GRASP with Path-Relinking for the Maximum Diversity Problem

  • Marcos R. Q. de Andrade
  • Paulo M. F. de Andrade
  • Simone L. Martins
  • Alexandre Plastino
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)


The Maximum Diversity Problem (MDP) consists in identifying, in a population, a subset of elements, characterized by a set of attributes, that present the most diverse characteristics between themselves. The identification of such solution is an NP-hard problem. This paper presents a GRASP heuristic associated with the path-relinking technique developed to obtain high-quality solutions for this problem in a competitive computational time. Experimental results illustrate the effectiveness of using the path-relinking method to improve results generated by pure GRASP.


Local Search Subset Size Restricted Candidate List Adaptive Search Procedure Grasp Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Aiex, R.M., Resende, M.G.C., Ribeiro, C.C.: Probability distribution of solution time in GRASP: An experimental investigation. J. of Heuristics 8, 343–373 (2002)zbMATHCrossRefGoogle Scholar
  2. 2.
    Andrade, P.M.F., Plastino, A., Ochi, L.S., Martins, S.L.: GRASP for the Maximum Diversity Problem. In: Procs. of MIC 2003. CD-ROM Paper: MIC03_15 (2003)Google Scholar
  3. 3.
    Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. of Global Optimization 6, 109–133 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Ghosh, J.B.: Computational aspects of the maximum diversity problem. Operations Research Letters 19, 175–181 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Glover, F., Laguna, M., Marti, R.: Fundamentals of scatter search and path-relinking. Control and Cybernetics 19, 653–684 (1977)MathSciNetGoogle Scholar
  6. 6.
    Glover, F., Hersh, G., McMillan, C.: Selecting subsets of maximum diversity, MS/IS Report No. 77-9, University of Colorado at Boulder (1977)Google Scholar
  7. 7.
    Glover, F., Kuo, C.-C., Dhir, K.S.: Integer programming and heuristic approaches to the minimum diversity problem. J. of Bus. and Management 4, 93–111 (1996)Google Scholar
  8. 8.
    Kochenberger, G., Glover, F.: Diversity data mining. Working Paper. The University of Mississipi (1999)Google Scholar
  9. 9.
    Resende, M.G.C., Ribeiro, C.C.: GRASP with path-relinking: Recent advances and applications. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Metaheuristics: Progress as Real Problem Solvers, pp. 29–63 (2005)Google Scholar
  10. 10.
    Ribeiro, C.C., Uchoa, E., Werneck, R.F.: A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS J. on Computing 14, 228–246 (2002)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Silva, G.C., Ochi, L.S., Martins, S.L.: Experimental comparison of greedy randomized adaptive search procedures for the maximum diversity problem. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004, vol. 3059, pp. 498–512. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Weitz, R., Lakshminarayanan, S.: An empirical comparison of heuristic methods for creating maximally diverse groups. J. of the Op. Res. Soc. 49, 635–646 (1998)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Marcos R. Q. de Andrade
    • 1
  • Paulo M. F. de Andrade
    • 1
  • Simone L. Martins
    • 1
  • Alexandre Plastino
    • 1
  1. 1.Departamento de Ciência da ComputaçãoUniversidade Federal FluminenseNiteróiBrazil

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