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Landscape properties of the very large-scale and the variable neighborhood search metaheuristics for the multidimensional assignment problem

Author

Listed:
  • Alla Kammerdiner

    (Eglin Air Force Base)

  • Alexander Semenov

    (The University of Florida Research and Engineering Educational Facility (REEF)
    University of Florida)

  • Eduardo L. Pasiliao

    (Eglin Air Force Base)

Abstract

We study the recent metaheuristic search algorithm for the multidimensional assignment problem (MAP) using fitness landscape theory. The analyzed algorithm performs a very large-scale neighborhood search on a set of feasible solutions to the problem. We derive properties of the landscape graphs that represent these very large-scale search algorithms acting on the solutions of the MAP. In particular, we show that the search graph is a generalization of a hypercube. We extend and generalize the original very large-scale neighborhood search to develop the variable neighborhood search. The new search is capable of searching even larger large-scale neighborhoods. We perform numerical analyses of the search graph structures for various problem instances of the MAP and different neighborhood structures of the MAP algorithm based on a very large-scale search. We also investigate the correlation between fitness (i.e., objective values) and distance (i.e., path lengths) of the local minima (i.e., sinks of the landscape). Our results can be used to design improved search-based metaheuristics for the MAP.

Suggested Citation

  • Alla Kammerdiner & Alexander Semenov & Eduardo L. Pasiliao, 2024. "Landscape properties of the very large-scale and the variable neighborhood search metaheuristics for the multidimensional assignment problem," Journal of Global Optimization, Springer, vol. 88(3), pages 653-683, March.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:3:d:10.1007_s10898-023-01285-w
    DOI: 10.1007/s10898-023-01285-w
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    References listed on IDEAS

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    1. Kammerdiner, A.R. & Pasiliao, E.L., 2014. "In and out forests on combinatorial landscapes," European Journal of Operational Research, Elsevier, vol. 236(1), pages 78-84.
    2. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    3. Terry Jones & Stephanie Forrest, 1995. "Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms," Working Papers 95-02-022, Santa Fe Institute.
    4. Daolio, Fabio & Tomassini, Marco & Vérel, Sébastien & Ochoa, Gabriela, 2011. "Communities of minima in local optima networks of combinatorial spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1684-1694.
    5. 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. Ilias Kotsireas & Panos Pardalos & Julius Žilinskas, 2024. "Preface," Journal of Global Optimization, Springer, vol. 88(3), pages 531-532, March.

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