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DOI: 10.4230/OASIcs.ATMOS.2013.137

Column Generation for Bi-Objective Vehicle Routing Problems with a Min-Max Objective

Authors: Boadu Mensah Sarpong, Christian Artigues, and Nicolas Jozefowiez

Published in: OASIcs, Volume 33, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2013)

Abstract

Column generation has been very useful in solving single objective vehicle routing problems (VRPs). Its role in a branch-and-price algorithm is to compute a lower bound which is then used in a branch-and-bound framework to guide the search for integer solutions. In spite of the success of the method, only a few papers treat its application to multi-objective problems and this paper seeks to contribute in this respect. We study how good lower bounds for bi-objective VRPs in which one objective is a min-max function can be computed by column generation. A way to model these problems as well as a strategy to effectively search for columns are presented. We apply the ideas to two VRPs and our results show that strong lower bounds for this class of problems can be obtained in "reasonable" times if columns are intelligently managed. Moreover, the quality of the bounds obtained from the proposed model are significantly better than those obtained from the corresponding "standard" approach.

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Boadu Mensah Sarpong, Christian Artigues, and Nicolas Jozefowiez. Column Generation for Bi-Objective Vehicle Routing Problems with a Min-Max Objective. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 33, pp. 137-149, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{sarpong_et_al:OASIcs.ATMOS.2013.137,
  author =	{Sarpong, Boadu Mensah and Artigues, Christian and Jozefowiez, Nicolas},
  title =	{{Column Generation for Bi-Objective Vehicle Routing Problems with a Min-Max Objective}},
  booktitle =	{13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{137--149},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-58-3},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{33},
  editor =	{Frigioni, Daniele and Stiller, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2013.137},
  URN =		{urn:nbn:de:0030-drops-42500},
  doi =		{10.4230/OASIcs.ATMOS.2013.137},
  annote =	{Keywords: Multi-objective optimization, column generation, integer programming, vehicle routing}
}

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Column Generation for Bi-Objective Vehicle Routing Problems with a Min-Max Objective

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