Advertisement

A new hybrid genetic algorithm for the maximally diverse grouping problem

  • Kavita Singh
  • Shyam SundarEmail author
Original Article
  • 40 Downloads

Abstract

This paper presents a new hybrid approach (\(\mathcal {N}\)SGGA) combining steady-state grouping genetic algorithm with a local search for the maximally diverse grouping problem (MDGP) related to equal group-size. The MDGP is a well-known \(\mathcal {NP}\)-Hard combinatorial optimization problem and finds numerous applications in real world. \(\mathcal {N}\)SGGA employs particularly (a) crossover operator (b) the effective way of utilization of local search and (c) the additional replacement strategy, making it different from the existing genetic algorithm for the MDGP. On a set of large benchmark instances, \(\mathcal {N}\)SGGA is competitive in comparison to the existing best-known approaches in the literature and performs particularly well on large-size instances. Some important ingredients of \(\mathcal {N}\)SGGA that shed some light on the adequacy of \(\mathcal {N}\)SGGA are analyzed.

Keywords

Maximally diverse grouping problem Steady-state genetic algorithm Crossover Replacement strategy Local search 

Notes

References

  1. 1.
    Arani T, Lotfi V (1989) A three phased approach to final exam scheduling. IIE Trans 21(1):86–96CrossRefGoogle Scholar
  2. 2.
    Bhadury J, Mighty EJ, Damar H (2000) Maximizing workforce diversity in project teams: a network flow approach. Omega 28(2):143–153CrossRefGoogle Scholar
  3. 3.
    Brimberg J, Mladenovic N, Urošević D (2015) Solving the maximally diverse grouping problem by skewed general variable neighborhood search. Inf Sci 295:650–675CrossRefGoogle Scholar
  4. 4.
    Duarte A, Martí R (2007) Tabu search and GRASP for the maximum diversity problem. Eur J Oper Res 178:71–84MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Falkenauer E (1998) Genetic algorithms and grouping problems. Wiley, ChicesterzbMATHGoogle Scholar
  6. 6.
    Fan ZP, Chen Y, Ma J, Zeng S (2011) A hybrid genetic algorithmic approach to the maximally diverse grouping problem. JORS 62(1):92–99CrossRefGoogle Scholar
  7. 7.
    Feo TA, Khellaf M (1990) A class of bounded approximation algorithms for graph partitioning. Networks 20(2):181–195MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Galinier P, Hao J (1999) Hybrid evolutionary algorithms for graph coloring. J Comb Optim 3(4):379–397MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the cec’2005 special session on real parameter optimization. J Heuristics 15(6):617–644CrossRefzbMATHGoogle Scholar
  10. 10.
    Goldberg DE (1989) Genetic algorithms in search optimization and machine learning. Addison-Wesley, BostonzbMATHGoogle Scholar
  11. 11.
    Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control and artificial intelligence. MIT Press, CambridgeCrossRefGoogle Scholar
  12. 12.
    Krass D, Ovchinnikov A (2010) Constrained group balancing: why does it work. Eur J Oper Res 206(1):144–154MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lai X, Hao J (2016) Iterated maxima search for the maximally diverse grouping problem. Eur J Oper Res 254(3):780–800MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Palubeckis G, Karciauskas E, Riskus A (2011) Comparative performance of three metaheuristic approaches for the maximally diverse grouping problem. ITC 40(4):277–285CrossRefGoogle Scholar
  15. 15.
    Palubeckis G, Ostreika A, Rubliauskas D (2015) Maximally diverse grouping: an iterated tabu search approach. JORS 66(4):579–592CrossRefGoogle Scholar
  16. 16.
    Rodríguez FJ, Lozano M, García-Martínez C, González-Barrera JD (2013) An artificial bee colony algorithm for the maximally diverse grouping problem. Inf Sci 230:183–196MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Singh A, Gupta AK (2007) Two heuristics for the one-dimensional bin-packing problem. OR Spectrum 29(4):765–781MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Sundar S (2014) A steady-state genetic algorithm for the dominating tree problem. In: Simulated evolution and learning—10th international conference, SEAL 2014, Dunedin, New Zealand, December 15–18, 2014. Proceedings, pp 48–57Google Scholar
  19. 19.
    Sundar S, Singh A (2015) Metaheuristic approaches for the blockmodel problem. IEEE Syst J 9(4):1237–1247CrossRefGoogle Scholar
  20. 20.
    Urošević D (2014) Variable neighborhood search for maximum diverse grouping problem. Yugosl J Oper Res 24:21–33MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Weitz R, Lakshminarayanan S (1997) An empirical comparison of heuristic and graph theoretic methods for creating maximally diverse groups, vlsi design, and exam scheduling. Omega 25:473–482CrossRefGoogle Scholar
  22. 22.
    Weitz R, Lakshminarayanan S (1998) An empirical comparison of heuristic methods for creating maximally diverse groups. J Oper Res Soc 49(6):635–646CrossRefzbMATHGoogle Scholar
  23. 23.
    Weitz R, Jelassi Tawfik M (1992) Assigning students to groups: a multi-criteria decision support system approach. Decision Sci 23(3):746–757CrossRefGoogle Scholar
  24. 24.
    Yeoh HK, Nor M, Iskandr M (2011) An algorithm to form balanced and diverse groups of students. Comput Appl Eng Educ 19:582–590CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer ApplicationsNational Institute of Technology RaipurRaipurIndia

Personalised recommendations