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Models and algorithms for the traffic assignment problem with link capacity constraints


  • Nie, Yu
  • Zhang, H. M.
  • Lee, Der-Horng


This paper explores the models as well as solution techniques for the link capacitated traffic assignment problem (CTAP) that is capable of offering more realistic traffic assignment results. CTAP can be approximated by the uncapacitated TAP using different dual/penalty strategies. Two important and distinctive approaches in this category are studied and implemented efficiently. The inner penalty function (IPF) approach establishes a barrier on the boundary of the feasible set so that constraints are not violated in the solution process, and the augmented Lagrangian multiplier (ALM) approach combines the exterior penalty with primal-dual and Lagrangian multipliers concepts. In both implementations, a gradient projection (GP) algorithm was adopted as the uniform subproblem solver for its excellent convergence property and reoptimization capability. Numerous numerical results demonstrated through efficient implementations of either the IPF or the ALM approach that CTAP is computationally tractable even for large-scale problems. Moreover, the relative efficiency of IPF and ALM was explored and their sensitivity to different algorithmic issues was investigated.

Suggested Citation

  • Nie, Yu & Zhang, H. M. & Lee, Der-Horng, 2004. "Models and algorithms for the traffic assignment problem with link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 285-312, May.
  • Handle: RePEc:eee:transb:v:38:y:2004:i:4:p:285-312

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    References listed on IDEAS

    1. Yang, Hai & Yagar, Sam, 1995. "Traffic assignment and signal control in saturated road networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 125-139, March.
    2. Jayakrishnan, R. & Tsai, Wei T. & Prashker, Joseph N. & Rajadhyaksha, Subodh, 1994. "A Faster Path-Based Algorithm for Traffic Assignment," University of California Transportation Center, Working Papers qt2hf4541x, University of California Transportation Center.
    3. Yang, Hai & Yagar, Sam, 1994. "Traffic assignment and traffic control in general freeway-arterial corridor systems," Transportation Research Part B: Methodological, Elsevier, vol. 28(6), pages 463-486, December.
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    Cited by:

    1. Wang, David Z.W. & Liu, Haoxiang & Szeto, W.Y., 2015. "A novel discrete network design problem formulation and its global optimization solution algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 213-230.
    2. repec:kap:netspa:v:17:y:2017:i:2:d:10.1007_s11067-016-9335-9 is not listed on IDEAS
    3. Ernesto Cipriani & Michael Florian & Michael Mahut & Marialisa Nigro, 2010. "Investigating the Efficiency of a Gradient Approximation Approach for the Solution of Dynamic Demand Estimation Problems," Chapters,in: New Developments in Transport Planning, chapter 18 Edward Elgar Publishing.
    4. Chen, Anthony & Choi, Keechoo, 2017. "Solving the combined modal split and traffic assignment problem with two types of transit impedance functionAuthor-Name: Ryu, Seungkyu," European Journal of Operational Research, Elsevier, vol. 257(3), pages 870-880.
    5. Yang, Hai & Wang, Xiaolei, 2011. "Managing network mobility with tradable credits," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 580-594, March.
    6. Bliemer, Michiel C.J. & Raadsen, Mark P.H. & Smits, Erik-Sander & Zhou, Bojian & Bell, Michael G.H., 2014. "Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 363-384.
    7. repec:eee:transb:v:106:y:2017:i:c:p:293-320 is not listed on IDEAS
    8. Seungkyu Ryu & Anthony Chen & Xiangdong Xu & Keechoo Choi, 2014. "A Dual Approach for Solving the Combined Distribution and Assignment Problem with Link Capacity Constraints," Networks and Spatial Economics, Springer, vol. 14(2), pages 245-270, June.
    9. Liu, Jiangtao & Zhou, Xuesong, 2016. "Capacitated transit service network design with boundedly rational agents," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 225-250.
    10. Bagloee, Saeed Asadi & Sarvi, Majid & Wolshon, Brian & Dixit, Vinayak, 2017. "Identifying critical disruption scenarios and a global robustness index tailored to real life road networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 98(C), pages 60-81.
    11. Nie, Yu (Marco), 2017. "On the potential remedies for license plate rationing," Economics of Transportation, Elsevier, vol. 9(C), pages 37-50.

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