多目标优化算法综述

102206OverviewOfMulti-objectiveOptimizationAlgorithmsGaopeng(CollegeofElectricandElectronicEngineering,NorthChinaElectricPowerUniversity,Beijing,102206)Abstract:BackgroundofMulti-objectiveoptimizationalgorithmsissummarizedinthispaper.ThenmathematicaldescriptiontotheproblemofMulti-objectiveoptimizationisdiscussed.Theadvantagesanddisadvantagesoftraditionalalgorithmformulti-objectiveoptimizationproblemarecomparedandclassificationsofthealgorithmsarediscussed.Moreover,Multi-objectiveevolutionaryalgorithmsareanalyzed,suchasNSGAPAESSPEA;Atlast,theclonalselectionalgorithmsbasedonimmuneprincipleisanalyzedandsomeimportantresearchareasofMulti-objectiveoptimizationareaddressed.Keywords:multi-objectiveoptimization,evolutionaryalgorithms,artificialimmunealgorithms,Paretonon-dominance,NSGAPAESSPEA,,,Pareto1.,,,NSGAPAESSPEA2.(Multi-objectiveoptimizationproblemMop),(vector)1772FranklinV.pareto1896ParetoParetoParetoParetoParetoMin12()[(),(),...()]kfxfxfxfx=..st()0,1,2,igxih==LnxR∈()(1)ifxik≤≤()(1,2,)igxih=Lnkh,,,Pareto:1Pareto0x1x01()xxp01()(),1,2,,;iifxfxik≤∀=L01()(),1,2,,.iifxfxik∃=L2ParetoPareto0xPareto110:.xxx∃p3ParetoPareto010{|.}sPxxx=∃p4ParetoPareto12{()((),(),())|}fksPfxfxfxfxxp==∈L3.ParetoPareto:12.:(Pareto)3.4.:3.1::1122max()()()()ikfxwfxwfxwfx=⋅+⋅++⋅L.stfxX∈0iw≥1iw=∑ParetoPareto:Paretoiz(1,2)ik=Lgoal()iifxz≥i∂:min1kiiiwδ=∑.st()iiifxzδ+≥1,2ik=L0iδ≥1,2ik=LxS∈ParetoPareto3.2ParetoParetoNSGAPAESSPEANSGA-II2.2.1NSGANSGASrimivasDeb1994[4],IEEEEvolutionaryComputationNSGAGoldberg,,:,,,,,Pareto,NSGA,,;Pareto,,3.2.2PAESPAESJoshuaD.KnowelesDavidW.Cone2000[5]PAES1+1,,,PAES,O(aMN),a,M,N3.2.3SPEAEckartZitzler1999(StrengthParetoEvolutionaryAlgorithm)[3],,,MOGASPEA,,ParetoSPEAPareto,Pareto,,SPEA,,,,,SPEA,:,SPEASPEA,2001ZitzlerSPEASPEA2,:1233.2.4NSGA-IISrinivasDebNSGA(non-dominatedsortinggeneticalgorithm)[1](:stochasticremainderproportionateselection)(no-dominated)(:)non-dominated3.2.5BCastro[2],[6]114.,,1.2.--3.5.,,,6.[1]KalyanmoyDebSamirAgrawalAmritPratabandT.Meyarivan.AFastElitistNon-DominatedSortingGenetieAigorithm:NSGA-II.KanGALrePort200001IndianInstituteofTechnologyKanPurIndia2000[2]L.N.deCasrtoFenrandoJV.ZubenlearningandOptimizationUsingtheClonalSelectionPrinciple.IEEETransonEvolutionaryComputation20026(3):239-251.[3]ZitzlerE,ThieleL.Multi-objectiveOptimizationUsingEvolutionaryAlgorithms-AComparativeStudy.In:EibenAE,ed.ParallelProblemSolvingfromNatureV,Amsterdam,September1998.292~301[4]SrinivasN,DebK.MultiobjectiveOptimizationUsingNon-dominatedSortinginGeneticAlgorithms.EvolutionaryComputation,1994,2(3):221~248[5]KnowlesJD,CorneDW.ApproximatingtheNon-dominatedFrontUsingtheParetoArchivedEvolutionStrategy.EvolutionaryComputation,2000,8(2):149~172[6]...2005.20多目标优化算法综述作者：高鹏作者单位：华北电力大学,电气与电子工程学院,北京,102206本文读者也读过(3条)1.许婧祺多目标优化算法研究综述[期刊论文]-科技信息2010(32)2.赵亮.雎刚.吕剑虹.ZHAOLiang.JUGang.L(U)Jian-hong一种改进的遗传多目标优化算法及其应用[期刊论文]-中国电机工程学报2008,28(2)3.刘楠楠基于进化算法的多目标优化算法及应用研究[学位论文]2010引用本文格式：高鹏多目标优化算法综述[会议论文]2007