Using Gaussian Processes for Metamodeling in Robust Optimization Problems

Abstract

This article proposes an approach based on Gaussian Processes for building metamodels for robust optimization problems that seek to reduce the computational effort required to quantify uncertainties. The approach is applied to two cases: a low-dimensional benchmark problem and a high-dimensional structural design, which consists of minimizing the mass of a structure formed by bars of different materials and diameters, subjected to point loads in different locations. The cases are modeled as robust optimization problems, where the objective function is estimated by a Gaussian Process and the optimization procedure uses a population meta-heuristic. The results indicate that the proposed approach is effective in reducing the number of objective function evaluations required to obtain a robust solution, with no significant statistical differences in the quality of solutions achieved.