A PENALTY FUNCTION METHOD FOR SOLVING ILL-POSED BILEVEL PROGRAMMING PROBLEM VIA WEIGHTED SUMMATION

(整期优先)网络出版时间:2013-06-16
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Forill-posedbilevelprogrammingproblem,theoptimisticsolutionisalwaysthebestdecisionfortheupperlevelbutitisnotalwaysthebestchoiceforbothlevelsiftheauthorsconsiderthemodel'ssatisfactorydegreeinapplication.Toacquireamoresatisfyingsolutionthantheoptimisticonetorealizethetwolevels'mostprofits,thispaperconsidersbothlevels'satisfactorydegreeandconstructsaminimizationproblemofthetwoobjectivefunctionsbyweightedsummation.Then,usingthedualitygapofthelowerlevelasthepenaltyfunction,theauthorstransferthesetwolevelsproblemtoasingleoneandproposeacorrespondingalgorithm.Finally,theauthorsgiveanexampletoshowamoresatisfyingsolutionthantheoptimisticsolutioncanbeachievedbythisalgorithm.