Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm

This letter presents a formal stochastic convergence analysis of the standard particle swarm optimization (PSO) algorithm, which involves with randomness. By regarding each particle's position on each evolutionary step as a stochastic vector, the standard PSO algorithm determined by non-negative real parameter tuple {omega, c(1), c(2)) is analyzed using stochastic process theory. The stochastic convergent condition of the particle swarm system and corresponding parameter selection guidelines are derived. (c) 2006 Elsevier B.V. All rights reserved.