Adaptive robust optimization with objective uncertainty

Boris Detienne (1, 2) , Henri Lefebvre (3) , Enrico Malaguti (3) , Michele Monaci (3)

1 Realopt - Reformulations based algorithms for Combinatorial Optimization
2 IMB - Institut de Mathématiques de Bordeaux
3 DEI - Department of electrical, electronic and information engineering "GUGLIELMO MARCONI" [Bologna]

In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and involve mixed-integer variables, thus extending the existing literature to a much wider class of problems. We show how these problems can be reformulated using Fenchel duality, allowing to derive an enumerative exact algorithm, for which we prove-convergence in a finite number of operations. An implementation of the resulting algorithm, embedding a column generation scheme, is then computationally evaluated on two different problems, using instances that are derived starting from the existing literature. To the best of our knowledge, this is the first approach providing results on the practical solution of this class of problems.

Mots clés: Branch-and-bound; Two-stage robust optimization; Reformulation; Fenchel duality; Column generation; Computational experiments

Domaines: Optimisation et contrôle [math.OC]

Boris Detienne, Henri Lefebvre, Enrico Malaguti, Michele Monaci. Adaptive robust optimization with objective uncertainty. 2021. ⟨hal-03371438⟩