Abstract
In this paper, we investigate solving the Maximum Dispersion Problem (MaxDP). For a given set of weighted objects, the MaxDP consists in partitioning this set into a predefined number of groups, such that the overall dispersion of elements, assigned to the same group, is maximized. Furthermore, each group has a target weight and the total weight of each group must be within a specific interval around the target weight. It has been proven that the MaxDP is NP-hard and, consequently, difficult to solve by classical exact methods. In this work, we use variants of Variable Neighborhood Search (VNS) for solving the MaxDP. In order to evaluate the efficiency of VNS, we carried out some numerical experiments on randomly generated instances. The results of the VNS is compared with the solutions provided by the solver Gurobi. According to our results, the VNS gives high quality solutions for small instances and, in solving large instances, it provides some decent solutions for all instances; however, Gurobi fails to provide any solution for some of them.
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References
Baker, K.R., Powell, S.G.: Methods for assigning students to groups: a study of alternative objective functions. J. Oper. Res. Soc. 53(4), 397–404 (2002)
Brimberg, J., Mladenović, N., Urošević, D.: Solving the maximally diverse grouping problem by skewed general variable neighborhood search. Inf. Sci. 295, 650–675 (2015)
Erkut, E.: The discrete p-dispersion problem. Eur. J. Oper. Res. 46(1), 48–60 (1990)
Fernández, E., Kalcsics, J., Nickel, S., Ríos-Mercado, R.Z.: A novel maximum dispersion territory design model arising in the implementation of the WEEE-directive. J. Oper. Res. Soc. 61(3), 503–514 (2010)
Fernández, E., Kalcsics, J., Nickel, S.: The maximum dispersion problem. Omega 41(4), 721–730 (2013)
Glover, F., Ching-Chung, K., Dhir, K.: A discrete optimization model for preserving biological diversity. Appl. Math. Modell. 19(11), 696–701 (2010)
Hansen, P., Mladenović, N.: Variable neighborhood search. In: Glover, F., Knochenberger, G. (eds.) Handbook of Metaheuristics, pp. 145–184. Kluwer Academic Publisher (2003)
Martí, R., Gallego, M., Duarte, A.: A branch and bound algorithm for the maximum diversity problem. Eur. J. Oper. Res. 200(1), 36–44 (2010)
Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)
Palubeckis, G., Karčiauskas, E., Riškus, A.: Comperative performance of three metaheuristic approaches for the maximally diverse grouping problem. Inf. Technol. Control 40(4), 277–285 (2011)
Prokopyev, O., Kong, N., Martinez-Torres, D.: The equitable dispersion problem. Eur. J. Oper. Res. 197(1), 59–67 (2009)
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Moeini, M., Wendt, O. (2018). A Heuristic for Solving the Maximum Dispersion Problem. In: Fink, A., Fügenschuh, A., Geiger, M. (eds) Operations Research Proceedings 2016. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-55702-1_54
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DOI: https://doi.org/10.1007/978-3-319-55702-1_54
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