Bi-objective nonlinear programming with minimum energy consumption and passenger waiting time for metro systems, based on the real-world smart-card data

Songpo Yang, Jianjun Wu, Huijun Sun, Xin Yang, Ziyou Gao, Anthony Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)


Generally, a good metro system means not only a passenger-oriented timetable but also an eco-friendly speed profile. This study develops a bi-objective nonlinear programming model to determine the optimal timetable and speed profile, with minimum energy consumption and passenger waiting time. In the nonlinear formulation, the average passenger waiting time is calculated based on the dynamic passenger flow by using the real-world smart-card data, and the energy consumption is obtained based on the tractive and regenerative energy on each section. The high-dimensional nonlinear problem is converted to a classical quadratic programming by using the Taylor approximation for obtaining the optimal solution easily. Finally, we conduct a numerical example based on the real-world data from the Beijing Metro Yizhuang Line of China. The results show that the developed model can save energy consumption by 6.0% and reduce passenger waiting time by 10.9% in comparison with the current planned timetable.
Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalTransportmetrica B
Publication statusAccepted/In press - 26 Apr 2017


  • energy consumption
  • passenger waiting time
  • speed profile
  • Timetable

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Transportation

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