Automatic Dantzig–Wolfe reformulation of mixed integer programsReport as inadecuate

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1 RWTH Aachen University 2 D.E.I. - University of Bologna. 3 Università degli Studi di Milano 4 LAMSADE - Laboratoire d-analyse et modélisation de systèmes pour l-aide à la décision 5 LIPN - Laboratoire d-Informatique de Paris-Nord

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

Author: Martin Bergner - Alberto Caprara - Alberto Ceselli - Fabio Furini - Marco E. Lübbecke - Enrico Malaguti - Emiliano Traversi -



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