A Surrogate-Assisted Two-Stage Differential Evolution for Expensive Constrained Optimization

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) have been successfully employed for expensive optimization. However, most SAEAs are designed for expensive unconstrained optimization, and less attention has been paid to expensive optimization with inequality constraints. Therefore, this work proposes a novel SAEA, called surrogate-assisted two-stage differential evolution (SA-TSDE), for expensive constrained optimization. In the first search stage, surrogate-assisted hybrid differential evolution is adopted for prescreening promising solutions in the decision space for exploration. Moreover, an effective repair strategy, named surrogate based repair strategy, is introduced to move the infeasible solutions closer to the feasible region. In the second search stage, a clustering strategy of feasible solutions is proposed based on the information provided by the first search stage and historical search. The clustering strategy adaptively generates a number of clusters, each of which can form a promising local region for the local search. Afterwards, local surrogates are built for finding the predicted optima in each local region. During the search process, a good balance between exploration and exploitation can be obtained by interleaving the two search stages. Experimental results indicate that SA-TSDE is highly competitive compared with some state-of-the-art methods.