Sub-Symmetry-Breaking Inequalities for ILP with Structured Symmetry

Pascale Bendotti (1, 2) , Pierre Fouilhoux (2) , Cécile Rottner (1, 2)

1 EDF R&D OSIRIS - Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie
2 RO - Recherche Opérationnelle

We consider integer linear programs whose solutions are binary matrices and whose (sub-)symmetry groups are symmetric groups acting on (sub-)columns. We propose a framework to build (sub-)symmetry-breaking inequalities for such programs, by introducing one additional variable per sub-symmetry group considered. The proposed framework is applied to derive inequalities breaking both symmetries and sub-symmetries in the graph coloring problem and in the ramp constrained min-up/min-down unit commitment problem.

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

Pascale Bendotti, Pierre Fouilhoux, Cécile Rottner. Sub-Symmetry-Breaking Inequalities for ILP with Structured Symmetry. IPCO 2019 - 20th Conference on Integer Programming and Combinatorial Optimization, May 2019, Ann Arbor, Michigan, United States. pp.57-71, ⟨10.1007/978-3-030-17953-3_5⟩. ⟨hal-01876358⟩