基于增強型差分進化算法求解廣義Nash均衡問題
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Solving generalized Nash equilibrium problem based on enhanced differential evolutionary algorithm
Wang Kaia，b，Jia Wenshenga，bt （a.Collgeofts&istis，rocalybotofeecisioaing&tolSeuzUesit 550025，China）
Abstract：Addressng theproblems thatclassicalmathematical methods forsolvingthegeneralizedNashequilibriumproblem face，suchasrelianceoninitialpointseletion，highdiferentiabilityrequirements，informationlossduringproblemtrasfor mation，andinsuffcientperformanceofmeta-heuristicalgorithms，thispaperproposedanenhanceddiferentialevolutionalg rithmtodirectlysolvethegeneralizedNashequilibriumproblemusingtheNikaido-Isoda function.Firstly，toimprovethediversityandconvergence speedofthediferentialevolutionalgorithm，itintroducedtheideasof tent chaotic mapping，adaptive coeficients，andtheslme mouldalgorithmtodesignanimprovedversionofthediferentialevolutionalgorithm.Italsoprovied atheoretical proofofthealgorithm’sconvergence.Secondly，itdefinedadominancestrategyandarelativefitnessfunction using the Nikaido-Isoda function toenhancepopulationvariationand selectioninthediferentialevolutionalgorithm.Finaly， theresultsofarithmeticcases indiferentdimensionsdemonstratethatthealgorithmsuccessullyresolves thegeneralized Nash equilibrium problem.Therefore，theproposedmethodforsolvingthegeneralizedNashequilibriumproblemdoesnotrelyoninitialpointslectinorfereiabilityanditvidsiformationlossduringprblmtansforatineringcrtaindvntges and effectiveness.
Keywords：generalized Nashequilibrium；Nikaido-Isoda function；bimodal variants；dominance strategies；meta-heuristic algorithms
0 引言
Nash均衡是非合作博弈中非常重要的概念，它在經(jīng)濟學(xué)、管理學(xué)、人工智能等[1＼～3]領(lǐng)域都有廣泛的應(yīng)用。（剩余16041字）