Chaos-based second-order bas for multimodal function optimization

Abstract

Aiming at solving a drawback of the second-order beetle antenna search (SOBAS), a variant of the beetle antenna search (BAS), that it is difficult to find the global optimal solution and the low convergence accuracy when applied to the multimodal optimization functions with high dimension or large variable region, a chaotic-based second-order BAS algorithm (CSOBAS) is proposed by introducing chaos theory into the SOBAS. The algorithm mainly has three innovations: 1) chaos initialization: choosing the one with the smallest fitness function value from twenty beetles with different positions for iterative search; 2) using chaotic map to tune the randomization parameter in the detection rule; 3) imposing a chaotic perturbation on the current beetle to hope to help the search to jump out the local optimal solution. Eight different chaotic maps are used to demonstrate their impact on the simulation results. With six typical multimodal functions, performance comparisons between the CSOBAS and the SOBAS are conducted, validating the effectiveness of the CSOBAS and its superiority compared to the SOBAS. What?s more, the CSOBAS with an appropriate chaotic map can achieve a very good convergence quality compared to other swarm intelligence optimization algorithms while maintaining an individual.