Multiple Surrogate-Model-Based Optimization Method Using the Multimodal Expected Improvement Criterion for Expensive Problems

Abstract

In this article, a multiple surrogate-model-based optimization method using the multimodal expected improvement criterion (MSMEIC) is proposed. In MSMEIC, an important region is first identified and used alternately with the whole space. Then, in each iteration, three common surrogate models, kriging, radial basis function (RBF), and quadratic response surface (QRS), are constructed, and a multipoint expected improvement (EI) criterion that selects the highest peak and other peaks of EI is proposed to obtain several potential candidates. Furthermore, the optimal predictions of the three surrogate models are regarded as potential candidates. After deleting redundant candidates, the remaining points are saved as the new sampling points. Finally, several well-known benchmark functions and an engineering application are employed to assess the performance of MSMEIC. The testing results demonstrate that, compared with four recent counterparts, the proposed method can obtain more precise solutions more efficiently and with strong robustness.