A method of parameter optimization for particle swarm optimization based on stochastic processes

The convergence speed is a major concern in using particle swarm optimization (PSO) in practice, especially when real-time computations are required. This paper proposes a method of parameter optimization for particle swarm optimization that has fast convergence speed in the stochastic sense. Using the theory of stochastic processes, a sufficient condition for the mean-square convergence of standard PSO is deduced. The mean spectral radius of the dynamical PSO model is constructed. It is shown that a smaller spectral radius leads to a faster convergence speed. To facilitate fast convergence, the mean spectral radius is minimized within the mean-square convergence region. Guidelines for parameter selection are presented. The proposed method is compared with two typical existing solutions through simulations on several common function optimization benchmarks. The results show that the proposed method a little better than the others in terms of both convergence speed and solution precision.