IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v99y2017icp167-182.html
   My bibliography  Save this article

A dynamic programming approach for optimizing train speed profiles with speed restrictions and passage points

Author

Listed:
  • Haahr, Jørgen Thorlund
  • Pisinger, David
  • Sabbaghian, Mohammad

Abstract

This paper considers a novel solution method for generating improved train speed profiles with reduced energy consumption. The solution method makes use of a time-space graph formulation which can be solved through Dynamic Programming. Instead of using uniform discretization of time and space as seen previously in the literature, we rely on an event-based decomposition that drastically reduces the search space. This approach is very flexible, making it easy to handle, e.g., speed limits, changes in altitude, and passage points that need to be crossed within a given time window. Based on solving an extensive number of real-life problem instances, our benchmarks show that the proposed solution method is able to satisfy all secondary constraints and still be able to decrease energy consumption by 3.3% on average compared to a commercial solver provided by our industrial collaborator, Cubris. The computational times are generally very low, making it possible to recompute the train speed profile in case of unexpected changes in speed restrictions or timings. This is a great advantage over static offline lookup tables. Also, the framework is very flexible, making it possible to handle a number of additional constraints on robustness, passenger comfort etc. Selected details of the method and benchmark are only described at a high level for confidentiality reasons.

Suggested Citation

  • Haahr, Jørgen Thorlund & Pisinger, David & Sabbaghian, Mohammad, 2017. "A dynamic programming approach for optimizing train speed profiles with speed restrictions and passage points," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 167-182.
    • Handle: RePEc:eee:transb:v:99:y:2017:i:c:p:167-182
    DOI: 10.1016/j.trb.2016.12.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261516301667
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2016.12.016?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. Villeneuve, Daniel & Desaulniers, Guy, 2005. "The shortest path problem with forbidden paths," European Journal of Operational Research, Elsevier, vol. 165(1), pages 97-107, August.
    2. Thomas Albrecht, 2009. "The Influence of Anticipating Train Driving on the Dispatching Process in Railway Conflict Situations," Networks and Spatial Economics, Springer, vol. 9(1), pages 85-101, March.
    3. Phil Howlett, 2000. "The Optimal Control of a Train," Annals of Operations Research, Springer, vol. 98(1), pages 65-87, December.
    4. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
    5. 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.
    6. 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.
    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. He, Deqiang & Yang, Yanjie & Chen, Yanjun & Deng, Jianxin & Shan, Sheng & Liu, Jianren & Li, Xianwang, 2020. "An integrated optimization model of metro energy consumption based on regenerative energy and passenger transfer," Applied Energy, Elsevier, vol. 264(C).
    2. Luan, Xiaojie & Wang, Yihui & De Schutter, Bart & Meng, Lingyun & Lodewijks, Gabriel & Corman, Francesco, 2018. "Integration of real-time traffic management and train control for rail networks - Part 2: Extensions towards energy-efficient train operations," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 72-94.
    3. Lai, Qingying & Liu, Jun & Haghani, Ali & Meng, Lingyun & Wang, Yihui, 2020. "Energy-efficient speed profile optimization for medium-speed maglev trains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    4. Şafak, Özge & Çavuş, Özlem & Selim Aktürk, M., 2018. "Multi-stage airline scheduling problem with stochastic passenger demand and non-cruise times," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 39-67.
    5. Xu, Peijuan & Corman, Francesco & Peng, Qiyuan & Luan, Xiaojie, 2017. "A train rescheduling model integrating speed management during disruptions of high-speed traffic under a quasi-moving block system," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 638-666.
    6. Fei Shang & Jingyuan Zhan & Yangzhou Chen, 2020. "An Online Energy-Saving Driving Strategy for Metro Train Operation Based on the Model Predictive Control of Switched-Mode Dynamical Systems," Energies, MDPI, vol. 13(18), pages 1-14, September.
    7. Kyoungho Ahn & Ahmed Aredah & Hesham A. Rakha & Tongchuan Wei & H. Christopher Frey, 2023. "Simple Diesel Train Fuel Consumption Model for Real-Time Train Applications," Energies, MDPI, vol. 16(8), pages 1-15, April.
    8. Zhuang Xiao & Pengfei Sun & Qingyuan Wang & Yuqing Zhu & Xiaoyun Feng, 2018. "Integrated Optimization of Speed Profiles and Power Split for a Tram with Hybrid Energy Storage Systems on a Signalized Route," Energies, MDPI, vol. 11(3), pages 1-21, February.
    9. Zhaoxiang Tan & Shaofeng Lu & Kai Bao & Shaoning Zhang & Chaoxian Wu & Jie Yang & Fei Xue, 2018. "Adaptive Partial Train Speed Trajectory Optimization," Energies, MDPI, vol. 11(12), pages 1-33, November.
    10. 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.
    11. Ning, Jingjie & Zhou, Yonghua & Long, Fengchu & Tao, Xin, 2018. "A synergistic energy-efficient planning approach for urban rail transit operations," Energy, Elsevier, vol. 151(C), pages 854-863.
    12. 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.

    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. Cheng Gong & Shiwen Zhang & Feng Zhang & Jianguo Jiang & Xinheng Wang, 2014. "An Integrated Energy-Efficient Operation Methodology for Metro Systems Based on a Real Case of Shanghai Metro Line One," Energies, MDPI, vol. 7(11), pages 1-25, November.
    2. Luan, Xiaojie & Wang, Yihui & De Schutter, Bart & Meng, Lingyun & Lodewijks, Gabriel & Corman, Francesco, 2018. "Integration of real-time traffic management and train control for rail networks - Part 2: Extensions towards energy-efficient train operations," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 72-94.
    3. Wang, Xuekai & Tang, Tao & Su, Shuai & Yin, Jiateng & Gao, Ziyou & Lv, Nan, 2021. "An integrated energy-efficient train operation approach based on the space-time-speed network methodology," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).
    4. Albrecht, Amie & Howlett, Phil & Pudney, Peter & Vu, Xuan & Zhou, Peng, 2018. "The two-train separation problem on non-level track—driving strategies that minimize total required tractive energy subject to prescribed section clearance times," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 135-167.
    5. Jie Yang & Limin Jia & Shaofeng Lu & Yunxiao Fu & Ji Ge, 2016. "Energy-Efficient Speed Profile Approximation: An Optimal Switching Region-Based Approach with Adaptive Resolution," Energies, MDPI, vol. 9(10), pages 1-27, September.
    6. Yang, Xin & Chen, Anthony & Ning, Bin & Tang, Tao, 2016. "A stochastic model for the integrated optimization on metro timetable and speed profile with uncertain train mass," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 424-445.
    7. Howlett, Phil, 2016. "A new look at the rate of change of energy consumption with respect to journey time on an optimal train journey," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 387-408.
    8. Luan, Xiaojie & Wang, Yihui & De Schutter, Bart & Meng, Lingyun & Lodewijks, Gabriel & Corman, Francesco, 2018. "Integration of real-time traffic management and train control for rail networks - Part 1: Optimization problems and solution approaches," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 41-71.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Wang, Chao & Meng, Xin & Guo, Mingxue & Li, Hao & Hou, Zhiqiang, 2022. "An integrated energy-efficient and transfer-accessible model for the last train timetabling problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    14. Xuesong Feng & Hanxiao Zhang & Yong Ding & Zhili Liu & Hongqin Peng & Bin Xu, 2013. "A Review Study on Traction Energy Saving of Rail Transport," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-9, September.
    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. 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.
    17. Zhaoxiang Tan & Shaofeng Lu & Kai Bao & Shaoning Zhang & Chaoxian Wu & Jie Yang & Fei Xue, 2018. "Adaptive Partial Train Speed Trajectory Optimization," Energies, MDPI, vol. 11(12), pages 1-33, November.
    18. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    19. Gutiérrez-Jarpa, Gabriel & Desaulniers, Guy & Laporte, Gilbert & Marianov, Vladimir, 2010. "A branch-and-price algorithm for the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows," European Journal of Operational Research, Elsevier, vol. 206(2), pages 341-349, October.
    20. Ann-Kathrin Rothenbächer & Michael Drexl & Stefan Irnich, 2018. "Branch-and-Price-and-Cut for the Truck-and-Trailer Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 52(5), pages 1174-1190, October.

    More about this item

    Statistics

    Access and download statistics

    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:99:y:2017:i:c:p:167-182. 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.