Experiments with Two-Row Cuts from Degenerate Tableaux

Authors:
Amitabh Basu;Pierre Bonami;Gé/rard Cornué/jols;Franç/ois Margot
Affiliations:
Department of Mathematics, University of California, Davis, Davis, California 95616;Laboratoire d'Informatique Fondamentale, Faculté/ des Sciences de Luminy, Université/ de Marseille, 13288 Marseille, France;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213/ and Laboratoire d'Informatique Fondamentale, Faculté/ des Sciences de Luminy, Université/ de Marseill ...;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Venue:
INFORMS Journal on Computing
Year:
2011

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Abstract

There has been a recent interest in cutting planes generated from two or more rows of the optimal simplex tableau. One can construct examples of integer programs for which a single cutting plane generated from two rows dominates the entire split closure. Motivated by these theoretical results, we study the effect of adding a family of cutting planes generated from two rows on a set of instances from the MIPLIB library. The conclusion of whether these cuts are competitive with Gomory mixed-integer cuts is very sensitive to the experimental setup. In particular, we consider the issue of reliability versus aggressiveness of the cut generators, an issue that is usually not addressed in the literature.