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A Relax-and-Cut Framework for Gomory’s Mixed-Integer Cuts

  • Conference paper
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6140))

Abstract

Gomory’s Mixed-Integer Cuts (GMICs) are widely used in modern branch-and-cut codes for the solution of Mixed-Integer Programs. Typically, GMICs are iteratively generated from the optimal basis of the current Linear Programming (LP) relaxation, and immediately added to the LP before the next round of cuts is generated. Unfortunately, this approach prone to instability.

In this paper we analyze a different scheme for the generation of rank-1 GMIC read from a basis of the original LP—the one before the addition of any cut. We adopt a relax-and-cut approach where the generated GMIC are not added to the current LP, but immediately relaxed in a Lagrangian fashion.

Various elaborations of the basic idea are presented, that lead to very fast—yet accurate—variants of the basic scheme. Very encouraging computational results are presented, with a comparison with alternative techniques from the literature also aimed at improving the GMIC quality, including those proposed very recently by Balas and Bonami and by Dash and Goycoolea.

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Author information

Authors and Affiliations

  1. DEI, University of Padova, Italy

    Matteo Fischetti

  2. DMPA, University of Padova, Italy

    Domenico Salvagnin

Authors
  1. Matteo Fischetti
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  2. Domenico Salvagnin
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Editor information

Editors and Affiliations

  1. DEIS, University of Bologna, Viale Risorgimento 2, 40136, Bologna, Italy

    Andrea Lodi , Michela Milano  & Paolo Toth ,  & 

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Fischetti, M., Salvagnin, D. (2010). A Relax-and-Cut Framework for Gomory’s Mixed-Integer Cuts. In: Lodi, A., Milano, M., Toth, P. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2010. Lecture Notes in Computer Science, vol 6140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13520-0_16

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  • DOI: https://doi.org/10.1007/978-3-642-13520-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13519-4

  • Online ISBN: 978-3-642-13520-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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