On counting lattice points and Chvátal-Gomory cutting planes

Authors:
Andrea Lodi;Gilles Pesant;Louis-Martin Rousseau
Affiliations:
DEIS, Università di Bologna;CIRRELT, École Polytechnique de Montréal;CIRRELT, École Polytechnique de Montréal
Venue:
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Year:
2011

Citing 5
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Abstract

The paper investigates the relationship between counting the lattice points belonging to an hyperplane and the separation of Chvátal-Gomory cutting planes. In particular, we show that counting can be exploited in two ways: (i) to strengthen the cuts separated, e.g., by Gomory classical procedure, and (ii) to heuristically evaluate the effectiveness of those cuts and possibly select only a subset of them. Empirical results on a small set of 0-1 Integer Programming instances are presented.