Table of Contents
ISRN Operations Research
Volume 2013 (2013), Article ID 203032, 10 pages
http://dx.doi.org/10.1155/2013/203032
Research Article

A New Formulation of the Set Covering Problem for Metaheuristic Approaches

École Polytechnique de Montréal, C.P. 6079, Succ. Centre-Ville, Montréal, QC, Canada H3C 3A7

Received 18 February 2013; Accepted 4 April 2013

Academic Editors: L. Buzna, P. Ekel, C. Mohan, and M. Wang

Copyright © 2013 Nehme Bilal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Caprara, M. Fischetti, and P. Toth, “Heuristic method for the set covering problem,” Operations Research, vol. 47, no. 5, pp. 730–743, 1999. View at Google Scholar · View at Scopus
  2. G. Lan, G. W. DePuy, and G. E. Whitehouse, “An effective and simple heuristic for the set covering problem,” European Journal of Operational Research, vol. 176, no. 3, pp. 1387–1403, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. E. Balas, Class of Location, Distribution and Scheduling Problems: Modeling and Solution Methods, Carnegie Mellon University. Design Research Center, New York, NY, USA, 1983.
  4. S. Ceria, “Set covering problem,” in Annotated Bibliographies in Combinatorial Optimization, 1997. View at Google Scholar
  5. M. Garey and D. Johnson, Computers and Intractability. A Guide To the Theory of NP-Completeness, W. H. Freeman, Oxford, UK, 1979.
  6. L. Lessing, I. Dumitrescu, and T. Stutzle, “A comparison between acoalgorithms for the set covering problem,” Ant Colony Optimization and Swarm Intelligence, pp. 105–122, 2004. View at Google Scholar
  7. M. Rahoual, R. Hadji, and V. Bachelet, “Parallel ant system for the set covering problem,” in Ant Algorithmspages, pp. 249–297, 2002. View at Google Scholar
  8. Z. Ren, Z. Feng, L. Ke, and H. Chang, “A fast and efficient ant colony optimization approach for the set covering problem,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '08), (IEEE World Congress on Computational Intelligence), pp. 1839–1844, IEEE, June 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. Z. G. Ren, Z. R. Feng, L. J. Ke, and Z. J. Zhang, “New ideas for applying ant colony optimization to the set covering problem,” Computers and Industrial Engineering, vol. 58, no. 4, pp. 774–784, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. B. Crawford and C. Castro, “Integrating lookahead and post processing procedures with aco for solving set partitioning and covering problems,” in proceedings of the 8th International Conference on Artificial Intelligence and Soft Computing (ICAISC '06), pp. 1082–1090, 2006.
  11. G. DePuy, G. Whitehouse, and R. Moraga, “Using the meta-raps approach to solve combinatorial problems,” in Proceedings of the 2002 Industrial Engineering Research Conference, vol. 19, p. 21, Citeseer, May 2002.
  12. T. A. Feo and M. G. C. Resende, “Greedy randomized adaptive search procedures,” Journal of Global Optimization, vol. 6, no. 2, pp. 109–133, 1995. View at Publisher · View at Google Scholar · View at Scopus
  13. J. E. Beasley and P. C. Chu, “A genetic algorithm for the set covering problem,” European Journal of Operational Research, vol. 94, no. 2, pp. 392–404, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Solar, V. Parada, and R. Urrutia, “A parallel genetic algorithm to solve the set-covering problem,” Computers and Operations Research, vol. 29, no. 9, pp. 1221–1235, 2002. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Orvosh and L. Davis, “Using a genetic algorithm to optimize problems with feasibility constraints,” in Proceedings of the 1st IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, pp. 548–553, IEEE, June 1994. View at Scopus
  16. T. Bäck, M. Schütz, and S. Khuri, “A comparative study of a penalty function, a repair heuristic, and stochastic operators with the set-covering problem,” in Artificial Evolution, pp. 320–332, Springer, New York, NY, USA, 1996. View at Google Scholar
  17. K. S. Al-Sultan, M. F. Hussain, and J. S. Nizami, “A genetic algorithm for the set covering problem,” Journal of the Operational Research Society, vol. 47, no. 5, pp. 702–709, 1996. View at Google Scholar · View at Scopus
  18. R. L. Wang and K. Okazaki, “An improved genetic algorithm with conditional genetic operators and its application to set-covering problem,” Soft Computing, vol. 11, no. 7, pp. 687–694, 2007. View at Publisher · View at Google Scholar · View at Scopus
  19. N. Musliu, “Local search algorithm for unicost set covering problem,” Advances in Applied Artificial Intelligence, vol. 4031, pp. 302–311, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Yagiura, M. Kishida, and T. Ibaraki, “A 3-flip neighborhood local search for the set covering problem,” European Journal of Operational Research, vol. 172, no. 2, pp. 472–499, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. E. Balas and M. C. Carrera, “A dynamic subgradient-based branch-and-bound procedure for set covering,” Operations Research, vol. 44, no. 6, pp. 875–890, 1996. View at Google Scholar · View at Scopus
  22. J. E. Beasley, “Lagrangian heuristic for set-covering problems,” Naval Research Logistics, vol. 37, no. 1, pp. 151–164, 1990. View at Google Scholar · View at Scopus
  23. G. Kinney and J. Barnes, “A group theoretic tabu search algorithm for set covering problems,” Working Paper, 2004, http://www.researchgate.net/publication/228734774_A_group_theoretic_tabu_search_algorithm_for_set_covering_problems. View at Google Scholar
  24. G. W. Kinney, J. W. Barnes, and B. W. Colletti, “A reactive tabu search algorithm with variable clustering for the Unicost set covering problem,” International Journal of Operational Research, vol. 2, no. 2, pp. 156–172, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. J. Bautista and J. Pereira, “A GRASP algorithm to solve the unicost set covering problem,” Computers and Operations Research, vol. 34, no. 10, pp. 3162–3173, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Caserta, “Tabu search-based metaheuristic algorithm for large-scale set covering problems,” Metaheuristics, vol. 39, pp. 43–63, 2007. View at Google Scholar
  27. M. L. Fisher, “The lagrangian relaxation method for solving integer programming problems,” Management Science, vol. 27, no. 1, pp. 1–18, 1981. View at Google Scholar · View at Scopus
  28. M. Held, P. Wolfe, and H. P. Crowder, “Validation of subgradient optimization,” Math Program, vol. 6, no. 1, pp. 62–88, 1974. View at Google Scholar · View at Scopus
  29. V. Chvatal, “A greedy heuristic for the set-covering problem,” Mathematics of Operations Research, vol. 4, no. 3, pp. 233–235, 1979. View at Publisher · View at Google Scholar
  30. J. Beasley, “OR-library: distributing test problems by electronic mail,” Journal of the Operational Research Society, vol. 41, no. 11, pp. 1069–1072, 1990. View at Google Scholar
  31. B. Yelbay, S. Birbil, and K. Bulbul, “The set covering problem revisited: an empirical study of the value of dual information,” Optimization Online, 2012. View at Google Scholar