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Min-max-min robust combinatorial optimization with few recourse solutions

Abstract : In this paper, we consider a variant of adaptive robust combinatorial optimization problems with cost uncertainty where the decision maker can prepare K solutions and choose the best among them upon knowledge of the true cost vectors. 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.
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https://hal.archives-ouvertes.fr/hal-02939356
Contributor : Michael Poss <>
Submitted on : Tuesday, September 15, 2020 - 3:19:26 PM
Last modification on : Sunday, October 11, 2020 - 3:10:52 AM

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  • HAL Id : hal-02939356, version 1

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Ayşe Arslan, Michael Poss, Marco Silva. Min-max-min robust combinatorial optimization with few recourse solutions. 2020. ⟨hal-02939356v1⟩

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