Model analysis of particle swarm optimizer

Particle swarm optimizer (PSO) exhibits good performance for optimization problems. However, there is little analysis about the kinetic characteristic, parameter selection and the situation where algorithm falls into stagnate to cause premature convergence. In the paper, the kinetic characteristic of three models of PSO (Gbest, Pbest, Common model) are analyzed. The largest covering space (LCS) of the Gbest model and the Pbest model are deduced without new information. Furthermore, under the condition that the Lipschitz constraint is reduced, the sufficient conditions for asymptotic stability of parameters are proved. And the inertia weight ω value is enhanced to (-1, 1).