Abstract: In the process of solving the Nash equilibrium problems related to N-person non-cooperative game, quantum uncertainty principle, co-evolution and antibody concentration suppression mechanism in immune algorithm were introduced into the classical particle swarm optimization, and a new improved quantum particle swarm optimization algorithm is designed to deal with Nash equilibrium problems. In the process of calculation, this algorithm utilizes antibody concentration and co-evolution to maintain the diversity characteristics of particle groups, and uses the uncertainty of quantum to decrease the time-consuming of iterative searching process. In addition, this algorithm not only effectively inherits the simplicity and convenience of particle swarm optimization, but also greatly improves the convergence speed and global search ability. The experimental results show that the improved algorithm can overcome the premature convergence of particles, and has better performance than genetic algorithm and immune particle swarm optimization.

Key words: Immune algorithm, coevolution, non-cooperative game, Nash equilibrium, improved quantum particle swarm optimization

摘要： 在N人非合作博弈Nash均衡问题求解过程中，将量子不确定性原理、协同演化以及免疫算法内的抗体浓度抑制机制引进到经典粒子群算法中，设计了一种新型改进量子粒子群算法来更好地处理Nash均衡问题。该算法在运算过程中，运用抗体浓度以及协同演化的方式来维系粒子群具备的多样性特征，并借助量子不确定性缩减迭代搜索耗时。该算法不仅有效地将粒子群算法运算简单与方便实现的特质承继下来，而且算法的收敛速度以及其全局搜索能力都获得了大幅度的提升。相关数值算例分析表明，改进的算法能够更好地处理粒子早熟，相较遗传算法以及免疫粒子群算法更具性能优越性。

关键词: 免疫算法, 协同演化, 非合作博弈, Nash均衡, 改进量子粒子群算法