Partial convexification of general MIPs by Dantzig-Wolfe reformulation

  • Authors:

  • Martin Bergner;Alberto Caprara;Fabio Furini;Marco E. Lübbecke;Enrico Malaguti;Emiliano Traversi

  • Affiliations:

  • Chair of Operations Research, RWTH Aachen University, Aachen, Germany;DEIS, Università di Bologna, Bologna, Italy;Chair of Operations Research, RWTH Aachen University, Aachen, Germany;Chair of Operations Research, RWTH Aachen University, Aachen, Germany;DEIS, Università di Bologna, Bologna, Italy;DEIS, Università di Bologna, Bologna, Italy

  • Venue:
  • IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
  • Year:
  • 2011

Quantified Score

Hi-index 0.01

Visualization

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 generalpurpose tool than previously acknowledged by the research community.