Automatic Dantzig–Wolfe reformulation of mixed integer programs
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 th...
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| Vydané v: | Mathematical programming Ročník 149; číslo 1-2; s. 391 - 424 |
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| Hlavní autori: | , , , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.02.2015
Springer Nature B.V |
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| ISSN: | 0025-5610, 1436-4646 |
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| 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. |
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| AbstractList | 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. |
| Author | Caprara, Alberto Malaguti, Enrico Bergner, Martin Traversi, Emiliano Furini, Fabio Ceselli, Alberto Lübbecke, Marco E. |
| Author_xml | – sequence: 1 givenname: Martin surname: Bergner fullname: Bergner, Martin organization: Operations Research, RWTH Aachen University – sequence: 2 givenname: Alberto surname: Caprara fullname: Caprara, Alberto organization: DEI, Università di Bologna – sequence: 3 givenname: Alberto surname: Ceselli fullname: Ceselli, Alberto organization: Dipartimento di Informatica, Università degli Studi di Milano – sequence: 4 givenname: Fabio surname: Furini fullname: Furini, Fabio organization: LAMSADE, Université Paris-Dauphine – sequence: 5 givenname: Marco E. surname: Lübbecke fullname: Lübbecke, Marco E. email: marco.luebbecke@rwth-aachen.de organization: Operations Research, RWTH Aachen University – sequence: 6 givenname: Enrico surname: Malaguti fullname: Malaguti, Enrico organization: DEI, Università di Bologna – sequence: 7 givenname: Emiliano surname: Traversi fullname: Traversi, Emiliano organization: LIPN, Équipe AOC, Université Paris 13 |
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| Keywords | Matrix re-ordering Column generation 65K05 Dantzig–Wolfe decomposition Hypergraph partitioning Block-diagonal matrix 90C11 Automatic reformulation 49M27 |
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