Computing with Multi-row Gomory Cuts

Cutting planes for mixed integer problems (MIP) are nowadays an integral part of all general purpose software to solve MIP. The most prominent,and computationally significant, class of general cutting planes are Gomory mixed integer cuts (GMI). However finding other classes of general cuts for MIP that work well in practice has been elusive. Recent advances on the understanding of valid inequalities derived from the infinite relaxation introduced by Gomory and Johnson for mixed integer problems, has opened a new possibility of finding such an extension. In this paper, we investigate the computational impact of using a subclass of minimal valid inequalities from the infinite relaxation, using different number of tableau rows simultaneously, based on a simple separation procedure.We test these ideas on a set of MIPs, including MIPLIB 3.0 and MIPLIB 2003, and show that they can improve MIP performance even when compared against commercial software performance.This research was partially funded by FONDECYT grant 1070749 and by ICM grant P05-004F