Computational efficiency of accelerated particle swarm optimization combined with different chaotic maps for global optimization

Abstract

A new hybrid chaos optimization algorithm (COA), namely, the accelerated particle swarm optimization combined with different chaotic maps (APSOC), is proposed for global optimization with continuous and discrete variables in this paper. Computational efficiency of APSOC and other three COAs (CPSO1–CPSO3) is compared for nonlinear benchmark functions. And the three influencing factors of chaotic maps on efficiency are considered, namely, the Lyapunov exponent (LE) which quantifies the search speed of chaotic sequence, the probability distribution function (PDF), and the dispersion degree of chaotic sequence which is defined as an index to measure the computational performance of evolutionary algorithm herein. To investigate the influence of CPSOs with different one-dimensional chaotic maps on efficiency of global optimization, three cases are examined, such as: different chaotic maps with close LE and different PDF; the same chaotic map with the same PDF and different LE; and the identical chaotic map with equal or close LE and different PDF. Optimization results demonstrate that the probability distribution, search speed, and dispersion degree of chaotic sequences affect remarkably the performance of CPSOs. Finally, statistic results and evolution curves of APSOC with Circle map are compared with those of other three COAs, and the optimal design of trusses with discrete variables are performed by APSOC. It is indicated that APSOC with Circle map is superior to other CPSOs and has greater exploration ability and faster convergence rate.