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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
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)
Aringhieri, R., Cordone, R.: Comparing local search metaheuristics for the maximum diversity problem. J. Oper. Res. Soc. 62, 266–280 (2011)
Aringhieri, R., Cordone, R., Melzani, Y.: Tabu Search versus GRASP for the maximum diversity problem. 4OR 6(1), 45–60 (2008)
Aringhieri, R., Cordone, R., Grosso, A.: Construction and improvement algorithms for dispersion problems. Eur. J. Oper. Res. 242(1), 1–13 (2014)
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)
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)
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)
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)
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)
Duarte, A., Martí, R.: Tabu search and grasp for the maximum diversity problem. Eur. J. Oper. Res. 178(1), 71–84 (2007)
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)
Galinier, P., Boujbel, Z., Fernandes, M.C.: An efficient memetic algorithm for the graph partitioning problem. Ann. Oper. Res. 191(1), 1–22 (2011)
Glover, F.: Multi-wave algorithms for metaheuristic optimization. J. Heurist. 22, 331–358 (2016)
Glover, F., Kuo, C.C., Dhir, K.S.: Heuristic algorithms for the maximum diversity problem. J. Inf. Optim. Sci. 19(1), 109–132 (1998)
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)
Lai, X., Hao, J.K.: A tabu based memetic algorithm for the max-mean dispersion problem. Comput. Oper. Res. 72, 118–127 (2016)
Martí, R., Sandoya, F.: GRASP and path relinking for the equitable dispersion problem. Comput. Oper. Res. 40, 3091–3099 (2013)
Martí, R., Gallego, M., Duarte, A., Pardo, E.G.: Heuristics and metaheuristics for the maximum diversity problem. J. Heurist. 19(4), 591–615 (2013)
Mladenović, N., Todosijević, R., Urošević, D.: Less is more: basic variable neighborhood search for minimum differential dispersion problem. Inf. Sci. 326, 160–171 (2016)
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)
Prokopyev, O.A., Kong, N., Martinez-Torres, D.L.: The equitable dispersion problem. Eur. J. Oper. Res. 197(1), 59–67 (2009)
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)
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)
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)
Wang, Y., Wu, Q., Glover, F.: Effective metaheuristic algorithms for the minimum differential dispersion problem. Eur. J. Oper. Res. 258, 829–843 (2017)
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)
Yang, B., Cheung, W., Liu, J.: Community mining from signed social networks. IEEE Trans. Knowl. Data Eng. 19(10), 1333–1348 (2007)
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).
About this article
Cite this article
Song, J., Wang, Y., Wang, H. et al. An effective multi-wave algorithm for solving the max-mean dispersion problem. J Heuristics 25, 731–752 (2019). https://doi.org/10.1007/s10732-018-9398-5
- Multi-wave algorithm
- Local search
- Adaptive memory
- Dispersion problems