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Complexity of Solutions Combination for the Three-Index Axial Assignment Problem

Author

Listed:
  • Lev G. Afraimovich

    (Institute of Information Technology, Mathematics and Mechanics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia)

  • Maxim D. Emelin

    (Institute of Information Technology, Mathematics and Mechanics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603022, Russia)

Abstract

In this work we consider the NP-hard three-index axial assignment problem. We formulate and investigate a problem of combining feasible solutions. Such combination can be applied in a wide range of heuristic and approximate algorithms for solving the assignment problem, instead of the commonly used strategy of selecting the best solution among the found feasible solutions. We discuss approaches to a solution of the combination problem and prove that it becomes NP-hard already in the case of combining four solutions.

Suggested Citation

  • Lev G. Afraimovich & Maxim D. Emelin, 2022. "Complexity of Solutions Combination for the Three-Index Axial Assignment Problem," Mathematics, MDPI, vol. 10(7), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1062-:d:779720
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    References listed on IDEAS

    as
    1. Egon Balas & Matthew J. Saltzman, 1991. "An Algorithm for the Three-Index Assignment Problem," Operations Research, INFORMS, vol. 39(1), pages 150-161, February.
    2. 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.
    3. Huang, Gaofeng & Lim, Andrew, 2006. "A hybrid genetic algorithm for the Three-Index Assignment Problem," European Journal of Operational Research, Elsevier, vol. 172(1), pages 249-257, July.
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