Communication Dans Un Congrès Année : 2025

Solving two-stage distributionally robust optimization with mixed-integer ambiguity sets via a hybrid Benders and column-and-constraint decomposition method

Résumé

We propose a decomposition algorithm to approximately solve two-stage distributionally robust optimization problems with mixed-integer ambiguity sets. Such settings are particularly relevant in non-cooperative contexts, such as unplanned disruptions or interdictions, where an adversary reacts to the defender's decisions. DRO is a natural fit, but resulting problems are difficult to reformulate as solvable MILPs unless the ambiguity set follows a specific structure. Therefore, we propose a data-driven approach to find an upper bound to the original problem. The ambiguity set is split into integer and continuous sets, so that the recourse model is easily reformulated into a tractable form by relying on known strong duality results. The resulting problem is solved using a traditional decomposition approach combining Benders’ decomposition and column-and-constraint generation. We demonstrate our approach on a network design problem with interdiction constraints.

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Dates et versions

hal-05198453 , version 1 (04-08-2025)

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  • HAL Id : hal-05198453 , version 1

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Pascal Quach, Yiping Fang, Anne Barros. Solving two-stage distributionally robust optimization with mixed-integer ambiguity sets via a hybrid Benders and column-and-constraint decomposition method. XVIIth International Conference on Stochastic Programming, Jul 2025, Champs-sur-Marne (Marne-la-Vallée), France. ⟨hal-05198453⟩
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