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Journal of Heuristics

, Volume 25, Issue 4–5, pp 731–752 | Cite as

An effective multi-wave algorithm for solving the max-mean dispersion problem

  • Jiawei Song
  • Yang WangEmail author
  • Haibo Wang
  • Qinghua Wu
  • Abraham P. Punnen
Article
  • 113 Downloads

Abstract

We propose an effective multi-wave algorithm organized in multiple search phases for the max-mean dispersion problem, which offers enhancement of neighborhood search algorithms by incorporating the notion of persistent attractiveness in memory based strategies. In each wave, a vertical phase and a horizontal phase are first alternated to reach a boundary solution. Then a concluding horizontal phase is executed to search around this boundary solution for further solution refinement. Finally, an oscillation phase and a diversified initial solution generation phase focus on search diversification to build well-diversified initial solutions for subsequent waves and passes. Experimental results show that the proposed approach performs quite competitive with state-of-the-art algorithms in the literature. Additional analysis discloses the benefits of the key ingredients in the proposed algorithm.

Keywords

Multi-wave algorithm Local search Adaptive memory Dispersion problems 

Notes

Acknowledgements

We are grateful to the reviewers whose comments have helped to improve our paper. This work was supported by the National Natural Science Foundation of China (Grant No. 71501157).

References

  1. Amirgaliyeva, Z., Mladenović, N., Todosijević, R.: Solving the maximum min-sum dispersion by alternating formulations of two different problems. Eur. J. Oper. Res. 260(2), 444–459 (2017)MathSciNetzbMATHGoogle Scholar
  2. Aringhieri, R., Cordone, R.: Comparing local search metaheuristics for the maximum diversity problem. J. Oper. Res. Soc. 62, 266–280 (2011)Google Scholar
  3. Aringhieri, R., Cordone, R., Melzani, Y.: Tabu Search versus GRASP for the maximum diversity problem. 4OR 6(1), 45–60 (2008)MathSciNetzbMATHGoogle Scholar
  4. Aringhieri, R., Cordone, R., Grosso, A.: Construction and improvement algorithms for dispersion problems. Eur. J. Oper. Res. 242(1), 1–13 (2014)MathSciNetzbMATHGoogle Scholar
  5. Brimberg, J., Mladenović, N., Todosijević, R., Urošević, D.: Less is more: solving the max-mean diversity problem with variable neighborhood search. Inf. Sci. 382, 179–200 (2017)Google Scholar
  6. Brimberg, J., Mladenović, N., Todosijević, R., Urošević, D.: A basic variable neighborhood search heuristic for the uncapacitated multiple allocation phub center problem. Optim. Lett. 11(2), 313–327 (2017)MathSciNetzbMATHGoogle Scholar
  7. Carrasco, R., Pham, A., Gallego, M., Gortázar, F., Martí, R., Duarte, A.: Tabu search for the MaxCMean dispersion problem. Knowl.-Based Syst. 85, 256–264 (2015)Google Scholar
  8. Della, C.F., Grosso, A., Locatelli, M.: A heuristic approach for the max-min diversity problem based on max-clique. Comput. Oper. Res. 36(8), 2429–2433 (2009)MathSciNetzbMATHGoogle Scholar
  9. Della, C.F., Garraffa, M., Salassa, F.: A hybrid three-phase approach for the max-mean dispersion problem. Comput. Oper. Res. 71, 16–22 (2016)MathSciNetzbMATHGoogle Scholar
  10. Duarte, A., Martí, R.: Tabu search and grasp for the maximum diversity problem. Eur. J. Oper. Res. 178(1), 71–84 (2007)MathSciNetzbMATHGoogle Scholar
  11. Duarte, A., Sánchez-Oro, J., Resende, M.G.C., Glover, F., Martí, R.: Greedy randomized search procedure with exterior path relinking for differential dispersion minimization. Inf. Sci. 296(1), 46–60 (2014)MathSciNetGoogle Scholar
  12. Galinier, P., Boujbel, Z., Fernandes, M.C.: An efficient memetic algorithm for the graph partitioning problem. Ann. Oper. Res. 191(1), 1–22 (2011)MathSciNetzbMATHGoogle Scholar
  13. Glover, F.: Multi-wave algorithms for metaheuristic optimization. J. Heurist. 22, 331–358 (2016)Google Scholar
  14. Glover, F., Kuo, C.C., Dhir, K.S.: Heuristic algorithms for the maximum diversity problem. J. Inf. Optim. Sci. 19(1), 109–132 (1998)zbMATHGoogle Scholar
  15. Kerchove, C., Dooren, P.V.: The page trust algorithm: how to rank web pages when negative links are allowed? In: Proceedings SIAM International Conference on Data Mining, pp. 346–352 (2008)Google Scholar
  16. Lai, X., Hao, J.K.: A tabu based memetic algorithm for the max-mean dispersion problem. Comput. Oper. Res. 72, 118–127 (2016)zbMATHGoogle Scholar
  17. Martí, R., Sandoya, F.: GRASP and path relinking for the equitable dispersion problem. Comput. Oper. Res. 40, 3091–3099 (2013)MathSciNetzbMATHGoogle Scholar
  18. Martí, R., Gallego, M., Duarte, A., Pardo, E.G.: Heuristics and metaheuristics for the maximum diversity problem. J. Heurist. 19(4), 591–615 (2013)Google Scholar
  19. Mladenović, N., Todosijević, R., Urošević, D.: Less is more: basic variable neighborhood search for minimum differential dispersion problem. Inf. Sci. 326, 160–171 (2016)Google Scholar
  20. Porumbel, D.C., Hao, J.K., Glover, F.: A simple and effective algorithm for the MaxMin diversity problem. Ann. Oper. Res. 186(1), 275–293 (2011)zbMATHGoogle Scholar
  21. Prokopyev, O.A., Kong, N., Martinez-Torres, D.L.: The equitable dispersion problem. Eur. J. Oper. Res. 197(1), 59–67 (2009)MathSciNetzbMATHGoogle Scholar
  22. Resende, M.G.C., Mart, R., Gallego, M., Duarte, A.: GRASP and path relinking for the max-min diversity problem. Comput. Oper. Res. 37(3), 498–508 (2010)MathSciNetzbMATHGoogle Scholar
  23. Silver, G.C., Ochi, L.S., Martins, S.L.: Experimental comparisons of greedy randomized adaptive search procedures for the maximum diversity problem. In: Ribeiro, C.C., Martins, S.L. (eds.) Experimental and Efficient Algorithms. Lecture Notes in Computer Science, vol. 3059, pp. 498–512. Springer, Angra dos Reis, Brazil (2004)Google Scholar
  24. Wang, Y., Hao, J.K., Glover, F., Lü, Z.: A tabu search based memetic search for the maximum diversity problem. Eng. Appl. Artif. Intell. 27, 103–114 (2014)Google Scholar
  25. Wang, Y., Wu, Q., Glover, F.: Effective metaheuristic algorithms for the minimum differential dispersion problem. Eur. J. Oper. Res. 258, 829–843 (2017)MathSciNetzbMATHGoogle Scholar
  26. Wilson, T., Wiebe, J., Hoffmann, P.: Recognizing contextual polarity in phrase-level sentiment analysis, In: Proceedings of the Conference on Human Language Technology and Empirical Methods in Natural Language Processing, pp. 347–354 (2005)Google Scholar
  27. Yang, B., Cheung, W., Liu, J.: Community mining from signed social networks. IEEE Trans. Knowl. Data Eng. 19(10), 1333–1348 (2007)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jiawei Song
    • 1
  • Yang Wang
    • 2
    Email author
  • Haibo Wang
    • 3
  • Qinghua Wu
    • 1
  • Abraham P. Punnen
    • 4
  1. 1.School of ManagementHuazhong University of Science and TechnologyWuhanChina
  2. 2.School of ManagementNorthwestern Polytechnical UniversityXi’anChina
  3. 3.Sanchez School of BusinessTexas A&M International UniversityLaredoUSA
  4. 4.Department of MathematicsSimon Fraser University SurreySurreyCanada

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