粒子群优化算法的收敛性分析  

Convergence analysis of particle swarm optimization algorithm

作　　者：徐刚[1] 江美珍[1] 吴志华 饶兰香 

机构地区：[1]南昌大学数学系,江西南昌330031 [2]江西省计算技术研究所,江西南昌330002

出　　处：《南昌大学学报（理科版）》2015年第4期315-318,共4页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(61175127);江西省自然科学基金资助项目(20142BAB211021)

摘　　要：根据粒子群优化(Particle swarm optimization,PSO)算法的数学模型定义粒子状态序列和群体状态序列,并分析其马尔可夫性质,引入了粒子转移概率,证明了粒子及种群的最优状态集的封闭性;进一步基于随机过程理论证明了群体状态以概率转到最优状态集,从而证明了标准粒子群算法以一定概率收敛于全局最优。According to the particle swarm optimization(PSO)mathematic model,the particle state sequence and swarm state sequence are defined first,and their Markov property are analyzed,the transition probabili-ty of a particle is introduced,after that,it is proved that the particle optimal state set and swarm optimal state set are closed set;furthermore,based on stochastic process theory,the swarm state sequence conver-ges to the swarm optimal state set in probability,thereby,it is proved that standard PSO algorithm reaches the global optimum in probability.

关 键 词：粒子群优化算法 MARKOV链 收敛性 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]