Multiple Metamodels for Robustness Estimation in Multi-objective Robust Optimization

Due to the excessive cost of Monte Carlo simulation, metamodel is now frequently used to accelerate the process of robustness estimation. In this paper, we explore the use of multiple metamodels for robustness evaluation in multi-objective evolutionary robust optimization under parametric uncertainty. The concept is to build several different metamodel types, and employ cross-validation to pick the best metamodel or to create an ensemble of metamodels. Three types of metamodel were investigated: sparse polynomial chaos expansion (PCE), Kriging, and 2\(^\text {nd}\) order polynomial regression (PR). Numerical study on robust optimization of two test problems was performed. The result shows that the ensemble approach works well when all the constituent metamodel is sufficiently accurate, while the best scheme is more favored when there is a constituent metamodel with poor quality. Moreover, besides the accuracy, we found that it is also important to preserve the trend and smoothness of the decision variables-robustness relationship. PR, which is the less accurate metamodel from all, can found a better representation of the Pareto front than the sparse PCE.