Surrogate-Assisted Differential Evolution With Region Division for Expensive Optimization Problems With Discontinuous Responses

A considerable number of surrogate-assisted evolutionary algorithms (SAEAs) have been developed to solve expensive optimization problems (EOPs) with continuous objective functions. However, in the real-world applications, we may face EOPs with discontinuous objective functions, which are also called EOPs with discontinuous responses (EOPDRs). Indeed, EOPDRs pose a great challenge to current SAEAs. In this article, a surrogate-assisted differential evolution (DE) algorithm with region division is proposed, named ReDSADE. ReDSADE includes three main strategies: 1) the region division strategy; 2) the Kriging-based search; and 3) the radial basis function (RBF)-based local search. In the region division strategy, we define a new distance measure, called the objective-decision distance. Based on this distance, the evaluated solutions are partitioned into several clusters, and several support vector machine (SVM) classifiers are trained to classify them. These SVM classifiers divide the decision space into several subregions, with the aim of making the objective function continuous in them. In the Kriging-based search, a Kriging model is established in each subregion and combined with DE to search for the optimal solution. In the RBF-based local search, DE is coupled with RBF to search around the best solution found so far, thus accelerating the convergence. By combining these three strategies, ReDSADE is able to solve EOPDRs with limited function evaluations. Three sets of test problems and a real-world application are utilized to verify the effectiveness of ReDSADE. The results demonstrate that ReDSADE exhibits good convergence accuracy and convergence speed.