Computational Experiments with Cross and Crooked Cross Cuts

In a recent paper, Dash, Dey and Günlük (2010) showed that many families of inequalities for the two-row continuous group relaxation and variants of this relaxation are cross cuts or crooked cross cuts, both of which generalize split cuts. Li and Richard (2008) recently studied t-branch split cuts for mixedinteger programs for integers t ≥ 1. Split cuts are just 1-branch split cuts, and cross cuts are 2-branch split cuts. In this paper, we study whether cross and crooked cross cuts can be separated in an effective manner for practical MIPs, and can yield a non-trivial improvement over the bounds obtained by split cuts. We also study whether such cuts obtained from two simplex tableau rows at a time can strengthen the bounds obtained by GMI cuts based on single tableau rows. We give positive answers to both these questions for MIPLIB 3.0 problems.