###### Abstract
[43] proposed a multi-objective programming model consisting of three objective functions to minimize the energy consumption, passenger waiting time at stations and waiting time of transfer passengers at transfer stations. In recent years, data-driven energy saving control methods have been applied in URT systems. A series of machine learning method are employed in data-driven multi-train energy control strategy optimization. [PERSON] et al. [44] presented a cooperative control method to optimize each switching point of the driving regimes. [PERSON] et al. [45] used a deep neural network (DNN) to improve the performance of train energy control. [PERSON] et al. [46] proposed a policy-based reinforcement learning train control approach to reduce the traction energy consumption of the train. [PERSON] et al. [47] applied a model predictive control method to the minimum safety tracking interval. Due to the multiple parameters of the trains' dynamics, [PERSON] et al. [48] and [PERSON], [PERSON] and [PERSON] [49] applied proportional integral differential (PID) and fuzzy controllers to optimize train control and the speed-time curve. [PERSON] and [PERSON] [50] built a dynamic planning model using rail running time to find the optimal control strategy. [PERSON] et al. [51] proposed multi-train timetable optimization based on the improved Seeker Optimization Algorithm (SOA). [PERSON] et al. [52] proposed a novel distance measurement on hesitant fuzzy sets (HFSs) based on equal-probability transformation and their application to decision-making regarding traffic control. In a word, the above research mainly focuses on the passenger waiting time at the station, and does not consider actual constraints such as train multi-stage traction energy consumption, actual train capacity, safety speed limit, etc. The established mathematical model has not yet been perfected and adapted to the actual operation conditions. Nevertheless, there are significant limitations to the previous studies. First, the above studies mainly focus on the passenger waiting time at the station, and do not consider actual constraints such as train multi-stage traction energy consumption, actual train capacity, safety speed limit, etc. The established mathematical model has not yet been perfected and adapted to the actual operation conditions. Second, reducing passenger waiting time and energy consumption through train scheduling has a great impact on improving service quality and energy efficiency from an operational perspective [43]. However, there is a lack of studies on coordinated optimization of train traction energy consumption of multiple trains that also consider time-varying passenger demand and train operating state variation. Third, the above studies reduce the total energy consumption by optimizing the timetable or speed profile, respectively. However, the train timetable and speed profile are not independent elements of train operation. Both have a direct impact on traction energy consumption and the utilization of regenerative braking energy, and should be considered together. In summary, at present, both research on single train energy-saving operation and multi-train timetable optimization have achieved rich findings, but there are still some urgent problems regarding energy-saving train control that deserve in-depth study. On one hand, in terms of train control, the energy-saving control method and mathematical model, based on the combination of time-varying passenger flow and multi-train operating conditions, have not been fully established. When multiple trains run at the same time, due to the short departure interval, any slight change in the train operation process will affect the operation of other trains in the network and indirectly influence the use of train traction energy consumption.