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1、EducationManagementInnovation0LectureNotesinSocialScienceVol.3?2016ChinaScientificResearchPublishingCo.LimitedHongKongISSN2414455XAGeicAlgithmfSolvingaClassofMultiobjectiveBilevelProgrammingProblemsShanfengZhangKeqiangLi

2、（名前，姓后）DepartmentofComputerUniversityGuangzhou810008ChinaAbstractAtpresentmostoftheresearchesonbilevelprogrammingproblemsarefocusedonsingleobjectivecases.Thispaperdiscussesabilevelprogrammingproblemwithupperlevelmultiobj

3、ectiveoptimization.Indertosolvetheproblemefficientlywepresentageicalgithmusinginterpolation.Thismethoddoesnotrequiresolvingloweroptimizationproblemfrequently.Intheproposedalgithmfirstlytheinterpolationfunctionsareadopted

4、toapproximatelowerlevelsolutionfunctions.Asaresulttheiginalproblemcanbeapproximatedbyasinglelevelmultiobjectiveprogramming.Inadditionthecrespondinginterpolationfunctionsareupdatedsuchthatthesefunctionscanapproximatethelo

5、werlevelsolutionfunctionverywell.Finallythemultiobjectiveprogrammingissolvedfobtaininganoptimalsolutionsetoftheiginalproblem.Thesimulationontwoexamplesindicatestheproposedalgithmiseffectivefeasible.Keywds:multiobjectiveb

6、ilevelprogramminggeicalgithminterpolation.1IntroductionBilevelprogrammingproblem(BLPP)isahierarchicaloptimizationproblemwhichincludesanupperlevelsdecisionmakeralowerlevelsdecisionmaker.Bothofthemhavetheobjectivefunctions

7、constraintconditions.ThisproblemwasproposedbyStackelberg[1]knownasStackelbergproblem.Themathematicalmodelofthiskindofproblemscanbewrittenasfollows:EducationManagementInnovation2LectureNotesinSocialScienceVol.3?2016ChinaS

8、cientificResearchPublishingCo.LimitedHongKongISSN2414455X(2)???????????0)(..)(min0)(..))()()((min21yxgtsyxfyxGtsyxFyxFyxFYymXx?21|)(21piuxlRxxxXiiipTp???????21|)21qiuylRyyyYiiiqTq???????Somebasicconceptsassociatedwiththe

9、problemarepresentedasfollowsSearchspace：|)(YyXxyx????Constraintregion：0)(0)(|)(?????yxgyxGyxSProjectionofontotheleader’sdecisionspace:S).(.|)(SyxtsyXxXS????Feasiblesetfthefollowerfeachfixed:)(XSx?)(minarg|)(SyyxfyYyxM???

10、?Inducibleregion:)(|)(xMySyxIR???Definition1FanytwopointsifthefollowingconditionsareIRyxyx?)()(2211satisfied:i)Fanywehave21mi??)()(2211xxFyxFii?ii)Thereexistsasuchthat21mj??)()(2211xxFyxFjj?Thenwecalleddominates.)(11yx)(

11、22yxDefinition2Fpointifanysolutionindoesnotdominatesthen)(yxIR)(yx)(yxisaParetooptimalsolution.Twoassumptionsaregivenasfollows:i)isNonemptycompact.Sii)Feachvariablevalueisunique.Xx?)(xy3.Thelowersolutionbasedoninterpolat

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