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Heuristic solution approaches for the maximum minsum dispersion problem

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Abstract

The Maximum Minsum Dispersion Problem (Max-Minsum DP) is a strongly NP-Hard problem that belongs to the family of equitable dispersion problems. When dealing with dispersion, the operations research literature has focused on optimizing efficiency-based objectives while neglecting, for the most part, measures of equity. The most common efficiency-based functions are the sum of the inter-element distances or the minimum inter-element distance. Equitable dispersion problems, on the other hand, attempt to address the balance between efficiency and equity when selecting a subset of elements from a larger set. The objective of the Max-Minsum DP is to maximize the minimum aggregate dispersion among the chosen elements. We develop tabu search and GRASP solution procedures for this problem and compare them against the best in the literature. We also apply LocalSolver, a commercially available black-box optimizer, to compare our results. Our computational experiments show that we are able to establish new benchmarks in the solution of the Max-Minsum DP.

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Acknowledgments

This research has been partially supported by the Ministerio de Economía y Competitividad of Spain (Grant Refs. TIN2012-35632-C02 and TIN2015-65460-C2), the Generalitat Valenciana (ACOMP/2014/A/241 and Prometeo 2013/049), and the University of Valencia (UV-INV-PRECOMP13-115334).

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de Valencia, Valencia, Spain

    Anna Martínez-Gavara, Vicente Campos & Rafael Martí

  2. Leeds School of Business, University of Colorado Boulder, Boulder, CO, USA

    Manuel Laguna

Authors
  1. Anna Martínez-Gavara
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  2. Vicente Campos
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  3. Manuel Laguna
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  4. Rafael Martí
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Correspondence to Rafael Martí.

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Martínez-Gavara, A., Campos, V., Laguna, M. et al. Heuristic solution approaches for the maximum minsum dispersion problem. J Glob Optim 67, 671–686 (2017). https://doi.org/10.1007/s10898-016-0429-1

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  • DOI: https://doi.org/10.1007/s10898-016-0429-1

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