Partial Convexification of General MIPs by Dantzig-Wolfe Reformulation

  • Martin Bergner
  • Alberto Caprara
  • Fabio Furini
  • Marco E. Lübbecke
  • Enrico Malaguti
  • Emiliano Traversi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6655)

Abstract

Dantzig-Wolfe decomposition is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs) in practice. However, the method is not implemented in any state-of-the-art MIP solver: it needs tailoring to the particular problem; the decomposition must be determined from the typical bordered block-diagonal matrix structure; the resulting column generation subproblems must be solved efficiently; etc. We provide a computational proof-of-concept that the process can be automated in principle, and that strong dual bounds can be obtained on general MIPs for which a solution by a decomposition has not been the first choice. We perform an extensive computational study on the 0-1 dynamic knapsack problem (without block-diagonal structure) and on general MIPLIB2003 instances. Our results support that Dantzig-Wolfe reformulation may hold more promise as a general-purpose tool than previously acknowledged by the research community.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin Bergner
    • 1
  • Alberto Caprara
    • 2
  • Fabio Furini
    • 1
  • Marco E. Lübbecke
    • 1
  • Enrico Malaguti
    • 2
  • Emiliano Traversi
    • 2
  1. 1.Chair of Operations ResearchRWTH Aachen UniversityAachenGermany
  2. 2.DEISUniversità di BolognaBolognaItaly

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