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Very Large-Scale Neighborhood Search for the Multidimensional Assignment Problem

In: Optimization Methods and Applications

Author

Listed:
  • Alla R. Kammerdiner

    (New Mexico State University)

  • Charles F. Vaughan

    (Joint Navigation Warfare Center)

Abstract

The multidimensional assignment problem is an extension of the linear assignment problem to higher dimensions. This NP-hard problem in combinatorial optimization has applications in scheduling, multiple target tracking, and healthcare. In combinatorial optimization, algorithms utilizing very large-scale neighborhood search are proven to be particularly effective for some computationally difficult problems. In this chapter, we present two such algorithms, which are some of the first proposed for this problem in the literature. The two algorithms are distinct. One uses theory of cyclic transfers to construct and exploit the improvement graph. Another relies on polynomial schemes for finding optimal permutation. Because both methods depend on multiple restarts for effective exploration of search space, we propose and discuss some new multi-start strategies motivated by the design of experiments.

Suggested Citation

  • Alla R. Kammerdiner & Charles F. Vaughan, 2017. "Very Large-Scale Neighborhood Search for the Multidimensional Assignment Problem," Springer Optimization and Its Applications, in: Sergiy Butenko & Panos M. Pardalos & Volodymyr Shylo (ed.), Optimization Methods and Applications, pages 251-262, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-68640-0_12
    DOI: 10.1007/978-3-319-68640-0_12
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    Cited by:

    1. Alla Kammerdiner & Alexander Semenov & Eduardo L. Pasiliao, 2022. "Multidimensional Assignment Problem for Multipartite Entity Resolution," Journal of Global Optimization, Springer, vol. 84(2), pages 491-523, October.

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