Multi-surrogate assisted PSO with adaptive speciation for expensive multimodal multi-objective optimization

Expensive multimodal multi-objective optimization problems (MMOPs) commonly arise in real-world situations, in which multiple Pareto solutions correspond to the same objective values. In order to provide satisfactory solutions for decision makers, plenty of evolutionary algorithms (EAs) have been used to solve MMOPs. However, the traditional EAs is limited in practice due to the time-consuming problem caused by a large number of fitness evaluations. To tackle this issue, a multi-surrogate assisted particle swarm optimization with adaptive speciation is proposed in this paper. In the proposed algorithm, a multi-surrogate model using adaptive scheduling strategy is introduced to reveal the many-to-one mapping relationship between decision space and objective space. To trade-off between convergence and diversity in both decision and objective space, a speciation method with adaptive niche radius is designed to perform species self-organization and evolution. Moreover, a surrogate assisted evolution with leader updating strategy is performed to guide the evolution of species. In order to verify the effectiveness of the proposed method, the benchmark problem (from IEEE Congress on evolutionary computation 2019) is analyzed experimentally. The experimental results show that the proposed method is superior to the state-of-the-art multimodal multi-objective evolutionary algorithm in term of maintaining the diversity of solutions in the decision and objective space.(c) 2023 Published by Elsevier B.V.