The Standard Particle Swarm Optimization Algorithm Convergence Analysis and Parameter Selection

Formal sufficient and necessary condition for the deterministic standard PSO algorithm to converge to equilibrium point, diverge to infinity or oscillate within a range is derived based on the discrete time dynamic system theory. General guidelines for parameters selection are provided according to the theory analysis. It is pointed out that, strictly speaking, the currently popular view that small inertia weight will facilitate a local search is not accurate enough. And the condition for the view to hold is given. The simulation results of particle trajectories are given to illustrate and verify the theory analysis.