Decomposition-based approaches for a class of two-stage robust binary optimization problems

Ayşe N Arslan (1, 2) , Boris Detienne (3, 4, 5)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 INSA Rennes - Institut National des Sciences Appliquées - Rennes
3 IMB - Institut de Mathématiques de Bordeaux
4 Realopt - Reformulations based algorithms for Combinatorial Optimization
5 EDGE - Formulations étendues et méthodes de décomposition pour des problèmes génériques d'optimisation

In this paper, we study a class of two-stage robust binary optimization problems with objective uncertainty where recourse decisions are restricted to be mixed-binary. For these problems, we present a deterministic equivalent formulation through the convexification of the recourse feasible region. We then explore this formulation under the lens of a relaxation, showing that the specific relaxation we propose can be solved using the branch-and-price algorithm. We present conditions under which this relaxation is exact, and describe alternative exact solution methods when this is not the case. Despite the two-stage nature of the problem, we provide NP-completeness results based on our reformulations. Finally, we present various applications in which the methodology we propose can be applied. We compare our exact methodology to those approximate methods recently proposed in the literature under the name K-adaptability. Our computational results show that our methodology is able to produce better solutions in less computational time compared to the K-adaptability approach, as well as to solve bigger instances than those previously managed in the literature.

Domaines: Optimisation et contrôle [math.OC]; Recherche opérationnelle [math.OC]

Ayşe N Arslan, Boris Detienne. Decomposition-based approaches for a class of two-stage robust binary optimization problems. INFORMS Journal on Computing, 2022, 34 (2), ⟨10.1287/ijoc.2021.1061⟩. ⟨hal-02190059v4⟩