Min-Sup-Min Robust Combinatorial Optimization with Few Recourse Solutions

In this paper, we consider a variant of adaptive robust combinatorial optimization problems where the decision maker can prepare K solutions and choose best among them upon knowledge true data realizations. We suppose that uncertainty may affect objective constraints through functions are not necessarily linear. propose new exact algorithm for solving these when feasible set nominal problem does contain too many good solutions. Our enumerates solutions, generates dynamically scenarios from set, assigns to generated using vertex p-center formulation, solved by binary search algorithm. numerical results on shortest path knapsack with conflicts show our compares favorably methods proposed in literature. additionally heuristic extension method handle it is prohibitive enumerate all This shown provide within reasonable solution time limit problem. Finally, illustrate how approach handles nonlinear an all-or-nothing subset taken Summary Contribution: paper describes Its development relies progressive relaxation augmented row-and-column generation technique. efficient execution requires reformulation relaxation, coupled dominance rules The amenable exploiting special structures considered as illustrated various applications throughout paper. A practical view provided proposition variant. computational experiments outperforms existing methodologies therefore pushes envelope class considered.