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' DotNumerics Simplex Extender
' Copyright 2015 Gregor Reichert, Daniel Wagner O. de Medeiros
'
' This file is part of DWSIM.
'
' DWSIM 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 3 of the License, or
' (at your option) any later version.
'
' DWSIM 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 DWSIM. If not, see <http://www.gnu.org/licenses/>.
Imports DotNumerics.Optimization
Public Module SimplexExtender
Public Delegate Function ObjectiveFunction(ByVal x() As Double) As Double
''' <summary>
''' Simplified implementation of Nelder-Mead-Simplex-Downhill algorithm. No "Reduction" and no "Expansion" implemented yet.
''' https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method
''' </summary>
''' <param name="simplexsolver">simplex solver instance</param>
''' <param name="objfunc">objective function delegate</param>
''' <param name="Var">optimization variables</param>
''' <returns>the values of the variables that minimize the objective function value</returns>
''' <remarks></remarks>
<System.Runtime.CompilerServices.Extension()> Public Function ComputeMin2(simplexsolver As Simplex, objfunc As ObjectiveFunction, ByVal Var() As OptBoundVariable) As Double()
Dim cnt As Integer = 0
Dim i, k, IdxMax As Integer
Dim Dx, FVnew, LF, LF1 As Double
Dim Beta As Double = 0.5
'Dimension 0: point number
'Dimension 1: coordinates of points; last column = 1 is indicating "at limiting border"
Dim Points(Var.Length, Var.Length - 1) As Double
Dim FuncVal(Var.Length) As Double
Dim Pt(Var.Length - 1) As Double
Dim CenterPt(Var.Length - 1) As Double
'Calculate initial value
For i = 0 To Var.Length - 1
'Pt(i) = (Var(i).UpperBound - Var(i).LowerBound) / 2
'Pt(i) = 0
Pt(i) = Var(i).InitialGuess
Next
'Initialise points
For k = 0 To Var.Length 'points
For i = 0 To Var.Length - 1 'coordinates
Points(k, i) = Pt(i)
Next
Next
For k = 1 To Var.Length
Dx = (Var(k - 1).UpperBound - Var(k - 1).LowerBound) / 10
Points(k, k - 1) += Dx
Next
'Calculate point values
For k = 0 To Var.Length
For i = 0 To Var.Length - 1
Pt(i) = Points(k, i)
Next
FuncVal(k) = objfunc(Pt)
Next
Do
cnt += 1
'Search worst value e.g. maximum Gibbs Enthalpy
IdxMax = 0
For k = 1 To Var.Length
If FuncVal(k) > FuncVal(IdxMax) Then IdxMax = k
Next
'Calculate center point as average from all points except max
For i = 0 To Var.Length - 1
CenterPt(i) = 0
Next
For k = 0 To Var.Length
If k <> IdxMax Then
For i = 0 To Var.Length - 1
CenterPt(i) += Points(k, i) / Var.Length
Next
End If
Next
'reflect worst point at center point
LF = 1
For i = 0 To Var.Length - 1
LF1 = 1
Pt(i) = CenterPt(i) + CenterPt(i) - Points(IdxMax, i)
'Check if point is inside bounds
If Pt(i) < Var(i).LowerBound Then
LF1 = (Var(i).LowerBound - CenterPt(i)) / (Points(IdxMax, i) - CenterPt(i))
End If
If LF1 < LF Then LF = LF1
If Pt(i) > Var(i).UpperBound Then
LF1 = (Var(i).UpperBound - CenterPt(i)) / (Points(IdxMax, i) - CenterPt(i))
End If
If LF1 < LF Then LF = -LF1
Next
If LF < 1 Then
For i = 0 To Var.Length - 1
Pt(i) = CenterPt(i) + LF * (CenterPt(i) - Points(IdxMax, i))
Next
End If
FVnew = objfunc(Pt)
If FVnew < FuncVal(IdxMax) Then
'replace worst point by new one
FuncVal(IdxMax) = FVnew
For i = 0 To Var.Length - 1
Points(IdxMax, i) = Pt(i)
Next
Else
'contract worst point to center point
For i = 0 To Var.Length - 1
Pt(i) = 0.5 * CenterPt(i) + 0.5 * Points(IdxMax, i)
Next
FVnew = objfunc(Pt)
'check if solution is not improving anymore
If FVnew > FuncVal(IdxMax) - simplexsolver.Tolerance Or cnt > simplexsolver.MaxFunEvaluations Then Exit Do
'and replace worst value by contracted value
FuncVal(IdxMax) = FVnew
For i = 0 To Var.Length - 1
Points(IdxMax, i) = Pt(i)
Next
End If
Loop
'Search best value to be returned e.g. minimum Gibbs Enthalpy
IdxMax = 0
For k = 1 To Var.Length
If FuncVal(k) < FuncVal(IdxMax) Then IdxMax = k
Next
For i = 0 To Var.Length - 1
Pt(i) = Points(IdxMax, i)
Next
Return Pt
End Function
End Module
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