Trade-off Between Robustness and Worst-Case Performance in Min-Max Optimization

Abstract

Min-max optimization is an approach to avoid the risk of obtaining a solution whose performance is satisfactory in a simulation scenario but significantly degraded in real-world scenarios, thereby obtaining a robust solution under the worst case in the considered scenarios. However, owing to the trade-off between robustness and worst-case performance, it is often difficult to design a set of scenarios in simulation-based optimization, known as the uncertainty set, which can be a practical barrier to applying min-max optimization. In this study, we propose a novel approach to obtaining the Pareto front of the bi-objective optimization for the size of the uncertainty set and worst-case performance under the uncertainty set. The proposed approach aims to obtain a set of solutions that cover the worst-case performance effectively but are better than a given performance threshold. The effectiveness of each algorithmic component was evaluated through numerical experiments using a synthetic problem. Applications to automatic ship berthing tasks demonstrate the usefulness of the proposed approach and its limitations.