Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14266
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Main Title: On Compact Formulations for Integer Programs Solved by Column Generation
Author(s): Villeneuve, Daniel
Desrosiers, Jacques
Lübbecke, Marco E.
Soumis, Francois
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15493
http://dx.doi.org/10.14279/depositonce-14266
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: Column generation has become a powerful tool in solving large scale integer programs. It is well known that most of the often reported compatibility issues between pricing subproblem and branching rule disappear when branching decisions are based on imposing constraints on the subproblem's variables. This can be generalized to branching on variables of a so-called compact formulation. We constructively show that such a formulation always exists under mild assumptions. It has a block diagonal structure with identical subproblems, each of which contributes only one column in an integer solution. This construction has an interpretation as reversing a Dantzig-Wolfe decomposition. Our proposal opens the way for the development of branching rules adapted to the subproblem's structure and to the linking constraints.
Subject(s): integer programming
branch and bound
column generation
compact formulations
integer program
Issue Date: 2003
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 90C10 Integer programming
49M27 Decomposition methods
65K05 Mathematical programming algorithms
90C06 Large-scale problems
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2003, 25
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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