Reduce-and-Split Cuts: Improving the Performance of Mixed-Integer Gomory Cuts

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.

• 저널Management Science · 51(11) · 1720–1732
• 토픽Complexity and Algorithms in Graphs · Computational Theory and Mathematics
• DOI10.1287/mnsc.1050.0382
• 저자Kent Andersen, Gérard Cornuéjols, Yanjun Li