A Two-Level Model Management-Based Surrogate-Assisted Evolutionary Algorithm for Medium-Scale Expensive Multiobjective Optimization

Medium-scale expensive multiobjective optimization problems (EMOPs) present a significant challenge to most existing surrogate-assisted evolutionary algorithms (SAEAs). Because the algorithms must balance convergence and diversity with a limited number of fitness evaluations (FEs), while managing the uncertainty in surrogate predictions within the medium-scale decision space. Therefore, this work proposes a surrogate-assisted multiobjective evolutionary algorithm based on two-level model management (SAMOEA-TL2M) to effectively address medium-scale EMOPs. In SAMOEA-TL2M, infill solutions are selected using the proposed two-level model management strategy. In the first level, the estimated non-dominated solutions with good shift-based density estimation (SDE) values are selected for the balance of convergence and diversity. In the second level, the estimated non-dominated solutions and high uncertainty solutions are considered. To quantify uncertainty, an inverse distance weighting (IDW) is introduced. Moreover, an accuracy rate indicator (ARI) is proposed for the optimization state assessment, providing guidance for adaptively executing the two model management levels. Extensive experiments on three widely used instances and time-varying ratio error estimation (TREE) problems with up to 120 dimensions demonstrate the superiority of SAMOEA-TL2M over five state-of-the-art SAEAs in solving medium-scale EMOPs.