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A Class of Hard Small 0—1 Programs

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Integer Programming and Combinatorial Optimization (IPCO 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1412))

Abstract

In this paper, we consider a class of 0–1 programs which, although innocent looking, is a challenge for existing solution methods. Solving even small instances from this class is extremely difficult for conventional branch-and-bound or branch-and-cut algorithms. We also experimented with basis reduction algorithms and with dynamic pro- gramming without much success. The paper then examines the perfor- mance of two other methods: a group relaxation for 0,1 programs, and a sorting-based procedure following an idea of Wolsey. Although the re- sults with these two methods are somewhat better than with the other four when it comes to checking feasibility, we offer this class of small 0,1 programs as a challenge to the research community. As of yet, instances from this class with as few as seven constraints and sixty 0–1 variables are unsolved.

This work was supported in part by NSF grant DMI-9424348.

Part of the work was done while this author was affiliated with Carnegie Mellon University.

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Author information

Authors and Affiliations

  1. Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols

  2. IBM, T. J. Watson Research Center, Yorktown Heights, NY, 10598, USA

    Milind Dawande

Authors
  1. Gérard Cornuéjols
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  2. Milind Dawande
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Editor information

Editors and Affiliations

  1. Department of Computational and Applied Mathematics, Rice University, 6020 Annapolis, Houston, TX, 77005, USA

    Robert E. Bixby

  2. PROS Strategic Solutions, 3223 Smith Street, Houston, TX, 77006, USA

    E. Andrew Boyd

  3. Department of Industrial, Engineering, Texas A&M University, 1000 Country Place Dr. Apt. 69, Houston, TX, 77079, USA

    Roger Z. Ríos-Mercado

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© 1998 Springer-Verlag Berlin Heidelberg

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Cornuéjols, G., Dawande, M. (1998). A Class of Hard Small 0—1 Programs. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_22

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  • DOI: https://doi.org/10.1007/3-540-69346-7_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64590-0

  • Online ISBN: 978-3-540-69346-8

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