We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the implementation of decisions requires preparing the ground. We focus on the case that the set of possible scenarios is described through a budgeted uncertainty set and provide three algorithms for the problem. The first algorithm solves heuristically the dualized problem, a non-convex mixed-integer non-linear program (MINLP), via an alternating optimization approach. The second algorithm solves the MINLP exactly for $k=2$ through a dedicated spatial branch-and-bound algorithm. The third approach enumerates $k$-tuples, relying on strong bounds to avoid a complete enumeration. We test our methods on shortest path instances that were used in the previous literature and on randomly generated knapsack instances, and find that our methods considerably outperform previous approaches. Many instances that were previously not solved within hours can now be solved within few minutes, often even faster.
Robust single-stage selection problems with budgeted interval uncertainty
LS2N, University of Nantes（南特大学）；National Academy of Sciences of Belarus（白俄罗斯国家科学院）；University of Siegen（锡根大学）；HHL Leipzig Graduate School of Management（德国莱比锡商学院）
VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control Performance Optimization with Unmodeled Constraints
Mitsubishi Electric Research Laboratories（三菱电机研究院）；École polytechnique fédérale de Lausanne（洛桑联邦理工学院）；Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科学与技术实验室）
