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1、EducationandManagementInnovation 7AGeneticAlgorithmforSolvingaClassofMulti-objectiveBilevelProgrammingProblemsShanfengZhang,KeqiangLi（名前，姓后）DepartmentofComputer,******University,Guangzhou,810008,ChinaAbstractAtpresent,mostoftheresearchesonbilevelprogrammingproblemsarefocused
2、onsingleobjectivecases.Thispaperdiscussesabilevelprogrammingproblemwithupperlevelmulti-objectiveoptimization.Inordertosolvetheproblemefficiently,wepresentageneticalgorithmusinginterpolation.Thismethoddoesnotrequiresolvingloweroptimizationproblemfrequently.Intheproposedalgorit
3、hm,firstly,theinterpolationfunctionsareadoptedtoapproximatelowerlevelsolutionfunctions.Asaresult,theoriginalproblemcanbeapproximatedbyasingle-levelmulti-objectiveprogramming.Inaddition,thecorrespondinginterpolationfunctionsareupdatedsuchthatthesefunctionscanapproximatethelowe
4、rlevelsolutionfunctionverywell.Finally,themulti-objectiveprogrammingissolvedforobtaininganoptimalsolutionsetoftheoriginalproblem.Thesimulationontwoexamplesindicatestheproposedalgorithmiseffectiveandfeasible.Keywords:multi-objectivebilevelprogramming,geneticalgorithm,interpola
5、tion.1IntroductionBilevelprogrammingproblem(BLPP)isahierarchicaloptimizationproblem,whichincludesanupperlevelsdecisionmakerandalowerlevelsdecisionmaker.Bothofthemhavetheobjectivefunctionsandconstraintconditions.ThisproblemwasproposedbyStackelberg[1],andknownasStackelbergprobl
6、em.Themathematicalmodelofthiskindofproblemscanbewrittenasfollows:LectureNotesinSocialScience,Vol.3©2016ChinaScientificResearchPublishingCo.,Limited,HongKongISSN2414-455XEducationandManagementInnovation 7(1)Wherearedecisionvariables,areobjectivefunctionsandareconstraintfuncti
7、ons;aretheothersconstraint,suchasupperandlowerboundsorintegerconstraints.Bilevelprogrammingproblemsoccurinvariousapplications,suchaseconomicsandmanagement[2],engineering[3],transportationandothers.Mostofthesemodelsarebilevelsingleobjectiveproblems.Infact,therearelotsofreal-wo
8、rldproblemsthatcanbemodeledasmulti-objectivebilevelprogrammingproble
