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Local search heuristics for multi-index assignment problems with decomposable costs

Author

Listed:
  • H-J Bandelt

    (Universität Hamburg)

  • A Maas

    (Maastricht University)

  • F C R Spieksma

    (Katholieke Universiteit Leuven)

Abstract

The multi-index assignment problem (MIAP) with decomposable costs is a natural generalization of the well-known assignment problem. Applications of the MIAP arise, for instance, in the field of multi-target multi-sensor tracking. We describe an (exponentially sized) neighbourhood for a solution of the MIAP with decomposable costs, and show that one can find a best solution in this neighbourhood in polynomial time. Based on this neighbourhood, we propose a local search algorithm. We empirically test the performance of published constructive heuristics and the local search algorithm on random instances; a straightforward iterated local search algorithm is also tested. Finally, we compute lower bounds to our problem, which enable us to assess the quality of the solutions found.

Suggested Citation

  • H-J Bandelt & A Maas & F C R Spieksma, 2004. "Local search heuristics for multi-index assignment problems with decomposable costs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(7), pages 694-704, July.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:7:d:10.1057_palgrave.jors.2601723
    DOI: 10.1057/palgrave.jors.2601723
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    References listed on IDEAS

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    1. Crama, Yves & Spieksma, Frits C. R., 1992. "Approximation algorithms for three-dimensional assignment problems with triangle inequalities," European Journal of Operational Research, Elsevier, vol. 60(3), pages 273-279, August.
    2. Spieksma, Frits C. R. & Woeginger, Gerhard J., 1996. "Geometric three-dimensional assignment problems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 611-618, June.
    3. William P. Pierskalla, 1968. "Letter to the Editor—The Multidimensional Assignment Problem," Operations Research, INFORMS, vol. 16(2), pages 422-431, April.
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    Cited by:

    1. Walteros, Jose L. & Vogiatzis, Chrysafis & Pasiliao, Eduardo L. & Pardalos, Panos M., 2014. "Integer programming models for the multidimensional assignment problem with star costs," European Journal of Operational Research, Elsevier, vol. 235(3), pages 553-568.
    2. Duc Manh Nguyen & Hoai An Le Thi & Tao Pham Dinh, 2014. "Solving the Multidimensional Assignment Problem by a Cross-Entropy method," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 808-823, May.
    3. Gregory Tauer & Rakesh Nagi & Moises Sudit, 2013. "The graph association problem: Mathematical models and a lagrangian heuristic," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(3), pages 251-268, April.

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