Surrogate-assisted Multi-population Differential Evolution Algorithm Based on Region Decomposition

In expensive optimization problems, if the optimal solution of the problem was not unique, such prob lems were referred to as expensive multimodal optimization problems. However, it was extremely difficult to obtain multiple optimal solutions with limited computational resources. Moreover, existing surrogate-assisted evolutionary algorithms paid less attention to multimodal attributes. In view of this, a surrogate-assisted multi-population differ ential evolution algorithm based on region decomposition was proposed to solve expensive multimodal optimization problems. Firstly, in the population individual initialization stage, the correlation between inter-individual distances and objective values was used to detect potential sub-regions, and sub-populations were divided to explore multiple optimal solutions. Secondly, in the early stage of evolution, the differential evolution algorithm was used to perform global search in each sub-population to capture multiple optimal solutions. After multiple optimal individuals were obtained in the early stage of evolution, the covariance matrix adaptive evolution strategy was adopted to carry out local search on them to improve the quality of optimal solutions. In addition, an infilling criterion was proposed, which could adaptively select appropriate individuals for real evaluation according to specific parameters to improve the accuracy and generalization ability of the surrogate model. Finally, the proposed algorithm was compared with seven other algorithms on 20 test functions. The results showed that the proposed algorithm achieved optimal per formance on 13 functions with the PR metric, and was slightly inferior to the comparison algorithms on at most 5 functions. Overall, the proposed algorithm exhibited excellent performance in solving expensive multimodal optimi zation problems.