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International Workshop on Hybrid Metaheuristics

HM 2014: Hybrid Metaheuristics pp 155–168Cite as

JAM: A Tabu-Based Two-Stage Simulated Annealing Algorithm for the Multidimensional Arrangement Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8457))

Abstract

In this paper we study a version of the Multidimensional Arrangement Problem (MAP) that embeds a graph into a multidimensional array minimizing the aggregated (Manhattan) distance of the embedded edges. This problem includes the minimum Linear Arrangement Problem (minLA) as a special case, among others. We propose JAM, a tabu-based two-stage simulated annealing heuristic for this problem. Our algorithm relies on existing techniques for the minimum linear arrangement (minLA) problem, which are non-trivially adapted to work in multiple dimensions. Due to the scarcity of specific benchmarks for MAP, we have tested the performance of our algorithm with benchmarks for the minLA and Quadratic Assignment Problems (with more than 80 graphs). For each graph in these benchmarks, we provide results for 1, 2 and 3-dimensional instances of MAP, enlarging, hence, the benchmarking resources for the research community. The results obtained show the practicality of JAM, often matching the best known result and even improving some of them.

This research was supported in part by the Comunidad de Madrid grant S2009TIC-1692, Spanish MICINN grant TEC2011-29688-C02-01, and National Natural Science Foundation of China grant 61020106002.

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Author information

Authors and Affiliations

  1. Universidad Carlos III de Madrid, Madrid, Spain

    Jordi Arjona Aroca

  2. IMDEA Networks Institute, Madrid, Spain

    Antonio Fernández Anta

Authors
  1. Jordi Arjona Aroca
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  2. Antonio Fernández Anta
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Editor information

Editors and Affiliations

  1. Dept. Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Jordi Girona 1-3, edif. Omega, 08034, Barcelona, Spain

    Maria J. Blesa

  2. Dept. of Computer Science, IKERBASQUE and University of the Basque Country, Paseo Manuel Lardizabal 1, 20018, Donostia, Spain

    Christian Blum

  3. Dept. of Business and Informatics, University of Hamburg, Institute of Information Systems, Von-Melle-Park 5, 20146, Hamburg, Germany

    Stefan Voß

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Aroca, J.A., Anta, A.F. (2014). JAM: A Tabu-Based Two-Stage Simulated Annealing Algorithm for the Multidimensional Arrangement Problem. In: Blesa, M.J., Blum, C., Voß, S. (eds) Hybrid Metaheuristics. HM 2014. Lecture Notes in Computer Science, vol 8457. Springer, Cham. https://doi.org/10.1007/978-3-319-07644-7_12

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  • DOI: https://doi.org/10.1007/978-3-319-07644-7_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07643-0

  • Online ISBN: 978-3-319-07644-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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