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Memetic self-adaptive evolution strategies applied to the maximum diversity problem

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Abstract

The maximum diversity problem consists in finding a subset of elements which have maximum diversity between each other. It is a very important problem due to its general aspect, that implies many practical applications such as facility location, genetics, and product design. We propose a method based on evolution strategies with local search and self-adaptation of the parameters. For all time limits from 1 to 300 s as well as for time to converge to the best solutions known, this method leads to better results when compared to other state-of-the-art algorithms.

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Notes

  1. All additional information mentioned in this paper, such as source codes and results, is available from the authors on www.alandefreitas.com/downloads/problem-instances/maximum-diversity-problem.php.

  2. http://www.optsicom.es/mdp.

References

  1. Agrafiotis, D.K.: Stochastic algorithms for maximizing molecular diversity. J. Chem. Inf. Comput. Sci. 37(5), 841–851 (1997). doi:10.1021/ci9700337

    Google Scholar 

  2. Aringhieri, R., Bruglieri, M., Cordone, R.: Optimal results and tight bounds for the maximum diversity problem. Found. Comput. Decision Sci. 34(2), 73–86 (2009)

    MATH  Google Scholar 

  3. Aringhieri, R., Cordone, R.: Comparing local search metaheuristics for the maximum diversity problem. J. Operational Res. Soc. 62(2), 266–280 (2011)

    Article  Google Scholar 

  4. Back, T.: Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, USA (1996)

    Google Scholar 

  5. Berretta, R., Moscato, P.: New ideas in optimization chap. The number partitioning problem: an open challenge for evolutionary computation? pp. 261–278. McGraw-Hill Ltd., UK, Maidenhead, UK, England (1999). http://dl.acm.org/citation.cfm?id=329055.329082

  6. Brimberg, J., Mladenovic, N., Urosevic, D., Ngai, E.: Variable neighborhood search for the heaviest-subgraph. Comput. Operat. Res. 36(11), 2885–2891 (2009). doi:10.1016/j.cor.2008.12.020

    Google Scholar 

  7. Duarte, A., Marti, R.: Tabu search and grasp for the maximum diversity problem. Eur. J. Operational Res. 178(1), 71–84 (2007). doi:10.1016/j.ejor.2006.01.021

    Google Scholar 

  8. Ghosh, J.B.: Computational aspects of the maximum diversity problem. Operat. Res. Lett. 19(4), 175–181 (1996). doi:10.1016/0167-6377(96)00025-9

  9. Glover, F., Kuo, C., Dhir, K.: Heuristic algorithms for the maximum diversity problem. J. Inf. Optimization Sci. 19(1), 109–132 (1998)

    Article  MATH  Google Scholar 

  10. Hansen, P., Mladenović, N.: First vs. best improvement: an empirical study. Discrete Appl. Math. 154(5), 802–817 (2006). doi:10.1016/j.dam.2005.05.020

  11. Kuo, C.C., Glover, F., Dhir, K.S.: Analyzing and modeling the maximum diversity problem by zero-one programming. Decision Sci. 24(6), 1171–1185 (1993). doi:10.1111/j.1540-5915.1993.tb00509.x

    Google Scholar 

  12. Lozano, M., Molina, D., Garcí-a-Martí-nez, C.: Iterated greedy for the maximum diversity problem. Eur. J. Operational Res. 214(1), 31–38 (2011). doi:10.1016/j.ejor.2011.04.018

    Google Scholar 

  13. Martí, R., Gallego, M., Duarte, A.: A branch and bound algorithm for the maximum diversity problem. Eur. J. Operational Res. 200(1), 36–44 (2010). doi:10.1016/j.ejor.2008.12.023

  14. Martí, R., Gallego, M., Duarte, A., Pardo, E.: Heuristics and metaheuristics for the maximum diversity problem. J. Heuristics 1–25 (2011). doi:10.1007/s10732-011-9172-4

  15. Palubeckis, G.: Iterated tabu search for the maximum diversity problem. Appl. Math. Comput. 189(1), 371–383 (2007). doi:10.1016/j.amc.2006.11.090

    Google Scholar 

  16. Resende, M., Martí, R., Gallego, M., Duarte, A.: Grasp and path relinking for the max-min diversity problem. Comput. Operat. Res. 37(3), 498–508 (2010). doi:10.1016/j.cor.2008.05.011 (Metaheuristics)

  17. Resende, M.G.C., Ribeiro, C.C., Glover, F., Martí, R.: Scatter search and path-relinking: Fundamentals, advances, and applications. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics, International Series in Operations Research and Management Science, vol. 146, pp. 87–107. Springer US (2010). doi:10.1007/978-1-4419-1665-5_4

  18. Silva, G., Ochi, L., Martins, S.: Experimental comparison of greedy randomized adaptive search procedures for the maximum diversity problem. In: Ribeiro, C., Martins, S. (eds.) Experimental and Efficient Algorithms, Lecture Notes in Computer Science, vol. 3059, pp. 498–512. Springer, Heidelberg (2004). doi:10.1007/978-3-540-24838-5_37

  19. Silva, G.C., Andrade, M.R., Ochi, L.S., Martins, S.L., Plastino, A.: New heuristics for the maximum diversity problem. J. Heuristics 13(4), 315–336 (2007). doi:10.1007/s10732-007-9010-x

    Google Scholar 

  20. Wang, J., Zhou, Y., Cai, Y., Yin, J.: Learnable tabu search guided by estimation of distribution for maximum diversity problems. Soft Computing 16(4), 711–728 (2012). doi:10.1007/s00500-011-0780-6

    Google Scholar 

  21. Wang, J., Zhou, Y., Yin, J., Zhang, Y.: Competitive hopfield network combined with estimation of distribution for maximum diversity problems. Trans. Sys. Man Cyber. Part B 39(4), 1048–1066 (2009). doi:10.1109/TSMCB.2008.2010220

    Google Scholar 

  22. Weitz, R., Lakshminarayanan, S.: An empirical comparison of heuristic and graph theoretic methods for creating maximally diverse groups, vlsi design, and exam scheduling. Omega 25(4), 473–482 (1997). doi:10.1016/S0305-0483(97)00007-8

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Acknowledgments

We sincerely thank the reviewers for their valuable contribution to this paper. This work has been supported by the Brazilian agencies CAPES, CNPq, and FAPEMIG; and the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme.

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Authors and Affiliations

  1. UFMG, Belo Horizonte, Brazil

    Alan Robert Resende de Freitas, Frederico Gadelha Guimarães & Rodrigo César Pedrosa Silva

  2. UFOP, Ouro Preto, Brazil

    Marcone Jamilson Freitas Souza

Authors
  1. Alan Robert Resende de Freitas
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  2. Frederico Gadelha Guimarães
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  3. Rodrigo César Pedrosa Silva
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  4. Marcone Jamilson Freitas Souza
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Correspondence to Alan Robert Resende de Freitas.

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de Freitas, A.R.R., Guimarães, F.G., Pedrosa Silva, R.C. et al. Memetic self-adaptive evolution strategies applied to the maximum diversity problem. Optim Lett 8, 705–714 (2014). https://doi.org/10.1007/s11590-013-0610-0

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