Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 345049, 23 pages
http://dx.doi.org/10.1155/2015/345049
Research Article

A Universal Concept for Robust Solving of Shortest Path Problems in Dynamically Reconfigurable Graphs

Institute of Smart Systems Technologies, Transportation Informatics Group (TIG), Universität Klagenfurt, Klagenfurt, Austria

Received 27 May 2015; Accepted 4 November 2015

Academic Editor: John D. Clayton

Copyright © 2015 Jean Chamberlain Chedjou and Kyandoghere Kyamakya. 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.-H. Kim and H. Myung, “Evolutionary programming techniques for constrained optimization problems,” IEEE Transactions on Evolutionary Computation, vol. 1, no. 2, pp. 129–140, 1997. View at Publisher · View at Google Scholar · View at Scopus
  2. A. K. Qin, V. L. Huang, and P. N. Suganthan, “Differential evolution algorithm with strategy adaptation for global numerical optimization,” IEEE Transactions on Evolutionary Computation, vol. 13, no. 2, pp. 398–417, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Verblunsky, “On the shortest path through a number of points,” Proceedings of the American Mathematical Society, vol. 2, no. 6, pp. 904–913, 1951. View at Publisher · View at Google Scholar · View at MathSciNet
  4. S. Kim, M. E. Lewis, and C. C. White III, “Optimal vehicle routing with real-time traffic information,” IEEE Transactions on Intelligent Transportation Systems, vol. 6, no. 2, pp. 178–188, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. S.-T. Liu and C. Kao, “Network flow problems with fuzzy arc lengths,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 34, no. 1, pp. 765–769, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. A. R. Willms and S. X. Yang, “Real-time robot path planning via a distance-propagating dynamic system with obstacle clearance,” IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, vol. 38, no. 3, pp. 884–893, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. C. Chenghui and S. Ferrari, “Information-driven sensor path planning by approximate cell decomposition,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 39, no. 3, pp. 672–689, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. X. Zhu and W. E. Wilhelm, “Three-stage approaches for optimizing some variations of the resource constrained shortest-path sub-problem in a column generation context,” European Journal of Operational Research, vol. 183, no. 2, pp. 564–577, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Changming, “De-interlacing of video images using a shortest path technique,” IEEE Transactions on Consumer Electronics, vol. 47, no. 2, pp. 225–230, 2001. View at Publisher · View at Google Scholar · View at Scopus
  10. J. Cong, A. B. Kahng, and K.-S. Leung, “Efficient algorithms for the minimum shortest path steiner arborescence problem with applications to VLSI physical design,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 17, no. 1, pp. 24–39, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. T. Deschamps and L. D. Cohen, “Fast extraction of minimal paths in 3D images and applications to virtual endoscopy,” Medical Image Analysis, vol. 5, no. 4, pp. 281–299, 2001. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. Boykov and V. Kolmogorov, “An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1124–1137, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. L. Fu, “An adaptive routing algorithm for in-vehicle route guidance systems with real-time information,” Transportation Research Part B: Methodological, vol. 35, no. 8, pp. 749–765, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. M.-Y. Kao, Encyclopedia of Algorithms, Springer, New York, NY, USA, 2008.
  15. E. Nardelli, G. Proietti, and P. Widmayer, “Finding the most vital node of a shortest path,” Theoretical Computer Science, vol. 296, no. 1, pp. 167–177, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. A. Broder, R. Kumar, F. Maghoul et al., “Graph structure in the Web,” Computer Networks, vol. 33, no. 1, pp. 309–320, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. R. E. Bellman, Dynamic Programming, Princeton University Press, 1957. View at MathSciNet
  18. E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, no. 1, pp. 269–271, 1959. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. R. Bellman, “On a routing problem,” Quarterly of Applied Mathematics, vol. 16, pp. 87–90, 1958. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. L. R. Ford and D. R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, NJ, USA, 1962.
  21. L. Fu, D. Sun, and L. R. Rilett, “Heuristic shortest path algorithms for transportation applications: state of the art,” Computers & Operations Research, vol. 33, no. 11, pp. 3324–3343, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. G. Tsaggouris and C. Zaroliagis, “Non-additive shortest paths,” in Algorithms—ESA 2004, vol. 3221 of Lecture Notes in Computer Science, pp. 822–834, Springer, Berlin, Germany, 2004. View at Publisher · View at Google Scholar
  23. P. Narváez, K.-Y. Siu, and H.-Y. Tzeng, “New dynamic algorithms for shortest path tree computation,” IEEE/ACM Transactions on Networking, vol. 8, no. 6, pp. 734–746, 2000. View at Publisher · View at Google Scholar · View at Scopus
  24. A. V. Goldberg, “Scaling algorithms for the shortest paths problem,” SIAM Journal on Computing, vol. 24, no. 3, pp. 494–504, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  25. U. Zwick, “All pairs shortest paths using bridging sets and rectangular matrix multiplication,” Journal of the ACM, vol. 49, no. 3, pp. 289–317, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. S. Pettie, “A new approach to all-pairs shortest paths on real-weighted graphs,” Theoretical Computer Science, vol. 312, no. 1, pp. 47–74, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  27. M. Thorup, “Undirected single-source shortest paths with positive integer weights in linear time,” Journal of the ACM, vol. 46, no. 3, pp. 362–394, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. J. C. Nash, “The (Dantzig) simplex method for linear programming,” Computing in Science & Engineering, vol. 2, no. 1, pp. 29–31, 2000. View at Publisher · View at Google Scholar · View at Scopus
  29. C.-W. Ahn and R. S. Ramakrishna, “A genetic algorithm for shortest path routing problem and the sizing of populations,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 6, pp. 566–579, 2002. View at Publisher · View at Google Scholar · View at Scopus
  30. J. Zhang and A. C. Sanderson, “JADE: adaptive differential evolution with optional external archive,” IEEE Transactions on Evolutionary Computation, vol. 13, no. 5, pp. 945–958, 2009. View at Publisher · View at Google Scholar
  31. H. Beigy and M. R. Meybodi, “Utilizing distributed learning automata to solve stochastic shortest path problems,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 14, no. 5, pp. 591–615, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. B. Moradabadi and H. Beigy, “A new real-coded Bayesian optimization algorithm based on a team of learning automata for continuous optimization,” Genetic Programming and Evolvable Machines, vol. 15, no. 2, pp. 169–193, 2014. View at Publisher · View at Google Scholar · View at Scopus
  33. X. J. Wu and H. F. Xue, “Shortest path algorithm based on cellular automata extend model,” Computer Applications, vol. 24, pp. 92–103, 2004. View at Google Scholar
  34. M. Wang, Y. Qian, and X. Guang, “Improved calculation method of shortest path with cellular automata model,” Kybernetes, vol. 41, no. 3-4, pp. 508–517, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. C. W. Ahn, R. S. Ramakrishna, C. G. Kang, and I. C. Choi, “Shortest path routing algorithm using Hopfield neural network,” Electronics Letters, vol. 37, no. 19, pp. 1176–1178, 2001. View at Publisher · View at Google Scholar · View at Scopus
  36. M. K. Mehmet Ali and F. Kamoun, “Neural networks for shortest path computation and routing in computer networks,” IEEE Transactions on Neural Networks, vol. 4, no. 6, pp. 941–954, 1993. View at Publisher · View at Google Scholar · View at Scopus
  37. D.-C. Park and S.-E. Choi, “A neural network based multi-destination routing algorithm for communication network,” in Proceedings of the IEEE International Joint Conference on Neural Networks Proceedings, vol. 2, pp. 1673–1678, IEEE, Anchorage, Alaska, USA, May 1998. View at Publisher · View at Google Scholar
  38. J. J. Hopfield and D. W. Tank, “‘Neural’ computation of decisons in optimization problems,” Biological Cybernetics, vol. 52, no. 3, pp. 141–152, 1985. View at Google Scholar · View at MathSciNet · View at Scopus
  39. U.-P. Wen, K.-M. Lan, and H.-S. Shih, “A review of Hopfield neural networks for solving mathematical programming problems,” European Journal of Operational Research, vol. 198, no. 3, pp. 675–687, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  40. G. G. Lendaris, K. Mathia, and R. Saeks, “Linear Hopfield networks and constrained optimization,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 29, no. 1, pp. 114–118, 1999. View at Publisher · View at Google Scholar · View at Scopus
  41. F. Araújo, B. Ribeiro, and L. Rodrigues, “A neural network for shortest path computation,” IEEE Transactions on Neural Networks, vol. 12, no. 5, pp. 1067–1073, 2001. View at Publisher · View at Google Scholar · View at Scopus
  42. A. Nazemi and F. Omidi, “An efficient dynamic model for solving the shortest path problem,” Transportation Research Part C: Emerging Technologies, vol. 26, pp. 1–19, 2013. View at Publisher · View at Google Scholar · View at Scopus
  43. J. C. Chedjou and K. Kyamakya, “A universal concept based on cellular neural networks for ultrafast and flexible solving of differential equations,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 4, pp. 749–762, 2015. View at Publisher · View at Google Scholar · View at Scopus
  44. J. C. Chedjou and K. Kyamakya, “A Novel general and robust method based on NAOP for solving nonlinear ordinary differential equations and partial differential equations by cellular neural networks,” Journal of Dynamic Systems, Measurement, and Control, vol. 135, no. 3, Article ID 031014, 11 pages, 2013. View at Publisher · View at Google Scholar
  45. S. X. Yang and C. Luo, “A neural network approach to complete coverage path planning,” IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, vol. 34, no. 1, pp. 718–725, 2004. View at Publisher · View at Google Scholar · View at Scopus
  46. Z. Yi, J. C. Lv, and L. Zhang, “Output convergence analysis for a class of delayed recurrent neural networks with time-varying inputs,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 36, no. 1, pp. 87–95, 2006. View at Publisher · View at Google Scholar · View at Scopus
  47. K. E. Parsopoulos and M. N. Vrahatis, “On the computation of all global minimizers through particle swarm optimization,” IEEE Transactions on Evolutionary Computation, vol. 8, no. 3, pp. 211–224, 2004. View at Publisher · View at Google Scholar · View at Scopus