Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014 (2014), Article ID 258207, 13 pages
http://dx.doi.org/10.1155/2014/258207
Research Article

The Ordered Clustered Travelling Salesman Problem: A Hybrid Genetic Algorithm

Department of Computer Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 5701, Riyadh 11432, Saudi Arabia

Received 28 August 2013; Accepted 30 December 2013; Published 19 February 2014

Academic Editors: M. Rǎdulescu, L. Scrimali, and W. Szeto

Copyright © 2014 Zakir Hussain Ahmed. 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. J. A. Chisman, “The clustered traveling salesman problem,” Computers and Operations Research, vol. 2, no. 2, pp. 115–119, 1975. View at Google Scholar · View at Scopus
  2. M. Gendreau, A. Hertz, and G. Laporte, “The traveling salesman problem with backhauls,” Computers and Operations Research, vol. 23, no. 5, pp. 501–508, 1996. View at Publisher · View at Google Scholar · View at Scopus
  3. N. Guttmann-Beck, R. Hassin, S. Khuller, and B. Raghavachari, “Approximation algorithms with bounded performance guarantees for the clustered traveling salesman problem,” Algorithmica, vol. 28, no. 4, pp. 422–437, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. F. C. J. Lokin, “Procedures for travelling salesman problems with additional constraints,” European Journal of Operational Research, vol. 3, no. 2, pp. 135–141, 1979. View at Google Scholar · View at Scopus
  5. G. Laporte, J.-Y. Potvin, and F. Quilleret, “Tabu search heuristic using genetic diversification for the clustered traveling salesman problem,” Journal of Heuristics, vol. 2, no. 3, pp. 187–200, 1997. View at Google Scholar · View at Scopus
  6. G. Laporte and U. Palekar, “Some applications of the clustered travelling salesman problem,” Journal of the Operational Research Society, vol. 53, no. 9, pp. 972–976, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. Z. H. Ahmed, “Genetic algorithm for the traveling salesman problem using sequential constructive crossover operator,” International Journal of Biometrics & Bioinformatics, vol. 3, no. 6, pp. 96–105, 2010. View at Google Scholar
  8. Z. H. Ahmed, “A hybrid sequential constructive sampling algorithm for the bottleneck traveling salesman problem,” International Journal of Computational Intelligence Research, vol. 6, no. 3, pp. 475–484, 2010. View at Google Scholar
  9. T. Aramgiatisiris, “An exact decomposition algorithm for the traveling salesman problem with backhauls,” Journal of Research in Engineering and Technology, vol. 1, pp. 151–164, 2004. View at Google Scholar
  10. TSPLIB, 1995, http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/.
  11. Z. H. Ahmed, “An exact algorithm for the clustered traveling salesman problem,” Opsearch, vol. 50, no. 2, pp. 215–228, 2013. View at Google Scholar
  12. J. D. E. Little, K. G. Murthy, D. W. Sweeny, and C. Karel, “An algorithm for the travelling salesman problem,” Operations Research, vol. 11, pp. 972–989, 1963. View at Google Scholar
  13. K. Jongens and T. Volgenant, “The symmetric clustered traveling salesman problem,” European Journal of Operational Research, vol. 19, no. 1, pp. 68–75, 1985. View at Google Scholar · View at Scopus
  14. M. Gendreau, G. Laporte, and J. Y. Potvin, “Heuristics for the clustered traveling salesman problem,” Tech. Rep. CRT-94-54, Centre de Recherché sur les Transports, Universite de Montreal, Montreal, Canada, 1994. View at Google Scholar
  15. J.-Y. Potvin and F. Guertin, “A genetic algorithm for the clustered traveling salesman problem with an a priori order on the clusters,” Tech. Rep. CRT-95-06, Centre de recherchesur les transports, Université de Montréal, Montréal, Canada, 1995. View at Google Scholar
  16. J.-Y. Potvin and F. Guertin, “The clustered traveling salesman problem: a genetic approach,” in Meta-Heuristics: Theory & Applications, I. H. Osman and J. Kelly, Eds., pp. 619–631, Kluwer Academic, Norwell, Mass, USA, 1996. View at Google Scholar
  17. S. Anily, J. Bramel, and A. Hertz, “5/3-Approximation algorithm for the clustered traveling salesman tour and path problems,” Operations Research Letters, vol. 24, no. 1, pp. 29–35, 1999. View at Publisher · View at Google Scholar · View at Scopus
  18. N. Christofides, “Worst-case analysis of a new heuristic for the traveling salesman problem,” Tech. Rep. 388, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pa, USA, 1976. View at Google Scholar
  19. W. Sheng, N. Xi, M. Song, and Y. Chen, “Robot path planning for dimensional measurement in automotive manufacturing,” Journal of Manufacturing Science and Engineering, Transactions of the ASME, vol. 127, no. 2, pp. 420–428, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. C. Ding, Y. Cheng, and M. He, “Two-level genetic algorithm for clustered traveling salesman problem with application in large-scale TSPs,” Tsinghua Science and Technology, vol. 12, no. 4, pp. 459–465, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, New York, NY, USA, 1989.
  22. Z. H. Ahmed, “A hybrid genetic algorithm for the bottleneck traveling salesman problem,” ACM Transactions on Embedded Computing Systems, vol. 12, no. 1, article 9, 2013. View at Google Scholar
  23. K. Deb, Optimization for Engineering Design: Algorithms and Examples, Prentice Hall India, New Delhi, India, 1995.
  24. Z. H. Ahmed, “Multi-parent extension of sequential constructive crossover for the travelling salesman problem,” International Journal of Operational Research, vol. 11, no. 3, pp. 331–342, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. Z. H. Ahmed, “An experimental study of a hybrid genetic algorithm for the maximum travelling salesman problem,” Mathematical Sciences, vol. 7, no. 1, pp. 1–7, 2013. View at Google Scholar
  26. C.-X. Wang, D.-W. Cui, Z.-R. Wang, and D. Chen, “A novel ant colony system based on minimum 1-tree and hybrid mutation for TSP,” in Proceedings of the 1st International Conference on Natural Computation (ICNC '05), LNCS, pp. 1269–1278, Springer, Changsha, China, August 2005. View at Scopus