Particle swarm optimization in the presence of multiple global optima

Dynamic analyses of canonical particle swarm optimization (PSO) have indicated that parameter values of phi_max = 4.1 and constriction coefficient chi = 0.729 provide adequate exploration and prevent swarm explosion. This paper shows by example that these values do not prevent swarm explosion in some cases. In other examples it is shown that even when the swarm does not explode, the canonical PSO algorithm with these parameter values can still fail to converge indefinitely. A satisfactory analysis of PSO has yet to be made, and will require abandoning certain assumptions that oversimplify particle behavior.