COPASI / data /TestSuite /optimization /HolderTable2Function.cps
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<body xmlns="http://www.w3.org/1999/xhtml"><h1>Holder table 2 function</h1>
<p>Part of a set of benchmark functions for global optimisation</p>
<ul>
<li>variables: 2</li>
<li>interval: [-10,10] (all variables)</li>
<li>global minima: (8.05502,9.66459), (-8.05502,9.66459), (8.05502,-9.66459), (-8.05502,-9.66459)</li>
<li>minimum value: -19.20850</li>
</ul>
<p>f(x<sub>1</sub>,x<sub>2</sub>)=- abs(
sin(x<sub>1</sub>) cos(x<sub>2</sub>)
exp(
abs( 1 - sqrt(x<sub>1</sub><sup>2</sup> + x<sub>2</sub><sup>2</sup>) / &pi; )
) )</p>
<hr />
<p>The holder table function has four global minima close to the corners of the search space. In addition it has many other local minima, arranged in a regular pattern. The function is separable so in principle it could be minimized by two independent searches in one direction (each of the parameters).</p>
<p>Defined in: Mishra, S.K. (2006) Some new test functions for global optimization and performance of repulsive particle swarm method. <i>Munich Personal RePEc Archive</i> paper 2718 (<a href="http://mpra.ub.uni-muenchen.de/2718/">http://mpra.ub.uni-muenchen.de/2718/</a>).</p><p style="font-size:small"><b>CC0 1.0 Universal</b>: To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. Please refer to <a href="http://creativecommons.org/publicdomain/zero/1.0/" title="Creative Commons CC0">CC0 Public Domain Dedication</a> for more information.</p>
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This table outputs time and the target function of the optimization.
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<Object cn="Separator=&#x09;"/>
<Object cn="CN=Root,Vector=TaskList[Parameter Estimation],Problem=Parameter Estimation,Reference=Best Parameters"/>
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<Object cn="String=&#x0a;"/>
<Object cn="CN=Root,Vector=TaskList[Parameter Estimation],Object=Result"/>
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<Report key="Report_18" name="Metabolic Control Analysis" taskType="metabolicControlAnalysis" separator="&#x09;" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Metabolic Control Analysis],Object=Description"/>
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<Object cn="String=&#x0a;"/>
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</Report>
<Report key="Report_17" name="Lyapunov Exponents" taskType="lyapunovExponents" separator="&#x09;" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Lyapunov Exponents],Object=Description"/>
</Header>
<Footer>
<Object cn="String=&#x0a;"/>
<Object cn="CN=Root,Vector=TaskList[Lyapunov Exponents],Object=Result"/>
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</Report>
<Report key="Report_16" name="Time Scale Separation Analysis" taskType="timeScaleSeparationAnalysis" separator="&#x09;" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Time Scale Separation Analysis],Object=Description"/>
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<Footer>
<Object cn="String=&#x0a;"/>
<Object cn="CN=Root,Vector=TaskList[Time Scale Separation Analysis],Object=Result"/>
</Footer>
</Report>
<Report key="Report_15" name="Sensitivities" taskType="sensitivities" separator="&#x09;" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Sensitivities],Object=Description"/>
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<Footer>
<Object cn="String=&#x0a;"/>
<Object cn="CN=Root,Vector=TaskList[Sensitivities],Object=Result"/>
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</Report>
<Report key="Report_14" name="Linear Noise Approximation" taskType="linearNoiseApproximation" separator="&#x09;" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Linear Noise Approximation],Object=Description"/>
</Header>
<Footer>
<Object cn="String=&#x0a;"/>
<Object cn="CN=Root,Vector=TaskList[Linear Noise Approximation],Object=Result"/>
</Footer>
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<Report key="Report_13" name="Time-Course" taskType="timeCourse" separator="&#x09;" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Time-Course],Object=Description"/>
</Header>
<Footer>
<Object cn="CN=Root,Vector=TaskList[Time-Course],Object=Result"/>
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</Report>
<Report key="Report_11" name="Moieties" taskType="moieties" separator="&#x09;" precision="6">
<Comment>
Automatically generated report.
</Comment>
<Header>
<Object cn="CN=Root,Vector=TaskList[Moieties],Object=Description"/>
</Header>
<Footer>
<Object cn="String=&#x0a;"/>
<Object cn="CN=Root,Vector=TaskList[Moieties],Object=Result"/>
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</Report>
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<ListOfPlots>
<PlotSpecification name="Progress of Optimization" type="Plot2D" active="1" taskTypes="">
<Parameter name="log X" type="bool" value="0"/>
<Parameter name="log Y" type="bool" value="1"/>
<ListOfPlotItems>
<PlotItem name="target function" type="Curve2D">
<Parameter name="Line type" type="unsignedInteger" value="0"/>
<Parameter name="Line subtype" type="unsignedInteger" value="0"/>
<Parameter name="Line width" type="unsignedFloat" value="1"/>
<Parameter name="Symbol subtype" type="unsignedInteger" value="0"/>
<Parameter name="Color" type="string" value="auto"/>
<Parameter name="Recording Activity" type="string" value="during"/>
<ListOfChannels>
<ChannelSpec cn="CN=Root,Vector=TaskList[Optimization],Problem=Optimization,Reference=Function Evaluations"/>
<ChannelSpec cn="CN=Root,Vector=TaskList[Optimization],Problem=Optimization,Reference=Best Value"/>
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</PlotItem>
</ListOfPlotItems>
</PlotSpecification>
<PlotSpecification name="Create New" type="Plot2D" active="1" taskTypes="">
<Parameter name="log X" type="bool" value="0"/>
<Parameter name="log Y" type="bool" value="0"/>
<ListOfPlotItems>
<PlotItem name="Values[y].InitialValue/Values[f].InitialValue|Values[x].InitialValue" type="Spectogram">
<Parameter name="logZ" type="bool" value="0"/>
<Parameter name="bilinear" type="bool" value="1"/>
<Parameter name="contours" type="string" value=""/>
<Parameter name="maxZ" type="string" value=""/>
<Parameter name="colorMap" type="string" value="Default"/>
<Parameter name="Color" type="string" value="auto"/>
<Parameter name="Recording Activity" type="string" value="during"/>
<ListOfChannels>
<ChannelSpec cn="CN=Root,Model=Holder table 2 function,Vector=Values[x1],Reference=InitialValue"/>
<ChannelSpec cn="CN=Root,Model=Holder table 2 function,Vector=Values[x2],Reference=InitialValue"/>
<ChannelSpec cn="CN=Root,Model=Holder table 2 function,Vector=Values[Holder table 2 function],Reference=InitialValue"/>
</ListOfChannels>
</PlotItem>
</ListOfPlotItems>
</PlotSpecification>
</ListOfPlots>
<GUI>
</GUI>
<ListOfUnitDefinitions>
<UnitDefinition key="Unit_1" name="meter" symbol="m">
<MiriamAnnotation>
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Unit_0">
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</MiriamAnnotation>
<Expression>
m
</Expression>
</UnitDefinition>
<UnitDefinition key="Unit_5" name="second" symbol="s">
<MiriamAnnotation>
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Unit_4">
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<Expression>
s
</Expression>
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<UnitDefinition key="Unit_13" name="Avogadro" symbol="Avogadro">
<MiriamAnnotation>
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Unit_12">
</rdf:Description>
</rdf:RDF>
</MiriamAnnotation>
<Expression>
Avogadro
</Expression>
</UnitDefinition>
<UnitDefinition key="Unit_17" name="item" symbol="#">
<MiriamAnnotation>
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Unit_16">
</rdf:Description>
</rdf:RDF>
</MiriamAnnotation>
<Expression>
#
</Expression>
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<UnitDefinition key="Unit_35" name="liter" symbol="l">
<MiriamAnnotation>
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Unit_34">
</rdf:Description>
</rdf:RDF>
</MiriamAnnotation>
<Expression>
0.001*m^3
</Expression>
</UnitDefinition>
<UnitDefinition key="Unit_41" name="mole" symbol="mol">
<MiriamAnnotation>
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#Unit_40">
</rdf:Description>
</rdf:RDF>
</MiriamAnnotation>
<Expression>
Avogadro*#
</Expression>
</UnitDefinition>
</ListOfUnitDefinitions>
</COPASI>