Sub-symmetry-breaking inequalities and application to the Unit Commitment Problem

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 problems, by introducing one additional variable per sub-symmetry group considered. The proposed framework is applied to derive such inequalities when the symmetry group is the symmetric group acting on the columns. It is also applied to derive inequalities breaking both symmetries and sub-symmetries in the Min-up/min-down Unit Commitment Problem (MUCP). We show the effectiveness of the approach by presenting an experimental comparison with state-of-the-art symmetry-breaking formulations for the MUCP with or without ramp constraints.
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Submitted on : Tuesday, September 18, 2018 - 2:41:55 PM
Last modification on : Friday, July 5, 2019 - 3:26:03 PM

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Pascale Bendotti, Pierre Fouilhoux, Cécile Rottner. Sub-symmetry-breaking inequalities and application to the Unit Commitment Problem. Lecture Notes in Computer Science, Springer, In press, The 20th Conference on Integer Programming and Combinatorial Optimization May 22–24, 2019, Ann Arbor, Michigan, USA. ⟨hal-01876358⟩

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