NEO 2016 pp 183-202 | Cite as

A New Local Search Heuristic for the Multidimensional Assignment Problem

  • Sergio Luis  Pérez Pérez
  • Carlos E. Valencia
  • Francisco Javier Zaragoza Martínez
Part of the Studies in Computational Intelligence book series (SCI, volume 731)


The Multidimensional Assignment Problem (MAP) is a natural extension of the well-known assignment problem. The most studied case of the MAP is the 3-dimensional Assignment Problem (3AP), though in recent years some local search heuristics and a memetic algorithm were proposed for the general case. Until now, a memetic algorithm has been proven to be the best-known option to solve MAP instances and it uses some procedures called dimensionwise variation heuristics as part of the improvement of individuals. We propose a new local search heuristic, based on ideas from dimensionwise variation heuristics, which consider a bigger space of neighborhoods, providing higher quality solutions for the MAP. Our main contribution is a generalization of several local search heuristics known from the literature, the conceptualization of a new one, and the application of exact techniques to find local optimum solutions at its neighborhoods. The results of computational evaluation show how our heuristic outperforms the previous local search heuristics and its competitiveness against a state-of-the-art memetic algorithm.


Multidimensional assignment problem Local search Exact technique Heuristic Neighborhood 



We would like to thank to M. Saltzman who provided us with the instances used for him and E. Balas many years ago and, for show us his interest in the work that we are doing about this problem. We also want to thank to D. Karapetyan and G. Gutin who provided us with the instances that they used at both of their papers of 2011 about the MAP and, for provided us with the source code that they used for the generation of such families of instances, which was also very useful to accomplish this work. A special thanks to M. Vargas for provided us with a state-of-the-art implementation that solves 2AP through an auction algorithm. Finally, we also thank to the Mexican institutions Conacyt and Comecyt who supported to the realization of this researching work.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Sergio Luis  Pérez Pérez
    • 1
  • Carlos E. Valencia
    • 2
  • Francisco Javier Zaragoza Martínez
    • 3
  1. 1.Posgrado en OptimizaciónUniversidad Autónoma Metropolitana AzcapotzalcoMexico CityMexico
  2. 2.Departamento de MatemáticasCentro de Investigación y de Estudios Avanzados del IPNMexico CityMexico
  3. 3.Departamento de SistemasUniversidad Autónoma Metropolitana AzcapotzalcoMexico CityMexico

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