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. © 2011 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Lodi, A., Pesant, G., & Rousseau, L. M. (2011). On counting lattice points and chvátal-gomory cutting planes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6697 LNCS, pp. 131–136). https://doi.org/10.1007/978-3-642-21311-3_13
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