Reduce-and-Split Cuts: Improving the Performance of Mixed Integer Gomory Cuts
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 2005
- Accession Number
- AD1021103
Entities
People
- Gérard Cornuéjols
- Kent Andersen
- Yanjun Li
Organizations
- Carnegie Mellon University