Markov Chain and Adaptive Parameter Selection on Particle Swarm Optimizer

Particle Swarm Optimizer (PSO) is such a complex stochastic process so that analysis on the stochastic behavior of the PSO is not easy. The choosing of parameters plays an important role since it is critical in the performance of PSO. As far as our investigation is concerned, most of the relevant researches are based on computer simulations and few of them are based on theoretical approach. In this paper, theoretical approach is used to investigate the behavior of PSO. Firstly, a state of PSO is defined in this paper, which contains all the information needed for the future evolution. Then the memory-less property of the state defined in this paper is investigated and proved. Secondly, by using the concept of the state and suitably dividing the whole process of PSO into countable number of stages (levels), a stationary Markov chain is established. Finally, according to the property of a stationary Markov chain, an adaptive method for parameter selection is proposed