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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Vydáno v:Mathematical programming Ročník 149; číslo 1-2; s. 391 - 424
Hlavní autoři: Bergner, Martin, Caprara, Alberto, Ceselli, Alberto, Furini, Fabio, Lübbecke, Marco E., Malaguti, Enrico, Traversi, Emiliano
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2015
Springer Nature B.V
Témata:
Algorithms
Analysis
Automation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Communities
Construction
Decomposition
Estimates
Full Length Paper
Graph coloring
Integer programming
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Mixed integer
Numerical Analysis
Solvers
State of the art
Studies
Theoretical
Matrix re-ordering
Column generation
65K05
Dantzig–Wolfe decomposition
Hypergraph partitioning
Block-diagonal matrix
90C11
Automatic reformulation
49M27
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí: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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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-014-0761-5