中文摘要：

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。

英文摘要：

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.