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Mathematical Problems in Engineering
Volume 2017, Article ID 5839192, 11 pages
https://doi.org/10.1155/2017/5839192
Research Article

Designing Vehicle Turning Restrictions Based on the Dual Graph Technique

1College of Civil Engineering and Architecture, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, China
2School of Transportation and Logistics, Dalian University of Technology, No. 2, Linggong Road, Dalian, China

Correspondence should be addressed to Hongsheng Qi; nc.ude.ujz@gnehsgnohiq

Received 23 November 2016; Accepted 12 March 2017; Published 6 April 2017

Academic Editor: Salvatore Alfonzetti

Copyright © 2017 Lihui Zhang 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. Braess, “Über ein paradoxon aus der verkehrsplanung,” Unternehmenforschung, vol. 12, pp. 258–268, 1968. View at Google Scholar · View at MathSciNet
  2. W. H. K. Lam, “Optimization of transport investment and pricing policies: the role of transport pricing in network design,” Transportation Planning and Technology, vol. 13, no. 4, pp. 245–258, 1989. View at Publisher · View at Google Scholar · View at Scopus
  3. E. I. Pas and S. L. Principio, “Braess' paradox: some new insights,” Transportation Research Part B: Methodological, vol. 31, no. 3, pp. 265–276, 1997. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Nagurney, “Congested urban transportation networks and emission paradoxes,” Transportation Research Part D: Transport and Environment, vol. 5, no. 2, pp. 145–151, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Nagurney, “The negation of the Braess paradox as demand increases: the wisdom of crowds in transportation networks,” EPL, vol. 91, no. 4, Article ID 48002, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Long, Z. Gao, H. Zhang, and W. Y. Szeto, “A turning restriction design problem in urban road networks,” European Journal of Operational Research, vol. 206, no. 3, pp. 569–578, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. J. Q. Ying and H. Yang, “Sensitivity analysis of stochastic user equilibrium flows in a bi-modal network with application to optimal pricing,” Transportation Research Part B: Methodological, vol. 39, no. 9, pp. 769–795, 2005. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Q. Ying, H. Lu, and J. Shi, “An algorithm for local continuous optimization of traffic signals,” European Journal of Operational Research, vol. 181, no. 3, pp. 1189–1197, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. S. Bekhor, M. E. Ben-Akiva, and M. S. Ramming, “Route choice: choice set generation and probabilistic choice models,” in Proceedings of the 4th TRISTAN Conference, Azores, Portugal, 2001.
  10. R. B. Dial, “A probabilistic multipath traffic assignment model which obviates path enumeration,” Transportation Research, vol. 5, no. 2, pp. 83–111, 1971. View at Publisher · View at Google Scholar · View at Scopus
  11. H. X. Liu, X. He, and B. He, “Method of successive weighted averages (MSWA) and self-regulated averaging schemes for solving stochastic user equilibrium problem,” Networks and Spatial Economics, vol. 9, no. 4, pp. 485–503, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. Long, W. Y. Szeto, and H.-J. Huang, “A bi-objective turning restriction design problem in urban road networks,” European Journal of Operational Research, vol. 237, no. 2, pp. 426–439, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. D. Karaboga, “An idea based on honey bee swarm for numerical optimization,” Technical Report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, Kayseri, Turkey, 2005. View at Google Scholar
  14. L. R. Foulds, D. C. Duarte, H. A. do Nascimento, H. J. Longo, and B. R. Hall, “Turning restriction design in traffic networks with a budget constraint,” Journal of Global Optimization, vol. 60, no. 2, pp. 351–371, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. R. B. Potts and R. M. Oliver, Flows in Transportation Networks, Academic Press, London, UK, 1972. View at MathSciNet
  16. F. Palacios-gomez, L. Lasdon, and M. Engquist, “Nonlinear optimization by successive linear programming,” Management Science, vol. 28, no. 10, pp. 1106–1120, 1982. View at Google Scholar · View at Scopus
  17. H. D. Sherali, A. Narayanan, and R. Sivanandan, “Estimation of origin-destination trip-tables based on a partial set of traffic link volumes,” Transportation Research Part B: Methodological, vol. 37, no. 9, pp. 815–836, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. G. B. Dantzig and P. Wolfe, “Decomposition principle for linear programs,” Operations Research, vol. 8, no. 1, pp. 101–111, 1960. View at Publisher · View at Google Scholar
  19. G. Brønmo, M. Christiansen, K. Fagerholt, and B. Nygreen, “A multi-start local search heuristic for ship scheduling—a computational study,” Computers and Operations Research, vol. 34, no. 3, pp. 900–917, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Añez, T. De La Barra, and B. Pérez, “Dual graph representation of transport networks,” Transportation Research Part B: Methodological, vol. 30, no. 3, pp. 209–216, 1996. View at Publisher · View at Google Scholar · View at Scopus
  21. L. J. Leblanc, “Algorithm for the discrete network design problem,” Transportation Science, vol. 9, no. 3, pp. 183–199, 1975. View at Publisher · View at Google Scholar · View at Scopus
  22. L. Zhang, S. Lawphongpanich, and Y. Yin, “Reformulating and solving discrete network design problem via an active set technique,” in Proceedings of the 18th International Symposium on Transportation and Traffic Theory, W. H. K. Lam, S. C. Wong, and H. K. Lo, Eds., pp. 283–300, Springer, Hong Kong, 2009.
  23. S. Wang, Q. Meng, and H. Yang, “Global optimization methods for the discrete network design problem,” Transportation Research Part B: Methodological, vol. 50, pp. 42–60, 2013. View at Publisher · View at Google Scholar · View at Scopus
  24. M. Beckmann, C. Mcguire, and C. Winsten, Studies in the Economics of Transportation, Yale University Press, New Haven, Conn, USA, 1956.
  25. M. Aghassi, D. Bertsimas, and G. Perakis, “Solving asymmetric variational inequalities via convex optimization,” Operations Research Letters, vol. 34, no. 5, pp. 481–490, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. D. Z. W. Wang and H. K. Lo, “Global optimum of the linearized network design problem with equilibrium flows,” Transportation Research Part B: Methodological, vol. 44, no. 4, pp. 482–492, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. H. Farvaresh and M. M. Sepehri, “A single-level mixed integer linear formulation for a bi-level discrete network design problem,” Transportation Research Part E: Logistics and Transportation Review, vol. 47, no. 5, pp. 623–640, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. K. G. Murty, Linear Complementarity, Linear and Nonlinear Programming, vol. 3 of Sigma Series in Applied Mathematics, Heldermann, Berlin, Germany, 1988. View at MathSciNet
  29. J. Nocedal and S. J. Wright, Numerical Optimization, Springer Series in Operations Research and Financial Engineering, Springer, New York, NY, USA, 2nd edition, 2006. View at MathSciNet
  30. Y. Shafahi and R. Faturechi, “A new fuzzy approach to estimate the O–D matrix from link volumes,” Transportation Planning and Technology, vol. 32, no. 6, pp. 499–526, 2009. View at Publisher · View at Google Scholar
  31. A. Brooke, D. Kendrick, A. Meeraus, and R. Raman, GAMS: A User's Guide, GAMS Development Corporation, Washington, DC, USA, 2005.
  32. L. Zhang and J. Sun, “Dual-based heuristic for optimal cordon pricing design,” Journal of Transportation Engineering, vol. 139, no. 11, pp. 1105–1116, 2013. View at Publisher · View at Google Scholar · View at Scopus