高维多目标进化算法研究综述

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:2009208227.:973(2009CB320601);(60534010,60821063,60904079);111(B08015).:(1983),,,,;(1947),,,,,,.:100120920(2010)0320321206a,a,a,b(a.,b.,110004):23,4,,.,,;,.:Pareto;;;:TP301:ASurveyonlarge2dimensionalmulti2objectiveevolutionaryalgorithmsKONGWei2jiana,DINGJin2lianga,CHAITian2youa,b(a.KeyLaboratoryofIntegratedAutomationforProcessIndustry,MinistryofEducation,b.ResearchCenterofAutomation,NortheasternUniversity,Shenyang110004,China.Correspondent:KONGWei2jian,E2mail:[e-mail])Abstract:Theconventionalmulti2objectiveevolutionaryalgorithms(MOEAs)cansolvetwo2objectiveoptimizationproblemssuccessfully,buttheirsearchabilityandperformancewilldeterioratebadlywhenthenumberofobjectivesexceedsfour.So,large2dimensionalmulti2objectiveevolutionaryalgorithmsareattractingmoreattention.Thelarge2dimensionalmulti2objectiveevolutionaryalgorithmsaresurveyedsystematicallybycategories.Theinfluencesoflarge2dimensionalobjectivesbringingonoptimizationproblemsareanalyzed,andthevisualizationtechniquesareintroduced.Finally,theproposedalgorithmsareevaluatedandtopicsforfutureresearcharesuggested.Keywords:Paretodominance;Large2dimensionalobjectives;MOEA;Visualizationtechniques1(MOEA),MOGA[1](Multi2objectivegeneticalgorithm),NSGA2[2](Nondominatedsortinggeneticalgorithm2),SPEA[3](StrengthParetoevolutionaryalgorithm)PAES[4](Paretoarchivedevolutionstrategy)Pareto,Pareto[5,6],Pareto,[7,8].,MOEA,[9].Purshouse[10],4(),ParetoMOEA.,,Pareto.Hughes[11]ParetoMOEA(23),Pareto.,ParetoMOEA.MOEA[12],,.:1)Pareto,©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[13,14][15218].2)Pareto.Pareto,,[19],k2[20,21],2[22].3)Pareto.,[23225].,MOEA;;,.2m,minF(x)=[f1(x),f2(x),,fm(x)],s.t.xXn.(1):F(x)m,fi(x)i,xn,Xn.m4,.Pareto.,m,N,xixj,,ixixj50%.,Pareto,xi((2m-1)/2m)N,,((2m-1)/2m)N.,.Deb[26]DTLZ2,,.2,4,6,8,10,200,,10,1.NSGA2[2]MOEA,Pareto[10].Pareto,NSGA212NSGA2,2.,,,,Pareto,.,:1),ParetoPareto,.2),.3),,.3MOEAMOEA,.,3.3.1ParetoPareto,.Masahiro[27].Pareto,,,3.Horn[28],3,223©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[13],,.Branke[29],,,.Wierzbicki[30],Pareto.Deb[14]MOEA,Pareto.Deb[15,16],NSGA2[2].Pareto,,PCANSGA2,Pareto,Pareto.Brockhoff[17,18]Pareto,Pareto,.Jaimes[31][32],,.3.2ParetoPareto,.Drechsler[19].st,st.,,3s,t,u,st,tu,us,.Ikeda[22]2,xy,xy,yxy.Laumanns[33]e2,,x(1+e)y,,4.4e2e2,e.Sato[34],NSGA2,.5,x,y,z,Pareto,x,y,z,zy.5ParetoDi[20,21]k2,,,.3,x=(2,3,7),y=(3,2,9),z=(4,5,4),1,12,2313,3323©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[35,36].Pareto,.Zitzler[37](IBEA),,,,.[38],,[39].IBEAs[40242].Wagner[43]Pareto3,IBEAs.Pareto,1.Hughes[44]Pareto(MSOPS),Pareto,.,Pareto[12],.4,,Pareto;,.3,.Fleming[13][45].,,,6,5(1,8,2,6,3),(2,4,3,7,5),(7,1,5,2,2).[46],,,.,.Obayashi[47]Pareto[48].,,.,[49,50].65,.,:1)Pareto,.2)ParetoPareto,,,,,.3)Pareto,Pareto,,.:1)Pareto,,.Pareto,.2).Pareto,Pareto,,Pareto.3),,,.(References)[1]FonsecaCM,FlemingPJ.Geneticalgorithmformulti2objectiveoptimization:Formulation,discussionand423©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[C].Procof5thICGA.SanMateo:MorganKaufmannPublishers,1993:4162423.[2]DebK,AmritP,SameerA,etal.Afastandelitistmulti2objectivegeneticalgorithm:NSGA2[J].IEEETransonEvolutionaryComputation,2002,6(2):1822197.[3]ZitzlerE,ThieleL.Multi2objectiveevolutionaryalgorithms:acomparativecasestudyandthestrengthparetoapproach[J].IEEETransonEvolutionaryComputation,1999,3(4):2572271.[4]KnowlesJD,CorneDW.ApproximatingthenondominatedfrontusingtheParetoarchivedevolutionstrategy[J].EvolutionaryComputation,2000,8(2):1492172.[5]HajelaP,LinCY.Geneticsearchstrategiesinmulticriterionoptimaldesign[J].StructuralandMultidisciplinaryOptimization,1992,4(2):992107.[6]SchafferJD.Multipleobjectiveoptimizationwithvectorevaluatedgeneticalgorithms[C].Procof1stIntConfonGeneticAlgorithmsandTheirApplication.Hillsdale:L.ErlbaumAssociatesInc,1985:932100.[7]DebK.Multi2objectiveoptimizationusingevolutionaryalgorithms[M].Chichester:JohnWileyandSonsInc,2001.[8]CoelloCAC,LamontGB.Applicationsofmulti2objectiveevolutionaryalgorithms[M].Singapore:WorldScientificPublisher,2004.[9]CoelloCAC,LamontGB,VeldhuizenDAV.Evolutionaryalgorithmforsolvingmulti2objectiveproblems[M].NewYork:KluwerAcademicPublisher,2007.[10]PurshouseRC,FlemingPJ.Evolutionarymany2objectiveoptimization:Anexploratoryanalysis[C].Procof2003IEEECongressonEvolutionaryComputation.Canberra:IEEEServiceCenter,2003:206622073.[11]IshibuchiH,TsukamotoN,NojimaY.Evolutionarymany2objectiveoptimization:Ashortreview[C].ProcofIEEECongressonEvolutionaryComputation.HongKong:IEEEServiceCenter,2008:242422431.[12]HughesEJ.Evolutionarymany2objectiveoptimization:Manyonceoronemany[C].Procof2005IEEECongressonEvolutionaryComputation.Edinburg