Markov Chain and Adaptive Parameter Selection on Particle Swarm Optimizer

Abstract

Particle Swarm Optimizer (PSO) is such a complex stochastic process that analysis of the stochastic behaviour 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 research are based on computer simulations and few of them are based on theoretical approaches. In this paper, a theoretical approach is used to investigate the behaviour of PSO. Firstly, a state of PSO is defined in this paper, which contains all the information needed for 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 a 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.