Column-generation in integer linear programming

Nelson Maculan; Marcos de Mendonça Passini; José André de Moura Brito; Irene Loiseau[1]

  • [1] Departamento de Computación – Facultad de Ciencias Exactas y Naturales – Universidad de Buenos Aires, Argentina; Partially supported by grants UBACYT EX036, CONICET 644/98.

RAIRO - Operations Research - Recherche Opérationnelle (2003)

  • Volume: 37, Issue: 2, page 67-83
  • ISSN: 0399-0559

Abstract

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We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this approach to a telecommunications network planning problem.

How to cite

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Maculan, Nelson, et al. "Column-generation in integer linear programming." RAIRO - Operations Research - Recherche Opérationnelle 37.2 (2003): 67-83. <http://eudml.org/doc/245751>.

@article{Maculan2003,
abstract = {We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this approach to a telecommunications network planning problem.},
affiliation = {Departamento de Computación – Facultad de Ciencias Exactas y Naturales – Universidad de Buenos Aires, Argentina; Partially supported by grants UBACYT EX036, CONICET 644/98.},
author = {Maculan, Nelson, Passini, Marcos de Mendonça, Brito, José André de Moura, Loiseau, Irene},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {column-generation; integer programming; branch-and-price; column generation},
language = {eng},
number = {2},
pages = {67-83},
publisher = {EDP-Sciences},
title = {Column-generation in integer linear programming},
url = {http://eudml.org/doc/245751},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Maculan, Nelson
AU - Passini, Marcos de Mendonça
AU - Brito, José André de Moura
AU - Loiseau, Irene
TI - Column-generation in integer linear programming
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 2
SP - 67
EP - 83
AB - We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this approach to a telecommunications network planning problem.
LA - eng
KW - column-generation; integer programming; branch-and-price; column generation
UR - http://eudml.org/doc/245751
ER -

References

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