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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.

Keywords

Knapsack Problem Valid Inequality Coupling Constraint Dual Bound Dummy Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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