Journal of Heuristics

, Volume 19, Issue 4, pp 591–615 | Cite as

Heuristics and metaheuristics for the maximum diversity problem

  • Rafael Martí
  • Micael Gallego
  • Abraham Duarte
  • Eduardo G. Pardo


This paper presents extensive computational experiments to compare 10 heuristics and 20 metaheuristics for the maximum diversity problem (MDP). This problem consists of selecting a subset of maximum diversity from a given set of elements. It arises in a wide range of real-world settings and we can find a large number of studies, in which heuristic and metaheuristic methods are proposed. However, probably due to the fact that this problem has been referenced under different names, we have only found limited comparisons with a few methods on some sets of instances.

This paper reviews all the heuristics and metaheuristics for finding near-optimal solutions for the MDP. We present the new benchmark library MDPLIB, which includes most instances previously used for this problem, as well as new ones, giving a total of 315. We also present an exhaustive computational comparison of the 30 methods on the MDPLIB. Non-parametric statistical tests are reported in our study to draw significant conclusions.


Heuristic optimization Quadratic binary problem Metaheuristics 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Rafael Martí
    • 1
  • Micael Gallego
    • 2
  • Abraham Duarte
    • 2
  • Eduardo G. Pardo
    • 2
  1. 1.Departamento de Estadística e Investigación OperativaUniversidad de ValenciaValenciaSpain
  2. 2.Departamento de Ciencias de la ComputaciónUniversidad Rey Juan CarlosMadridSpain

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