IDEAS home Printed from https://ideas.repec.org/a/eee/transe/v177y2023ics1366554523002211.html
   My bibliography  Save this article

Integrating alternating direction method of multipliers and bush for solving the traffic assignment problem

Author

Listed:
  • Liu, Zhiyuan
  • Zhang, Honggang
  • Zhang, Kai
  • Zhou, Zihan

Abstract

This paper introduces two novel parallel algorithmic frameworks to address the user equilibrium traffic assignment problem (UE-TAP). Most of the existing solution algorithms for the UE-TAP are executed in a sequential manner. This study endeavors to explore parallel computing methods based on model decomposition. Considering that the TAPs can be decomposed based on their origins, thus, following the spirit of the alternating direction method of multipliers (ADMM), a new parallel algorithm B-ADMM is proposed, which integrates the concept of the bush. Subsequently, the convergence of the proposed algorithm is rigorously proven. To enhance the algorithmic parallelism while maintaining the convergence efficiency of the B-ADMM algorithm, this paper further employs the parallel block coordinate descent (PBCD) method to improve the B-ADMM algorithm. We develop a bi-level parallel algorithm PBCD-ADMM, in which the independent origins/bushes are separated into several blocks, and the origin/bush-based restricted subproblems in each block can be solved in parallel. Furthermore, for the given bush belonging to a block, the bush links can also be grouped into several sub-blocks based on the original link-blocking scheme. Thus, these link-based subproblems in each sub-block can also be solved in parallel. A numerical experiment is conducted to validate the proposed algorithms, which indicates that the two new parallel algorithms perform better in terms of convergence speed compared with the original ADMM algorithm.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:transe:v:177:y:2023:i:c:s1366554523002211
    DOI: 10.1016/j.tre.2023.103233
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1366554523002211
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tre.2023.103233?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    2. 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.
    3. B. S. He & H. Yang & S. L. Wang, 2000. "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 337-356, August.
    4. Jun Xie & Yu (Marco) Nie, 2019. "A New Algorithm for Achieving Proportionality in User Equilibrium Traffic Assignment," Transportation Science, INFORMS, vol. 53(2), pages 566-584, March.
    5. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    6. 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.
    7. 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.
    8. 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.
    9. Deren Han & Xiaoming Yuan, 2012. "A Note on the Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 227-238, October.
    10. Xingju Cai & Deren Han & Xiaoming Yuan, 2017. "On the convergence of the direct extension of ADMM for three-block separable convex minimization models with one strongly convex function," Computational Optimization and Applications, Springer, vol. 66(1), pages 39-73, January.
    11. 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.
    12. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    13. Huang, Ruqing & Han, Lee D. & Huang, Zhongxiang, 2022. "A new network equilibrium flow model: User-equilibrium with quantity adjustment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 163(C).
    14. 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.
    15. Fukushima, Masao, 1984. "A modified Frank-Wolfe algorithm for solving the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 169-177, April.
    16. 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).
    17. B. Feijoo & R. R. Meyer, 1988. "Piecewise-Linear Approximation Methods for Nonseparable Convex Optimization," Management Science, INFORMS, vol. 34(3), pages 411-419, March.
    18. 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).
    19. Zhang, Fang & Lu, Jian & Hu, Xiaojian, 2022. "Integrated path controlling and subsidy scheme for mobility and environmental management in automated transportation networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 167(C).
    20. 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.
    21. Noruzoliaee, Mohamadhossein & Zou, Bo & Zhou, Yan (Joann), 2021. "Truck platooning in the U.S. national road network: A system-level modeling approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Honggang & Liu, Zhiyuan & Dong, Yu & Zhou, Hongyue & Liu, Pan & Chen, Jun, 2024. "A novel network equilibrium model integrating urban aerial mobility," Transportation Research Part A: Policy and Practice, Elsevier, vol. 187(C).
    2. Liu, Zhiyuan & Dong, Yu & Zhang, Honggang & Zheng, Nan & Huang, Kai, 2024. "A novel parallel computing framework for traffic assignment problem: Integrating alternating direction method of multipliers with Jacobi over relaxation method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 189(C).
    3. Zhao, Wei & Liao, Qi & Qiu, Rui & Liu, Chunying & Xu, Ning & Yu, Xiao & Liang, Yongtu, 2024. "Pipe sharing: A bilevel optimization model for the optimal capacity allocation of natural gas network," Applied Energy, Elsevier, vol. 359(C).
    4. Honggang Zhang & Zhiyuan Liu & Yicheng Zhang & Weijie Chen & Chenyang Zhang, 2024. "A Distributed Computing Method Integrating Improved Gradient Projection for Solving Stochastic Traffic Equilibrium Problem," Networks and Spatial Economics, Springer, vol. 24(2), pages 361-381, June.
    5. Liu, Zhiyuan & Xie, Shen & Zhang, Honggang & Zhou, Dinghao & Yang, Yuwei, 2024. "A parallel computing framework for large-scale microscopic traffic simulation based on spectral partitioning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 181(C).
    6. Cheng, Qixiu & Lin, Yuqian & Zhou, Xuesong (Simon) & Liu, Zhiyuan, 2024. "Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters," European Journal of Operational Research, Elsevier, vol. 312(1), pages 182-197.

    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. 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.
    2. 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).
    3. Liu, Zhiyuan & Dong, Yu & Zhang, Honggang & Zheng, Nan & Huang, Kai, 2024. "A novel parallel computing framework for traffic assignment problem: Integrating alternating direction method of multipliers with Jacobi over relaxation method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 189(C).
    4. 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.
    5. 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).
    6. David Di Lorenzo & Alessandro Galligari & Marco Sciandrone, 2015. "A convergent and efficient decomposition method for the traffic assignment problem," Computational Optimization and Applications, Springer, vol. 60(1), pages 151-170, January.
    7. Feng, Liyang & Xie, Jun & Liu, Xiaobo & Tang, Youhua & Wang, David Z.W. & Nie, Yu (Marco), 2024. "Is order-2 proportionality good enough for approximating the most likely path flow in user equilibrium traffic assignment?," Transportation Research Part B: Methodological, Elsevier, vol. 186(C).
    8. 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.
    9. Wang, Xiaolei & Wang, Jun & Guo, Lei & Liu, Wei & Zhang, Xiaoning, 2021. "A convex programming approach for ridesharing user equilibrium under fixed driver/rider demand," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 33-51.
    10. 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.
    11. 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.
    12. 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.
    13. Hong Zheng, 2015. "Adaptation of Network Simplex for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 49(3), pages 543-558, August.
    14. Jun Xie & Yu (Marco) Nie, 2019. "A New Algorithm for Achieving Proportionality in User Equilibrium Traffic Assignment," Transportation Science, INFORMS, vol. 53(2), pages 566-584, March.
    15. Bar-Gera, Hillel & Boyce, David & Nie, Yu (Marco), 2012. "User-equilibrium route flows and the condition of proportionality," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 440-462.
    16. 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.
    17. Meng Li & Guowei Hua & Haijun Huang, 2018. "A Multi-Modal Route Choice Model with Ridesharing and Public Transit," Sustainability, MDPI, vol. 10(11), pages 1-14, November.
    18. Jaller, Miguel & Pahwa, Anmol & Zhang, Michael, 2021. "Cargo Routing and Disadvantaged Communities," Institute of Transportation Studies, Working Paper Series qt9qg2318x, Institute of Transportation Studies, UC Davis.
    19. 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.
    20. 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.

    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:transe:v:177:y:2023:i:c:s1366554523002211. 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/600244/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.