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Lexicography and degeneracy: can a pure cutting plane algorithm work?

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Abstract

We discuss an implementation of the lexicographic version of Gomory’s fractional cutting plane method for ILP problems and of two heuristics mimicking the latter. In computational testing on a battery of MIPLIB problems we compare the performance of these variants with that of the standard Gomory algorithm, both in the single-cut and in the multi-cut (rounds of cuts) version, and show that they provide a radical improvement over the standard procedure. In particular, we report the exact solution of ILP instances from MIPLIB such as stein15, stein27, and bm23, for which the standard Gomory cutting plane algorithm is not able to close more than a tiny fraction of the integrality gap. We also offer an explanation for this surprising phenomenon.

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Authors and Affiliations

  1. DEI, University of Padova, Padua, Italy

    Arrigo Zanette & Matteo Fischetti

  2. Carnegie Mellon University, Pittsburgh, PA, USA

    Egon Balas

Authors
  1. Arrigo Zanette
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  2. Matteo Fischetti
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  3. Egon Balas
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Corresponding author

Correspondence to Matteo Fischetti.

Additional information

The work of A. Zanette and M. Fischetti was supported by the Future and Emerging Technologies unit of the EC (IST priority), under contract no. FP6-021235-2 (project “ARRIVAL”) and by MiUR, Italy (PRIN 2006 project “Models and algorithms for robust network optimization”). The work of E. Balas was supported by National Science Foundation grant #DMI-0352885 and Office of Naval Research contract #N00014-03-1-0133.

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Zanette, A., Fischetti, M. & Balas, E. Lexicography and degeneracy: can a pure cutting plane algorithm work?. Math. Program. 130, 153–176 (2011). https://doi.org/10.1007/s10107-009-0335-0

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  • DOI: https://doi.org/10.1007/s10107-009-0335-0

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