Min-Sup-Min Robust Combinatorial Optimization with Few Recourse Solutions
研究决策者可以准备K个解并在得知真实数据后选择最佳解的自适应鲁棒组合优化问题，提出一种新的精确算法，通过枚举好解、动态生成场景并利用顶点p-中心公式分配解，在自适应最短路径和带冲突背包问题上优于现有方法。
In this paper, we consider a variant of adaptive robust combinatorial optimization problems where the decision maker can prepare K solutions and choose the best among them upon knowledge of the true data realizations. We suppose that the uncertainty may affect the objective and the constraints through functions that are not necessarily linear. We propose a new exact algorithm for solving these problems when the feasible set of the nominal optimization problem does not contain too many good solutions. Our algorithm enumerates these good solutions, generates dynamically a set of scenarios from the uncertainty set, and assigns the solutions to the generated scenarios using a vertex p-center formulation, solved by a binary search algorithm. Our numerical results on adaptive shortest path and knapsack with conflicts problems show that our algorithm compares favorably with the methods proposed in the literature. We additionally propose a heuristic extension of our method to handle problems where it is prohibitive to enumerate all good solutions. This heuristic is shown to provide good solutions within a reasonable solution time limit on the adaptive knapsack with conflicts problem. Finally, we illustrate how our approach handles nonlinear functions on an all-or-nothing subset problem taken from the literature. Summary of Contribution: Our paper describes a new exact algorithm for solving adaptive robust combinatorial optimization problems when the feasible set of the nominal optimization problems does not contain too many good solutions. Its development relies on a progressive relaxation of the problem augmented with a row-and-column generation technique. Its efficient execution requires a reformulation of this progressive relaxation, coupled with dominance rules and a binary search algorithm. The proposed algorithm is amenable to exploiting the special structures of the problems considered as illustrated with various applications throughout the paper. A practical view is provided by the proposition of a heuristic variant. Our computational experiments show that our proposed exact solution method outperforms the existing methodologies and therefore pushes the computational envelope for the class of problems considered.