A multi-objective perspective on robust ranking and selection

In this study, we consider the robust Ranking and Selection problems with input uncertainty. Instead of adopting the minimax analysis in the classical robust optimization, we propose a novel method to approach this problem from the perspective of multi-objective optimization and Pareto optimality. More specifically, the performances of each design under various scenarios are reformulated as multiple objectives, and in this case, robust Ranking and Selection becomes a multi-objective Ranking and Selection. In order to determine the number of simulation replications to various scenarios of each design, a bi-level convex optimization is formulated by maximizing the surrogate of the large deviation rate function of the probability of false selection. Numerical results show the efficiency of the proposed procedure (PR-OCBA) compared with other methods.