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1、443GDE3:ThethirdEvolutionStepofGeneralizedDifferentialEvolutionSakuKukkonenandJouniLampinenDepartmentofInformationTechnologyLappeenrantaUniversityofTechnologyP.O.Box20,FIN-53851Lappeenranta,Finlandsaku.kukkonen@lut.fiAbstract-anynumberofobjectivesandconstraint
2、s.Thelatestver-AdevelopedversionofGeneralizedDifferentialEvo-sion,GDE3,introducedinthispaperisanattempttoim-lution,GDE3,isproposed.GDE3isanextensionofDif-proveearlierversionsinthecaseofmultipleobjectives.ferentialEvolution(DE)forglobaloptimizationwithanarbitra
3、rynumberofobjectivesandconstraints.Inthe2Multi-ObjectiveOptimizationwithCon-caseofaproblemwithasingleobjectiveandwithoutstraintsconstraintsGDE3fallsbacktotheoriginalDE.GDE3improvesearlierGDEversionsinthecaseofmulti-Manypracticalproblemshavemultipleobjectivesan
4、dsev-objectiveproblemsbygivingabetterdistributedsolu-eralaspectscausemultipleconstraintstoproblems.Forex-tion.PerformanceofGDE3isdemonstratedwithasetample,mechanicaldesignproblemshaveseveralobjectivesoftestproblemsandtheresultsarecomparedwithothersuchasobtaine
5、dperformanceandmanufacturingcosts,andmethods.availableresourcesmaycauselimitations.Constraintscanbedividedintoboundaryconstraintsandconstraintfunc-1Introductiontions.Boundaryconstraintsareusedwhenthevalueofadecisionvariableislimitedtosomerange,andconstraintDur
6、ingthelast15years,EvolutionaryAlgorithms(EAs)functionsrepresentmorecomplicatedconstraints,whicharehavegainedpopularityinsolvingdifficultmulti-objectiveexpressedasfunctions.optimizationproblems(MOOPs)sinceEAsarecapableAmathematicallyconstrainedMOOPcanbepresente
7、dofdealingwithobjectivefunctions,whicharenotmathe-intheform:maticallywellbehaving,e.g.,discontinuous,non-convex,minimize{ff(x),f2(X),..*,fM(X)}multi-modal,andnon-differentiable.Multi-objectiveEAs(1)subjectto(gl(x),92(X),***,9K(X)<(MOEAs)arealsocapableofprovidi
8、ngmultiplesolutioncandidatesinasinglerun,whichisdesirablewithMOOPs.Thus,thereareMfunctionstobeoptimizedandKcon-DifferentialEvolution(DE)isarelativelynewEAandstraintfunctions.Maximi
