Computational Experiments with Cross and Crooked Cross Cuts
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Computational-Experiments-with-Cross.pdf
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Author(s)
Dash, Sanjeeb
Gunluk, Oktay
Vielma, Juan Pablo
Date Issued
June 2014
Journal
INFORMS Journal on Computing
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
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.
Version
Author's final manuscript
Abstract
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].
MIT Department
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/ijoc.2014.0598
