Bi-Objective Surrogate Feasibility Robust Design Optimization Utilizing Expected Non-Dominated Improvement With Relaxation

Abstract

Abstract Engineering design optimization problems often have two competing objectives as well as uncertainty. For these problems, quite often there is interest in obtaining feasibly robust optimum solutions. Feasibly robust here refers to solutions that are feasible under all uncertain conditions. In general, obtaining bi-objective feasibly robust solutions can be computationally expensive, even more so when the functions to evaluate are themselves computationally intensive. Although surrogates have begun to be utilized to decrease the computational costs of such problems, there is limited usage of Bayesian frameworks on problems of multiobjective optimization under interval uncertainty. This article seeks to formulate an approach for the solution of these problems via the expected improvement Bayesian acquisition function. The acquisition function is solved alternatingly with worst-case searches to find robust solutions. In this paper, a method is developed for iteratively relaxing the solutions to facilitate convergence to a set of non-dominated, robust optimal solutions. Additionally, a variation of the bi-objective expected improvement criterion is proposed to encourage variety and density of the robust bi-objective Pareto optimal (or non-dominated) solutions. Several examples are tested and compared against another bi-objective robust optimization approach with surrogate utilization. It is shown that the proposed method performs well at finding robustly optimized feasible solutions with limited function evaluations. Future directions for improving the proposed methodology are suggested.