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Measuring diversity. A review and an empirical analysis

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  • Parreño, Francisco
  • Álvarez-Valdés, Ramón
  • Martí, Rafael

Abstract

Maximum diversity problems arise in many practical settings from facility location to social networks, and constitute an important class of NP-hard problems in combinatorial optimization. There has been a growing interest in these problems in recent years, and different mathematical programming models have been proposed to capture the notion of diversity. They basically consist of selecting a subset of elements of a given set in such a way that a measure based on their pairwise distances is maximized to achieve dispersion or representativeness. In this paper, we perform an exhaustive comparison of four mathematical models to achieve diversity over the public domain library MDPLIB, studying the structure of the solutions obtained with each of them. We extend this library by including new Euclidean instances which permit to analyze the geometrical distribution of the solutions. Our study concludes which models are better suited for dispersion and which ones for representativeness in terms of the structure of their solutions, as well as which instances are difficult to solve. We also identify in our conclusions one of the models which is not recommended in any setting. We finalize by proposing two improvements, one related to the models and one to solving methods. The computational testing shows the value of the analysis and merit of our proposals.

Suggested Citation

  • Parreño, Francisco & Álvarez-Valdés, Ramón & Martí, Rafael, 2021. "Measuring diversity. A review and an empirical analysis," European Journal of Operational Research, Elsevier, vol. 289(2), pages 515-532.
  • Handle: RePEc:eee:ejores:v:289:y:2021:i:2:p:515-532
    DOI: 10.1016/j.ejor.2020.07.053
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    References listed on IDEAS

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    1. Duarte, Abraham & Marti, Rafael, 2007. "Tabu search and GRASP for the maximum diversity problem," European Journal of Operational Research, Elsevier, vol. 178(1), pages 71-84, April.
    2. R. Chandrasekaran & A. Daughety, 1981. "Location on Tree Networks: P -Centre and n -Dispersion Problems," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 50-57, February.
    3. Anna Martínez-Gavara & Vicente Campos & Manuel Laguna & Rafael Martí, 2017. "Heuristic solution approaches for the maximum minsum dispersion problem," Journal of Global Optimization, Springer, vol. 67(3), pages 671-686, March.
    4. Michael B. Teitz, 1968. "Toward A Theory Of Urban Public Facility Location," Papers in Regional Science, Wiley Blackwell, vol. 21(1), pages 35-51, January.
    5. Prokopyev, Oleg A. & Kong, Nan & Martinez-Torres, Dayna L., 2009. "The equitable dispersion problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 59-67, August.
    6. Micael Gallego & Abraham Duarte & Manuel Laguna & Rafael Martí, 2009. "Hybrid heuristics for the maximum diversity problem," Computational Optimization and Applications, Springer, vol. 44(3), pages 411-426, December.
    7. Erkut, Erhan & Neuman, Susan, 1989. "Analytical models for locating undesirable facilities," European Journal of Operational Research, Elsevier, vol. 40(3), pages 275-291, June.
    8. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    9. Şenay Ağca & Burak Eksioglu & Jay B. Ghosh, 2000. "Lagrangian solution of maximum dispersion problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(2), pages 97-114, March.
    10. Martí, Rafael & Gallego, Micael & Duarte, Abraham, 2010. "A branch and bound algorithm for the maximum diversity problem," European Journal of Operational Research, Elsevier, vol. 200(1), pages 36-44, January.
    11. Sayyady, Fatemeh & Fathi, Yahya, 2016. "An integer programming approach for solving the p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 253(1), pages 216-225.
    12. S. S. Ravi & D. J. Rosenkrantz & G. K. Tayi, 1994. "Heuristic and Special Case Algorithms for Dispersion Problems," Operations Research, INFORMS, vol. 42(2), pages 299-310, April.
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