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Computational Experiments with Cross and Crooked Cross Cuts

Sanjeeb Dash (sanjeebd***at***us.ibm.com)
Oktay Gunluk (gunluk***at***us.ibm.com)
Juan Pablo Vielma (jvielma***at***pitt.edu)

Abstract: In a recent paper, Dash, Dey and Gunluk (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 mixed-integer 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.

Keywords: Mixed-integer programs, split cuts, crooked cross cuts, two-row cuts, continuous group relaxation

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Citation:

Download: [PDF]

Entry Submitted: 06/22/2011
Entry Accepted: 06/22/2011
Entry Last Modified: 06/22/2011

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