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ARTICLES

Reduced gradient algorithm for user equilibrium traffic assignment problem

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Pages 1111-1135 | Received 02 Aug 2018, Accepted 02 Dec 2019, Published online: 19 Feb 2020

References

  • Babazadeh, A. 2005. “Equilibrium Transit Assignment Problem in Congested Networks: Formulation and Solution Algorithm.” Ph.D. diss., Sharif University of Technology, Tehran, Iran.
  • Babazadeh A., and H. Z. Aashtiani. 2005. “Algorithm for Equilibrium Transit Assignment Problem.” Transportation Research Record: Journal of the Transportation Research board 1923: 227–235. doi: 10.1177/0361198105192300124
  • Bar-Gera, H. 2002. “Origin-Based Algorithm for the Traffic Assignment Problem.” Transportation Science 36 (4): 398–417. doi: 10.1287/trsc.36.4.398.549
  • Bar-Gera, H. 2010. “Traffic Assignment by Paired Alternative Segments.” Transportation Research Part B: Methodological 44 (8): 1022–1046. doi: 10.1016/j.trb.2009.11.004
  • Bar-Gera, H. 2015. Transportation Test Networks. Accessed June, 2015. http://www.bgu.ac.il/~bargera/tntp.
  • Bazaraa, M. S., H. D. Sherali, and C. M. Shetty. 2006. Nonlinear Programming: Theory and Algorithms. 3rd ed. Hoboken: John Wiley & Sons.
  • Beckmann, M., C. B. McGuire, and C. B. Winsten. 1956. Studies in the Economics of Transportation. New Haven, Connecticut: Yale University Press.
  • Bertsekas, D. 1976. “On the Goldstein-Levitin-Polyak Gradient Projection Method.” IEEE Transactions on Automatic Control 21 (2): 174–184. doi: 10.1109/TAC.1976.1101194
  • Chen, A. 2001. “Effects of Flow Update Strategies on Implementation of the Frank-Wolfe Algorithm for the Traffic Assignment Problem.” Transportation Research Record: Journal of the Transportation Research Board 1771: 132–139. doi: 10.3141/1771-17
  • Chen, A., R. Jayakrishnan, and W. K. Tsai. 2002. “Faster Frank-Wolfe Traffic Assignment with New Flow Update Scheme.” Journal of Transportation Engineering 128 (1): 31–39. doi: 10.1061/(ASCE)0733-947X(2002)128:1(31)
  • Chen, A., and D. H. Lee. 1999. “Path-Based Algorithms for Large Scale Traffic Equilibrium Problems: A Comparison Between DSD and GP.” In 78th Annual Meeting of the Transportation Research Board, Washington, DC.
  • Chen, A., D. H. Lee, and R. Jayakrishnan. 2002. “Computational Study of State-of-the-Art Path-Based Traffic Assignment Algorithms.” Mathematics and Computers in Simulation 59 (6): 509–518. doi: 10.1016/S0378-4754(01)00437-2
  • Chen, A., X. Xu, S. Ryu, and Z. Zhou. 2013. “A Self-Adaptive Armijo Stepsize Strategy with Application to Traffic Assignment Models and Algorithms.” Transportmetrica A: Transport Science 9 (8): 695–712. doi: 10.1080/18128602.2011.653999
  • Dafermos, S. C., and F. T. Sparrow. 1969. “The Traffic Assignment Problem for a General Network.” Journal of Research of the National Bureau of Standards B 73 (2): 91–118.
  • Dial, R. B. 2006. “A Path-Based User-Equilibrium Traffic Assignment Algorithm That Obviates Path Storage and Enumeration.” Transportation Research Part B: Methodological 40 (10): 917–936. doi: 10.1016/j.trb.2006.02.008
  • Di Lorenzo, D., A. Galligari, and M. Sciandrone. 2015. “A Convergent and Efficient Decomposition Method for the Traffic Assignment Problem.” Computational Optimization and Applications 60 (1): 151–170. doi: 10.1007/s10589-014-9668-6
  • Emme release 4.3.5. 2017. INRO Consultants, Inc., Montreal, Canada.
  • Florian, M., I. Constantin, and D. Florian. 2009. “A New Look at Projected Gradient Method for Equilibrium Assignment.” Transportation Research Record: Journal of the Transportation Research Board 2090: 10–16. doi: 10.3141/2090-02
  • Florian, M., and S. Nguyen. 1974. “A Method for Computing Network Equilibrium with Elastic Demands.” Transportation Science 8 (4): 321–332. doi: 10.1287/trsc.8.4.321
  • Frank, M., and P. Wolfe. 1956. “An Algorithm for Quadratic Programming.” Naval Research Logistics Quarterly 3 (1-2): 95–110. doi: 10.1002/nav.3800030109
  • Galligari, A., and M. Sciandrone. 2018. “A Convergent and Fast Path Equilibration Algorithm for the Traffic Assignment Problem.” Optimization Methods and Software 33 (2): 354–371. doi: 10.1080/10556788.2017.1332621
  • General Algebraic Modeling System (GAMS) release 25.1.2. 2018. GAMS Development Corporation, Fairfax, VA, USA.
  • Gentile, G. 2014. “Local User Cost Equilibrium: a Bush-Based Algorithm for Traffic Assignment.” Transportmetrica A: Transport Science 10 (1): 15–54. doi: 10.1080/18128602.2012.691911
  • Gentile, G. 2016. “Solving a Dynamic User Equilibrium model based on splitting rates with Gradient Projection algorithms.” Transportation Research Part B: Methodological 92: 120–147. doi: 10.1016/j.trb.2016.02.005
  • Holmgren, J., and P. O. Lindberg. 2014. “Upright Stiff: Subproblem Updating in the FW Method for Traffic Assignment.” EURO Journal on Transportation and Logistics 3 (3-4): 205–225. doi: 10.1007/s13676-013-0031-3
  • Inoue, S. I., and T. Maruyama. 2012. “Computational Experience on Advanced Algorithms for User Equilibrium Traffic Assignment Problem and its Convergence Error.” Procedia-Social and Behavioral Sciences 43: 445–456. doi: 10.1016/j.sbspro.2012.04.118
  • Javani, B., and A. Babazadeh. 2017. “Origin-Destination-Based Truncated Quadratic Programming Algorithm for Traffic Assignment Problem.” Transportation Letters 9 (3): 166–176. doi: 10.1080/19427867.2016.1227531
  • Jayakrishnan, R., W. T. Tsai, J. N. Prashker, and S. Rajadhyaksha. 1994. “A Faster Path-Based Algorithm for Traffic Assignment.” Transportation Research Record: Journal of the Transportation Research Board 1443: 75–83.
  • Kumar, A., and S. Peeta. 2010. “Slope-Based Multipath Flow Update Algorithm for Static User Equilibrium Traffic Assignment Problem.” Transportation Research Record: Journal of the Transportation Research Board 2196: 1–10. doi: 10.3141/2196-01
  • Kumar, A., and S. Peeta. 2014a. “Slope-Based Path Shift Propensity Algorithm for the Static Traffic Assignment Problem.” International Journal for Traffic and Transport Engineering 4 (3): 297–319. doi: 10.7708/ijtte.2014.4(3).05
  • Kumar, A., and S. Peeta. 2014b. “Strategies to Enhance the Performance of Path-Based Static Traffic Assignment Algorithms.” Computer-Aided Civil and Infrastructure Engineering 29 (5): 330–341. doi: 10.1111/mice.12056
  • Kumar, A., S. Peeta, and Y. Nie. 2012. “Update Strategies for Restricted Master Problems for User Equilibrium Traffic Assignment Problem: Computational Study.” Transportation Research Record: Journal of the Transportation Research Board 2283: 131–142. doi: 10.3141/2283-14
  • Larsson, T., and M. Patriksson. 1992. “Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem.” Transportation Science 26 (1): 4–17. doi: 10.1287/trsc.26.1.4
  • LeBlanc, L. J., E. K. Morlok, and W. P. Pierskalla. 1975. “An Efficient Approach to Solving the Road Network Equilibrium Traffic Assignment Problem.” Transportation Research 9 (5): 309–318. doi: 10.1016/0041-1647(75)90030-1
  • Lee, D. H., Y. Nie, and A. Chen. 2003. “A Conjugate Gradient Projection Algorithm for the Traffic Assignment Problem.” Mathematical and Computer Modelling 37 (7-8): 863–878. doi: 10.1016/S0895-7177(03)00090-6
  • Luenberger, D. G., and Y. Ye. 2008. Linear and Nonlinear Programming. 3rd ed. Volume 116 of International Series in Operations Research & Management Science. New York: Springer.
  • McCormick, G. P. 1970. “The Variable Reduction Method for Nonlinear Programming.” Management Science 17 (3): 146–160. doi: 10.1287/mnsc.17.3.146
  • Mitradjieva, M., and P. O. Lindberg. 2013. “The Stiff is Moving—Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment.” Transportation Science 47 (2): 280–293. doi: 10.1287/trsc.1120.0409
  • Nguyen, S. 1974. “An Algorithm for the Traffic Assignment Problem.” Transportation Science 8 (3): 203–216. doi: 10.1287/trsc.8.3.203
  • Nie, Y. M. 2010. “A Class of Bush-Based Algorithms for the Traffic Assignment Problem.” Transportation Research Part B: Methodological 44 (1): 73–89. doi: 10.1016/j.trb.2009.06.005
  • Open Channel Foundation. 2014. Accessed October, 2014. http://www.openchannelfoundation.org.
  • Patriksson, M. 1994. The Traffic Assignment Problem: Models and Methods. Utrecht, Netherlands: VSP.
  • Perederieieva, O., M. Ehrgott, A. Raith, and J. Y. Wang. 2015. “A Framework for and Empirical Study of Algorithms for Traffic Assignment.” Computers & Operations Research 54: 90–107. doi: 10.1016/j.cor.2014.08.024
  • Perederieieva, O., M. Ehrgott, A. Raith, and J. Y. Wang. 2016. “Numerical Stability of Path-Based Algorithms for Traffic Assignment.” Optimization Methods and Software 31 (1): 53–67. doi: 10.1080/10556788.2015.1047018
  • Rosen, J. B. 1960. “The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints.” Journal of the Society for Industrial and Applied Mathematics 8 (1): 181–217. doi: 10.1137/0108011
  • Sheffi, Y. 1985. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Englewood Cliffs, NJ: Prentice Hall.
  • Visum release 16.01-12. 2016. PTV Group., Karlsruhe, Germany.
  • Wardrop, J. G. 1952. “Road Paper. Some Theoretical Aspects of Road Traffic Research.” Proceedings of the Institution of Civil Engineers 1 (3): 325–362. doi: 10.1680/ipeds.1952.11259
  • Wolfe, P. 1967. “Methods of Nonlinear Programming. Chapter 6 of Nonlinear Programming.” In Interscience, edited by J. Abadie, 97–131. New York: John Wiley.
  • Wolfe, P. 1972. “On the Convergence of Gradient Methods Under Constraint.” IBM Journal of Research and Development 16 (4): 407–411. doi: 10.1147/rd.164.0407
  • Xie, J., Y. Nie, and X. Liu. 2018. “A Greedy Path-Based Algorithm for Traffic Assignment.” In Transportation Research Board 97th Annual Meeting, Washington DC, USA, January 7–11. Transportation Research Board.
  • Xie, J., and C. Xie. 2015. “Origin-Based Algorithms for Traffic Assignment: Algorithmic Structure, Complexity Analysis, and Convergence Performance.” Transportation Research Record: Journal of the Transportation Research Board 2498: 46–55. doi: 10.3141/2498-06
  • Zangwill, W. I. 1969. Nonlinear Programming: A Unified Approach. Englewood Cliffs, NJ: Prentice-Hall.
  • Zheng, H. 2015. “Adaptation of Network Simplex for the Traffic Assignment Problem.” Transportation Science 49 (3): 543–558. doi: 10.1287/trsc.2014.0574

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