IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v119y2019icp102-121.html
   My bibliography  Save this article

Tolerance-based strategies for extending the column generation algorithm to the bounded rational dynamic user equilibrium problem

Author

Listed:
  • Wang, Dong
  • Liao, Feixiong
  • Gao, Ziyou
  • Timmermans, Harry

Abstract

The column generation (CG) algorithm has been widely applied to traffic assignment problems due to its capability of circumventing path enumeration. Incorporating bounded rationality (BR) and dynamics, this paper proposes four tolerance-based strategies for extending the CG algorithm to the bounded rational dynamic user equilibrium model (BR-DUE): (i) a tolerance-based minimum disutility path search strategy is developed to allow travelers seeking satisfactory paths; (ii) a self-adjusted convergence threshold strategy is applied for fast convergence at the intermediate iterations; (iii) a varied temporal resolution scheme, combining exploration and exploitation, is suggested to assign flows to narrow time regions rather than to the whole time horizon; and (iv) a path search skipping strategy is introduced by comparing the lower bound of travel disutility and the minimum disutility between the OD pairs. With these strategies, an efficient tolerance-based column generation (TBCG) algorithm for BR-DUE is developed. Numerical examples are provided to demonstrate that the TBCG algorithm leads to significant computation time reductions without the expense of solution quality, of which the speedup factors are around two compared with using the original CG algorithm.

Suggested Citation

  • Wang, Dong & Liao, Feixiong & Gao, Ziyou & Timmermans, Harry, 2019. "Tolerance-based strategies for extending the column generation algorithm to the bounded rational dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 102-121.
    • Handle: RePEc:eee:transb:v:119:y:2019:i:c:p:102-121
    DOI: 10.1016/j.trb.2018.11.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261518307598
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2018.11.008?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. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    2. Rubio-Ardanaz, J. M. & Wu, J. H. & Florian, M., 2003. "Two improved numerical algorithms for the continuous dynamic network loading problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(2), pages 171-190, February.
    3. Long, Jiancheng & Szeto, W.Y. & Gao, Ziyou & Huang, Hai-Jun & Shi, Qin, 2016. "The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 179-206.
    4. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Li, Xinwei, 2018. "Day-to-day departure time choice under bounded rationality in the bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 832-849.
    5. Michael Levin & Matt Pool & Travis Owens & Natalia Juri & S. Travis Waller, 2015. "Improving the Convergence of Simulation-based Dynamic Traffic Assignment Methodologies," Networks and Spatial Economics, Springer, vol. 15(3), pages 655-676, September.
    6. 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.
    7. Richard Mounce & Malachy Carey, 2015. "On the Convergence of the Method of Successive Averages for Calculating Equilibrium in Traffic Networks," Transportation Science, INFORMS, vol. 49(3), pages 535-542, August.
    8. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    9. Lu, Chung-Cheng & Liu, Jiangtao & Qu, Yunchao & Peeta, Srinivas & Rouphail, Nagui M. & Zhou, Xuesong, 2016. "Eco-system optimal time-dependent flow assignment in a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 217-239.
    10. Tong, C. O. & Wong, S. C., 2000. "A predictive dynamic traffic assignment model in congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 625-644, November.
    11. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    12. Chen, Anthony & Lo, Hong K. & Yang, Hai, 2001. "A self-adaptive projection and contraction algorithm for the traffic assignment problem with path-specific costs," European Journal of Operational Research, Elsevier, vol. 135(1), pages 27-41, November.
    13. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    14. Nie, Xiaojian & Zhang, H.M., 2005. "Delay-function-based link models: their properties and computational issues," Transportation Research Part B: Methodological, Elsevier, vol. 39(8), pages 729-751, September.
    15. Lu, Chung-Cheng & Mahmassani, Hani S. & Zhou, Xuesong, 2009. "Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 345-364, March.
    16. Di, Xuan & Liu, Henry X., 2016. "Boundedly rational route choice behavior: A review of models and methodologies," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 142-179.
    17. D. Zhang & A. Nagurney, 1997. "Formulation, Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 417-444, May.
    18. Malachy Carey & Y. Ge, 2012. "Comparison of Methods for Path Flow Reassignment for Dynamic User Equilibrium," Networks and Spatial Economics, Springer, vol. 12(3), pages 337-376, September.
    19. Serdar Çolak & Antonio Lima & Marta C. González, 2016. "Understanding congested travel in urban areas," Nature Communications, Nature, vol. 7(1), pages 1-8, April.
    20. Liu, Peng & Liao, Feixiong & Huang, Hai-Jun & Timmermans, Harry, 2015. "Dynamic activity-travel assignment in multi-state supernetworks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 656-671.
    21. Anna Nagurney & Ding Zhang, 1997. "Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-Demand Traffic Network Equilibria," Transportation Science, INFORMS, vol. 31(2), pages 147-158, May.
    22. Mounce, Richard & Carey, Malachy, 2011. "Route swapping in dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 102-111, January.
    23. Han, Lanshan & Ukkusuri, Satish & Doan, Kien, 2011. "Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1749-1767.
    24. Jiancheng Long & Hai-Jun Huang & Ziyou Gao & W. Y. Szeto, 2013. "An Intersection-Movement-Based Dynamic User Optimal Route Choice Problem," Operations Research, INFORMS, vol. 61(5), pages 1134-1147, October.
    25. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "Existence of simultaneous route and departure choice dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 17-30.
    26. Lo, Hong K. & Szeto, W. Y., 2002. "A cell-based variational inequality formulation of the dynamic user optimal assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 421-443, June.
    27. Fosgerau, Mogens & Karlström, Anders, 2010. "The value of reliability," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 38-49, January.
    28. Han, Ke & Szeto, W.Y. & Friesz, Terry L., 2015. "Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 16-49.
    29. Guo, Xiaolei & Liu, Henry X., 2011. "Bounded rationality and irreversible network change," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1606-1618.
    30. Li, Qing & Liao, Feixiong & Timmermans, Harry J.P. & Huang, Haijun & Zhou, Jing, 2018. "Incorporating free-floating car-sharing into an activity-based dynamic user equilibrium model: A demand-side model," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 102-123.
    31. Szeto, W. Y. & Lo, Hong K., 2004. "A cell-based simultaneous route and departure time choice model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 38(7), pages 593-612, August.
    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. Wang, Dong & Liao, Feixiong, 2021. "Analysis of first-come-first-served mechanisms in one-way car-sharing services," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 22-41.
    2. Wang, Dong & Liao, Feixiong & Gao, Ziyou & Tian, Qiong, 2022. "Analysis of activity duration-related charging behavioral responses of electric vehicle travelers to charging services," Transport Policy, Elsevier, vol. 123(C), pages 73-81.
    3. Ma, Jie & Xu, Min & Meng, Qiang & Cheng, Lin, 2020. "Ridesharing user equilibrium problem under OD-based surge pricing strategy," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 1-24.
    4. Li, Qing & Liao, Feixiong, 2020. "Incorporating vehicle self-relocations and traveler activity chains in a bi-level model of optimal deployment of shared autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 151-175.
    5. Xu, Zhandong & Chen, Anthony & Li, Guoyuan & Li, Zhengyang & Liu, Xiaobo, 2024. "Elastic-demand bi-criteria traffic assignment under the continuously distributed value of time: A two-stage gradient projection algorithm with graphical interpretations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 183(C).
    6. 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).
    7. Liu, Peng & Liao, Feixiong & Tian, Qiong & Huang, Hai-Jun & Timmermans, Harry, 2020. "Day-to-day needs-based activity-travel dynamics and equilibria in multi-state supernetworks," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 208-227.
    8. Fu, Daocheng & Cai, Pinlong & Lin, Yilun & Mao, Song & Wen, Licheng & Li, Yikang, 2023. "Incremental path planning: Reservation system in V2X environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    9. Wang, Dong & Liao, Feixiong, 2023. "Incentivized user-based relocation strategies for moderating supply–demand dynamics in one-way car-sharing services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 171(C).
    10. 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).

    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. 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).
    2. Ren-Yong Guo & Hai Yang & Hai-Jun Huang, 2018. "Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?," Transportation Science, INFORMS, vol. 52(3), pages 603-620, June.
    3. Han, Ke & Friesz, Terry L. & Szeto, W.Y. & Liu, Hongcheng, 2015. "Elastic demand dynamic network user equilibrium: Formulation, existence and computation," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 183-209.
    4. Long, Jiancheng & Szeto, W.Y. & Gao, Ziyou & Huang, Hai-Jun & Shi, Qin, 2016. "The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 179-206.
    5. Liu, Peng & Liao, Feixiong & Tian, Qiong & Huang, Hai-Jun & Timmermans, Harry, 2020. "Day-to-day needs-based activity-travel dynamics and equilibria in multi-state supernetworks," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 208-227.
    6. Wang, Dong & Liao, Feixiong, 2023. "Incentivized user-based relocation strategies for moderating supply–demand dynamics in one-way car-sharing services," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 171(C).
    7. Qixiu Cheng & Zhiyuan Liu & Feifei Liu & Ruo Jia, 2017. "Urban dynamic congestion pricing: an overview and emerging research needs," International Journal of Urban Sciences, Taylor & Francis Journals, vol. 21(0), pages 3-18, August.
    8. Jiayang Li & Zhaoran Wang & Yu Marco Nie, 2023. "Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice," Papers 2304.02500, arXiv.org, revised Feb 2024.
    9. Lu, Chung-Cheng & Mahmassani, Hani S. & Zhou, Xuesong, 2009. "Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 345-364, March.
    10. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
    11. Long, Jiancheng & Szeto, W.Y. & Huang, Hai-Jun & Gao, Ziyou, 2015. "An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 182-217.
    12. Hongbo Ye & Hai Yang, 2017. "Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium," Transportation Science, INFORMS, vol. 51(3), pages 968-980, August.
    13. Friesz, Terry L. & Han, Ke & Bagherzadeh, Amir, 2021. "Convergence of fixed-point algorithms for elastic demand dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 336-352.
    14. Song, Wenjing & Han, Ke & Wang, Yiou & Friesz, Terry L. & del Castillo, Enrique, 2018. "Statistical metamodeling of dynamic network loading," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 740-756.
    15. Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.
    16. Li, Qing & Liao, Feixiong, 2020. "Incorporating vehicle self-relocations and traveler activity chains in a bi-level model of optimal deployment of shared autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 151-175.
    17. Peeta, Srinivas, 2016. "A marginal utility day-to-day traffic evolution model based on one-step strategic thinkingAuthor-Name: He, Xiaozheng," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 237-255.
    18. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Tan, Zhijia, 2015. "Link-based day-to-day network traffic dynamics and equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 248-260.
    19. Long, Jiancheng & Wang, Chao & Szeto, W.Y., 2018. "Dynamic system optimum simultaneous route and departure time choice problems: Intersection-movement-based formulations and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 166-206.
    20. Malachy Carey & Y. Ge, 2012. "Comparison of Methods for Path Flow Reassignment for Dynamic User Equilibrium," Networks and Spatial Economics, Springer, vol. 12(3), pages 337-376, September.

    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:119:y:2019:i:c:p:102-121. 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.