Evolutionary Multitask Framework With Bi-Knowledge Transfer for Multimodal Optimization Problems

Abstract

Solving multimodal optimization problems (MMOPs) is a challenging task which needs locating multiple global optimal solutions simultaneously with high accuracy. Current popular niching-based evolutionary algorithms (EAs) for solving MMOPs usually divide the population into several separate species to search for different optimal solutions. However, achieving effective information exchange between species to enhance the performance of overall algorithm remains a challenge in current niching-based EAs, which will directly affect the efficiency of the multimodal optimization algorithm. In this article, the process of the different species locating peaks in MMOPs is regarded as an evolutionary multitask (EMT) optimization problem and an EMT framework with bi-knowledge transfer for MMOPs is proposed. An explicit knowledge transfer (E-KT) strategy is designed to transfer the optimal individual of the species with the fastest convergence speed to other species, thereby facilitating the acceleration their convergence. Moreover, in order to further improve the information exchange between species, a species-center-based implicit knowledge transfer (I-SCKT) strategy is designed to improve the diversity of the population. The performance of ${\mathrm { MTBKT}}_{\mathrm { MMOP}}$ is tested on the widely used CEC’2013 benchmark and five practical flexible job shop problems. The experimental results of ${\mathrm { MTBKT}}_{\mathrm { MMOP}}$ are compared with nine state-of-the-art MMOPs algorithms and show that our ${\mathrm { MTBKT}}_{\mathrm { MMOP}}$ is superior to all of them. Besides, the experimental results also show that the ${\mathrm { MTBKT}}_{\mathrm { MMOP}}$ achieves breakthroughs in handling with a large number of optimal solutions or high-dimensional MMOPs, which provides a new and effective method for dealing with MMOPs.