Stability analysis of particle swarm optimization without Lipschitz constraint

There are some adjustable parameters which directly influence the performance and stability of Particle Swarm Optimization algorithm. In this paper, stabilities of PSO with constant parameters and time-varying parameters are analyzed without Lipschitz constraint. Necessary and sufficient stability conditions for acceleration factor P and inertia weight w are presented. Experiments on benchmark functions show the good performance of PSO satisfying the stability condition, even without Lipschitz constraint. And the inertia weight ω value is enhanced to (-1,1).