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.
@article{RO_2003__37_2_67_0,
author = {Maculan, Nelson and Passini, Marcos de Mendon\c{c}a and Brito, Jos\'e Andr\'e de Moura and Loiseau, Irene},
title = {Column-generation in integer linear programming},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {67--83},
publisher = {EDP-Sciences},
volume = {37},
number = {2},
year = {2003},
doi = {10.1051/ro:2003014},
mrnumber = {2010413},
zbl = {1036.90076},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro:2003014/}
}
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 SP - 67 EP - 83 VL - 37 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2003014/ DO - 10.1051/ro:2003014 LA - en ID - RO_2003__37_2_67_0 ER -
%0 Journal Article %A Maculan, Nelson %A Passini, Marcos de Mendonça %A Brito, José André de Moura %A Loiseau, Irene %T Column-generation in integer linear programming %J RAIRO - Operations Research - Recherche Opérationnelle %D 2003 %P 67-83 %V 37 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2003014/ %R 10.1051/ro:2003014 %G en %F RO_2003__37_2_67_0
Maculan, Nelson; Passini, Marcos de Mendonça; Brito, José André de Moura; Loiseau, Irene. Column-generation in integer linear programming. RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 2, pp. 67-83. doi : 10.1051/ro:2003014. http://archive.numdam.org/articles/10.1051/ro:2003014/
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