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Chvatal-Gomory cutting planes (CG-cuts for short) are a fundamental tool inInteger Programming. Given any single CG-cut, one can derive an entire familyof CG-cuts, by `iterating' its multiplier vector modulo one. This leadsnaturally to two questions: first, which iterates correspond to the strongestcuts, and, second, can we find such strong cuts efficiently? We answer thefirst question empirically, by showing that one specific approach for selectingthe iterate tends to perform much better than several others. The approachessentially consists in solving a nonlinear optimization problem over a speciallattice associated with the CG-cut. We then provide a partial answer to thesecond question, by presenting a polynomial-time algorithm that yields aniterate that is strong in a certain well-defined sense. The algorithm is basedon results from the algorithmic geometry of numbers.

Iterated Chvatal-Gomory Cuts and the Geometry of Numbers