Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 854218, 8 pages
http://dx.doi.org/10.1155/2015/854218
Research Article

Solving Large-Scale TSP Using a Fast Wedging Insertion Partitioning Approach

1School of Science, Central South University of Forestry and Technology, Changsha, Hunan 410004, China
2China Electric Power Research Institute, Beijing 100192, China
3Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
4State Grid Fujian Electric Power Research Institute, Fuzhou, Fujian 350007, China

Received 10 November 2014; Accepted 18 May 2015

Academic Editor: P. Balasubramaniam

Copyright © 2015 Zuoyong Xiang 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. D. S. Johnson and L. A. McGeoch, “Experimental analysis of heuristics for the STSP,” in The Traveling Salesman Problem and Its Variations, pp. 369–443, Berlin, Germany, Springer, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. Held and R. M. Karp, “The traveling-salesman problem and minimum spanning trees,” Operations Research, vol. 18, pp. 1138–1162, 1970. View at Publisher · View at Google Scholar · View at MathSciNet
  3. K. H. Hansen and J. Krarup, “Improvements of the Held-Karp algorithm for the symmetric traveling-salesman problem,” Mathematical Programming, vol. 7, no. 1, pp. 87–96, 1974. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. X. Goemans and D. J. Bertsimas, “Probabilistic analysis of the Held and Karp lower bound for the euclidean traveling salesman problem,” Mathematics of Operations Research, vol. 16, no. 1, pp. 72–89, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  5. G. Gutin and A. P. Punnen, The Traveling Salesman Problem and Its Variations, vol. 12, Springer Science & Business Media, 2002.
  6. J. Beardwood, J. H. Halton, and J. M. Hammersley, “The shortest path through many points,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 55, no. 4, pp. 299–327, 1959. View at Publisher · View at Google Scholar
  7. R. M. Karp and J. M. Steele, “Probabilistic analysis of heuristics,” in The Traveling Salesman Problem, chapter 6, pp. 181–205, John Wiley & Sons, 1985. View at Google Scholar
  8. D. S. Johnson, L. A. McGeoch, and E. E. Rothberg, “Asymptotic experimental analysis for the held-karp traveling salesman bound,” in Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 341–350, Atlanta, Ga, USA, January 1996.
  9. J. J. Bentley, “Fast algorithms for geometric traveling salesman problems,” ORSA Journal on Computing, vol. 4, no. 4, pp. 387–411, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  10. R. M. Karp, “Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane,” Mathematics of Operations Research, vol. 2, no. 3, pp. 209–224, 1977. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. R. Bellman, “Dynamic programming treatment of the travelling salesman problem,” Journal of the ACM, vol. 9, no. 1, pp. 61–63, 1962. View at Publisher · View at Google Scholar
  12. T. A. Feo and M. G. 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 MathSciNet · View at Scopus
  13. K. Holmqvist, A. Migdalas, and P. M. Pardalos, “Parallel continuous non-convex optimization,” in Parallel Computing in Optimization, Appl. Optim., pp. 471–527, Springer, Berlin, Germany, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  14. K. Holmqvist, A. Migdalas, and P. M. Pardalos, “Parallelized heuristics for combinatorial search,” in Parallel Computing in Optimization, pp. 269–294, Springer, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. G. C. Resende and C. C. Ribeiro, “Greedy randomized adaptive search procedures,” in Handbook of Metaheuristics, pp. 219–249, Kluwer Academic, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  16. D. Applegate and W. Cook, “Solving large-scale matching problems,” in Network Flows and Matching: First DIMACS Implementation Challenge, pp. 557–576, American Mathematical Society, Boston, Mass, USA, 1993. View at Google Scholar
  17. J. R. Allwright and D. B. Carpenter, “A distributed implementation of simulated annealing for the travelling salesman problem,” Parallel Computing. Theory and Applications, vol. 10, no. 3, pp. 335–338, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. M. G. A. Verhoeven, E. H. L. Aarts, and P. C. J. Swinkels, “A parallel 2-opt algorithm for the traveling salesman problem,” Future Generation Computer Systems, vol. 11, no. 2, pp. 175–182, 1995. View at Publisher · View at Google Scholar · View at Scopus
  19. E. L. Lawler, The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley-Interscience Series in Discrete Mathematics, Wiley-Interscience, 1985.
  20. G. Laporte, “The traveling salesman problem: an overview of exact and approximate algorithms,” European Journal of Operational Research, vol. 59, no. 2, pp. 231–247, 1992. View at Publisher · View at Google Scholar · View at Scopus
  21. D. Applegate, W. Cook, and A. Rohe, “Chained lin-kernighan for large traveling salesman problems,” INFORMS Journal on Computing, vol. 15, no. 1, pp. 82–92, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. K. Helsgaun, “An effective implementation of the Lin-Kernighan traveling salesman heuristic,” European Journal of Operational Research, vol. 126, no. 1, pp. 106–130, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. D. S. Johnson and L. A. McGeoch, “The traveling salesman problem: a case study in local optimization,” in Local Search in Combinatorial Optimization, vol. 1, pp. 215–310, John Wiley & Sons, 1997. View at Google Scholar
  24. F. Glover, M. Laguna, and R. Marti, “Scatter search and path relinking: advances and applications,” in Handbook of Metaheuristics, pp. 1–35, Springer, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  25. X. Gao, Y. Chen, J. Liu, and J. Zhou, “Personalized 3D caricature generation based on PCA subspace,” in Advances in Multimedia Information Processing—PCM 2008, vol. 5353 of Lecture Notes in Computer Science, pp. 713–720, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar
  26. Z. Chen, J. Zhou, X. Gao, L. Li, and J. Liu, “A novel method for pencil drawing generation in non-photo-realistic rendering,” in Advances in Multimedia Information Processing—PCM 2008, pp. 931–934, Springer, 2008. View at Google Scholar
  27. J. Liu, Y. Chen, C. Miao, X. Gao, J. Xie, and W. Gao, “Automatic 3D caricature generation by learning in enlarged manifold space,” in Proceedings of the 1st ACM SIGGRAPH Conference and Exhibition in Asia (SIGGRAPH Asia '08), ACM, Singapore, December 2008.
  28. J. Liu, Y. Chen, J. Xie, X. Gao, and W. Gao, “Semi-supervised learning of caricature pattern from manifold regularization,” in Proceedings of the 15th International Multimedia Modeling Conference (MMM '09), pp. 413–424, Sophia-Antipolis, France, January 2009.
  29. J. Xie, Y. Chen, J. Liu, C. Miao, and X. Gao, “Interactive 3D caricature generation based on double sampling,” in Proceedings of the 17th ACM International Conference on Multimedia (MM '09), pp. 745–748, ACM, Beijing, China, October 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. X. Gao, Y. Chen, J. Zhou, J. Liu, C. Miao, and Z. Chen, “Genetic sampling in eigenspace for 3d caricature synthesis,” in Proceedings of the 7th International Conference on Information, Communications and Signal Processing (ICICS '09), pp. 1–4, IEEE, December 2009.
  31. J. Liu, Y. Chen, C. Miao et al., “Semi-supervised learning in reconstructed manifold space for 3D caricature generation,” Computer Graphics Forum, vol. 28, no. 8, pp. 2104–2116, 2009. View at Publisher · View at Google Scholar · View at Scopus
  32. H. Zhang, Y. Liu, and Z. Ma, “Fusing inherent and external knowledge with nonlinear learning for cross-media retrieval,” Neurocomputing, vol. 119, pp. 10–16, 2013. View at Publisher · View at Google Scholar · View at Scopus
  33. X. Gao, J. Cao, Z. Jin, X. Li, and J. Li, “GeSoDeck: a geo-social event detection and tracking system,” in Proceedings of the 21st ACM International Conference on Multimedia (MM '13), pp. 471–472, Catalunya, Spain, October 2013. View at Publisher · View at Google Scholar · View at Scopus
  34. X. Gao, J. Cao, Q. He, and J. Li, “A novel method for geographical social event detection in social media,” in Proceedings of the 5th International Conference on Internet Multimedia Computing and Service (ICIMCS '13), pp. 305–308, ACM, August 2013. View at Publisher · View at Google Scholar · View at Scopus
  35. X. Gao, S. C. H. Hoi, Y. Zhang, J. Wan, and J. Li, “Soml: sparse online metric learning with application to image retrieval,” in Proceedings of the 28th AAAI Conference on Artificial Intelligence, AAAI, Quebec City, Canada, July 2014.
  36. Z. Chen, Y. Chen, S. Wang, and Z. Zhao, “A supervised learning based semantic location extraction method using mobile phone data,” in Proceedings of the IEEE International Conference on Computer Science and Automation Engineering (CSAE '12), vol. 3, pp. 548–551, IEEE, Zhangjiajie, China, May 2012. View at Publisher · View at Google Scholar · View at Scopus
  37. Z. Zhao, Y. Chen, S. Wang, and Z. Chen, “Fallalarm: smart phone based fall detecting and positioning system,” in Proceedings of the 3rd International Conference on Ambient Systems, Networks and Technologies (ANT '12), the 9th International Conference on Mobile Web Information Systems (MobiWIS '12), pp. 617–624, Niagara Falls, Canada, August 2012.
  38. Y. Chen, Z. Chen, J. Liu, D. H. Hu, and Q. Yang, “Surrounding context and episode awareness using dynamic bluetooth data,” in Proceedings of the 14th International Conference on Ubiquitous Computing (UbiComp '12), pp. 629–630, September 2012. View at Scopus
  39. Y. Chen, Z. Zhao, S. Wang, and Z. Chen, “Extreme learning machine-based device displacement free activity recognition model,” Soft Computing, vol. 16, no. 9, pp. 1617–1625, 2012. View at Publisher · View at Google Scholar · View at Scopus
  40. Z. Chen, “Mining individual behavior pattern based on significant locations and spatial trajectories,” in Proceedings of the IEEE International Conference on Pervasive Computing and Communications Workshops (PERCOM Workshops '12), pp. 540–541, Lugano, Switzerland, March 2012. View at Publisher · View at Google Scholar · View at Scopus
  41. Z. Chen, S. Wang, Y. Chen, Z. Zhao, and M. Lin, “InferLoc: calibration free based location inference for temporal and spatial fine-granularity magnitude,” in Proceedings of the 15th IEEE International Conference on Computational Science and Engineering (CSE '12), pp. 453–460, Nicosia, Cyprus, December 2012. View at Publisher · View at Google Scholar · View at Scopus
  42. S. Wang, Y. Chen, and Z. Chen, “Recognizing transportation mode on mobile phone using probability fusion of extreme learning machines,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 21, supplement 2, pp. 13–22, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  43. C.-W. You, N. D. Lane, F. Chen et al., “CarSafe app: alerting drowsy and distracted drivers using dual cameras on smartphones,” in Proceedings of the 11th Annual International Conference on Mobile Systems, Applications, and Services (MobiSys '13), pp. 13–26, ACM, Taipei, Taiwan, June 2013. View at Publisher · View at Google Scholar · View at Scopus
  44. Z. Chen, M. Lin, F. Chen et al., “Unobtrusive sleep monitoring using smartphones,” in Proceedings of the 7th International Conference on Pervasive Computing Technologies for Healthcare and Workshops (PervasiveHealth '13), pp. 145–152, May 2013. View at Publisher · View at Google Scholar · View at Scopus
  45. Z. Chen, S. Wang, Z. Shen, Y. Chen, and Z. Zhao, “Online sequential ELM based transfer learning for transportation mode recognition,” in Proceedings of the 6th IEEE International Conference on Cybernetics and Intelligent Systems (CIS '13), pp. 78–83, IEEE, Manila, Philippines, November 2013. View at Publisher · View at Google Scholar · View at Scopus
  46. Z. Chen, Y. Chen, S. Wang, J. Liu, X. Gao, and A. T. Campbell, “Inferring social contextual behavior from bluetooth traces,” in Proceedings of the ACM Conference on Ubiquitous Computing (UbiComp '13), pp. 267–270, Zurich, Switzerland, September 2013. View at Publisher · View at Google Scholar · View at Scopus
  47. Z. Zhao, Z. Chen, Y. Chen, S. Wang, and H. Wang, “A class incremental extreme learning machine for activity recognition,” Cognitive Computation, vol. 6, no. 3, pp. 423–431, 2014. View at Publisher · View at Google Scholar · View at Scopus
  48. Z. Chen, Y. Chen, L. Hu et al., “ContextSense: unobtrusive discovery of incremental social context using dynamic bluetooth data,” in Proceedings of the ACM International Joint Conference on Pervasive and Ubiquitous Computing (UbiComp '14), pp. 23–26, ACM, Seattle, Wash, USA, September 2014. View at Publisher · View at Google Scholar · View at Scopus
  49. L. Hu, Y. Chen, S. Wang, and Z. Chen, “b-COELM: a fast, lightweight and accurate activity recognition model for mini-wearable devices,” Pervasive and Mobile Computing, vol. 15, pp. 200–214, 2014. View at Publisher · View at Google Scholar · View at Scopus
  50. L. K. Platzman and I. Bartholdi, “Spacefilling curves and the planar travelling salesman problem,” Journal of the ACM, vol. 36, no. 4, pp. 719–737, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  51. Y. Zhang, C. Yan, F. Dai, and Y. Ma, “Efficient parallel framework for H.264/AVC deblocking filter on many-core platform,” IEEE Transactions on Multimedia, vol. 14, no. 3, pp. 510–524, 2012. View at Publisher · View at Google Scholar · View at Scopus
  52. C. Yan, Y. Zhang, J. Xu et al., “A highly parallel framework for HEVC coding unit partitioning tree decision on many-core processors,” IEEE Signal Processing Letters, vol. 21, no. 5, pp. 573–576, 2014. View at Publisher · View at Google Scholar · View at Scopus
  53. C. Yan, Y. Zhang, J. Xu et al., “Efficient parallel framework for HEVC motion estimation on many-core processors,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 24, no. 12, pp. 2077–2089, 2014. View at Publisher · View at Google Scholar · View at Scopus