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

Metro is considered as an efficient transport mode to alleviate traffic congestion in big cities because of its large transport capacity. 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.