Stagnation Analysis in Particle Swarm Optimization

Particle swarm optimization (PSO) has shown to be an efficient, robust and simple optimization algorithm, and has been successfully applied to many different kinds of problems. But it is still an open problem that why PSO can be successful. Most of current PSO studies are empirical, with only a few theoretical analyses, and these theoretical studies concentrate mainly on simplified PSO systems, discarding randomness. In order to improve the understanding of real stochastic PSO algorithm, this paper presents a formal stochastic analysis of the stochastic PSO algorithm, which involves with randomness. The stochastic properties of particle trajectories in stagnation phase are studied in details