Inverse multi-objective robust evolutionary design optimization in the presence of uncertainty

In many real-world design problems, uncertainties are often present and practically impossible to avoid. Many existing works on Evolutionary Algorithm (EA) for handling uncertainty have emphasized on introducing some prior structure of the uncertainty or noise to the variable domain and conducting sensitivity analysis based on the assumed information. In this paper, we present an evolutionary design optimization that handles the presence of uncertainty with respect to the desired robust performance in mind, which we call an inverse robust design. The scheme, unlike others developed to represent uncertainty does not assume any structure of the uncertainty involved; hence it is particularly useful when there is very little information about the uncertainties available. In our formulation, we model the clustering of uncertain events in families of nested sets using a multi-level optimization searches within the multi-objective evolutionary search. Empirical studies were conducted on synthetic functions to demonstrate that our algorithm converges to a set of designs with non-dominated nominal performances and robustness to the presence of uncertainties.