基于粒子群优化求解纳什均衡的演化算法

基于粒子群优化方法从群智能的角度建立了博弈的演化模型，为求解有限n人非合作博弈的纳什均衡设计了一种粒子群优化算法．通过随机初始点的可行化以及对迭代步长的控制，保证粒子群在算法的迭代过程中始终保持在博弈的可行策略空间内，避免了在随机搜索中产生无效的粒子，因此提高了粒子群优化算法求解纳什均衡的计算性能．给出了算法的数值例子并分析了该算法的计算性能，通过粒子群算法与遗传算法的比较显示了粒子群算法求解博弈纳什均衡解的高效性．

Evolutionary Algorithm for Solving Nash Equilibrium Based on Particle Swarm Optimization

From the view of Swarm Intelligence Theory,an evolutionary model based on the method of Particle Swarm Optimization(PSO) is presented,and the PSO algorithm for solving the Nash equilibriums for n persons' non-cooperative game is proposed.In addition,the compute performance of the PSO algorithm is improved by setting the initial particle swarm in the feasible strategy space and controlling the iterative step lengths.Finally,we give numerical examples and the performance analyses of the algorithm.Comparing with the genetic algorithm,we show that the PSO algorithm is effective and practical for solving Nash equilibrium.