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1、ABSTRACTAsamostimportantbranchofoptimizationtheoryanditsapplications,multi-objectiveoptimization’stheoreticalresearchrelatedtomanybranchessuchasconvexanalysis,nonsmoothanalysis,nonlinearanalysis,etc.Atthesametime,multi-objectiveoptimizationalsohasimportantapplicationsinmanyareas
2、ofnationallife.Inmulti-objectiveoptimizationproblems,therearestillsomemeaningfulhotissues,suchasthetheoreticalresearchofapproximatesolution,intelligentoptimizationalgorithm,applicationsinpracticalproblemsandsoon.Manyauthorshavegainedalotofresults.Inspiredbytheseresults,wediscuss
3、edsomequestionsfocusingon-quasiweaklyefficientsolutioninmulti-objectiveoptimization,non-dominatedsortinggeneticalgorithmwithelitestrategy(NSGA-II),multi-objectiveoptimizationinfinancialinvestment.Ourmainworkwasasfollows:InchapterI,welookedbackonsomeresearchinmulti-objectiveopti
4、mizationandintroducedthepreliminaries.InchapterII,firstofall,onthebasisof[1],maintainningconvexityassumptionsunchanged,weincreasedtheequalityconstraintoftheMPandextendedittotheVPwithsomegeneralconstraints.WedefinedaweaksaddlepointofVP,andintroducedadualmodel.Wegetalotofresults,s
5、uchastheexistenceofsufficientandnecessaryconditionsof-quasiweaklyefficientsolutionandthesaddlepointinmultiobjectiveoptimizationofVPproblemandweprovedthecorrespondingdualitytheorem.Then,underthesemi-convexityassumptions,necessaryandsufficientconditionswereobtainedfortheexistence
6、of-quasiweaklyefficientsolutioninmultiobjectiveoptimizationproblemandthedualitytheoremwasproved.InchapterIII,onthebasisofthereviewoftheexistingmulti-objectiveoptimizationalgorithm,wediscussedaclassofintelligentoptimizationalgorithmsofmulti-objectiveoptimization-NSGA-II(non-domi
7、natedsortinggeneticalgorithmwithelitestrategy).WegavetheideasofNSGA-IIanditsprocesses,analyzedParetorankingstrategyusedinthenon-dominatedsortinglink’sdefects,andproposedtheimprovementofthecumulativesortingfitnessassignmentstrategyalgorithm,andmadeacomparisonbetweentheimprovedalg
8、orithmandtheoriginaloneintermsofconvergence,and
