马尔科夫链的粒子群优化算法全局收敛性分析

摘要

本文对粒子群优化算法的全局收敛性进行了分析,给出了粒子速度和位置的一步转移概率,然后从粒子状态所构成的马尔科夫链着手,分析了此马尔科夫链的一系列性质,证明了粒子状态空间的可约性和非齐次性,并验证粒子状态空间是非常返态的,最后表明马尔科夫链不存在平稳过程的条件,继而从转移概率的角度证明了算法不是全局收敛的.%We analyze the global convergence of particle swarm optimization(PSO) algorithm. The one-step transition probabilities of particle velocity and particle position are calculated. Several properties about this Markov chain are investigated. The reducibility and nonhomogeneity are proved. It is shown that the particle state space is non-recurrent. These properties show the nonexistence of conditions for this Markov chain to be a stationary process. Thus, we confirm from the transition probability that the PSO algorithm is not global convergent.