基于增强型差分进化算法求解广义Nash均衡问题

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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，它在经济学、管理学、人工智能等[1＼～3]领域都有广泛的应用。（剩余16041字）