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Automatic Dantzig-Wolfe Reformulation of Mixed Integer Programs

Martin Bergner (bergner***at***or.rwth-aachen.de)
Alberto Caprara (***at***)
Alberto Ceselli (alberto.ceselli***at***unimi.it)
Fabio Furini (fabio.furini***at***unibo.it)
Marco Lübbecke (marco.luebbecke***at***rwth-aachen.de)
Enrico Malaguti (enrico.malaguti***at***unibo.it)
Emilio Traversi (emiliano.traversi***at***math.tu-dortmund.de)

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

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Citation: Accepted to mathematical programming.

Download: [PDF]

Entry Submitted: 09/21/2012
Entry Accepted: 09/22/2012
Entry Last Modified: 11/08/2013

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