Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 750968, 18 pages
http://dx.doi.org/10.1155/2011/750968
Research Article

A Data-Guided Lexisearch Algorithm for the Asymmetric Traveling Salesman Problem

Department of Computer Science, Al-Imam Muhammad Ibn Saud Islamic University, P.O. Box 5701, Riyadh 11432, Saudi Arabia

Received 23 October 2010; Revised 15 March 2011; Accepted 26 April 2011

Academic Editor: Tamas Kalmar-Nagy

Copyright © 2011 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. C. P. Ravikumar, “Solving larege-scale travelling salesperson problems on parallel machines,” Microprocessors and Microsystems, vol. 16, no. 3, pp. 149–158, 1992. View at Publisher · View at Google Scholar
  2. R. G. Bland and D. F. Shallcross, “Large traveling salesman problems arising from experiments in x-ray crystallography: a preliminary report on computation,” Operations Research Letters, vol. 8, no. 3, pp. 125–128, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. C. H. Papadimitriou and K. Steglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice Hall of India Private Limited, New Delhi, India, 1997.
  4. R. Jonker and T. Volgenant, “Transforming asymmetric into symmetric traveling salesman problems,” Operations Research Letter 2, vol. 2, pp. 161–163, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. D. Naddef, “Polyhedral theory and branch-and-cut-algorithms for the symmetric TSP,” in The Traveling Salesman Problem and Its Variations, G. Gutin and A. P. Punnen, Eds., vol. 12 of Computational Optimization, pp. 29–116, Kluwer Academic Publishers, Dodrecht, The Netherlands, 2002. View at Google Scholar · View at Zentralblatt MATH
  6. M. Fischetti, A. Lodi, and P. Toth, “Exact methods for the asymmetric traveling salesman problem,” in The Traveling Salesman Problem and Its Variations, G. Gutin and A. P. Punnen, Eds., vol. 12 of Computational Optimization, pp. 169–205, Kluwer Academic Publishers, Dodrecht, The Netherlands, 2002. View at Google Scholar · View at Zentralblatt MATH
  7. Z. H. Ahmed, “A lexisearch algorithm for the bottleneck traveling salesman problem,” International Journal of Computer Science and Security, vol. 3, no. 6, pp. 569–577, 2010. View at Google Scholar
  8. S. N. N. Pandit, “The loading problem,” Operations Research, vol. 10, no. 5, pp. 639–646, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. N. N. Pandit and K. Srinivas, “A lexisearch algorithm for the traveling salesman problem,” in Proceedings of the IEEE International Joint Conference on Neural Networks, vol. 3, pp. 2521–2527, November 1991.
  10. Z. H. Ahmed, “A data-guided lexisearch algorithm for the bottleneck traveling salesman problem,” International Journal of Operational Research. In press.
  11. H. D. Sherali, S. C. Sarin, and Pei-F Tsai, “A class of lifted path and flow-based formulations for the asymmetric traveling salesman problem with and without precedence constraints,” Discrete Optimization, vol. 3, no. 1, pp. 20–32, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. G. B. Dantzig, D. R. Fulkerson, and S. M. Johnson, “Solution of a large-scale traveling-salesman problem,” Operational Research Society Journal, vol. 2, pp. 393–410, 1954. View at Google Scholar
  13. S. C. Sarin, H. D. Sherali, and A. Bhootra, “New tighter polynomial length formulations for the asymmetric traveling salesman problem with and without precedence constraints,” Operations Research Letters, vol. 33, no. 1, pp. 62–70, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. T. Öncan, Ï. K. Altinel, and G. Laporte, “A comparative analysis of several asymmetric traveling salesman problem formulations,” Computers & Operations Research, vol. 36, no. 3, pp. 637–654, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. E. Balas and P. Toth, “Branch and bound methods,” in The Traveling Salesman Problem, E. L. Lawler, J. K. Lenstra, A. H .G. Rinnooy Kan et al., Eds., Wiley Series in Discrete Mathematics & Optimization, pp. 361–401, John Wiley & Sons, Chichester, UK, 1985. View at Google Scholar · View at Zentralblatt MATH
  16. G. Carpaneto, M. Dell'Amico, and P. Toth, “Exact solution of large-scale, asymmetric traveling salesman problems,” Association for Computing Machinery. Transactions on Mathematical Software, vol. 21, no. 4, pp. 394–409, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. D. L. Miller and J. H. Pekny, “Exact solution of large asymmetric traveling salesman problems,” Science, vol. 251, no. 4995, pp. 754–761, 1991. View at Publisher · View at Google Scholar
  18. M. Turkensteen, D. Ghosh, B. Goldengorin, and G. Sierksma, “Tolerance-based branch and bound algorithms for the ATSP,” European Journal of Operational Research, vol. 189, no. 3, pp. 775–788, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. S. N. N. Pandit, “An Intelligent approach to travelling salesman problem,” Symposium in Operations Research, Khragpur: Indian Institute of Technology (1964).
  20. M. S. Murthy, Some Combinatorial Search Problems (A Pattern Recognition Approach), Ph.D. thesis, Kakatiya University, Warangal, India, 1979.
  21. K. Srinivas, Data Guided Algorithms in Optimization and Pattern Recognition, Ph.D. thesis, University Of Hyderabad, Hyderabad, India, 1989.
  22. Z. H. Ahmed, A Sequential Constructive Sampling and Related Approaches to Combinatorial Optimization, Ph.D. thesis, Tezpur University, Assam, India, 2000.
  23. Z. H. Ahmed and S. N. N. Pandit, “The travelling salesman problem with precedence constraints,” Opsearch, vol. 38, no. 3, pp. 299–318, 2001. View at Google Scholar
  24. S. N. N. Pandit, S. C. Jain, and R. Misra, “Optimal machine allocation,” Journal of Institute of Engineers, vol. 44, pp. 226–240, 1964. View at Google Scholar
  25. TSPLIB, http://www2.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/.
  26. D. S. Johnson, Machine comparison site, http://public.research.att.com/~dsj/chtsp/speeds.html.