空间科学与技术学院学术论文集西安电子科技大学Word下载.docx

空间科学与技术学院学术论文集西安电子科技大学Word下载.docx

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空间科学与技术学院学术论文集西安电子科技大学@#@ADecompositionBasedMulti-objectiveParticleSwarmOptimizerforConstraintHandling@#@WeikangNing,BaolongGuo,YunyiYan,JinfuWu,DanZhao@#@（SchoolofAerospaceScience&@#@Technology,XidianUniv.,Xi’an710071,China;@#@）@#@Abstract:

@#@Multi-objectiveparticleswarmoptimization（MOPSO）algorithmsbasedondecompositionhavedrawnalotattentionrecently.DespitethesuccessofdecompositionbasedMOPSO（MOPSO/D）algorithms,itsuseinconstrainedmulti-objectiveoptimizationproblems（CMOPs）remainstobefurtherstudied.MostMOPSO/Dalgorithmsproposedrecentlyaredesignedforunconstrainedproblems.ThusweaimtoextendtheabilityofMOPSO/Dalgorithmsinourstudy.AframeworkofdecompositionbasedMOPSOforconstrainthandling（cMOPSO/D）isfirstproposedinthispaper.ThentwotypicalconstrainthandlingtechniquesarecombinedwithcMOPSO/Dasacomparison,whichresultsintwoversionsofcMOPSO/D:

@#@cMOPSO/Dusingpenaltyfunction（cMOPSO/D-P）andcMOPSO/Dusinglexicographicordering（cMOPSO/D-LO）.ThealgorithmsproposedaretestedontenCMOPsandarecomparedwiththreestate-of-the-artalgorithms,cMOEA/D,D2MOPSOandOMOPSO.Experimentalresultssupportedbythestatisticalanalysisofthreequantitativemetrics,togetherwithsometheoreticalanalysis,suggestthattheproposedalgorithmsareeffective,competitiveandpromising.@#@Keywords:

@#@Multi-objectiveoptimization,Decomposition,PSO,Constrainthandling,Penaltyfunction,Lexicographicordering@#@1.Introduction@#@Asaparadigmofevolutionaryalgorithm（EA）,particleswarmoptimization（PSO）hasbeensuccessfullyappliedtosolvingmulti-objectiveoptimizationproblems（MOPs）[22,20,11].Intherealworld,however,manyproblemstobesolvedoftenneedtosatisfyseveralequalityand/orinequalityconstraints,andthispresentsanadditionalchallengeformulti-objectiveevolutionaryalgorithms（MOEAs）.Solvingconstrainedmulti-objectiveproblems（CMOPs）ideallyoftenrequiresthesearchmakingabalancebetweenthefeasibleandinfeasibleregions,thustheinformationcarriedbytheinfeasiblesolutionscouldbefullyexploited.@#@Manyconstrainthandlingtechniquesareproposedandhavebeenstudiedforalongtimeinsingleobjectiveoptimization[7,13].Penaltyfunctioniswidelyusedforitssimplicity[28,18,33,2].Thefitnessofasolutioniscalculatedbasedonitsobjectivevalueandapenaltyterm.Buthowtodeterminetheamountofpenalizationisratherhard.Toalleviatethisdrawback,someadaptivepenaltyfunctionsarereportedintheliterature[17,8,3,5].Besides,differentconstrainthandlingtechniquesbasedonlexicographicorderingarealsowidelystudied.Deb[9]proposedabinarytournamentselectionoperatortocomparetwosolutions.Basedonthesatisfactionlevelfortheconstraints,TakahamaandSakaiproposedanαconstrainedmethod@#@[29]thatusesαlevelcomparisontocomparetwosolutions.Asanimprovementofαcon-strainedmethod,εconstrainedmethod,whichwasproposedbyTakahamaandSakai[30],adoptsanεlevelcomparisonto@#@comparetwosolutions.AdynamiccontrolofεwasalsoproposedandthecomparisonschemewascombinedwithPSO.Becauseitishardtostriketherightbalancebetweentheobjectiveandthepenaltyterminpenaltyfunctions,RunarssonandYao[23]proposedastatisticrankingmethodinwhichtheconstraintviolationisignoredwithsomeprobability.@#@InrelativelytraditionalParetodominancebasedMOEAs,constraint-dominanceisawidelyusedconstrainthandlingtechnique.Inspiredbythebinarytournamentselectionoperator[9]usedinconstrainedsingleobjectiveoptimization,aconstraint-dominancerelationshipwasproposedbyDeb[10]inNSGA-IItocomparetwosolutions.SimilarconstrainthandlingstrategiesareadoptedbyMOPSO[6]andOMOPSO[27].Besides,penaltyfunctionbasedconstrainthandlingtechniquesarealsoused.Anadaptivepenaltybasedconstrainedhandlingtechniquewasincorporatedwithnon-dominatedsortingbyWoldesenbet[32].Inthismethod,eachobjectivevalueofasolutionismodifiedfirstbasedonitsconstraintviolationandthennon-dominatedsortingisused.@#@Theconceptofdecomposition,whichwasproposedbyZhang[37]recently,hasproventobeefficientinhandlingmanycomplexMOPs.Thefitnessassignmentmechanismadoptedbymulti-objectiveevolutionaryalgorithmbasedondecomposition（MOEA/D）makesiteasierforMOEA/Dtoincorporatemanyconstrainthandlingtechniquesoriginallyinventedforsingleobjectiveoptimization.JanandZhang[14]proposedapenaltyfunctionbasedMOEA/Dforconstrainthandling.Thepenaltyfunctionadoptedusesanadaptivethresholdtocontrolhowheavyaninfeasiblesolutionispunished.Besides,twolexicographicorderingbasedMOEA/Darealsoreported.Asafuddoula[4]introducedanallowableviolationthresholdtodetermineifaninfeasiblesolutionisconsideredasfeasible.Thethre