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International Conference on Operations Research and Enterprise Systems

ICORES 2014: Operations Research and Enterprise Systems pp 95–107Cite as

Adjacency Variables Formulation for the Minimum Linear Arrangement Problem

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 509))

Abstract

We present a new integer linear formulation using \(O(n^2)\) variables, called adjacency variables, to solve the Minimum Linear Arrangement problem (MinLA). We give a couple of valid equalities and inequalities for this formulation, some of them deriving from on a new general partitioning approach that is not limited to our formulation. We numerically tested the lower bound provided by the linear relaxation using instances of the matrix market library. Our results are compare with the best known lower bounds, in terms of quality, as well computing times.

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Notes

  1. 1.

    http://math.nist.gov/MatrixMarket/.

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Acknowledgements

This work was financially supported by the region of Haute- Normandie (France) and the European Union. This support is gratefully acknowledged.

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Authors and Affiliations

  1. Laboratoire d’Informatique d’Avignon (LIA), 339, chemin des Meinajaries, Agroparc, B.P. 91228, 84911, Avignon Cedex 9, France

    Serigne Gueye

  2. Laboratoire de Mathmatiques Appliques du Havre (LMAH), 25 rue Philippe Lebon, B.P. 540, Le Havre Cedex, France

    Sophie Michel

  3. Centre de Recherche en Informatique de Lens (CRIL), Rue Jean Souvraz, SP 18, 62307, Lens Cedex, France

    Mahdi Moeini

  4. Chair of Business Information Systems and Operations Research (BISOR), Technical University of Kaiserslautern, Postfach 3049, Erwin-Schroedinger-Str., Room 42-426, D-67653, Kaiserslautern, Germany

    Mahdi Moeini

Authors
  1. Serigne Gueye
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  2. Sophie Michel
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  3. Mahdi Moeini
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Corresponding author

Correspondence to Serigne Gueye .

Editor information

Editors and Affiliations

  1. IMA, LISA, Angers, France

    Eric Pinson

  2. Polytechnic Institute of Setúbal, Setúbal, Portugal

    Fernando Valente

  3. Complutense University, Madrid, Spain

    Begoña Vitoriano

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Gueye, S., Michel, S., Moeini, M. (2015). Adjacency Variables Formulation for the Minimum Linear Arrangement Problem. In: Pinson, E., Valente, F., Vitoriano, B. (eds) Operations Research and Enterprise Systems. ICORES 2014. Communications in Computer and Information Science, vol 509. Springer, Cham. https://doi.org/10.1007/978-3-319-17509-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-17509-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17508-9

  • Online ISBN: 978-3-319-17509-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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