Abstract
We propose new heuristic procedures for the maximally diverse grouping problem (MDGP). This NP-hard problem consists of forming maximally diverse groups—of equal or different size—from a given set of elements. The most general formulation, which we address, allows for the size of each group to fall within specified limits. The MDGP has applications in academics, such as creating diverse teams of students, or in training settings where it may be desired to create groups that are as diverse as possible. Search mechanisms, based on the tabu search methodology, are developed for the MDGP, including a strategic oscillation that enables search paths to cross a feasibility boundary. We evaluate construction and improvement mechanisms to configure a solution procedure that is then compared to state-of-the-art solvers for the MDGP. Extensive computational experiments with medium and large instances show the advantages of a solution method that includes strategic oscillation.
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References
Arani T and Lotfi V (1989). A three phased approach to final exam scheduling. IIE Transactions 21 (1): 86–96.
Baker KR and Powell SG (2002). Methods for assigning students to groups: A study of alternative objective functions. Journal of the Operational Research Society 53 (4): 397–404.
Bhadury J, Mighty EJ and Damar H (2000). Maximizing workforce diversity in project teams: A network flow approach. Omega 28 (2): 143–153.
Chen CC (1986). Placement and partitioning methods for integrated circuit layout. PhD Dissertation, EECS Department, University of California, Berkeley.
Chen Y, Fan ZP, Ma J and Zeng S (2011). A hybrid grouping genetic algorithm for reviewer group construction problem. Expert Systems with Applications 38 (3): 2401–2411.
Duarte A and Martí R (2007). Tabu search and GRASP for the maximum diversity problem. European Journal of Operational Research 178 (1): 71–84.
Falkenauer E (1998). Genetic Algorithms for Grouping Problems. Wiley: New York.
Fan ZP, Chen Y, Ma J and Zeng S (2011). A hybrid genetic algorithmic approach to the maximally diverse grouping problem. Journal of the Operational Research Society 62 (1): 92–99.
Feo T and Khellaf M (1990). A class of bounded approximation algorithms for graph partitioning. Networks 20 (2): 181–195.
Feo T, Goldschmidt O and Khellaf M (1992). One-half approximation algorithms for the k-partition problem. Operations Research 40 (Supplement 1): S170–S173.
Gallego M, Duarte A, Laguna M and Martí R (2009). Hybrid heuristics for the maximum diversity problem. Journal of Computational Optimization and Application 44 (3): 411–426.
Glover F and Laguna M (1997). Tabu Search. Kluwer Academic Publisher: Boston, MA.
Glover F, Kuo CC and Dhir KS (1998). Heuristic algorithms for the maximum diversity problem. Journal of Information and Optimization Sciences 19 (1): 109–132.
Hettich S and Pazzani MJ (2006). Mining for element reviewers: Lessons learned at the national science foundation. In: Proceedings of the KDD’06. ACM: New York, NY, pp 862–871.
Kral J (1965). To the problem of segmentation of a program. Information Processing Machines 2 (1): 116–127.
Lotfi V and Cerveny R (1991). A final-exam-scheduling package. Journal of the Operational Research Society 42 (3): 205–216.
Martí R and Sandoya F (2012). GRASP and path relinking for the equitable dispersion problem. Computers and Operations Research, In press, http://dx.doi.org/10.1016/j.cor.2012.04.005.
Martí R, Gallego M and Duarte A (2012). Heuristics and metaheuristics for the maximum diversity problem. Journal of Heuristics, doi: 10.1007/s10732-011-9172-4.
Miller J, Potter W, Gandham R and Lapena C (1993). An evaluation of local improvement operators for genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics 23 (5): 1340–1351.
Mingers J and O'Brien FA (1995). Creating students groups with similar characteristics: A heuristic approach. Omega 23 (3): 313–321.
O'Brien FA and Mingers J (1995). The equitable partitioning problem: A heuristic algorithm applied to the allocation of university student accommodation. Warwick Business School, Research Paper no. 187.
Resende MGC, Martí R, Gallego M and Duarte A (2010). GRASP and path relinking for the max-min diversity problem. Computers and Operations Research 37 (3): 498–508.
Ribeiro CC, Uchoa E and Werneck RF (2002). A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS Journal on Computing 14 (3): 228–246.
Vasko FJ, Knolle PJ and Spiegel DS (2005). An empirical study of hybrid genetic algorithms for the set covering problem. The Journal of the Operational Research Society 56 (10): 1213–1223.
Weitz RR and Jelassi MT (1992). Assigning students to groups: A multi-criteria decision support system approach. Decision Sciences 23 (3): 746–757.
Weitz RR and Lakshminarayanan S (1996). On a heuristic for the final exam scheduling problem. Journal of the Operational Research Society 47 (4): 599–600.
Weitz RR and Lakshminarayanan S (1998). An empirical comparison of heuristic methods for creating maximally diverse groups. Journal of the Operational Research Society 49 (6): 635–646.
Acknowledgements
This research has been partially supported by the Ministerio de Education y Ciencia of Spain (Grant Ref. TIN2009-07516) and by the University Rey Juan Carlos (in the program ‘Ayudas a la Movilidad 2010’).
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Gallego, M., Laguna, M., Martí, R. et al. Tabu search with strategic oscillation for the maximally diverse grouping problem. J Oper Res Soc 64, 724–734 (2013). https://doi.org/10.1057/jors.2012.66
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DOI: https://doi.org/10.1057/jors.2012.66