New Metropolis coefficients of Particle Swarm Optimization

This paper is presented to improve the optimizing efficiency and stability of the Particle Swarm Optimization (PSO) algorithm in real number space by developing the learning coefficients of the PSO. The new variable coefficients, which are named Metropolis coefficients due to the originality and similarity of the Metropolis probability in the Simulated Annealing, are presented as nonlinear functions of the generation of particles and the distances from each particle to the private and social optimal position in the problem space. This approach about the Metropolis coefficients is not only the graft but the fusion of PSO and Simulated Annealing. The application tests show that the improved PSO with the Metropolis coefficients can get the optimal position in the problem space by using less iteration steps than the traditional PSO, and the added computation of the variable coefficients does not increase the single iteration computing time much. So the new Metropolis coefficients can save both the iteration and time of the optimization computing of PSO.