=[100]; + termFN='maxGenTerm'; +end +if n<12 %Default muatation information + if opts(2)==1 %Float GA + mutFNs=['boundaryMutation multiNonUnifMutation nonUnifMutation unifMutation']; + mutOps=[4 0 0;6 termOps(1) 3;4 termOps(1) 3;4 0 0]; + else %Binary GA + mutFNs=['binaryMutation']; + mutOps=[0.05]; + end +end +if n<10 %Default crossover information + if opts(2)==1 %Float GA + xOverFNs=['arithXover heuristicXover simpleXover']; + xOverOps=[2 0;2 3;2 0]; + else %Binary GA + xOverFNs=['simpleXover']; + xOverOps=[0.6]; + end +end +if n<9 %Default select opts only i.e. roullete wheel. + selectOps=[]; +end +if n<8 %Default select info + selectFN=['normGeomSelect']; + selectOps=[0.08]; +end +if n<6 %Default termination information + termOps=[100]; + termFN='maxGenTerm'; +end +if n<4 %No starting population passed given + startPop=[]; +end +if startPop==[] %Generate a population at random + %startPop=zeros(80,size(bounds,1)+1); + startPop=initialize(80,bounds,evalFN,evalOps,opts(1:2)); +end + +if opts(2)==0 %binary + bits=calcbits(bounds,opts(1)); +end + +xOverFNs=parse(xOverFNs); +mutFNs=parse(mutFNs); + +xZomeLength = size(startPop,2); %Length of the xzome=numVars+fittness +numVar = xZomeLength-1; %Number of variables +popSize = size(startPop,1); %Number of individuals in the pop +endPop = zeros(popSize,xZomeLength); %A secondary population matrix +c1 = zeros(1,xZomeLength); %An individual +c2 = zeros(1,xZomeLength); %An individual +numXOvers = size(xOverFNs,1); %Number of Crossover operators +numMuts = size(mutFNs,1); %Number of Mutation operators +epsilon = opts(1); %Threshold for two fittness to differ +oval = max(startPop(:,xZomeLength)); %Best value in start pop +bFoundIn = 1; %Number of times best has changed +done = 0; %Done with simulated evolution +gen = 1; %Current Generation Number +collectTrace = (nargout>3); %Should we collect info every gen +floatGA = opts(2)==1; %Probabilistic application of ops +display = opts(3); %Display progress + +while(~done) + %Elitist Model + [bval,bindx] = max(startPop(:,xZomeLength)); %Best of current pop + best = startPop(bindx,:); + + if collectTrace + traceInfo(gen,1)=gen; %current generation + traceInfo(gen,2)=startPop(bindx,xZomeLength); %Best fittness + traceInfo(gen,3)=mean(startPop(:,xZomeLength)); %Avg fittness + end + + if ( (abs(bval - oval)>epsilon) | (gen==1)) %If we have a new best sol + if display + fprintf(1,'\n%d %f\n',gen,bval); %Update the display + end + if floatGA + bPop(bFoundIn,:)=[gen startPop(bindx,:)]; %Update bPop Matrix + else + bPop(bFoundIn,:)=[gen b2f(startPop(bindx,1:numVar),bounds,bits)... + startPop(bindx,xZomeLength)]; + end + bFoundIn=bFoundIn+1; %Update number of changes + oval=bval; %Update the best val + else + if display + fprintf(1,'%d ',gen); %Otherwise just update num gen + end + end + + endPop = feval(selectFN,startPop,[gen selectOps]); %Select + + if floatGA %Running with the model where the parameters are numbers of ops + for i=1:numXOvers, + for j=1:xOverOps(i,1), + a = rand*(popSize-1)+1; %Pick a parent + b = rand*(popSize-1)+1; %Pick another parent + xN=deblank(xOverFNs(i,:)); %Get the name of crossover function + [c1 c2] = feval(xN,endPop(a,:),endPop(b,:),bounds,[gen xOverOps(i,:)]); + + if c1(1:numVar)==endPop(a,(1:numVar)) %Make sure we created a new + c1(xZomeLength)=endPop(a,xZomeLength); %solution before evaluating + elseif c1(1:numVar)==endPop(b,(1:numVar)) + c1(xZomeLength)=endPop(b,xZomeLength); + else + %[c1(xZomeLength) c1] = feval(evalFN,c1,[gen evalOps]); + eval(e1str); + end + if c2(1:numVar)==endPop(a,(1:numVar)) + c2(xZomeLength)=endPop(a,xZomeLength); + elseif c2(1:numVar)==endPop(b,(1:numVar)) + c2(xZomeLength)=endPop(b,xZomeLength); + else + %[c2(xZomeLength) c2] = feval(evalFN,c2,[gen evalOps]); + eval(e2str); + end + + endPop(a,:)=c1; + endPop(b,:)=c2; + end + end + + for i=1:numMuts, + for j=1:mutOps(i,1), + a = rand*(popSize-1)+1; + c1 = feval(deblank(mutFNs(i,:)),endPop(a,:),bounds,[gen mutOps(i,:)]); + if c1(1:numVar)==endPop(a,(1:numVar)) + c1(xZomeLength)=endPop(a,xZomeLength); + else + %[c1(xZomeLength) c1] = feval(evalFN,c1,[gen evalOps]); + eval(e1str); + end + endPop(a,:)=c1; + end + end + + else %We are running a probabilistic model of genetic operators + for i=1:numXOvers, + xN=deblank(xOverFNs(i,:)); %Get the name of crossover function + cp=find(rand(popSize,1)4 +12 123 131 10 44 D[<126012F0A21260>4 4 123 131 10 46 +D[<1303A3497EA2497E130BA2EB11E0A3EB20F0A2497E1478A2497EA33801FFFEEB001E 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+Fa(Bersini,)j(H.)e(and)f(Renders,)k(B.)c Fw(1994.)e(Hybridizing)g +(genetic)g(algorithms)f(with)i(hill-clim)o(bing)d(meth-)328 +1749 y(o)q(ds)i(for)h(global)f(optimization)o(:)17 b(Tw)o(o)d(p)q +(ossible)e(w)o(a)o(ys.)h(In)g Fu(1994)j(IEEE)e(International)h(Symp)n +(osium)328 1791 y(Evolutionary)f(Computation)p Fw(,)e(Orlando,)e(Fl,)h +(pp.)g(312{317.)265 1837 y Fa(Corana,)i(A.)p Fw(,)d Fa(Mar)o(chesi,)j +(M.)p Fw(,)d Fa(Mar)n(tini,)h(C.)p Fw(,)f Fa(and)g(Ridella,)j(S.)d +Fw(1987.)d(Minimizing)g(m)o(ultimo)q(dal)f(func-)328 +1879 y(tions)i(of)i(con)o(tin)o(uous)c(v)n(ariables)i(with)h(the)g +(\\sim)o(ulated)e(annealing")g(algorithm.)f Fu(A)o(CM)11 +b(T)m(r)n(ansactions)328 1921 y(on)i(Mathematic)n(al)h(Softwar)n(e)h +(13,)d Fw(3,)f(262{280.)265 1967 y Fa(D)o(a)m(vis,)k(L.)e +Fw(1991.)d Fu(The)j(Handb)n(o)n(ok)i(of)e(Genetic)h(A)o(lgorithms)p +Fw(.)e(V)m(an)g(Nostrand)e(Reingold,)f(New)j(Y)m(ork.)265 +2014 y Fa(Goldber)o(g,)21 b(D.)d Fw(1989.)e Fu(Genetic)i(A)o(lgorithms) 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b(conjunction)d(with)j(genetic)f(algorithms.)e(T)m(ec)o +(hnical)i(Rep)q(ort)g(NCSU-IE)i(T)m(ec)o(hnical)e(Rep)q(ort)g(95,)328 +2403 y(North)f(Carolina)f(State)g(Univ)o(ersit)o(y)m(.)265 +2449 y Fa(Joines,)15 b(J.)e(and)g(Houck,)h(C.)f Fw(1994.)e(On)h(the)g +(use)f(of)h(non-stationa)o(ry)d(p)q(enalt)o(y)h(functions)g(to)i(solv)o +(e)f(con-)328 2491 y(strained)d(optimization)f(problems)h(with)j +(genetic)d(algorithms.)g(In)i Fu(1994)j(IEEE)f(International)g(Sym-)328 +2532 y(p)n(osium)h(Evolutionary)h(Computation)p Fw(,)e(Orlando,)e(Fl,)h +(pp.)g(579{584.)p eop +%%Page: 14 14 +14 13 bop 225 125 a Fs(14)71 b Fr(\001)78 b Fs(C.)12 +b(Houck)h(et)g(al.)265 233 y Fa(Michalewicz,)21 b(Z.)d +Fw(1994.)e Fu(Genetic)i(A)o(lgorithms)i(+)e(Data)g(Structur)n(es)h(=)f +(Evolution)i(Pr)n(o)n(gr)n(ams)p Fw(.)e(AI)328 274 y(Series.)10 +b(Springer-V)m(erla)o(g,)e(New)13 b(Y)m(ork.)p eop +%%Trailer +end +userdict /end-hook known{end-hook}if +%%EOF diff --git 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"a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/gaotindex.html" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/gaotindex.html" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c28476c63a0dcca861e66ebb96176e5b9baafaf3674930ffaf8e0082812670de -size 3317 + + + + + +

Genetic Algorithm Optimization Toolbox (GAOT)

+
+
+The following files are in the distribution:
+
+Main interface
+
+ ga.m                   The Genetic Algorithm  
+ initialize.m           Initialization function Used by ga.m   
+
+Operators used during simulated evolution
+
+ Crossover Operators
+  heuristicXover.m       Operator for the Algorithm Used by ga.m 
+  arithXover.m           Operator for the Algorithm Used by ga.m 
+  simpleXover.m          Operator for the Algorithm Used by ga.m 
+
+ Mutation Operators
+  binaryMutation.m       Operator for the Algorithm Used by ga.m 
+  boundaryMutation.m     Operator for the Algorithm Used by ga.m 
+  multiNonUnifMutation.m Operator for the Algorithm Used by ga.m 
+  nonUnifMutation.m      Operator for the Algorithm Used by ga.m 
+  unifMutation.m         Operator for the Algorithm Used by ga.m
+
+ Selection Functions
+  normGeomSelect.m       Selection function Used by ga.m
+  roulette.m             Selection function Used by ga.m
+  tournSelect.m          Selection function Used by ga.m
+
+ Termination Functions
+  maxGenTerm.m           Termination function Used by ga.m
+  optMaxGenTerm.m        Termination function Used by ga.m
+
+Functions used for binary representation
+  calcbits.m             Binary precision function used by ga.m
+  f2b.m                  Float to Binary conversion used by ga.m
+  b2f.m                  Binary to Float conversion used by ga.m
+
+Utility functions
+  parse.m                Parse blank separated names used by ga.m
+  delta.m                Used by nonUnifMutation.m and mult...m
+
+Demonstrations
+  gademo1.m              Introductory demo of GAOT
+  gademo2.m              Multi-dimensional demo of GAOT
+  gademo3.m              Reference for GAOT
+
+ Functions used in Demonstrations
+  gademo1eval1.m         Example eval function used by gademo1.m
+  coranaEval.m           Calculate Corana functions used by gademo2.m
+  coranaMin.m            Calculate negative of Corana used by gademo2.m
+  gaEval.m               Calculation of Corana used for testing
+  gaGradEval.m           Evaluation Used for Testing      
+  gaGradGrad.m           Gradient used for SQP during Testing
+
+ + + +
+
Jeff Joines (jjoine@eos.ncsu.edu)
+ +Last modified: Wed Feb 7 10:21:44 1996 + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/heuristicXover.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/heuristicXover.m" index 75e29ac38918fb7f133502174712b80e4ffa56d0..b599da8daf8b16b458cfacd1aeb23ace7da8443c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/heuristicXover.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/heuristicXover.m" @@ -1,3 +1,68 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ef01a21a13157ae9fb77cbaf9f5f3a50bc14a9c48da3d3696e88247ab0bdf0e4 -size 2139 +function [c1,c2] = heuristicXover(p1,p2,bounds,Ops) +% Heuristic crossover takes two parents P1,P2 and performs an extrapolation +% along the line formed by the two parents outward in the direction of the +% better parent. +% +% function [c1,c2] = heuristicXover(p1,p2,bounds,Ops) +% p1 - the first parent ( [solution string function value] ) +% p2 - the second parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options for heuristic crossover, [gen #heurXovers number_of_retries] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +retry=Ops(3); % Number of retries +i=0; +good=0; +b1=bounds(:,1)'; +b2=bounds(:,2)'; +numVar = size(p1,2)-1; +% Determine the best and worst parent +if(p1(numVar+1) > p2(numVar+1)) + bt = p1; + wt = p2; +else + bt = p2; + wt = p1; +end +while i= b1)) + i = retry; + good=1; + else + i = i + 1; + end +end + +% If new child is not feasible just return the new children +if(~good) + c1 = wt; +end + +% Crossover functions return two children therefore return the best +% and the new child created +c2 = bt; +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/index.html" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/index.html" index cc439ae0c450f19275890518eb9a166c3975360f..cbe0f3b61a39898713bb6b0b1deb9e8096e56199 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/index.html" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/index.html" @@ -1,3 +1,71 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:95b0c4dd9ef900b4e1baf5746c463ad819bf32cfd0fadf60b372358911f50016 -size 2600 + +Genetic Algorithm Optimization Toolbox + + + +
+

Genetic Algorithm Optimization Toolbox (GAOT)

+ +GAOT implements simulated evolution in the Matlab environment using +both binary and real representations. (Ordered base representation is +in the debugging stage.) This implemenation is very flexible in the +genetic operators, selection functions, termination functions as well +as the evaluation functions that can be used. The implemination is +described in a companion paper submitted to ACM Transactions on +Mathematical Software. For now, the paper can be referenced as +follows: + +

"A Genetic Algorithm for Function +Optimization: A Matlab Implementation" by Chris Houck, Jeff +Joines, and Mike Kay, NCSU-IE TR 95-09, 1995.

+ + +The entire toolbox can be download +either as a compressed tar archive ( +GAOT.tar.gz) or a ZIP file (GAOT.zip). +This includes the postscript and dvi versions of the companion paper. + +

Copyright information

+ +This toolbox is copyrighted by the authors and is free software. You +can redistribute it and/or modify it under the terms of the GNU +General Public License (GPL) as published by the Free Software +Foundation; either version 2 of the License, or (at your option) any +later version. + +

Requirements

+ +The only requirement is that you have Matlab version 4 or later. The +toolbox should work without any modifications. + +

Documentation

+ +The companion paper (gaot.ps) describes the +implementation. A README describes how to +install GAOT on your system. To get a listing of the toolbox get help on GAOT in matlab. Three +demonstrations are provided to help the user

+ +

Comments, Problems and Suggestions

+ +Should you experience any problem downloading the files or using the +tool box, feel free to email +me. If you have any comments or suggestions for improvement or +modifications please email me as well. If you would like to be put on +a mailing list when the files are updated or modified, drop me an +email. + +

Other GA related Papers

+ +
    +
  • +
+ + +
+
Jeff Joines (jjoine@eos.ncsu.edu)
+ +Last modified: Wed Feb 7 10:32:15 1996 + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/initialize.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/initialize.m" index d231aca7698c2b3ad15146638590634bfe44f27e..0b2c934cfded84a4ee5ae1e68d14b50a8897d67c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/initialize.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/initialize.m" @@ -1,3 +1,79 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b0aae211bd3d017d80af0852cd13c90f99e366c5e30fc466363d10149c1f800c -size 3199 +function [pop] = initialize(num,bounds,evalFN,evalOps,options) +% function [pop]=initialize(populationSize, variableBounds,evalFN, +% evalOps,options) +% initialize creates a matrix of random numbers with +% a number of rows equal to the populationSize and a number +% columns equal to the number of rows in bounds plus 1 for +% the f(x) value which is found by applying the evalFN. +% +% pop - the initial, evaluated, random population +% populatoinSize - the size of the population, i.e. the number to create +% variableBounds - a matrix which contains the bounds of each variable, i.e. +% [var1_high var1_low; var2_high var2_low; ....] +% evalFN - the evaluation fn, usually the name of the .m file for +% evaluation +% evalOps - any options to be passed to the eval function defaults [] +% options - options to the initialize function, ie. +% [eps float/binary prec] where eps is the epsilon value +% and the second option is 1 for float and 0 for binary, +% prec is the precision of the variables defaults [1e-6 1] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +if nargin<5 + options=[1e-6 1]; +end +if nargin<4 + evalOps=[]; +end + +if any(evalFN<48) %Not a .m file + if options(2)==1 %Float GA + estr=['x=pop(i,:); pop(i,xZomeLength)=', evalFN ';']; + else %Binary GA + estr=['x=b2f(pop(i,:),bounds,bits); pop(i,xZomeLength)=', evalFN ';']; + end +else %A .m file + if options(2)==1 %Float GA + estr=['[pop(i,xZomeLength) pop(i,:)]=' evalFN '(pop(i,:),[0 evalOps]);']; + else %Binary GA + estr=['x=b2f(pop(i,:),bounds,bits);[v x]=' evalFN ... + '(x,[0 evalOps]); pop(i,:)=[f2b(x,bounds,bits) v];']; + end +end + + +numVars = size(bounds,1); %Number of variables +rng = (bounds(:,2)-bounds(:,1))'; %The variable ranges' + +if options(2)==1 %Float GA + xZomeLength = numVars+1; %Length of string is numVar + fit + pop = zeros(num,xZomeLength); %Allocate the new population + pop(:,1:numVars)=(ones(num,1)*rng).*(rand(num,numVars))+... + (ones(num,1)*bounds(:,1)'); +else %Binary GA + bits=calcbits(bounds,options(1)); + xZomeLength = sum(bits)+1; %Length of string is numVar + fit + pop = round(rand(num,sum(bits)+1)); +end + +for i=1:num + eval(estr); +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/maxGenTerm.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/maxGenTerm.m" index 67b8118150f688691017d5661b6cab7d6963ffb2..7073cbaa3cb61edb3a847a46622bae2d251e2c13 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/maxGenTerm.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/maxGenTerm.m" @@ -1,3 +1,28 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:486c85caf44d78be1603c1fb88819ea294c342bc4b9effa876ee51c9ad40df3a -size 1265 +function [done] = maxGenTerm(ops,bPop,endPop) +% function [done] = maxGenTerm(ops,bPop,endPop) +% ops - a vector of options [current_gen maximum_generation] +% bPop - a matrix of best solutions [generation_found solution_string] +% endPop - the current generation of solutions + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +currentGen = ops(1); +maxGen = ops(2); +done = currentGen >= maxGen; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/multiNonUnifMutation.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/multiNonUnifMutation.m" index 2bfc45dfa0044aef8a2af3885d907b135438e464..50b10867686579caabc8cb447910c72fcd140cfc 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/multiNonUnifMutation.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/multiNonUnifMutation.m" @@ -1,3 +1,45 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:63cb60366f073527d546094319f0769a62a191bb4568620626638e886fee67af -size 1991 +function [parent] = multiNonUnifMutation(parent,bounds,Ops) +% Multi-Non uniform mutation changes all of the parameters of the parent +% based on a non-uniform probability distribution. This Gaussian +% distribution starts wide, and narrows to a point distribution as the +% current generation approaches the maximum generation. +% +% function [newSol] = multiNonUnifMutate(parent,bounds,Ops) +% parent - the first parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options for multiNonUnifMutation +% [gen #MultiNonUnifMutations maxGen b] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +cg=Ops(1); % Current Generation +mg=Ops(3); % Maximum Number of Generations +b=Ops(4); % Shape parameter +df = bounds(:,2) - bounds(:,1); % Range of the variables +numVar = size(parent,2)-1; % Get the number of variables +% Now mutate that point +md = round(rand(1,numVar)); +for i = 1:numVar + if md(i) + parent(i)=parent(i)+delta(cg,mg,bounds(i,2)-parent(i),b); + else + parent(i)=parent(i)-delta(cg,mg,parent(i)-bounds(i,1),b); + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/nonUnifMutation.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/nonUnifMutation.m" index 43b4ec73833d70799f26765da4bfb353ee90d58c..913cc2a9ad75da2bb35ba303cf0bbc704eb62f17 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/nonUnifMutation.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/nonUnifMutation.m" @@ -1,3 +1,45 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2c8713c06a631c80c4bc4f325b3a5d03bffec23cdfeb9e00120d193600da6748 -size 2193 +function [parent] = nonUnifMutate(parent,bounds,Ops) +% Non uniform mutation changes one of the parameters of the parent +% based on a non-uniform probability distribution. This Gaussian +% distribution starts wide, and narrows to a point distribution as the +% current generation approaches the maximum generation. +% +% function [newSol] = multiNonUnifMutate(parent,bounds,Ops) +% parent - the first parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options for nonUnifMutate[gen #NonUnifMutations maxGen b] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +cg=Ops(1); % Current Generation +mg=Ops(3); % Maximum Number of Generations +b=Ops(4); % Shape parameter +df = bounds(:,2) - bounds(:,1); % Range of the variables +numVar = size(parent,2)-1; % Get the number of variables +% Pick a variable to mutate randomly from 1 to number of vars +mPoint = round(rand * (numVar-1)) + 1; +md = round(rand); % Choose a direction of mutation +if md % Mutate towards upper bound + newValue=parent(mPoint)+delta(cg,mg,bounds(mPoint,2)-parent(mPoint),b); +else % Mutate towards lower bound + newValue=parent(mPoint)-delta(cg,mg,parent(mPoint)-bounds(mPoint,1),b); +end +parent(mPoint) = newValue; % Make the child +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/normGeomSelect.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/normGeomSelect.m" index 0f07af6db5e1a270c470c7bd924af1a36d8f531b..e87822a86fa3dc23cfff4a08eaec309c4aa763ba 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/normGeomSelect.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/normGeomSelect.m" @@ -1,3 +1,50 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f1c4675b3d99f25bd0d51efdc519453ecba055ca46590bc8d6c54a8a3801c57a -size 2311 +function[newPop] = normGeomSelect(oldPop,options) +% NormGeomSelect is a ranking selection function based on the normalized +% geometric distribution. +% +% function[newPop] = normGeomSelect(oldPop,options) +% newPop - the new population selected from the oldPop +% oldPop - the current population +% options - options to normGeomSelect [gen probability_of_selecting_best] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +q=options(2); % Probability of selecting the best +e = size(oldPop,2); % Length of xZome, i.e. numvars+fit +n = size(oldPop,1); % Number of individuals in pop +newPop = zeros(n,e); % Allocate space for return pop +fit = zeros(n,1); % Allocates space for prob of select +x=zeros(n,2); % Sorted list of rank and id +x(:,1) =[n:-1:1]'; % To know what element it was +[y x(:,2)] = sort(oldPop(:,e)); % Get the index after a sort +r = q/(1-(1-q)^n); % Normalize the distribution, q prime +fit(x(:,2))=r*(1-q).^(x(:,1)-1); % Generates Prob of selection +fit = cumsum(fit); % Calculate the cumulative prob. func +rNums=sort(rand(n,1)); % Generate n sorted random numbers +fitIn=1; newIn=1; % Initialize loop control +while newIn<=n % Get n new individuals + if(rNums(newIn)= maxGen) | ((optimal - bestSolVal) <= epsilon); \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/parse.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/parse.m" index e9f351bc9cbae25567ae437b343e50db9b025c3e..4281e6167b2789aa7b781719b54259d078ea794b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/parse.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/parse.m" @@ -1,3 +1,42 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:4cac9baa65366e9604e3bf061005c8c9c73254320accbad0508aab2e733e3330 -size 1459 +function [x] = parse(inStr) +% parse is a function which takes in a string vector of blank separated text +% and parses out the individual string items into a n item matrix, one row +% for each string. +% +% function [x] = parse(inStr) +% x - the return matrix of strings +% inStr - the blank separated string vector + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +sz=size(inStr); +strLen=sz(2); +x=blanks(strLen); +wordCount=1; +last=0; +for i=1:strLen, + if inStr(i) == ' ' + wordCount = wordCount + 1; + x(wordCount,:)=blanks(strLen); + last=i; + else + x(wordCount,i-last)=inStr(i); + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/roulette.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/roulette.m" index 4245fe11f864548cbc67ed869b92f3447e1ca78c..440f53dfa8d7298b36076377cd5ea4a95cd428e8 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/roulette.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/GAOT/roulette.m" @@ -1,3 +1,50 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:7f54031a43bf3eadb6aa75569d51938f0c479d70df78fd1e7b07720bf1476826 -size 1781 +function[newPop] = roulette(oldPop,options) +% roulette is the traditional selection function with the probability of +% surviving equal to the fitness of i / sum of the fitness of all individuals +% +% function[newPop] = roulette(oldPop,options) +% newPop - the new population selected from the oldPop +% oldPop - the current population +% options - options [gen] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +% Get the parameters of the population +numVars = size(oldPop,2); +numSols = size(oldPop,1); + +% Generate the relative probabilities of selection +totalFit = sum(oldPop(:,numVars)); +prob=oldPop(:,numVars) / totalFit; +prob=cumsum(prob); + +rNums=sort(rand(numSols,1)) % Generate random numbers + +% Select individuals from the oldPop to the new +fitIn=1;newIn=1; +while newIn<=numSols + if(rNums(newIn) + + + Genetic Algorithms toolbox for Matlab + + + + +

Genetic Algorithms toolbox for Matlab (by Michael B. Gordy)

+ +
From: m1mbg00@newfed.frb.gov (Michael B Gordy)

+Reply-To: m1mbg00@frb.gov

+Newsgroups: comp.ai.genetic,comp.soft-sys.matlab

+Subject: Re: Genetic Algorithms toolbox for Matlab

+Date: Wed, 7 Feb 1996 17:08:52 GMT

+Organization: Federal Reserve Board

+Message-ID: DMF0yt.ACr@glendora.uucp

+References: 4edofo$j19@ftp.ee.vill.edu 4ekssr$pjp@bond.nexus.se

+

+

+There seems to be much unmet demand for a GA routine in Matlab, so I'll 

+make mine available.  It's easy to use, as its syntax is fairly close

+to Matlab's fmins routine.  It works, but I can't make any claims for 

+sophistication.  (Hey, I'm an economist, not a computer scientist, and

+I don't follow the GA literature closely.)

+

+Use at your own risk, of course.  I can't provide support in any formal

+sense, but would be happy to try to incorporate suggested improvements.

+

+-- Michael Gordy

+   Federal Reserve Board
+ +

+
+ +
View/Download renamed Matlab file gagordy.m (identical to ga.m below)
+ +

+
% ----------------------- cut here for ga.m -------------------------

+function [beta,stopcode]=ga(funstr,parspace,options,p1,p2,p3,p4,p5,p6,p7,p8,p9)

+%[beta,stopcode]=ga(funstr,parspace,options,p1,p2,p3,p4,p5,p6,p7,p8,p9)

+% Genetic Algorithm for function maximization.

+% Especially useful for functions with kinks and discontinuities,

+% and where a good "starting point" is unavailable.

+%    See Dorsey and Mayer, 

+%    Journal of Business and Economic Statistics, January 1995, 13(1)

+% Program by Michael Gordy <m1mbg00@frb.gov>

+% Version 1.12, 7 February 1996

+%

+% OUTPUTS:

+%  beta       = (1 x K) parameter vector maximizing funstr

+%  stopcode   = code for terminating condition

+%                == 1 if terminated normally

+%                == 2 if maximum number of iterations exceeded

+%

+% INPUTS:

+%  funstr     = name of function to be maximized (string).

+%  parspace   = (2 x K) matrix is [min; max] of parameter space dimensions

+%               or, if (3 x K), then bottom row is a good starting value

+%  options    = vector of option settings

+%  p1,p2,...,p9 are optional parameters to be passed to funstr

+%

+% where:

+% options(1) = m (size of generation, must be even integer)

+% options(2) = eta (crossover rate in (0,1); use Booker's VCO if < 0)

+% options(3) = gamma (mutation rate in (0,1))

+% options(4) = printcnt (print status once every printcnt iterations)

+%                Set printcnt to zero to suppress printout.

+% options(5) = maxiter (maximum number of iterations)

+% options(6) = stopiter (minimum number of gains < epsln before stop)

+% options(7) = epsln (smallest gain worth recognizing)

+% options(8) = rplcbest (every rplcbest iterations, insert best-so-far)

+% options(9) = 1 if function is vectorized (i.e., if the function

+%                can simultaneously evaluate many parameter vectors).

+%    Default option settings: [20,-1,0.12,10,20000,2000,1e-4,50,0]

+%

+% Note: 

+%    The function is maximized with respect to its first parameter,

+%    which is expressed as a row vector.

+%    Example: 

+%      Say we want to maximize function f with respect to vector p,

+%      and need also to pass to f data matrices x,y,z.  Then,

+%      write the function f so it is called as f(p,x,y,z).  GA will

+%      assume that p is a row vector.

+

+gaver='1.12';

+defopt=[24,-1,0.12,10,20000,2000,1e-4,50,0];

+months = ['Jan';'Feb';'Mar';'Apr';'May';'Jun';...

+          'Jul';'Aug';'Sep';'Oct';'Nov';'Dec'];

+

+if nargin>2

+   if isempty(options)

+        options=defopt;

+   end

+else

+   options=defopt;

+end

+m=options(1); eta=options(2); gam=options(3);

+printcnt=options(4);

+maxiter=options(5);

+stopiter=options(6); epsln=options(7);

+rplcbest=options(8);

+vecfun=options(9);

+

+% Use Booker's VCO if eta==-1

+vco=(eta<0);  eta=abs(eta);

+

+% Cancel rplcbest if <=0

+if rplcbest<=0, rplcbest=maxiter+1; end

+

+K=size(parspace,2);

+

+% Draw initial Generation

+G=rand(m,K).*(parspace(2*ones(m,1),:)-parspace(ones(m,1),:))...

+       +parspace(ones(m,1),:);

+b0rows=size(parspace,1)-2;

+if b0rows>0

+  G(1:b0rows,:)=parspace(3:b0rows+2,:);

+  parspace=parspace([1 2],:);

+end

+

+% Initial 'best' holders

+inarow=0;

+bestfun=-Inf; beta=zeros(1,K);

+

+% Score for each of m vectors

+f=zeros(m,1);

+

+% Setup function string for evaluations

+paramstr=',p1,p2,p3,p4,p5,p6,p7,p8,p9';

+evalstr = [funstr,'(G'];

+if ~vecfun

+        evalstr=[evalstr, '(i,:)'];

+end

+if nargin>3, evalstr=[evalstr,paramstr(1:3*(nargin-3))]; end

+evalstr = [evalstr, ')'];

+

+% Print header

+if printcnt>0

+   disp(['GA (Genetic Algorithm), Version ',gaver,' by Michael Gordy'])

+   disp(['Maximization of function ',funstr])

+   disp('i      = Current generation')

+   disp('best_i = Best function value in generation i')

+   disp('best   = Best function value so far')

+   disp('miss   = Number of generations since last hit')

+   disp('psi    = Proportion of unique genomes in generation')

+   disp(sprintf(['\n',blanks(20),'i     best_i        best     miss   psi']))

+end

+

+iter=0;  stopcode=0;

+oldpsi=1;  % for VCO option

+while stopcode==0

+   iter=iter+1;

+   % Call function for each vector in G

+   if vecfun

+        f=eval(evalstr);

+   else

+     for i=1:m

+        f(i)=eval(evalstr);

+     end

+   end

+   f0=f;

+   [bf0,bx]=max(f);

+   bf=max([bf0 bestfun]);

+   fgain=(bf-bestfun);

+   if fgain>epsln

+        inarow=0;

+   else

+        inarow=inarow+1;

+   end

+   if fgain>0

+        bestfun=bf;

+        beta=G(bx(1),:);

+   end

+   if printcnt>0 & rem(iter,printcnt)==1

+        psi=length(unique(G))/m;

+        ck=clock;

+        ckhr=int2str(ck(4)+100);  ckday=int2str(ck(3)+100);

+        ckmin=int2str(ck(5)+100); cksec=int2str(ck(6)+100);

+        timestamp=[ckday(2:3),months(ck(2),:),' ',...

+           ckhr(2:3),':',ckmin(2:3),':',cksec(2:3),' '];

+        disp([timestamp,sprintf('%6.0f %8.5e %8.5e %5.0f %5.3f',...

+                [iter bf0 bestfun inarow psi])])

+        save gabest beta timestamp iter funstr

+   end

+   % Reproduction

+   f=(f-min(f)).^(1+log(iter)/100);

+   pcum=cumsum(f)/sum(f);

+   r=rand(1,m); r=sum(r(ones(m,1),:)>pcum(:,ones(1,m)))+1;

+   G=G(r,:);

+   % Crossover

+   if vco

+        psi=length(unique(G))/m;

+        eta=max([0.2 min([1,eta-psi+oldpsi])]);

+        oldpsi=psi;

+   end   

+   y=sum(rand(m/2,1)<eta);

+   if y>0

+     % choose crossover point

+     x=floor(rand(y,1)*(K-1))+1;

+     for i=1:y

+        tmp=G(i,x(i)+1:K);

+        G(i,x(i)+1:K)=G(i+m/2,x(i)+1:K);

+        G(i+m/2,x(i)+1:K)=tmp;

+     end

+   end

+   % Mutation

+   M=rand(m,K).*(parspace(2*ones(m,1),:)-parspace(ones(m,1),:))...

+       +parspace(ones(m,1),:);

+   domuta=find(rand(m,K)<gam);

+   G(domuta)=M(domuta);

+   % Once every rplcbest iterations, re-insert best beta

+   if rem(iter,rplcbest)==0

+        G(m,:)=beta;

+   end

+   stopcode=(inarow>stopiter)+2*(iter>maxiter);

+end

+

+if printcnt>0

+   if stopcode==1

+        disp(sprintf('GA: No improvement in %5.0f generations.\n',stopiter))

+   else

+        disp(sprintf('GA: Maximum number of iterations exceeded.\n'))

+   end

+end

+% end of GA.M

+

+
+ +
created by: Mitch +Rauth (last changed 10. May 1996)
+ +
updated and changed by: Hartmut Pohlheim +(September 1996)
+ + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaMichEval.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaMichEval.m" index dc6c61acc20babc52554d24f88aaaed8dfcff6ad..cf346e70a1700c433f92a1fff7aa1a4c7ea77c33 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaMichEval.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaMichEval.m" @@ -1,3 +1,4 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1b736ca4c5c087ab5f01d52661fc5f6137a230f4285b8a043bc96598b65aa598 -size 193 +function [val,sol] = gaTestEval(sol,options) +val = 21.5 + sol(1) * sin(4*pi*sol(1)) + sol(2)*sin(20*pi*sol(2)); +%G=zeros(0); +%val = sqrt(sol(1)) * sin(2*sol(1)) + sqrt(sol(1))*cos(5*sol(1))+5; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaSimpleEval.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaSimpleEval.m" index dc6c61acc20babc52554d24f88aaaed8dfcff6ad..cf346e70a1700c433f92a1fff7aa1a4c7ea77c33 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaSimpleEval.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaSimpleEval.m" @@ -1,3 +1,4 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1b736ca4c5c087ab5f01d52661fc5f6137a230f4285b8a043bc96598b65aa598 -size 193 +function [val,sol] = gaTestEval(sol,options) +val = 21.5 + sol(1) * sin(4*pi*sol(1)) + sol(2)*sin(20*pi*sol(2)); +%G=zeros(0); +%val = sqrt(sol(1)) * sin(2*sol(1)) + sqrt(sol(1))*cos(5*sol(1))+5; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaZBGrad.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaZBGrad.m" index 9dacee10640fda7aec8c5d191b3973bd1f34adfc..b1a32611030c23d145f27c6518df4e5aaaa07112 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaZBGrad.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaZBGrad.m" @@ -1,3 +1,5 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b5a2df3af293828b22600cff26452e96d7a50ac2de08e40cfa89cc43d676563c -size 174 +function [val,G] = gaZBGrad(sol) + +% Constrain minimizes so we have to take the - to maximize +val = -(21.5 + sol(1) * sin(4*pi*sol(1)) + sol(2)*sin(20*pi*sol(2))); +G=zeros(0); \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaZBGradEval.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaZBGradEval.m" index aa6b379f661c6097fbfbd067ed615c731d3da4a1..710d643ca2903eb93bc721921260755f850f6c57 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaZBGradEval.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gaZBGradEval.m" @@ -1,3 +1,22 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1ab07a9cafc850137759649eeeb15345ca16f1d8a2a3c9067034e0206c7a6cc6 -size 683 +function [val,nsol] = gaZBGradEval(sol,options) + +% This evaluation function takes in a potential solution and two options +% options(3) is the percent of time to perform the gradient heuristic to the +% potential solution +% options(4) is the percentage of time to update the solution based on the +% outcome of the gradient heuristic +% options [currentGen maxGen eval_with_constr update_with_constr] +nsol=sol; +if (rand4 +12 123 131 10 44 D[<126012F0A21260>4 4 123 131 10 46 +D[<1303A3497EA2497E130BA2EB11E0A3EB20F0A2497E1478A2497EA33801FFFEEB001E +0002131F80A248EB0780A2120C001E14C039FF803FFC>30 29 126 +156 27 65 D[26 28 125 +155 26 I[<90380FE02090387018603801C00439030003E000061301000E13004814605A +15201278127000F01400A80070142012781238A26C14407E000614806CEB01003801C006 +38007018EB0FE0>27 30 125 156 26 I[28 +28 125 155 27 I[<90381FC04090387030C03801C00C38030003000E1301120C001C13 +005A15401278127000F01400A6EC7FF8EC07C00070130312781238A27E120C120E000313 +053801C008390070304090381FC000>29 30 125 156 28 71 D[<39FFF0FFF0390F000F +00AC90B5FCEB000FAD39FFF0FFF0>28 28 125 155 27 I[<380FFF8038007C00133CB3 +127012F8A21338EA7078EA4070EA30E0EA0F80>17 29 125 155 +19 74 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1412 y(ematical)j +(capabilities.)23 b(The)16 b(to)q(olb)q(o)o(x)e(has)i(b)q(een)h(tested) +h(on)d(a)g(series)j(of)d(non-linear,)g(non-)225 1461 +y(con)o(v)o(ex,)f(m)o(ulti-modal)d(functions.)20 b(The)15 +b(results)h(of)e(these)i(tests)g(sho)o(w)e(that)h(the)g(algorithm)225 +1511 y(is)f(capable)g(of)f(\014nding)g(b)q(etter)j(solutions)d(with)g +(less)i(function)e(ev)n(aluations)g(than)h(sim)o(ulated)225 +1561 y(annealing.)225 1650 y Fw(REFERENCES)265 1708 y +Fa(Bersini,)j(H.)e(and)f(Renders,)k(B.)c Fw(1994.)e(Hybridizing)g +(genetic)g(algorithms)f(with)i(hill-clim)o(bing)d(meth-)328 +1749 y(o)q(ds)i(for)h(global)f(optimization)o(:)17 b(Tw)o(o)d(p)q +(ossible)e(w)o(a)o(ys.)h(In)g Fu(1994)j(IEEE)e(International)h(Symp)n +(osium)328 1791 y(Evolutionary)f(Computation)p Fw(,)e(Orlando,)e(Fl,)h +(pp.)g(312{317.)265 1837 y Fa(Corana,)i(A.)p Fw(,)d Fa(Mar)o(chesi,)j +(M.)p Fw(,)d Fa(Mar)n(tini,)h(C.)p Fw(,)f Fa(and)g(Ridella,)j(S.)d +Fw(1987.)d(Minimizing)g(m)o(ultimo)q(dal)f(func-)328 +1879 y(tions)i(of)i(con)o(tin)o(uous)c(v)n(ariables)i(with)h(the)g +(\\sim)o(ulated)e(annealing")g(algorithm.)f Fu(A)o(CM)11 +b(T)m(r)n(ansactions)328 1921 y(on)i(Mathematic)n(al)h(Softwar)n(e)h +(13,)d Fw(3,)f(262{280.)265 1967 y Fa(D)o(a)m(vis,)k(L.)e +Fw(1991.)d Fu(The)j(Handb)n(o)n(ok)i(of)e(Genetic)h(A)o(lgorithms)p +Fw(.)e(V)m(an)g(Nostrand)e(Reingold,)f(New)j(Y)m(ork.)265 +2014 y Fa(Goldber)o(g,)21 b(D.)d Fw(1989.)e Fu(Genetic)i(A)o(lgorithms) +h(in)f(Se)n(ar)n(ch,)i(Optimization,)g(and)e(Machine)h(L)n(e)n(arning)p +Fw(.)328 2055 y(Addison-W)m(esley)m(.)265 2102 y Fa(Holland,)e(J.)e +Fw(1975.)d Fu(A)n(daptation)17 b(in)d(natur)n(al)i(and)g(arti\014cial)f +(systems)p Fw(.)f(The)g(Univ)o(ersit)o(y)e(of)h(Mic)o(higan)328 +2143 y(Press,)d(Ann)i(Arb)q(or.)265 2190 y Fa(Houck,)20 +b(C.)p Fw(,)e Fa(Joines,)i(J.)p Fw(,)f Fa(and)e(Ka)n(y,)i(M.)e +Fw(1995a.)e(A)i(comparison)d(of)i(genetic)e(algorithms,)h(random)328 +2232 y(restart,)9 b(and)g(t)o(w)o(o-opt)g(switc)o(hing)g(for)h(solving) +f(large)g(lo)q(cation-allocati)o(on)e(problems.)h Fu(Computers)k(&)328 +2273 y(Op)n(er)n(ations)i(R)n(ese)n(ar)n(ch)i(forthc)n(oming)e(in)f(sp) +n(e)n(cial)h(issue)e(on)h(evolution)h(c)n(omputation)p +Fw(.)265 2320 y Fa(Houck,)f(C.)p Fw(,)e Fa(Joines,)i(J.)p +Fw(,)e Fa(and)g(Ka)n(y,)i(M.)e Fw(1995b.)e(The)h(e\013ectiv)o(e)e(use)i +(of)g(lo)q(cal)f(impro)o(v)o(emen)n(t)e(pro)q(cedures)328 +2361 y(in)13 b(conjunction)d(with)j(genetic)f(algorithms.)e(T)m(ec)o +(hnical)i(Rep)q(ort)g(NCSU-IE)i(T)m(ec)o(hnical)e(Rep)q(ort)g(95,)328 +2403 y(North)f(Carolina)f(State)g(Univ)o(ersit)o(y)m(.)265 +2449 y Fa(Joines,)15 b(J.)e(and)g(Houck,)h(C.)f Fw(1994.)e(On)h(the)g +(use)f(of)h(non-stationa)o(ry)d(p)q(enalt)o(y)h(functions)g(to)i(solv)o +(e)f(con-)328 2491 y(strained)d(optimization)f(problems)h(with)j +(genetic)d(algorithms.)g(In)i Fu(1994)j(IEEE)f(International)g(Sym-)328 +2532 y(p)n(osium)h(Evolutionary)h(Computation)p Fw(,)e(Orlando,)e(Fl,)h +(pp.)g(579{584.)p eop +%%Page: 14 14 +14 13 bop 225 125 a Fs(14)71 b Fr(\001)78 b Fs(C.)12 +b(Houck)h(et)g(al.)265 233 y Fa(Michalewicz,)21 b(Z.)d +Fw(1994.)e Fu(Genetic)i(A)o(lgorithms)i(+)e(Data)g(Structur)n(es)h(=)f +(Evolution)i(Pr)n(o)n(gr)n(ams)p Fw(.)e(AI)328 274 y(Series.)10 +b(Springer-V)m(erla)o(g,)e(New)13 b(Y)m(ork.)p eop +%%Trailer +end +userdict /end-hook known{end-hook}if +%%EOF diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gas.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gas.m" index d3057a4663b1b65e5c63b40a07ef54a0f6ee1aee..32d7674a604b804147743b24de133cc330a171bc 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gas.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/gas.m" @@ -1,3 +1,3 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:22e923000ba3ac417d65e319e67513cdc218431c1e8b2bba399db5fa5529ff8d -size 65 +function [val,sol] = gaTestEval(sol,options) +val=sum(sol(1:3)); + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/seed.mat" 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"b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/seed.mat" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/seed2.mat" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/seed2.mat" index 0a491ea72acf5ca9ea9d8893c99238043f790e8c..a3d262ff3d71969a00955fd45f60d7be9317eca1 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/seed2.mat" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/seed2.mat" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/startup.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/startup.m" index 3f4ab22a9f50cc36132ebe10cf16568feb0a435c..fdb41ce4ddaaed9a6317eb0e31adc35a52a21dcb 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/startup.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\261/Genetic Algorithms/startup.m" @@ -1,3 +1,2 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:7a31db6b29276c6ca2dc034bb836520ca19dbf905b4af001a50177a412757e25 -size 49 +path(path,'/afs/eos/info/ie/ie589k_info/GAOT'); + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/Contents.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/Contents.m" index 5e5152828b7245d52d069c3ca7eaaf2b68f7611b..9e8efbd34e3b15bd2def20ca5cd10f1070c08741 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/Contents.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/Contents.m" @@ -1,3 +1,105 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:bdc1510c462c71a35c44243fcdb2c23f364d5e617aae2c21822199e992430ac8 -size 4761 +% Genetic Optimization Toolbox +% +% Main interface +% ga.m The Genetic Algorithm +% initializega.m Initialization function for float and binary +% representation Used by ga.m +% initializeoga.m Initialization function for order-based +% representation +% +% Operators used during simulated evolution +% +% Crossover Operators +% +% Float and Binary Representation +% simpleXover.m Operator for the Algorithm Used by ga.m +% +% Float Representation +% heuristicXover.m Operator for the Algorithm Used by ga.m +% arithXover.m Operator for the Algorithm Used by ga.m +% +% Order-based Representation +% cyclicXover.m Operator for the Algorithm Used by ga.m +% erXover.m Operator for the Algorithm Used by ga.m +% enhancederXover.m Operator for the Algorithm Used by ga.m +% linerorderXover.m Operator for the Algorithm Used by ga.m +% orderbasedXover.m Operator for the Algorithm Used by ga.m +% partmapXover.m Operator for the Algorithm Used by ga.m +% singleptXover.m Operator for the Algorithm Used by ga.m +% uniformXover.m Operator for the Algorithm Used by ga.m +% +% Mutation Operators +% +% Binary Representation +% binaryMutation.m Operator for the Algorithm Used by ga.m +% +% Float Representation +% boundaryMutation.m Operator for the Algorithm Used by ga.m +% multiNonUnifMutation.m Operator for the Algorithm Used by ga.m +% nonUnifMutation.m Operator for the Algorithm Used by ga.m +% unifMutation.m Operator for the Algorithm Used by ga.m +% +% Binary and Order-Based Representation +% inversionMutation.m Operator for the Algorithm Used by ga.m +% +% Order-Based Representation +% adjswapMutation.m Operator for the Algorithm Used by ga.m +% shiftMutation.m Operator for the Algorithm Used by ga.m +% swapMutation.m Operator for the Algorithm Used by ga.m +% threeswapMutation.m Operator for the Algorithm Used by ga.m +% +% Selection Functions +% normGeomSelect.m Selection function Used by ga.m +% roulette.m Selection function Used by ga.m +% tournSelect.m Selection function Used by ga.m +% +% Termination Functions +% maxGenTerm.m Termination function Used by ga.m +% optMaxGenTerm.m Termination function Used by ga.m +% +% Functions used for binary representation +% calcbits.m Binary precision function used by ga.m +% f2b.m Float to Binary conversion used by ga.m +% b2f.m Binary to Float conversion used by ga.m +% +% Utility functions +% parse.m Parse blank separated names used by ga.m +% delta.m Used by nonUnifMutation.m and mult...m +% +% Demonstrations +% gademo1.m Introductory demo of GAOT +% gademo2.m Multi-dimensional demo of GAOT +% gademo3.m Reference for GAOT +% floatExample.m Example using float representation +% floatGradExample.m Example exploring learning(Lamarckian and Baldwinian) +% binaryExample.m Example using binary representation +% orderBasedExample.m Example using order-based representation +% +% Functions used in Demonstrations +% gademo1eval1.m Example eval function used by gademo1.m +% coranaEval.m Calculate Corana functions used by gademo2.m +% coranaMin.m Calculate negative of Corana used by gademo2.m +% gaEval.m Calculation of Corana used for testing +% gaMichEval.m Michalewicz 2-variable problem evaluation +% gaZBGradEval.m Michalewicz Evaluation Used for Learning example +% gaZBGrad.m Gradient used for SQP during learning +% tspEval.m Function used in orderBasedExample + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/EER.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/EER.m" index c24167760c7f73cc7c5b96daaab0d0fda461590c..316a8c79134a9b69667c41a7d65594ef184163e9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/EER.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/EER.m" @@ -1,3 +1,45 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:762691dc8e7525c08c615904262ca850290f4be8544d2d27d1da941345275921 -size 1586 +function [c1,c2]=er(p1,p2,bounds,genInfo,ops) +sz=size(p1,2); +%fprintf(1,'======EER======\n'); +%fprintf(1,'%d ',p1(1:sz-1)); fprintf(1,'\n'); +%fprintf(1,'%d ',p2(1:sz-1)); fprintf(1,'\n'); + +right=[2:sz-1 1]; +left =[sz-1 1:(sz-2)]; +p1i(p1(1:sz-1))=1:sz-1; %Generate index +p2i(p2(1:sz-1))=1:sz-1; %Generate index + +adj=sort([-1:-1:-sz+1;p1(right(p1i));p1(left(p1i));p2(right(p2i));p2(left(p2i))])'; %' +repeats=find(diff(adj(:,2:5)')'==0); +adj(repeats+sz-1)=zeros(size(repeats)); %Zero repeat +adj(repeats+2*(sz-1))=-1*adj(repeats+2*(sz-1)); %Leftover is negative +adj=[adj sum(abs(sign(adj(:,2:5)))')']; + +curr_site = round(rand*(sz-1) + 0.5); %Pick random start site +%curr_site=5; +%curr_site=8; +for site=1:(sz-2) + c1(site)=curr_site; + adj_cities=adj(curr_site,1+find(adj(curr_site,2:5))); %Cities adjacent + i=find(adj_cities<0); + adj_cities=abs(adj_cities); + %Zero out this site in adj table + [cai caj]=find(abs(adj(adj_cities,2:5))==curr_site); + adj(abs(adj(adj_cities(cai),1))+(sz-1)*caj)=zeros(size(cai,1),1); + adj(curr_site,1:6)=[0 0 0 0 0 0]; + %Update nonzero count + adj(adj_cities,6)=adj(adj_cities,6)-ones(size(cai,1),1); + %Pick the destination city + if(i==[]) %No negative city + [v i]=min(adj(adj_cities,6)); + if (v==[]) %No cities left ERROR + i=find(adj(:,1)<0); adj_cities=abs(adj(i,1)); i=1; + %adj_cities=abs(adj(i,1)); + %i=1; + end %No Cities left Error + end %If no negative cities + curr_site=abs(adj_cities(i(1))); +end +c1(sz-1:sz)=[curr_site p1(sz)]; %Tag on fittness +c2=p1; %Create other child +%fprintf(1,'%d ',c1(1:sz-1)); fprintf(1,'\n'); \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/adjswapMutation.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/adjswapMutation.m" index 74cb2e09bbe3009df891fe56f68d88fa307b479f..73d82347975777c52733d4c5480cf0f037c3b749 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/adjswapMutation.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/adjswapMutation.m" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f1c6423ad469455dc554836a6109a0d90fe154c5962d0e336f28db30677badff -size 1419 +function [child] = adjswapmutation(par,bounds,genInfo,Ops) +% Adjswap mutation performs a swap of two adjacent +% genes in a permutation +% +% function [newSol] = adjswapmutation(parent,bounds,Ops) +% parent - the first parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options for binaryMutation [gen prob_of_mutation] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +sz = size(par,2)-1; +pos = round(rand*(sz-1) + 0.5); %Generate U(1,n-1) +child = par; +child(pos:pos+1)=[par(pos+1) par(pos)]; + + + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/arithXover.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/arithXover.m" index 7e7d08b3a662e600a8038c08c366cdbbf833ab09..ab2ae473a023b6aad077708afc3a9db64f895d54 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/arithXover.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/arithXover.m" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:07c8dff039578a7d8f917cb28482454c1f97a417c2e5d8349b0d80be41937812 -size 1487 +function [c1,c2] = arithXover(p1,p2,bounds,Ops) +% Arith crossover takes two parents P1,P2 and performs an interpolation +% along the line formed by the two parents. +% +% function [c1,c2] = arithXover(p1,p2,bounds,Ops) +% p1 - the first parent ( [solution string function value] ) +% p2 - the second parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options matrix for arith crossover [gen #ArithXovers] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +% Pick a random mix amount +a = rand; + +% Create the children +c1 = p1*a + p2*(1-a); +c2 = p1*(1-a) + p2*a; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/b2f.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/b2f.m" index c7660a6d44ddfd1e95a2270591d4ab73f72df405..f712bf281fc3c26e160ba09ed6e2696adb905a8c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/b2f.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/b2f.m" @@ -1,3 +1,36 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:06b62dd9938e52d9911900f1a3aec805331dc31a0f57acbae7f35c36cf808dcd -size 1495 +function [fval] = b2f(bval,bounds,bits) +% function [fval] = b2f(bval,bounds,bits) +% +% Return the float number corresponing to the binary representation of bval. +% +% fval - the float representation of the number +% bval - the binary representation of the number +% bounds - the bounds on the variables +% bits - the number of bits to represent each variable + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables +numV=size(bounds,1); +cs=[0 cumsum(bits)]; +for i=1:numV + a=bval((cs(i)+1):cs(i+1)); + fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/binaryExample.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/binaryExample.m" index 95e4e55159d343eb099a18412f259778616f6ec2..68f4961aef6835b8cfd0a6213e09ebc70cd1cf21 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/binaryExample.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/binaryExample.m" @@ -1,3 +1,108 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:89f5e525a80056b24067284d85d969277e896f5115bbd290f7cd7ed7d26e72af -size 2080 +echo on +% This script shows how to use the ga using a float representation. +% You should see the demos for +% more information as well. gademo1, gademo2, gademo3 +global bounds + +% Setting the seed back to the beginning for comparison sake +rand('seed',0) + +% Crossover Operators +xFns = 'simpleXover'; +xOpts = [.4]; + +% Mutation Operators +mFns = 'binaryMutation'; + +mOpts = [0.005]; + +% Termination Operators +termFns = 'maxGenTerm'; +termOps = [200]; % 200 Generations + +% Selection Function +selectFn = 'roulette' +selectOps = []; + +% Evaluation Function +evalFn = 'gaMichEval'; +evalOps = []; + +type gaMichEval + +% Bounds on the variables +bounds = [-3 12.1; 4.1 5.8]; + +% GA Options [epsilon float/binar display] +gaOpts=[1e-6 0 1]; + +% Generate an intialize population of size 20 +startPop = initializega(20,bounds,'gaMichEval',[],[1e-6 0]); + +% Lets run the GA +% Hit a return to continue +pause + +[x endPop bestPop trace]=ga(bounds,evalFn,evalOps,startPop,gaOpts,... + termFns,termOps,selectFn,selectOps,xFns,xOpts,mFns,mOpts); + +% x is the best solution found +x +% Hit a return to continue +pause + +% endPop is the ending population +endPop +% Hit a return to continue +pause + +% trace is a trace of the best value and average value of generations +trace +% Hit a return to continue +pause + +% Plot the best over time +clf +plot(trace(:,1),trace(:,2)); +% Hit a return to continue +pause + +% Add the average to the graph +hold on +plot(trace(:,1),trace(:,3)); +% Hit a return to continue +pause + +% Lets increase the population size by running the defaults +% +rand('seed',0) +termOps=[100]; +[x endPop bestPop trace]=ga(bounds,evalFn,evalOps,[],gaOpts,termFns,termOps,... + selectFn,selectOps); + +% x is the best solution found +x +% Hit a return to continue +pause + +% endPop is the ending population +endPop +% Hit a return to continue +pause + +% trace is a trace of the best value and average value of generations +trace +% Hit a return to continue +pause + +% Plot the best over time +clf +plot(trace(:,1),trace(:,2)); +% Hit a return to continue +pause + +% Add the average to the graph +hold on +plot(trace(:,1),trace(:,3)); + +echo off \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/binaryMutation.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/binaryMutation.m" index 633def667fcbdd8a7e1c5d407a0f10bc57386e7e..48aebd343f99634d2a6d4ec1607d7f41ed3d0148 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/binaryMutation.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/binaryMutation.m" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c61b13138ccae83459b9fe051ea934766e342d6e55845ae463f34f1cbf28bf70 -size 1504 +function [parent] = binaryMutate(parent,bounds,Ops) +% Binary mutation changes each of the bits of the parent +% based on the probability of mutation +% +% function [newSol] = binaryMutate(parent,bounds,Ops) +% parent - the first parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options for binaryMutation [gen prob_of_mutation] + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +pm=Ops(2); +numVar = size(parent,2)-1; % Get the number of variables +% Pick a variable to mutate randomly from 1-number of vars +rN=rand(1,numVar)1) + r=.99; + % disp(sprintf('max gen %d < current gen %d setting ratio = 1',mt,ct)); +end +change = y*(rand*(1-r))^b; + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/dists.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/dists.m" index 39584834b99e9361921e3df19fad0afc9c375314..70a799fb2329e682eb5385217b146f4ed592af8e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/dists.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/dists.m" @@ -1,3 +1,192 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f779b6feefc12c89600cb008a0e1b6987a2ce79aac68a189ca7f5dd70024930e -size 6837 +function D = dists(X1,X2,p,e) +%DISTS Calculates distances between vectors of points. +% D = dists(X1,X2,p,e) +% X1 = n x d matrix of n d-dimensional points +% X2 = m x d matrix of m d-dimensional points +% D = n x m matrix of distances +% = (n-1) x 1 vector of distances between X1 points, if X2 = [] +% p = 2, Euclidean (default): D(i,j) = sqrt(sum((X1(i,:) - X2(j,:))^2)) +% = 1, rectilinear: D(i,j) = sum(abs(X1(i,:) - X2(j,:)) +% = Inf, Chebychev dist: D(i,j) = max(abs(X1(i,:) - X2(j,:)) +% = (1 Inf), lp norm: D(i,j) = sum(abs(X1(i,:) - X2(j,:))^p)^(1/p) +% = 'rad', great circle distance in radians of a sphere +% (where X1 and X2 are decimal degree latitudes and longitudes) +% = 'mi' or 'sm', great circle distance in statute miles on the earth +% = 'km', great circle distance in kilometers on the earth +% e = epsilon for hyperboloid approximation gradient estimation +% = 0 (default); no error checking if any non-empty 'e' input +% ~= 0 => general lp used for rect., Cheb., and p outside [1,2] +% +% Great circle distances are calculated using the Haversine Formula (from R.W. +% Sinnott, "Virtues of the Haversine", Sky and Telescope, vol. 68, no. 2, 1984 +% p. 159, as reported in "http://www.census.gov/cgi-bin/geo/gisfaq?Q5.1") + +% Copyright (c) 1998 by Michael G. Kay +% Matlog Version 1.0 Apr-3-98 + +% Input Error Checking ******************************************************* +if nargin == 4 & ~isempty(e) % No error checking is 'e' input + [n,d] = size(X1); + m = size(X2,1); +else % Do error checking + error(nargchk(1,4,nargin)); + e = 0; % 'e' default + [n,d] = size(X1); + if n == 0 | ~isreal(X1) + error('X1 must be non-empty real matrix'); + end + if nargin < 2 | isempty(X2) % Calc intra-seq dist b/w X1 points + m = 0; % X2 default + if n < 2 + error('X1 must have more than 1 point'); + end + else % Calc dist b/w X1 and X2 points + [m,dX2] = size(X2); + if m == 0 | ~isreal(X2) + error('X2 must be non-empty real matrix'); + end + if d ~= dX2 + error('Rows of X1 and X2 must have same dimensions'); + end + end + if nargin < 3 | isempty(p) + p = 2; % 'p' default + elseif ~ischar(p) % lp distances + if length(p(:)) ~= 1 | ~isreal(p) + error('''p'' must be a real scalar number'); + end + elseif ischar(p) % Great circle distances + p = lower(p); + if d ~= 2 + error('Points must be 2-dimensional for great-circle distances'); + end + if ~any(strcmp(p,{'rad','mi','sm','km'})) + error('''p'' must be either ''rad,'' ''mi,'' ''sm,'' or ''km'''); + end + else + error('''p'' not valid value'); + end +end +% End (Input Error Checking) *********************************************** + +% Interchange if X2 is the only 1 point +intrchg = 0; +if n > 1 & m == 1 + tmp = X2; X2 = X1; X1 = tmp; + m = n;n = 1; + intrchg = 1; +end + +% 1-dimensional points +if d == 1 + if e == 0 + if m ~= 0 + D = abs(X1(:,ones(1,m)) - X2(:,ones(1,n))'); + else + D = abs(X1(1:n-1) - X1(2:n))'; % X1 intra-seq. dist. + end + else + if m ~= 0 + D = sqrt((X1(:,ones(1,m)) - X2(:,ones(1,n))').^2 + e); + else + D = sqrt((X1(1:n-1) - X1(2:n)).^2 + e)'; + end + end + +% X1 only 1 point or intra-seq dist +elseif n == 1 | m == 0 + if n == 1 % Expand X1 to match X2 + X1 = X1(ones(1,m),:); + n = m; + else % X1 intra-seq. dist. + X2 = X1(2:n,:); % X2 = ending points + n = n - 1; + X1 = X1(1:n,:); % X1 = beginning points + end + if p == 2 % Euclidean distance + D = sqrt(sum(((X1 - X2).^2 + e)')); + elseif ischar(p) % Great-circle distance + X1 = pi*X1/180;X2 = pi*X2/180; + D = 2*asin(min(1,sqrt(sin((X1(:,1) - X2(:,1))/2).^2 + ... + cos(X1(:,1)).*cos(X2(:,1)).* ... + sin((X1(:,2) - X2(:,2))/2).^2)))'; + elseif p == 1 & e == 0 % Rectilinear distance + D = sum(abs(X1 - X2)'); + elseif (p >= 1 & p <= 2) | (e ~= 0 & p > 0) % General lp distance + D = sum((((X1 - X2).^2 + e).^(p/2))').^(1/p); + elseif p == Inf & e == 0 % Chebychev distance + D = max(abs(X1 - X2)'); + else % Otherwise + D = zeros(1,n); + for j = 1:n + D(j) = norm(X1(j,:) - X2(j,:),p); + end + end + +% X1 and X2 are 2-dimensional points +elseif d == 2 + if p == 2 % Euclidean distance + D = sqrt((X1(:, ones(1,m)) - X2(:, ones(1,n))').^2 + e + ... + (X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))').^2 + e); + elseif ischar(p) % Great-circle distance + X1 = pi*X1/180;X2 = pi*X2/180; + cosX1lat = cos(X1(:,1));cosX2lat = cos(X2(:,1)); + D = 2*asin(min(1,sqrt(... + sin((X1(:,ones(1,m)) - X2(:,ones(1,n))')/2).^2 + ... + cosX1lat(:,ones(1,m),1).*cosX2lat(:,ones(1,n))'.* ... + sin((X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))')/2).^2))); + elseif p == 1 & e == 0 % Rectilinear distance + D = abs(X1(:,ones(1,m)) - X2(:,ones(1,n))') + ... + abs(X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))'); + elseif (p >= 1 & p <= 2) | (e ~= 0 & p > 0) % General lp distance + D = (((X1(:, ones(1,m)) - X2(:, ones(1,n))').^2 + e).^(p/2) + ... + ((X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))').^2 + e).^(p/2)).^(1/p); + elseif p == Inf & e == 0 % Chebychev distance + D = max(abs(X1(:,ones(1,m)) - X2(:,ones(1,n))'),... + abs(X1(:,2*ones(1,m)) - X2(:,2*ones(1,n))')); + else % Otherwise + D = zeros(n,m); + for i = 1:n + for j = 1:m + D(i,j) = norm(X1(i,:) - X2(j,:),p); + end + end + end + +% X1 and X2 are 3 or more dim. point +else + if p == 2 % Euclidean distance + D = sqrt(sum((repmat(reshape(X1,[n 1 k]),1,m) - ... + repmat(reshape(X2,[1 m k]),n,1)).^2 + e,3)); + elseif p == 1 & e == 0 % Rectilinear distance + D = sum(abs(repmat(reshape(X1,[n 1 k]),1,m) - ... + repmat(reshape(X2,[1 m k]),n,1)),3); + elseif (p >= 1 & p <= 2) | (e ~= 0 & p > 0) % General lp distance + D = sum(((repmat(reshape(X1,[n 1 k]),1,m) - ... + repmat(reshape(X2,[1 m k]),n,1)).^2 + e).^(p/2),3).^(1/p); + elseif p == Inf & e == 0 % Chebychev distance + D = max(abs(repmat(reshape(X1,[n 1 k]),1,m) - ... + repmat(reshape(X2,[1 m k]),n,1)),[],3); + else % Otherwise + D = zeros(n,m); + for i = 1:n + for j = 1:m + D(i,j) = norm(X1(i,:) - X2(j,:),p); + end + end + end +end + +% Transpose D if X2 was interchanged or X1 intra-seq distances +if intrchg == 1 | m == 0 + D = D.'; +end + +% Convert 'rad' to 'km' or 'mi' (or 'sm') +if ischar(p) & ~strcmp(p,'rad') + if strcmp(p,'km') + D = (6378.388 - 21.476*abs(sin(mean([X1(:,1);X2(:,1)]))))*D; + else % 'mi' or 'sm' + D = (3963.34 - 13.35*abs(sin(mean([X1(:,1);X2(:,1)]))))*D; + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/enhancederXover.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/enhancederXover.m" index 2b357e693d5f17fa2bc63ef51770dd1f3a04016b..6f9ee743396129726146e7b9738ebf5a944a7bf9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/enhancederXover.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/enhancederXover.m" @@ -1,3 +1,56 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b9520ee3bbee6f509ff02c77571322ba098749a8525a0a299ea6067ae0af36e9 -size 2348 +function [c1,c2]=enhancederXover(p1,p2,bounds,ops) +% EnhancederXover crossover takes two parents P1,P2 and performs +% enhanced edge recombination crossover on permutation strings. +% +% function [c1,c2] = enhancederXover(p1,p2,bounds,Ops) +% p1 - the first parent ( [solution string function value] ) +% p2 - the second parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options matrix for simple crossover [gen #SimpXovers]. + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +sz=size(p1,2); +right=[2:sz 1]; +left =[sz 1:(sz-1)]; +p1i(p1)=1:10; %Generate index +p2i(p2)=1:10; %Generate index +adj=sort([-1:-1:-sz;p1(right(p1i));p1(left(p1i));p2(right(p2i));p2(left(p2i))])'; +repeats=find(diff(adj(:,2:5)')'==0); +adj(repeats+sz)=zeros(size(repeats)); %Zero repeat +adj(repeats+2*sz)=-1*adj(repeats+2*sz); %Leftover is negative + +curr_site = round(rand*sz + 0.5); %Pick random start site +for site=1:(sz-1) + c1(site)=curr_site; + inAdj=find(abs(adj(:,2:5))==curr_site); %Find this site in adjacency table + adj(inAdj+sz)=zeros(size(inAdj)); %Take this out of the adjacency table + %Find the element with fewest remaining links + lz=colperm(adj'); + lzi(lz)=1:size(lz,2); %create index + adj_cities=adj(curr_site,1+(find(adj(curr_site,2:5)))); + if(prod(sign(adj_cities))==-1) %One negative city + i=find(adj_cities<0); + else + [v i]=min(lzi(abs(adj_cities))); + end + curr_site=abs(adj_cities(i)); +end +c1(sz)=curr_site; +c2=p1; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/erXover.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/erXover.m" index 57df255503aeb53606e38792978539db680dbb0d..473104dddf55cbf169adf7e37d6c336c0eff7ee3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/erXover.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/erXover.m" @@ -1,3 +1,51 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ddfc0092e8a0d0098e1abbc134c68f3081ebf3b197102706174a95a6d0f1e8da -size 2118 +function [c1,c2]=er(p1,p2,bounds,ops) +% Er crossover takes two parents P1,P2 and performs edge recombination +% crossover on permutation strings. +% +% function [c1,c2] = er(p1,p2,bounds,Ops) +% p1 - the first parent ( [solution string function value] ) +% p2 - the second parent ( [solution string function value] ) +% bounds - the bounds matrix for the solution space +% Ops - Options matrix for simple crossover [gen #SimpXovers]. + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. +sz=size(p1,2)-1; +right=[2:sz 1]; +left =[sz 1:(sz-1)]; +p1i(p1)=1:sz; %Generate index +p2i(p2)=1:sz; %Generate index +adj=sort([-1:-1:-sz;p1(right(p1i));p1(left(p1i));p2(right(p2i));p2(left(p2i))])'; +repeats=find(diff(adj(:,2:5)')'==0); +adj(repeats+sz)=zeros(size(repeats)); + +curr_site = round(rand*sz + 0.5); %Pick random start site +for site=1:(sz-1) + c1(site)=curr_site; + inAdj=find(adj(:,2:5)==curr_site); %Find this site in adjacency table + adj(inAdj+sz)=zeros(size(inAdj)); %Take this out of the adjacency table + %Find the element with fewest remaining links + lz=colperm(adj'); + lzi(lz)=1:size(lz,2); %create index + adj_cities=adj(curr_site,1+(find(adj(curr_site,2:5)))); + [v i]=min(lzi(adj_cities)); + curr_site=adj_cities(i); +end +c1(sz)=curr_site; +c2=p1; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/f2b.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/f2b.m" index e0a9dd0b40c563ece33e9f3b2ce7264b4bdbcb04..6cc1d3db4c90b9143446dfc8580b9d4c886d7ca3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/f2b.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/f2b.m" @@ -1,3 +1,37 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9d0c56367accb6b52ffd399e00977ba60d30b57bf1b8d13c52bafe3dd4d1c9bb -size 1501 +function [bval] = function(fval,bounds,bits) +% function [bval] = f2b(fval,bounds,bits) +% +% Return the binary representation of the float number fval. +% +% fval - the float representation of the number +% bval - the binary representation of the number +% bounds - the bounds on the variables +% bits - the number of bits to represent each variable + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +scale=(2.^bits-1)./ (bounds(:,2)-bounds(:,1))'; %The range of the variables +numV=size(bounds,1); +cs=[0 cumsum(bits)]; +bval=[]; +for i=1:numV + fval(i)=(fval(i)-bounds(i,1)) * scale(i); + bval=[bval rem(floor(fval(i)*pow2(1-bits(i):0)),2)]; +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/floatExample.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/floatExample.m" index 6b0719019a8ae9205f4f3f635f60643430529c13..ff9b3f28623675336c0a6d3f8e4e88ba99643057 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/floatExample.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/floatExample.m" @@ -1,3 +1,130 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c258d04942bc8c752c890590c4ae1d894ed341e1c493905141b80578cbb0bc0f -size 2322 +echo on +% This script shows how to use the ga using a float representation. +% You should see the demos for +% more information as well. gademo1, gademo2, gademo3 +global bounds + +% Setting the seed to the same for binary +rand('seed',156789) + +% Crossover Operators +xFns = 'arithXover heuristicXover simpleXover'; +xOpts = [1 0; 1 3; 1 0]; + +% Mutation Operators +mFns = 'boundaryMutation multiNonUnifMutation nonUnifMutation unifMutation'; + +mOpts = [2 0 0;3 200 3;2 200 3;2 0 0]; + +% Termination Operators +termFns = 'maxGenTerm'; +termOps = [200]; % 200 Generations + +% Selection Function +selectFn = 'normGeomSelect'; +selectOps = [0.08]; + +% Evaluation Function +evalFn = 'gaMichEval'; +evalOps = []; + +type gaMichEval + +% Bounds on the variables +bounds = [-3 12.1; 4.1 5.8]; + +% GA Options [epsilon float/binar display] +gaOpts=[1e-6 1 1]; + +% Generate an intialize population of size 20 +startPop = initializega(20,bounds,'gaMichEval',[1e-6 1]) + +% Lets run the GA +% Hit a return to continue +pause + + +[x endPop bestPop trace]=ga(bounds,evalFn,evalOps,startPop,gaOpts,... + termFns,termOps,selectFn,selectOps,xFns,xOpts,mFns,mOpts); + + +% x is the best solution found +x +% Hit a return to continue +pause + + +% endPop is the ending population +endPop +% Hit a return to continue +pause + + +% bestPop is the best solution tracked over generations +bestPop +% Hit a return to continue +pause + + +% trace is a trace of the best value and average value of generations +trace +% Hit a return to continue +pause + + +% Plot the best over time +clf +plot(trace(:,1),trace(:,2)); +% Hit a return to continue +pause + + +% Add the average to the graph +hold on +plot(trace(:,1),trace(:,3)); +% Hit a return to continue +pause + + +% Lets increase the population size by running the defaults +% + +[x endPop bestPop trace]=ga(bounds,evalFn,evalOps,[],gaOpts); + +% x is the best solution found +x +% Hit a return to continue +pause + + +% endPop is the ending population +endPop +% Hit a return to continue +pause + + +% bestPop is the best solution tracked over generations +bestPop +% Hit a return to continue +pause + + +% trace is a trace of the best value and average value of generations +trace +% Hit a return to continue +pause + + +% Plot the best over time +clf +plot(trace(:,1),trace(:,2)); +% Hit a return to continue +pause + + +% Add the average to the graph +hold on +plot(trace(:,1),trace(:,3)); + + +echo off \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/floatGradExample.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/floatGradExample.m" index 0786dc8c301f76a43b143423838e0457f721d9d8..8cc71e322ad44bab62d81dbc1a29f945a20b9385 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/floatGradExample.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/floatGradExample.m" @@ -1,3 +1,101 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b54d6fd57f4891488aaf42a1a15e3b96dee82b61d05f7f84a16217e84d9b4dee -size 2137 +echo off +%load seed.mat +rand('seed',0); +echo on +% This script shows how to use the ga. You should see the demos for +% more information as well. gademo1, gademo2, gademo3 +global bounds + +% Crossover Operators +xFns = 'arithXover heuristicXover simpleXover'; +xOpts = [2 0; 2 3; 2 0]; + +% Mutation Operators +mFns = 'boundaryMutation multiNonUnifMutation nonUnifMutation unifMutation'; +mOpts = [4 0 0;6 10 3;4 10 3;4 0 0]; + +% Termination Operators +termFns = 'maxGenTerm'; +termOps = [10]; + +% Selection Function +selectFn = 'normGeomSelect'; +selectOps = [0.06]; + +% Evaluation Function takes two options +% prob to use gradient, prob to perform Lamarkian evolution +evalFn = 'gaZBGradEval'; +evalOps = [1.00 1.00]; + +% Bounds on the variables +bounds = [-3 12.1; 4.1 5.8]; + +% GA Options [epsilon float/binar display] +gaOpts=[1e-6 1 1]; + +% Generate an intialize population of size 80 +startPop = initializega(80,bounds,evalFn,evalOps,[1e-6 1]); +evalOps = [1.00 0.00]; % 1 - Peform learning 0-Do not update + +% Lets run the GA using Baldwinian Evolution + +[x endPop bestPop trace]=ga(bounds,evalFn,evalOps,startPop,gaOpts,... + termFns,termOps,selectFn,selectOps,xFns,xOpts,mFns,mOpts); + +% x is the best solution found +x +pause + +% endPop is the ending population +endPop +pause + +% bestPop is the best solution tracked over generations +bestPop +pause + +% trace is a trace of the best value and average value of generations +trace +pause + +% Plot the best over time +clf +plot(trace(:,1),trace(:,2)); +pause + +% Add the average to the graph +hold on +plot(trace(:,1),trace(:,3)); +pause + +% Lets run the GA using Lamarkian Evolution +evalOps = [1.00 1.00]; + +[x endPop bestPop trace]=ga(bounds,evalFn,evalOps,startPop,gaOpts,... + termFns,termOps,selectFn,selectOps,xFns,xOpts,mFns,mOpts); + +% x is the best solution found +x +pause + +% endPop is the ending population +endPop +pause + +% bestPop is the best solution tracked over generations +bestPop +pause + +% trace is a trace of the best value and average value of generations +trace +pause + +% Plot the best over time +clf +plot(trace(:,1),trace(:,2)); +pause + +% Add the average to the graph +hold on +plot(trace(:,1),trace(:,3)); +pause diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/ga.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/ga.m" index 900bbeb1d5efecd1494e540f0d90e3869bc81760..e92aa4221779661af676b6a036d61b7695e77b01 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/ga.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\351\201\227\344\274\240\347\256\227\346\263\225@\351\201\227\344\274\240\351\200\200\347\201\253\347\256\227\346\263\225\357\274\210\347\256\227\346\263\225\347\256\200\344\273\213+\347\274\226\347\250\213\346\212\200\345\267\247+\345\267\245\345\205\267\347\256\261+\345\272\224\347\224\250\345\244\247\345\205\250\357\274\211\357\274\210\345\220\253\346\272\220\344\273\243\347\240\201\357\274\211/\345\267\245\345\205\267\347\256\261/\351\201\227\344\274\240\347\256\227\346\263\225\345\267\245\345\205\267\347\256\2612/\351\201\227\344\274\240\345\267\245\345\205\267\347\256\261/ga.m" @@ -1,3 +1,304 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ff5f9c4abe9f08af1a79c5a3731b6b7d803de3b20050f09e8affbd4573ba538e -size 10805 +function [x,endPop,bPop,traceInfo] = ga(bounds,evalFN,evalOps,startPop,opts,... +termFN,termOps,selectFN,selectOps,xOverFNs,xOverOps,mutFNs,mutOps) +% GA run a genetic algorithm +% function [x,endPop,bPop,traceInfo]=ga(bounds,evalFN,evalOps,startPop,opts, +% termFN,termOps,selectFN,selectOps, +% xOverFNs,xOverOps,mutFNs,mutOps) +% +% Output Arguments: +% x - the best solution found during the course of the run +% endPop - the final population +% bPop - a trace of the best population +% traceInfo - a matrix of best and means of the ga for each generation +% +% Input Arguments: +% bounds - a matrix of upper and lower bounds on the variables +% evalFN - the name of the evaluation .m function +% evalOps - options to pass to the evaluation function ([NULL]) +% startPop - a matrix of solutions that can be initialized +% from initialize.m +% opts - [epsilon prob_ops display] change required to consider two +% solutions different, prob_ops 0 if you want to apply the +% genetic operators probabilisticly to each solution, 1 if +% you are supplying a deterministic number of operator +% applications and display is 1 to output progress 0 for +% quiet. ([1e-6 1 0]) +% termFN - name of the .m termination function (['maxGenTerm']) +% termOps - options string to be passed to the termination function +% ([100]). +% selectFN - name of the .m selection function (['normGeomSelect']) +% selectOpts - options string to be passed to select after +% select(pop,#,opts) ([0.08]) +% xOverFNS - a string containing blank seperated names of Xover.m +% files (['arithXover heuristicXover simpleXover']) +% xOverOps - A matrix of options to pass to Xover.m files with the +% first column being the number of that xOver to perform +% similiarly for mutation ([2 0;2 3;2 0]) +% mutFNs - a string containing blank seperated names of mutation.m +% files (['boundaryMutation multiNonUnifMutation ... +% nonUnifMutation unifMutation']) +% mutOps - A matrix of options to pass to Xover.m files with the +% first column being the number of that xOver to perform +% similiarly for mutation ([4 0 0;6 100 3;4 100 3;4 0 0]) + +% Binary and Real-Valued Simulation Evolution for Matlab +% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay +% +% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function +% optimization: A Matlab implementation. ACM Transactions on Mathmatical +% Software, Submitted 1996. +% +% This program is free software; you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation; either version 1, or (at your option) +% any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. A copy of the GNU +% General Public License can be obtained from the +% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. + +%%$Log: ga.m,v $ +%Revision 1.10 1996/02/02 15:03:00 jjoine +% Fixed the ordering of imput arguments in the comments to match +% the actual order in the ga function. +% +%Revision 1.9 1995/08/28 20:01:07 chouck +% Updated initialization parameters, updated mutation parameters to reflect +% b being the third option to the nonuniform mutations +% +%Revision 1.8 1995/08/10 12:59:49 jjoine +%Started Logfile to keep track of revisions +% + + +n=nargin; +if n<2 | n==6 | n==10 | n==12 + disp('Insufficient arguements') +end +if n<3 %Default evalation opts. + evalOps=[]; +end +if n<5 + opts = [1e-6 1 0]; +end +if isempty(opts) + opts = [1e-6 1 0]; +end + +if any(evalFN<48) %Not using a .m file + if opts(2)==1 %Float ga + e1str=['x=c1; c1(xZomeLength)=', evalFN ';']; + e2str=['x=c2; c2(xZomeLength)=', evalFN ';']; + else %Binary ga + e1str=['x=b2f(endPop(j,:),bounds,bits); endPop(j,xZomeLength)=',... + evalFN ';']; + end +else %Are using a .m file + if opts(2)==1 %Float ga + e1str=['[c1 c1(xZomeLength)]=' evalFN '(c1,[gen evalOps]);']; + e2str=['[c2 c2(xZomeLength)]=' evalFN '(c2,[gen evalOps]);']; + else %Binary ga + e1str=['x=b2f(endPop(j,:),bounds,bits);[x v]=' evalFN ... + '(x,[gen evalOps]); endPop(j,:)=[f2b(x,bounds,bits) v];']; + end +end + + +if n<6 %Default termination information + termOps=[100]; + termFN='maxGenTerm'; +end +if n<12 %Default muatation information + if opts(2)==1 %Float GA + mutFNs=['boundaryMutation multiNonUnifMutation nonUnifMutation unifMutation']; + mutOps=[4 0 0;6 termOps(1) 3;4 termOps(1) 3;4 0 0]; + else %Binary GA + mutFNs=['binaryMutation']; + mutOps=[0.05]; + end +end +if n<10 %Default crossover information + if opts(2)==1 %Float GA + xOverFNs=['arithXover heuristicXover simpleXover']; + xOverOps=[2 0;2 3;2 0]; + else %Binary GA + xOverFNs=['simpleXover']; + xOverOps=[0.6]; + end +end +if n<9 %Default select opts only i.e. roullete wheel. + selectOps=[]; +end +if n<8 %Default select info + selectFN=['normGeomSelect']; + selectOps=[0.08]; +end +if n<6 %Default termination information + termOps=[100]; + termFN='maxGenTerm'; +end +if n<4 %No starting population passed given + startPop=[]; +end +if isempty(startPop) %Generate a population at random + %startPop=zeros(80,size(bounds,1)+1); + startPop=initializega(80,bounds,evalFN,evalOps,opts(1:2)); +end + +if opts(2)==0 %binary + bits=calcbits(bounds,opts(1)); +end + +xOverFNs=parse(xOverFNs); +mutFNs=parse(mutFNs); + +xZomeLength = size(startPop,2); %Length of the xzome=numVars+fittness +numVar = xZomeLength-1; %Number of variables +popSize = size(startPop,1); %Number of individuals in the pop +endPop = zeros(popSize,xZomeLength); %A secondary population matrix +c1 = zeros(1,xZomeLength); %An individual +c2 = zeros(1,xZomeLength); %An individual +numXOvers = size(xOverFNs,1); %Number of Crossover operators +numMuts = size(mutFNs,1); %Number of Mutation operators +epsilon = opts(1); %Threshold for two fittness to differ +oval = max(startPop(:,xZomeLength)); %Best value in start pop +bFoundIn = 1; %Number of times best has changed +done = 0; %Done with simulated evolution +gen = 1; %Current Generation Number +collectTrace = (nargout>3); %Should we collect info every gen +floatGA = opts(2)==1; %Probabilistic application of ops +display = opts(3); %Display progress + +while(~done) + %Elitist Model + [bval,bindx] = max(startPop(:,xZomeLength)); %Best of current pop + best = startPop(bindx,:); + + if collectTrace + traceInfo(gen,1)=gen; %current generation + traceInfo(gen,2)=startPop(bindx,xZomeLength); %Best fittness + traceInfo(gen,3)=mean(startPop(:,xZomeLength)); %Avg fittness + traceInfo(gen,4)=std(startPop(:,xZomeLength)); + end + + if ( (abs(bval - oval)>epsilon) | (gen==1)) %If we have a new best sol + if display + fprintf(1,'\n%d %f\n',gen,bval); %Update the display + end + if floatGA + bPop(bFoundIn,:)=[gen startPop(bindx,:)]; %Update bPop Matrix + else + bPop(bFoundIn,:)=[gen b2f(startPop(bindx,1:numVar),bounds,bits)... + startPop(bindx,xZomeLength)]; + end + bFoundIn=bFoundIn+1; %Update number of changes + oval=bval; %Update the best val + else + if display + fprintf(1,'%d ',gen); %Otherwise just update num gen + end + end + + endPop = feval(selectFN,startPop,[gen selectOps]); %Select + + if floatGA %Running with the model where the parameters are numbers of ops + for i=1:numXOvers, + for j=1:xOverOps(i,1), + a = round(rand*(popSize-1)+1); %Pick a parent + b = round(rand*(popSize-1)+1); %Pick another parent + xN=deblank(xOverFNs(i,:)); %Get the name of crossover function + [c1 c2] = feval(xN,endPop(a,:),endPop(b,:),bounds,[gen xOverOps(i,:)]); + + if c1(1:numVar)==endPop(a,(1:numVar)) %Make sure we created a new + c1(xZomeLength)=endPop(a,xZomeLength); %solution before evaluating + elseif c1(1:numVar)==endPop(b,(1:numVar)) + c1(xZomeLength)=endPop(b,xZomeLength); + else + %[c1(xZomeLength) c1] = feval(evalFN,c1,[gen evalOps]); + eval(e1str); + end + if c2(1:numVar)==endPop(a,(1:numVar)) + c2(xZomeLength)=endPop(a,xZomeLength); + elseif c2(1:numVar)==endPop(b,(1:numVar)) + c2(xZomeLength)=endPop(b,xZomeLength); + else + %[c2(xZomeLength) c2] = feval(evalFN,c2,[gen evalOps]); + eval(e2str); + end + + endPop(a,:)=c1; + endPop(b,:)=c2; + end + end + + for i=1:numMuts, + for j=1:mutOps(i,1), + a = round(rand*(popSize-1)+1); + c1 = feval(deblank(mutFNs(i,:)),endPop(a,:),bounds,[gen mutOps(i,:)]); + if c1(1:numVar)==endPop(a,(1:numVar)) + c1(xZomeLength)=endPop(a,xZomeLength); + else + %[c1(xZomeLength) c1] = feval(evalFN,c1,[gen evalOps]); + eval(e1str); + end + endPop(a,:)=c1; + end + end + + else %We are running a probabilistic model of genetic operators + for i=1:numXOvers, + xN=deblank(xOverFNs(i,:)); %Get the name of crossover function + cp=find(rand(popSize,1)44 +D<126012F0A2126004047D830B>46 D<13101338A3135CA3138EA3EA0107A200031380EA 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