Article ID: | iaor2008970 |
Country: | United States |
Volume: | 51 |
Issue: | 11 |
Start Page Number: | 1720 |
End Page Number: | 1732 |
Publication Date: | Nov 2005 |
Journal: | Management Science |
Authors: | Cornujols Grard, Li Yanjun, Andersen Kent |
Keywords: | cutting plane algorithms |
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.