Multiple Additional Sampling by Expected Improvement Maximization in Efficient Global Optimization for Real-World Design Problems

Abstract

Efficient global optimization (EGO), based on the expected improvement maximization of the Kriging model, is a suitable optimization method for designs based on time-consuming evaluations such as computational fluid dynamics. However, the original formulation of EGO can find only one additional sample point after an initial sample point is acquired for the initial Kriging model construction. Therefore, the efficiency of EGO is decreased even if the designer is able to evaluate several designs using a large parallel computer because additional samples can only be obtained sequentially through the additional sampling process. In this study, a multiple additional sampling method is proposed to improve the efficiency of the additional sampling process in EGO while maintaining the performance of exploration based on EI maximization. The design performance of EGO with MAS is investigated by solving a test problem first, and then an airfoil design problem, which is a single objective problem. The results are compared with the original EGO in terms of the convergence of the objective function and the diversity of the design variables. According to these problems, the proposed method acquires optimum solutions as effectively as the original EGO, while the diversity of the solutions is improved. In addition, the total design time can be reduced compared with the original EGO in a parallel computational environment.