On Counting Lattice Points and Chvatal-Gomory Cutting Planes

摘要

The paper investigates the relationship between counting the lattice points belonging to an hyperplane and the separation of Chvatal-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.