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Sub-Symmetry-Breaking Inequalities for ILP with Structured Symmetry

Abstract : 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.
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Submitted on : Wednesday, February 12, 2020 - 2:51:29 PM
Last modification on : Saturday, February 15, 2020 - 1:34:27 AM

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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-01876358v2⟩

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