The Stability Of The Particle Swarm Optimization Analysis And Parameter Selection Strategy

Theory analysis of particle swarm optimization is always an important research topic. The current researchs mainly employ the dynamic system theory and stochastic process theory. Generally, the search supposes particle swarm optimization as a linear time-invariant system. It means the inertia weight, cognitive factor, social factor, personal historical best position pbest and historical best position formal by entire swarm gbest are constants. Therefore, in this paper, three different hypotheses are employed investigate the stability condition of particle swarm optimization.Firstly, particle swarm optimization is taken as a Linear time-invariant system, and Lyapunov stability analysis is used to discuss the stability condition, furthermore, the selection strategy of inertia weight is obtained.Secondly,we suppose the pbest abd gbest are time-varying variables, and the uniform asymptotic stability theory are employed to investigate the stability condition of particle swarm optimization. Then, the corresponding parameters selection strategies are discussed.Thirdly, we suppose inertia weight, cognitive factor, social factor, personal historical best position pbest and historical best position formal by entire swarm gbest are all time-varying variables and the stability condition is discussed with geometric speed stability theory. Then the parameter selection strategies are designed. Simulation results show all of these stability conditions can improve the performance significantly, especially for high dimensional multi-model optimization problems.