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基于几何变换的MAGA求解多纳什均衡
引用本文:顾佼佼,刘卫华,赵建军,刘吉伟.基于几何变换的MAGA求解多纳什均衡[J].计算机工程与科学,2016,38(1):108-113.
作者姓名:顾佼佼  刘卫华  赵建军  刘吉伟
作者单位:;1.海军航空工程学院科研部;2.国防科学技术大学计算机学院
基金项目:国家自然科学基金(61179018,61102165);航空科学基金(20135184008)
摘    要:针对粒子群优化PSO早熟收敛而且只能寻找一个极值的问题,提出基于几何变换的MAGA混合智能算法,并应用于博弈论求解多纳什均衡问题。算法由粒子群优化和禁忌搜索TS算法构成,对粒子群优化的改进包括对粒子运动松散控制和引入遗传算法GA增强粒子多样性;禁忌搜索算法对邻域空间深度搜索;引入Deflection-Repulsion几何变换对目标函数进行动态变换使算法能够寻找多极值。仿真结果表明,该算法在多纳什均衡求解问题表现突出,寻优速度快,准确率高,可扩展到其他多模态多极值问题领域。

关 键 词:纳什均衡  多极值  Memetic算法  几何变换
收稿时间:2014-06-09
修稿时间:2016-01-25

Multi-nash equilibrium computing based on geometric-transform MAGA
GU Jiao jiao,LIU Wei hua,ZHAO Jian jun,LIU Ji wei.Multi-nash equilibrium computing based on geometric-transform MAGA[J].Computer Engineering & Science,2016,38(1):108-113.
Authors:GU Jiao jiao  LIU Wei hua  ZHAO Jian jun  LIU Ji wei
Affiliation:(1.Department of Scientific Research,Naval Aeronautical and Astronautical University,Yantai 264001; 2.College of Computer,National University of Defense Technology,Changsha 410073,China)
Abstract:Concerning the premature convergence problem of particle swarm optimization (PSO) and the shortage of finding only one minimum, we propose a geometric transform based Memetic algorithm (MA) for detecting multi minima, which is applied in Nash Equilibria (NE) computing in game theory. The basic MA consists of PSO and Tabu Search (TS), which improves PSO in two ways: loosing constraint on particle movements and incorporating the genetic algorithm (GA) to maintain particle diversity. TS iterates through the neighborhood to get a local optimum. Furthermore, the deflection repulsion geometric transformation is incorporated to tune the search for multi minima. The performance is evaluated on a series of NE detecting examples. The results show that the proposed MA has a notable ability to detect multi minima while yielding high accuracy and performance.
Keywords:Nash Equilibrium  multi minima  Memetic algorithm (MA)  geometric transformation  
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