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

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

Abstract

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

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    1. 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.
    2. Torbjörn Larsson & Michael Patriksson, 1992. "Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 26(1), pages 4-17, February.
    3. 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.
    4. 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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