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Multi-train trajectory optimization for energy-efficient timetabling

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  • Wang, Pengling
  • Goverde, Rob M.P.

Abstract

This paper proposes a novel approach for energy-efficient timetabling by adjusting the running time allocation of given timetables using train trajectory optimization. The approach first converts the arrival and departure times to time window constraints in order to relax the given timetable. Then a train trajectory optimization method is developed to find optimal arrival/departure times and optimal energy-efficient speed profiles within the relaxed time windows. The proposed train trajectory optimization method includes two types, a single-train trajectory optimization (STTO), which focuses on optimizing individual train movements within the relaxed arrival and departure time windows, and a multi-train trajectory optimization (MTTO), which computes multi-train trajectories simultaneously with a shared objective of minimizing multi-train energy consumption and an additional target of eliminating conflicts between trains. The STTO and MTTO are re-formulated as a multiple-phase optimal control problem, which has the advantage of accurately incorporating varying gradients, curves and speed limits and different train routes. The multiple-phase optimal control problem is then solved by a pseudospectral method. The proposed approach is applied in case studies to fine-tune two timetables, for a single-track railway corridor and a double-track corridor of the Dutch railway. The results suggest that the proposed approach is able to improve the energy efficiency of a timetable.

Suggested Citation

  • Wang, Pengling & Goverde, Rob M.P., 2019. "Multi-train trajectory optimization for energy-efficient timetabling," European Journal of Operational Research, Elsevier, vol. 272(2), pages 621-635.
  • Handle: RePEc:eee:ejores:v:272:y:2019:i:2:p:621-635
    DOI: 10.1016/j.ejor.2018.06.034
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    1. Wang, Pengling & Goverde, Rob M.P., 2017. "Multi-train trajectory optimization for energy efficiency and delay recovery on single-track railway lines," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 340-361.
    2. U. Brännlund & P. O. Lindberg & A. Nõu & J.-E. Nilsson, 1998. "Railway Timetabling Using Lagrangian Relaxation," Transportation Science, INFORMS, vol. 32(4), pages 358-369, November.
    3. Canca, David & Zarzo, Alejandro, 2017. "Design of energy-Efficient timetables in two-way railway rapid transit lines," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 142-161.
    4. Huang, Yeran & Yang, Lixing & Tang, Tao & Gao, Ziyou & Cao, Fang, 2017. "Joint train scheduling optimization with service quality and energy efficiency in urban rail transit networks," Energy, Elsevier, vol. 138(C), pages 1124-1147.
    5. Bešinović, Nikola & Goverde, Rob M.P. & Quaglietta, Egidio & Roberti, Roberto, 2016. "An integrated micro–macro approach to robust railway timetabling," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 14-32.
    6. David Kraay & Patrick T. Harker & Bintong Chen, 1991. "Optimal Pacing of Trains in Freight Railroads: Model Formulation and Solution," Operations Research, INFORMS, vol. 39(1), pages 82-99, February.
    7. Yin, Jiateng & Tang, Tao & Yang, Lixing & Gao, Ziyou & Ran, Bin, 2016. "Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 178-210.
    8. Liu, Rongfang (Rachel) & Golovitcher, Iakov M., 2003. "Energy-efficient operation of rail vehicles," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(10), pages 917-932, December.
    9. Li, Xiang & Lo, Hong K., 2014. "An energy-efficient scheduling and speed control approach for metro rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 73-89.
    10. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    11. Li, Xiang & Lo, Hong K., 2014. "Energy minimization in dynamic train scheduling and control for metro rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 269-284.
    12. Ye, Hongbo & Liu, Ronghui, 2016. "A multiphase optimal control method for multi-train control and scheduling on railway lines," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 377-393.
    13. Albrecht, Amie & Howlett, Phil & Pudney, Peter & Vu, Xuan & Zhou, Peng, 2016. "The key principles of optimal train control—Part 1: Formulation of the model, strategies of optimal type, evolutionary lines, location of optimal switching points," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 482-508.
    14. Gupta, Shuvomoy Das & Tobin, J. Kevin & Pavel, Lacra, 2016. "A two-step linear programming model for energy-efficient timetables in metro railway networks," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 57-74.
    15. Scheepmaker, Gerben M. & Goverde, Rob M.P. & Kroon, Leo G., 2017. "Review of energy-efficient train control and timetabling," European Journal of Operational Research, Elsevier, vol. 257(2), pages 355-376.
    16. Phil Howlett, 2000. "The Optimal Control of a Train," Annals of Operations Research, Springer, vol. 98(1), pages 65-87, December.
    17. Yang, Lixing & Li, Keping & Gao, Ziyou & Li, Xiang, 2012. "Optimizing trains movement on a railway network," Omega, Elsevier, vol. 40(5), pages 619-633.
    18. Zhou, Leishan & Tong, Lu (Carol) & Chen, Junhua & Tang, Jinjin & Zhou, Xuesong, 2017. "Joint optimization of high-speed train timetables and speed profiles: A unified modeling approach using space-time-speed grid networks," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 157-181.
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    Cited by:

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    2. Andreas Bärmann & Alexander Martin & Oskar Schneider, 2021. "Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling," Transportation Science, INFORMS, vol. 55(3), pages 747-767, May.
    3. Zhang, Yongxiang & D'Ariano, Andrea & He, Bisheng & Peng, Qiyuan, 2019. "Microscopic optimization model and algorithm for integrating train timetabling and track maintenance task scheduling," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 237-278.
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    8. Jiang Liu & Tian-tian Li & Bai-gen Cai & Jiao Zhang, 2020. "Boundary Identification for Traction Energy Conservation Capability of Urban Rail Timetables: A Case Study of the Beijing Batong Line," Energies, MDPI, vol. 13(8), pages 1-25, April.
    9. Kang, Liujiang & Li, Hao & Sun, Huijun & Wu, Jianjun & Cao, Zhiguang & Buhigiro, Nsabimana, 2021. "First train timetabling and bus service bridging in intermodal bus-and-train transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 443-462.
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    11. Huang, Yu & Zhou, Wenliang & Qin, Jin & Deng, Lianbo, 2023. "Optimization of energy-efficiency train schedule considering passenger demand and rolling stock circulation plan of subway line," Energy, Elsevier, vol. 275(C).
    12. Zhan, Shuguang & Wang, Pengling & Wong, S.C. & Lo, S.M., 2022. "Energy-efficient high-speed train rescheduling during a major disruption," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
    13. Yang, Songpo & Chen, Yanyan & Dong, Zhurong & Wu, Jianjun, 2023. "A collaborative operation mode of energy storage system and train operation system in power supply network," Energy, Elsevier, vol. 276(C).
    14. Mariano Gallo & Marilisa Botte & Antonio Ruggiero & Luca D’Acierno, 2020. "A Simulation Approach for Optimising Energy-Efficient Driving Speed Profiles in Metro Lines," Energies, MDPI, vol. 13(22), pages 1-17, November.
    15. Li, Wenxin & Peng, Qiyuan & Wen, Chao & Wang, Pengling & Lessan, Javad & Xu, Xinyue, 2020. "Joint optimization of delay-recovery and energy-saving in a metro system: A case study from China," Energy, Elsevier, vol. 202(C).
    16. Zhou, Yu & Wang, Yun & Yang, Hai & Yan, Xuedong, 2019. "Last train scheduling for maximizing passenger destination reachability in urban rail transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 79-95.
    17. Lian, Deheng & Mo, Pengli & D’Ariano, Andrea & Gao, Ziyou & Yang, Lixing, 2024. "Energy-saving time allocation strategy with uncertain dwell times in urban rail transit: Two-stage stochastic model and nested dynamic programming framework," European Journal of Operational Research, Elsevier, vol. 317(1), pages 219-242.
    18. Gonzalo Sánchez-Contreras & Adrián Fernández-Rodríguez & Antonio Fernández-Cardador & Asunción P. Cucala, 2023. "A Two-Level Fuzzy Multi-Objective Design of ATO Driving Commands for Energy-Efficient Operation of Metropolitan Railway Lines," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    19. Xing, Zongyi & Zhang, Zhenyu & Guo, Jian & Qin, Yong & Jia, Limin, 2023. "Rail train operation energy-saving optimization based on improved brute-force search," Applied Energy, Elsevier, vol. 330(PA).

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