An Efficient Two-Stage Surrogate-Assisted Differential Evolution for Expensive Inequality Constrained Optimization

Constraint handling is a core part when using surrogate-assisted evolutionary algorithms (SAEAs) to solve expensive constrained optimization problems (ECOPs). However, most existing SAEAs for ECOPs train a surrogate for each constraint. With the number of constraints increasing, the training burden of surrogates becomes heavy and the efficiency of the algorithm is greatly reduced. To solve this issue, this article proposes an efficient two-stage surrogate-assisted differential evolution (eToSA-DE) algorithm to handle expensive inequality constraints. eToSA-DE trains one surrogate for the degree of constraint violation and the type of the surrogate varies during the evolution process. In the first stage when there are only a few feasible individuals, a Gaussian process regression model is trained to fit the degree of constraint violation. In the second stage when more feasible individuals are accumulated, a support vector machine classification model is trained to classify whether candidates are feasible. Both types of surrogates are constructed by individuals which are chosen by the boundary training data selection strategy. These selected individuals are located around the feasible boundaries and helpful for the surrogate to approximate the feasibility structure. Besides, a feasible exploration strategy is devised to search for promising areas. To alleviate the error caused by the regression model, a nearest neighbor rectification is adopted to modify the prediction results. Extensive experiments on benchmark test functions and two formulated engineering optimization problems demonstrate that the proposed method can get satisfactory optimization results and significantly improve the efficiency of the algorithm.