Particle swarm optimization with stochastic selection of perturbation-based chaotic updating system

In this paper, we consider the particle swarm optimization (PSO). In particular, we focus on an improved PSO called the CPSO-VQO, which uses a perturbation-based chaotic system and a threshold-based method of selecting from the standard and chaotic updating systems for each particle on the basis of the difference vector between its pbest and the gbest. Although it was reported that the CPSO-VQO performs well, it is not easy to select an amplitude of the perturbation and a threshold appropriately for an effective search. This is because the bifurcation structure of the chaotic system depends on the difference vector, and the difference vector varies widely between different stages of the search and between different problems.Therefore, we improve the CPSO-VQO by proposing a modified chaotic system whose bifurcation structure is irrelevant to the difference vector, and show theoretically desirable properties of the modified system. We also propose a new stochastic method that selects the updating system according to the ratio between the components of the difference vector for each particle, and restarting and acceleration techniques to develop the standard updating system used in the proposed PSO model. The proposed methods can maintain an appropriate balance between the identification and diversification aspects of the search. Moreover, we perform numerical experiments to evaluate the performance of the proposed PSOs: PSO-TPC, PSO-SPC, PSO-SDPC, IPSO-SPC and IPSO-SDPC. In particular, we demonstrate that the IPSO-SDPC finds high-quality solutions and is robust against variations in its parameter values.