A stagnation-resistant surrogate-assisted evolutionary algorithm for expensive multimodal problems

Identifying multiple global optimal solutions is a challenging task, especially when evaluating the objective function is computationally expensive. This type of problem is classified as an expensive multimodal optimization problem. Typically, surrogate models are employed to solve such problems. However, due to the difficulty of accurately fitting highly nonlinear multimodal shapes with surrogate models, evolutionary individuals are extremely prone to stagnation. To address this issue, this paper proposes a stagnation-resistant surrogate-assisted evolutionary algorithm, termed SREA-EMM. Specifically, a population initialization combined with clustering is utilized to select individuals with better diversity, forming multiple potential peak regions for search, thereby rapidly enhancing the level of local convergence. To cope with the stagnation situation, a dual-way guided restart mechanism is proposed, which guides individuals to restart through two kinds of solutions to balance the exploitation of existing modalities and the exploration of potential modalities. Besides, a strategy for migrating individuals based on stagnant information is designed, which aims to prevent restarted individuals from falling into previously converged regions, thereby improving restart efficiency and further enhancing the diversity of the population. The experiments on 20 test functions demonstrate that the proposed algorithm exhibits superior performance, outperforming current expensive multimodal algorithms and some classical multimodal algorithms on most functions. In addition, the effectiveness of SREA-EMM is further verified by the test results in the real-world vehicle task offloading problem.