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1、182IEEETRANSACTIONSONEVOLUTIONARYCOMPUTATION,VOL.6,NO.2,APRIL2002AFastandElitistMultiobjectiveGeneticAlgorithm:NSGA-IIKalyanmoyDeb,AssociateMember,IEEE,AmritPratap,SameerAgarwal,andT.MeyarivanAbstract—Multiobjectiveevolutionaryalgorithms(EAs)[20],[26].Theprimaryreasonforthisistheir
2、abilitytofindthatusenondominatedsortingandsharinghavebeencriti-multiplePareto-optimalsolutionsinonesinglesimulationrun.cizedmainlyfortheir:1)(3)computationalcomplexitySinceevolutionaryalgorithms(EAs)workwithapopulationof(whereisthenumberofobjectivesandisthepopulationsolutions,asimp
3、leEAcanbeextendedtomaintainadiversesize);2)nonelitismapproach;and3)theneedforspecifyingasharingparameter.Inthispaper,wesuggestanondominatedsetofsolutions.Withanemphasisformovingtowardthetruesorting-basedmultiobjectiveEA(MOEA),callednondominatedPareto-optimalregion,anEAcanbeusedtofi
4、ndmultiplesortinggeneticalgorithmII(NSGA-II),whichalleviatesallPareto-optimalsolutionsinonesinglesimulationrun.theabovethreedifficulties.Specifically,afastnondominated2Thenondominatedsortinggeneticalgorithm(NSGA)pro-sortingapproachwith()computationalcomplexityispresented.Also,asele
5、ctionoperatorispresentedthatcreatesaposedin[20]wasoneofthefirstsuchEAs.Overtheyears,thematingpoolbycombiningtheparentandoffspringpopulationsmaincriticismsoftheNSGAapproachhavebeenasfollows.andselectingthebest(withrespecttofitnessandspread)1)Highcomputationalcomplexityofnondominated
6、sorting:solutions.SimulationresultsondifficulttestproblemsshowthattheproposedNSGA-II,inmostproblems,isabletofindmuchThecurrently-usednondominatedsortingalgorithmhasabetterspreadofsolutionsandbetterconvergencenearthetruecomputationalcomplexityof(whereisthePareto-optimalfrontcompared
7、toPareto-archivedevolutionnumberofobjectivesandisthepopulationsize).Thisstrategyandstrength-ParetoEA—twootherelitistMOEAsthatmakesNSGAcomputationallyexpensiveforlargepopu-payspecialattentiontocreatingadiversePareto-optimalfront.lationsizes.ThislargecomplexityarisesbecauseoftheMoreo
8、ver,wemodifythedefinitiono
