IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v55y2021i3p592-615.html
   My bibliography  Save this article

Fast Calibration of Car-Following Models to Trajectory Data Using the Adjoint Method

Author

Listed:
  • Ronan Keane

    (Systems Science and Engineering, Cornell University, Ithaca, New York 14853)

  • H. Oliver Gao

    (Civil and Environmental Engineering, Cornell University, Ithaca, New York 14853)

Abstract

Before a car-following model can be applied in practice, it must first be validated against real data in a process known as calibration. This paper discusses the formulation of calibration as an optimization problem and compares different algorithms for its solution. The optimization consists of an arbitrary car following model, posed as either an ordinary or delay differential equation, being calibrated to an arbitrary source of trajectory data that may include lane changes. Typically, the calibration problem is solved using gradient free optimization. In this work, the gradient of the optimization problem is derived analytically using the adjoint method. The computational cost of the adjoint method does not scale with the number of model parameters, which makes it more efficient than evaluating the gradient numerically using finite differences. Numerical results are presented that show that quasi-Newton algorithms using the adjoint method are significantly faster than a genetic algorithm and also achieve slightly better accuracy of the calibrated model.

Suggested Citation

  • Ronan Keane & H. Oliver Gao, 2021. "Fast Calibration of Car-Following Models to Trajectory Data Using the Adjoint Method," Transportation Science, INFORMS, vol. 55(3), pages 592-615, May.
    • Handle: RePEc:inm:ortrsc:v:55:y:2021:i:3:p:592-615
    DOI: 10.1287/trsc.2020.1027
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.2020.1027
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.2020.1027?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
    ---><---

    References listed on IDEAS

    as
    1. Gipps, P.G., 1981. "A behavioural car-following model for computer simulation," Transportation Research Part B: Methodological, Elsevier, vol. 15(2), pages 105-111, April.
    2. Coifman, Benjamin & Li, Lizhe, 2017. "A critical evaluation of the Next Generation Simulation (NGSIM) vehicle trajectory dataset," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 362-377.
    3. Kerner, Boris S., 2014. "Three-phase theory of city traffic: Moving synchronized flow patterns in under-saturated city traffic at signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 76-110.
    4. Laval, Jorge A. & Daganzo, Carlos F., 2006. "Lane-changing in traffic streams," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 251-264, March.
    5. Fuchang Gao & Lixing Han, 2012. "Implementing the Nelder-Mead simplex algorithm with adaptive parameters," Computational Optimization and Applications, Springer, vol. 51(1), pages 259-277, January.
    6. Wong, G. C. K. & Wong, S. C., 2002. "A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(9), pages 827-841, November.
    7. Montanino, Marcello & Punzo, Vincenzo, 2015. "Trajectory data reconstruction and simulation-based validation against macroscopic traffic patterns," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 82-106.
    8. He, Zhengbing & Zheng, Liang & Guan, Wei, 2015. "A simple nonparametric car-following model driven by field data," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 185-201.
    9. Daganzo, Carlos F., 2006. "In traffic flow, cellular automata = kinematic waves," Transportation Research Part B: Methodological, Elsevier, vol. 40(5), pages 396-403, June.
    10. Tian, Junfang & Jiang, Rui & Jia, Bin & Gao, Ziyou & Ma, Shoufeng, 2016. "Empirical analysis and simulation of the concave growth pattern of traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 338-354.
    11. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    12. Davis, L.C., 2003. "Modifications of the optimal velocity traffic model to include delay due to driver reaction time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 557-567.
    13. Treiber, Martin & Kesting, Arne & Helbing, Dirk, 2006. "Delays, inaccuracies and anticipation in microscopic traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 71-88.
    14. Jiang, Rui & Hu, Mao-Bin & Zhang, H.M. & Gao, Zi-You & Jia, Bin & Wu, Qing-Song, 2015. "On some experimental features of car-following behavior and how to model them," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 338-354.
    15. Laval, Jorge A. & Leclercq, Ludovic, 2008. "Microscopic modeling of the relaxation phenomenon using a macroscopic lane-changing model," Transportation Research Part B: Methodological, Elsevier, vol. 42(6), pages 511-522, July.
    16. Laval, Jorge A. & Toth, Christopher S. & Zhou, Yi, 2014. "A parsimonious model for the formation of oscillations in car-following models," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 228-238.
    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. Yao, Handong & Li, Qianwen & Li, Xiaopeng, 2020. "A study of relationships in traffic oscillation features based on field experiments," Transportation Research Part A: Policy and Practice, Elsevier, vol. 141(C), pages 339-355.
    2. Tian, Junfang & Li, Guangyu & Treiber, Martin & Jiang, Rui & Jia, Ning & Ma, Shoufeng, 2016. "Cellular automaton model simulating spatiotemporal patterns, phase transitions and concave growth pattern of oscillations in traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 560-575.
    3. Jin, Wen-Long & Laval, Jorge, 2018. "Bounded acceleration traffic flow models: A unified approach," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 1-18.
    4. Laval, Jorge A. & Toth, Christopher S. & Zhou, Yi, 2014. "A parsimonious model for the formation of oscillations in car-following models," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 228-238.
    5. Jin, Wen-Long, 2013. "A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 361-377.
    6. Storm, Pieter Jacob & Mandjes, Michel & van Arem, Bart, 2022. "Efficient evaluation of stochastic traffic flow models using Gaussian process approximation," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 126-144.
    7. Treiber, Martin & Kesting, Arne, 2018. "The Intelligent Driver Model with stochasticity – New insights into traffic flow oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 613-623.
    8. Ngoduy, D., 2021. "Noise-induced instability of a class of stochastic higher order continuum traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 260-278.
    9. van Lint, J.W.C. & Calvert, S.C., 2018. "A generic multi-level framework for microscopic traffic simulation—Theory and an example case in modelling driver distraction," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 63-86.
    10. Li, Xiaopeng & Ouyang, Yanfeng, 2011. "Characterization of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1346-1361.
    11. Yibing Wang & Long Wang & Xianghua Yu & Jingqiu Guo, 2023. "Capacity Drop at Freeway Ramp Merges with Its Replication in Macroscopic and Microscopic Traffic Simulations: A Tutorial Report," Sustainability, MDPI, vol. 15(3), pages 1-27, January.
    12. Tang, Tie-Qiao & Zhang, Jian & Chen, Liang & Shang, Hua-Yan, 2017. "Analysis of vehicle’s safety envelope under car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 127-133.
    13. Sun, Lu & Jafaripournimchahi, Ammar & Kornhauser, Alain & Hu, Wushen, 2020. "A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    14. Bouadi, Marouane & Jia, Bin & Jiang, Rui & Li, Xingang & Gao, Zi-You, 2022. "Stochastic factors and string stability of traffic flow: Analytical investigation and numerical study based on car-following models," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 96-122.
    15. Zheng, Zuduo, 2014. "Recent developments and research needs in modeling lane changing," Transportation Research Part B: Methodological, Elsevier, vol. 60(C), pages 16-32.
    16. Yeo, Hwasoo, 2008. "Asymmetric Microscopic Driving Behavior Theory," University of California Transportation Center, Working Papers qt1tn1m968, University of California Transportation Center.
    17. Chiabaut, Nicolas & Leclercq, Ludovic & Buisson, Christine, 2010. "From heterogeneous drivers to macroscopic patterns in congestion," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 299-308, February.
    18. Tian, Junfang & Zhang, H.M. & Treiber, Martin & Jiang, Rui & Gao, Zi-You & Jia, Bin, 2019. "On the role of speed adaptation and spacing indifference in traffic instability: Evidence from car-following experiments and its stochastic model," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 334-350.
    19. Li, Xiaopeng & Wang, Xin & Ouyang, Yanfeng, 2012. "Prediction and field validation of traffic oscillation propagation under nonlinear car-following laws," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 409-423.
    20. Delpiano, Rafael & Laval, Jorge & Coeymans, Juan Enrique & Herrera, Juan Carlos, 2015. "The kinematic wave model with finite decelerations: A social force car-following model approximation," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 182-193.

    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:inm:ortrsc:v:55:y:2021:i:3:p:592-615. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.