Computational Experiments with Cross and Crooked Cross Cuts
Author(s)Dash, Sanjeeb; Gunluk, Oktay; Vielma, Juan Pablo
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In this paper, we study whether cuts obtained from two simplex tableau rows at a time can strengthen the bounds obtained by Gomory mixed-integer (GMI) cuts based on single tableau rows. We also study whether cross and crooked cross cuts, which generalize split cuts, can be separated in an effective manner for practical mixed-integer programs (MIPs) and can yield a nontrivial improvement over the bounds obtained by split cuts. We give positive answers to both these questions for MIPLIB 3.0 problems. Cross cuts are a special case of the t-branch split cuts studied by Li and Richard [Li Y, Richard J-PP (2008) Cook, Kannan and Schrijvers's example revisited. Discrete Optim. 5:724–734]. Split cuts are 1-branch split cuts, and cross cuts are 2-branch split cuts. Crooked cross cuts were introduced by Dash, Günlük, and Lodi [Dash S, Günlük O, Lodi A (2010) MIR closures of polyhedral sets. Math Programming 121:33–60] and were shown to dominate cross cuts by Dash, Günlük, and Molinaro [Dash S, Günlük O, Molinaro M (2012b) On the relative strength of different generalizations of split cuts. IBM Technical Report RC25326, IBM, Yorktown Heights, NY].
DepartmentSloan School of Management
INFORMS Journal on Computing
Institute for Operations Research and the Management Sciences (INFORMS)
Dash, Sanjeeb, Oktay Gunluk, and Juan Pablo Vielma. “Computational Experiments with Cross and Crooked Cross Cuts.” INFORMS Journal on Computing 26, no. 4 (November 2014): 780–797.
Author's final manuscript