Date of Original Version
1-20-2005
Type
Article
Published In
Management Science, Vol. 51, No. 11, November 2005, pp. 1720–1732
Abstract or Table of Contents
Mixed integer Gomory cuts have become an integral part of state-of-the-art software for solving mixed integer linear programming problems. Therefore, improvements in the performance of these cutting planes can be of great practical value. In this paper we present a simple and fast heuristic for improving the coefficients on the continuous variables in the mixed integer Gomory cuts. This is motivated by the fact that, in a mixed integer Gomory cut, the coefficient of an integer variable lies between 0 and 1, whereas for a continuous variable, there is no upper bound. The heuristic tries to reduce the coefficients of the continuous variables. We call the resulting cuts reduce-and-split cuts. We found that, on several test problems, reduce-and-split cuts can substantially enhance the performance of a branch-and-bound algorithm.