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.