A new expected-improvement algorithm for continuous minimax optimization

Worst-case design is important whenever robustness to adverse environmental conditions must be ensured regardless of their probability. It leads to minimax optimization, which is most often treated assuming that prior knowledge makes the worst environmental conditions obvious, or that a closed-form expression for the performance index is available. This paper considers the important situation where none of these assumptions is true and where the performance index must be evaluated via costly numerical simulations. Strategies to limit the number of these evaluations are then of paramount importance. One such strategy is proposed here, which further improves the performance of an algorithm recently presented that combines a relaxation procedure for minimax search with the well-knownKriging-based EGO algorithm. Expected Improvement is computed in the minimax optimization context, which allows to further reduce the number of costly evaluations of the performance index. The interest of the approach is demonstrated on test cases and a simple engineering problem from the literature, which facilitates comparison with alternative approaches.