基于自适应小生境粒子群算法的多重Nash均衡求解

SOLVING MULTIPLE NASH EQUILIBRIA BASED ON ADAPTIVE NICHED PARTICLE SWARM ALGORITHM

针对n人非合作博弈多重Nash均衡求解问题,提出一种自适应小生境粒子群算法。该算法融合了序列小生境技术、粒子群优化算法的思想,并加入了变异算子和自动生成小生境半径机制,使得所有粒子尽可能分布到整个搜索空间的不同局部峰值区域,从而有效地求得博弈问题的多重Nash均衡。最后给出几个数值算例,计算结果表明所提出的算法具有较好的性能。

This paper presents an adaptive niched particle swarm algorithm for solving the multiple Nash equilibria of n-persons＇ noncooperative game. The algorithm combines the ideas of the sequential niched technique and the particle swarm algorithm, and the mutation operator and the mechanism of automatic niche radius generation are added as well, so that all the particles are distributed to different local peak regions of entire search space as possible as can, thereby the multiple Nash equilibria of the game problem are effectively achieved. Finally, some numerical examples are given and the computation results demonstrate that the proposed algorithm has quite good performance.