Mathematical Programming

, Volume 149, Issue 1–2, pp 391–424 | Cite as

Automatic Dantzig–Wolfe reformulation of mixed integer programs

  • Martin Bergner
  • Alberto Caprara
  • Alberto Ceselli
  • Fabio Furini
  • Marco E. Lübbecke
  • Enrico Malaguti
  • Emiliano Traversi
Full Length Paper Series A

Abstract

Dantzig–Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs). However, the method is not implemented in any state-of-the-art MIP solver as it is considered to require structural problem knowledge and tailoring to this structure. We provide a computational proof-of-concept that the reformulation can be automated. That is, we perform a rigorous experimental study, which results in identifying a score to estimate the quality of a decomposition: after building a set of potentially good candidates, we exploit such a score to detect which decomposition might be useful for Dantzig–Wolfe reformulation of a MIP. We experiment with general instances from MIPLIB2003 and MIPLIB2010 for which a decomposition method would not be the first choice, and demonstrate that strong dual bounds can be obtained from the automatically reformulated model using column generation. Our findings support the idea that Dantzig–Wolfe reformulation may hold more promise as a general-purpose tool than previously acknowledged by the research community.

Keywords

Dantzig–Wolfe decomposition Column generation Block-diagonal matrix Matrix re-ordering Automatic reformulation Hypergraph partitioning 

Mathematics Subject Classification (2000)

90C11 49M27 65K05 

Supplementary material

10107_2014_761_MOESM1_ESM.pdf (1011 kb)
Supplementary material 1 (pdf 1010 KB)

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  • Martin Bergner
    • 1
  • Alberto Caprara
    • 4
  • Alberto Ceselli
    • 2
  • Fabio Furini
    • 3
  • Marco E. Lübbecke
    • 1
  • Enrico Malaguti
    • 4
  • Emiliano Traversi
    • 5
  1. 1.Operations ResearchRWTH Aachen UniversityAachenGermany
  2. 2.Dipartimento di InformaticaUniversità degli Studi di MilanoCremaItaly
  3. 3.LAMSADEUniversité Paris-DauphineParisFrance
  4. 4.DEIUniversità di BolognaBolognaItaly
  5. 5.LIPNÉquipe AOC, Université Paris 13VilletaneuseFrance

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