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Packing, Partitioning, and Covering Symresacks

Christopher Hojny(hojny***at***mathematik.tu-darmstadt.de)

Abstract: In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering (ppc) inequalities. To handle symmetries as well as ppc-constraints simultaneously, we introduce constrained symresacks which are the convex hull of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and which fulfill some ppc-constraints. We show that linear optimization problems over constrained symresacks can be solved in polynomial time. Furthermore, we derive complete linear descriptions of constrained symresacks for important classes of symmetries. These inequalities can then be used as strong cutting planes in a branch-and-bound procedure. Numerical experiments show that we can benefit from incorporating ppc-constraints into symmetry handling inequalities.

Keywords: symmetry, binary programming, complete linear description, extended formulation, total dual integral

Category 1: Integer Programming (0-1 Programming )

Citation: TU Darmstadt, Department of Mathematics, Research Group Optimization, Dolivostr. 15, 64293 Darmstadt, May 2017

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Entry Submitted: 05/03/2017
Entry Accepted: 05/03/2017
Entry Last Modified: 05/03/2017

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