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Journal of Applied Mathematics
Volume 2014, Article ID 818529, 10 pages
Research Article

Solving Dynamic Traveling Salesman Problem Using Dynamic Gaussian Process Regression

School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, University Road, Westville, Private Bag X 54001, Durban, 4000, South Africa

Received 4 January 2014; Accepted 11 February 2014; Published 7 April 2014

Academic Editor: M. Montaz Ali

Copyright © 2014 Stephen M. Akandwanaho 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. Simões and E. Costa, “Prediction in evolutionary algorithms for dynamic environments,” Soft Computing, pp. 306–315, 2013. View at Google Scholar
  2. J. Branke, T. Kaussler, H. Schmeck, and C. Smidt, A Multi-Population Approach to Dynamic Optimization Problems, Department of Computer Engineering, Yeditepe University, Istanbul, Turkey, 2000.
  3. K. S. Leung, H. D. Jin, and Z. B. Xu, “An expanding self-organizing neural network for the traveling salesman problem,” Neurocomputing, vol. 62, no. 1–4, pp. 267–292, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. M. Dorigo and L. M. Gambardella, “Ant colony system: a cooperative learning approach to the traveling salesman problem,” IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 53–66, 1997. View at Publisher · View at Google Scholar · View at Scopus
  5. C. Jarumas and J. Pichitlamken, “Solving the traveling salesman problem with gaussian process regression,” in Proceedings of the International Conference on Computing and Information Technology, 2011.
  6. K. Weicker, Evolutionary Algorithms and Dynamic Optimization Problems, University of Stuttgart, Stuttgart, Germany, 2003.
  7. K. Menger, Das botenproblem. Ergebnisse Eines Mathematischen Kolloquiums, 1932.
  8. G. Gutin, A. Yeo, and A. Zverovich, “Traveling salesman should not be greedy: domination analysis of greedy-type heuristics for the TSP,” Discrete Applied Mathematics, vol. 117, no. 1–3, pp. 81–86, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Hoffman and P. Wolfe, The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley, Chichester, UK, 1985.
  10. A. Punnen, “The traveling salesman problem: aplications, formulations and variations,” in The Traveling Salesman Problem and Its Variations, Combinatorial Optimization, 2002. View at Google Scholar
  11. E. Ozcan and M. Erenturk, A Brief Review of Memetic Algorithms for Solving Euclidean 2d Traveling Salesrep Problem, Department of Computer Engineering, Yeditepe University, Istanbul, Turkey.
  12. G. Clarke and J. Wright, “Scheduling of vehicles from a central depot to a number of delivery points,” Operations Research, vol. 12, no. 4, pp. 568–581, 1964. View at Google Scholar
  13. P. Miliotis, Integer Programming Approaches To the Traveling Salesman Problem, University of London, London, UK, 2012.
  14. R. Jonker and T. Volgenant, “Transforming asymmetric into symmetric traveling salesman problems,” Operations Research Letters, vol. 2, no. 4, pp. 161–163, 1983. View at Google Scholar · View at Scopus
  15. S. Gharan and A. Saberi, The Asymmetric Traveling Salesman Problem on Graphs with Bounded Genus, Springer, Berlin, Germany, 2012.
  16. P. Collard, C. Escazut, and A. Gaspar, “Evolutionary approach for time dependent optimization,” in Proceedings of the IEEE 8th International Conference on Tools with Artificial Intelligence, pp. 2–9, November 1996. View at Publisher · View at Google Scholar · View at Scopus
  17. H. Psaraftis, “Dynamic vehicle routing problems,” Vehicle Routing: Methods and Studies, 1988. View at Google Scholar
  18. M. Yang, C. Li, and L. Kang, “A new approach to solving dynamic traveling salesman problems,” in Simulated Evolution and Learning, vol. 4247 of Lecture Notes in Computer Science, pp. 236–243, Springer, Berlin, Germany, 2006. View at Google Scholar · View at Scopus
  19. S. S. Ray, S. Bandyopadhyay, and S. K. Pal, “Genetic operators for combinatorial optimization in TSP and microarray gene ordering,” Applied Intelligence, vol. 26, no. 3, pp. 183–195, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. E. Osaba, R. Carballedo, F. Diaz, and A. Perallos, “Simulation tool based on a memetic algorithm to solve a real instance of a dynamic tsp,” in Proceedings of the IASTED International Conference Applied Simulation and Modelling, 2012.
  21. R. Battiti and M. Brunato, The Lion Way, Machine Learning Plus Intelligent Optimization. Applied Simulation and Modelling, Lionsolver, 2013.
  22. D. Chuong, Gaussian Processess, Stanford University, Palo Alto, Calif, USA, 2007.
  23. W. Kongkaew and J. Pichitlamken, A Gaussian Process Regression Model For the Traveling Salesman Problem, Faculty of Engineering, Kasetsart University, Bangkok, Thailand, 2012.
  24. C. Rasmussen and C. Williams, MIT Press, Cambridge, UK, 2006.
  25. C. J. Paciorek and M. J. Schervish, “Spatial modelling using a new class of nonstationary covariance functions,” Environmetrics, vol. 17, no. 5, pp. 483–506, 2006. View at Google Scholar
  26. C. E. Rasmussen and H. Nickisch, “Gaussian processes for machine learning (GPML) toolbox,” Journal of Machine Learning Research, vol. 11, pp. 3011–3015, 2010. View at Google Scholar · View at Scopus
  27. F. Sinz, J. Candela, G. Bakir, C. Rasmussen, and K. Franz, “Learning depth from stereo,” in Pattern Recognition, vol. 3175 of Lecture Notes in Computer Science, pp. 245–252, Springer, Berlin, Germany, 2004. View at Google Scholar · View at Scopus
  28. J. Ko, D. J. Klein, D. Fox, and D. Haehnel, “Gaussian processes and reinforcement learning for identification and control of an autonomous blimp,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '07), pp. 742–747, Roma , Italy, April 2007. View at Publisher · View at Google Scholar · View at Scopus
  29. T. Idé and S. Kato, “Travel-time prediction using gaussian process regression: a trajectory-based approach,” in Proceedings of the 9th SIAM International Conference on Data Mining 2009 (SDM '09), pp. 1177–1188, May 2009. View at Scopus
  30. G. Reinelt, “Tsplib discrete and combinatorial optimization,” 1995,
  31. C. Paciorek, Nonstationary gaussian processes for regression and spatial modelling [Ph.D. thesis], Carnegie Mellon University, Pittsburgh, Pa, USA, 2003.
  32. D. Higdon, J. Swall, and J. Kern, Non-Stationary Spatial Modeling, Oxford University Press, New York, NY, USA, 1999.
  33. C. Plagemann, K. Kersting, and W. Burgard, “Nonstationary Gaussian process regression using point estimates of local smoothness,” in Machine Learning and Knowledge Discovery in Databases, vol. 5212 of Lecture Notes in Computer Science, no. 2, pp. 204–219, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar · View at Scopus
  34. G. Reinelt, “The tsplib symmetric traveling salesman problem instances,” 1995.
  35. J. Kirk, Matlab Central.
  36. X. Geng, Z. Chen, W. Yang, D. Shi, and K. Zhao, “Solving the traveling salesman problem based on an adaptive simulated annealing algorithm with greedy search,” Applied Soft Computing Journal, vol. 11, no. 4, pp. 3680–3689, 2011. View at Publisher · View at Google Scholar · View at Scopus
  37. A. Seshadri, Traveling Salesman Problem (Tsp) Using Simulated Annealing, IEEE, 2006.
  38. M. Nuhoglu, Shortest path heuristics (nearest neighborhood, 2 opt, farthest and arbitrary insertion) for travelling salesman problem, 2007.