The global convergence analysis of particle swarm optimization algorithm based on Markov chain
马尔科夫链的粒子群优化算法全局收敛性分析

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 con rm from the transition probability that the PSO algorithm is not global convergent.