IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v44y2010i1p73-89.html
   My bibliography  Save this article

A class of bush-based algorithms for the traffic assignment problem

Author

Listed:
  • Nie, Yu (Marco)

Abstract

This paper studies a class of bush-based algorithms (BA) for the user equilibrium (UE) traffic assignment problem, which promise to produce highly precise solutions by exploiting acyclicity of UE flows. Each of the two building blocks of BA, namely the construction of acyclic sub-networks (bush) and the solution of restricted master problems (RMP), is examined and further developed. Four Newton-type algorithms for solving RMP, which can be broadly categorized as route flow and origin flow based, are presented, of which one is newly developed in this paper. Similarities and differences between these algorithms, as well as the relevant implementation issues are discussed in great details. A comprehensive numerical study is conducted using both real and randomly generated networks, which reveals that the relative performance of the algorithms is consistent with the analysis. In particular, the results suggest that swapping flows between shortest and longest route segments consistently outperforms other RMP solution techniques.

Suggested Citation

  • Nie, Yu (Marco), 2010. "A class of bush-based algorithms for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 73-89, January.
  • Handle: RePEc:eee:transb:v:44:y:2010:i:1:p:73-89
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(09)00076-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    3. Dial, Robert B., 1999. "Minimal-revenue congestion pricing part I: A fast algorithm for the single-origin case," Transportation Research Part B: Methodological, Elsevier, vol. 33(3), pages 189-202, April.
    4. 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.
    5. Dial, Robert B., 2006. "A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 917-936, December.
    6. Stella C. Dafermos, 1971. "An Extended Traffic Assignment Model with Applications to Two-Way Traffic," Transportation Science, INFORMS, vol. 5(4), pages 366-389, November.
    7. T. Leventhal & G. Nemhauser & L. Trotter, 1973. "A Column Generation Algorithm for Optimal Traffic Assignment," Transportation Science, INFORMS, vol. 7(2), pages 168-176, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    2. Zheng, Hong & Peeta, Srinivas, 2014. "Cost scaling based successive approximation algorithm for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 17-30.
    3. Yu (Marco) Nie, 2012. "A Note on Bar-Gera's Algorithm for the Origin-Based Traffic Assignment Problem," Transportation Science, INFORMS, vol. 46(1), pages 27-38, February.
    4. Liu, Zhiyuan & Chen, Xinyuan & Hu, Jintao & Wang, Shuaian & Zhang, Kai & Zhang, Honggang, 2023. "An alternating direction method of multipliers for solving user equilibrium problem," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1072-1084.
    5. Xie, Chi, 2016. "New insights and improvements of using paired alternative segments for traffic assignmentAuthor-Name: Xie, Jun," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 406-424.
    6. Jafari, Ehsan & Pandey, Venktesh & Boyles, Stephen D., 2017. "A decomposition approach to the static traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 270-296.
    7. Xie, Jun & Nie, Yu (Marco) & Yang, Xiaoguang, 2013. "Quadratic approximation and convergence of some bush-based algorithms for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 15-30.
    8. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    9. Taesung Hwang, 2021. "Assignment of Freight Truck Shipment on the U.S. Highway Network," Sustainability, MDPI, vol. 13(11), pages 1-11, June.
    10. Rambha, Tarun & Boyles, Stephen D., 2016. "Dynamic pricing in discrete time stochastic day-to-day route choice models," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 104-118.
    11. Shen, Wei & Wynter, Laura, 2012. "A new one-level convex optimization approach for estimating origin–destination demand," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1535-1555.
    12. Maria Mitradjieva & Per Olov Lindberg, 2013. "The Stiff Is Moving---Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment ," Transportation Science, INFORMS, vol. 47(2), pages 280-293, May.
    13. Bai, Yun & Hwang, Taesung & Kang, Seungmo & Ouyang, Yanfeng, 2011. "Biofuel refinery location and supply chain planning under traffic congestion," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 162-175, January.
    14. Zhang, Honggang & Liu, Zhiyuan & Wang, Jian & Wu, Yunchi, 2023. "A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 174(C).
    15. Wang, Dong & Liao, Feixiong & Gao, Ziyou & Rasouli, Soora & Huang, Hai-Jun, 2020. "Tolerance-based column generation for boundedly rational dynamic activity-travel assignment in large-scale networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    16. Jafari, Ehsan & Boyles, Stephen D., 2016. "Improved bush-based methods for network contraction," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 298-313.
    17. Smith, Mike & Mounce, Richard, 2011. "A splitting rate model of traffic re-routeing and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1389-1409.
    18. Perederieieva, Olga & Raith, Andrea & Schmidt, Marie, 2018. "Non-additive shortest path in the context of traffic assignment," European Journal of Operational Research, Elsevier, vol. 268(1), pages 325-338.
    19. Liu, Zhiyuan & Zhang, Honggang & Zhang, Kai & Zhou, Zihan, 2023. "Integrating alternating direction method of multipliers and bush for solving the traffic assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    20. Wang, Aihu & Tang, Yuanhua & Mohmand, Yasir Tariq & Xu, Pei, 2022. "Modifying link capacity to avoid Braess Paradox considering elastic demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:44:y:2010:i:1:p:73-89. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.