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Bayesian optimization for congestion pricing problems: A general framework and its instability

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  • Huo, Jinbiao
  • Liu, Zhiyuan
  • Chen, Jingxu
  • Cheng, Qixiu
  • Meng, Qiang

Abstract

In this study, we proposed a generic Bayesian optimization (BO) framework to solve congestion pricing problems. In the BO framework, the Gaussian process (GP) serves as a surrogate model to approximate the highly nonlinear and expensive-to-evaluate objective functions. This study reveals that GP exhibits an instability phenomenon, which inherently limits the accuracy of BO. We investigate the sources and influences of instability from the perspective of error analysis, and then propose an improved GP (IGP) model to address the instability issue. The associated improvements are twofold: matrix inversion and matrix multiplication. A tailored preconditioner is developed to reduce the matrix inversion errors. To address multiplication errors, a tailored dot product algorithm in conjunction with a GP reformulation scheme is proposed. To validate the proposed models and methods, a link-based second-best congestion pricing problem is considered as an example. The results indicate that, in comparison to benchmark approaches (the sensitivity analysis method and genetic algorithm), the proposed BO framework shows higher computational efficiency and solution accuracy. With modifications on GP, the instability phenomenon is substantially mitigated in several instances, hence enhancing the accuracy of the BO framework.

Suggested Citation

  • Huo, Jinbiao & Liu, Zhiyuan & Chen, Jingxu & Cheng, Qixiu & Meng, Qiang, 2023. "Bayesian optimization for congestion pricing problems: A general framework and its instability," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 1-28.
    • Handle: RePEc:eee:transb:v:169:y:2023:i:c:p:1-28
    DOI: 10.1016/j.trb.2023.01.003
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    as
    1. Du, Muqing & Chen, Anthony, 2022. "Sensitivity analysis for transit equilibrium assignment and applications to uncertainty analysis," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 175-202.
    2. Jiang Qian Ying & Toshihiko Miyagi, 2001. "Sensitivity Analysis for Stochastic User Equilibrium Network Flows—A Dual Approach," Transportation Science, INFORMS, vol. 35(2), pages 124-133, May.
    3. Tay, Timothy & Osorio, Carolina, 2022. "Bayesian optimization techniques for high-dimensional simulation-based transportation problems," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 210-243.
    4. Liu, Zhiyuan & Wang, Shuaian & Meng, Qiang, 2014. "Optimal joint distance and time toll for cordon-based congestion pricing," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 81-97.
    5. Zheng, Liang & Xue, Xinfeng & Xu, Chengcheng & Ran, Bin, 2019. "A stochastic simulation-based optimization method for equitable and efficient network-wide signal timing under uncertainties," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 287-308.
    6. Gramacy, Robert B & Lee, Herbert K. H, 2008. "Bayesian Treed Gaussian Process Models With an Application to Computer Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1119-1130.
    7. Zhou, Bojian & Bliemer, Michiel & Yang, Hai & He, Jie, 2015. "A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 77-92.
    8. Zhang, Xiaoning & Yang, Hai, 2004. "The optimal cordon-based network congestion pricing problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 517-537, July.
    9. Younes Hamdouch & Siriphong Lawphongpanich, 2010. "Congestion Pricing for Schedule-Based Transit Networks," Transportation Science, INFORMS, vol. 44(3), pages 350-366, August.
    10. Wang, David Z.W. & Liu, Haoxiang & Szeto, W.Y., 2015. "A novel discrete network design problem formulation and its global optimization solution algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 213-230.
    11. Feng Xiao & H. M. Zhang, 2014. "Pareto-Improving and Self-Sustainable Pricing for the Morning Commute with Nonidentical Commuters," Transportation Science, INFORMS, vol. 48(2), pages 159-169, May.
    12. Anas, Alex, 2020. "The cost of congestion and the benefits of congestion pricing: A general equilibrium analysis," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 110-137.
    13. Carolina Osorio & Michel Bierlaire, 2013. "A Simulation-Based Optimization Framework for Urban Transportation Problems," Operations Research, INFORMS, vol. 61(6), pages 1333-1345, December.
    14. Yang Liu & Yu (Marco) Nie, 2017. "A Credit-Based Congestion Management Scheme in General Two-Mode Networks with Multiclass Users," Networks and Spatial Economics, Springer, vol. 17(3), pages 681-711, September.
    15. Zhang, Xiaoning & Yang, Hai & Huang, Hai-Jun, 2011. "Improving travel efficiency by parking permits distribution and trading," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 1018-1034, August.
    16. Aimé Kamgaing Kuiteingf & Patrice Marcotte & Gilles Savard, 2017. "Network Pricing of Congestion-Free Networks: The Elastic and Linear Demand Case," Transportation Science, INFORMS, vol. 51(3), pages 791-806, August.
    17. Bob Hickish & David I. Fletcher & Robert F. Harrison, 2020. "Investigating Bayesian Optimization for rail network optimization," International Journal of Rail Transportation, Taylor & Francis Journals, vol. 8(4), pages 307-323, October.
    18. A. Žilinskas, 1978. "Optimization of One‐Dimensional Multimodal Functions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 367-375, November.
    19. Gabriella Dellino & Jack P. C. Kleijnen & Carlo Meloni, 2012. "Robust Optimization in Simulation: Taguchi and Krige Combined," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 471-484, August.
    20. Michael Patriksson & R. Tyrrell Rockafellar, 2002. "A Mathematical Model and Descent Algorithm for Bilevel Traffic Management," Transportation Science, INFORMS, vol. 36(3), pages 271-291, August.
    21. Daganzo, Carlos F. & Lehe, Lewis J., 2015. "Distance-dependent congestion pricing for downtown zones," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 89-99.
    22. Wang, Shuaian & Zhang, Wei & Qu, Xiaobo, 2018. "Trial-and-error train fare design scheme for addressing boarding/alighting congestion at CBD stations," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 318-335.
    23. Di, Xuan & Liu, Henry X. & Ban, Xuegang (Jeff), 2016. "Second best toll pricing within the framework of bounded rationality," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 74-90.
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