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Sparsity of Lift-and-Project Cutting Planes

In: Operations Research Proceedings 2012

Author

Listed:
  • Matthias Walter

    (Otto-von-Guericke Universität Magdeburg)

Abstract

It is well-known that sparsity (i.e. having only a few nonzero coefficients) is a desirable property for cutting planes in mixed-integer programming. We show that on the MIPLIB 2003 problem instance set, using only 10 very dense cutting planes (compared to thousands of constraints in a model), leads to a run time increase of 25 % on average for the LP-solver. We introduce the concept of dual sparsity (a property of the row-multipliers of the cut) and show a strong correlation between dual and primal (the usual) sparsity. Lift-and-project cuts crucially depend on the choice of a so-called normalization, of which we compared several known ones with respect to their actual and possible sparsity. Then a new normalization is tested that improves the dual (and hence the primal) sparsity of the generated cuts.

Suggested Citation

  • Matthias Walter, 2014. "Sparsity of Lift-and-Project Cutting Planes," Operations Research Proceedings, in: Stefan Helber & Michael Breitner & Daniel Rösch & Cornelia Schön & Johann-Matthias Graf von der Schu (ed.), Operations Research Proceedings 2012, edition 127, pages 9-14, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-00795-3_2
    DOI: 10.1007/978-3-319-00795-3_2
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    Cited by:

    1. John Alasdair Warwicker & Steffen Rebennack, 2022. "A Comparison of Two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1042-1047, March.

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