###### Abstract  
With the traffic congestion problem deteriorating, people increasingly choose urban rail transit (URT) to travel. Although URT alleviates traffic congestion, the long-term operation of a large number of trains leads to huge energy consumption. In order to adapt the major social development concept of \"Low carbon\", a multi-train energy-saving control collaborative optimization method is proposed in this paper. First, the composition of single train operating conditions is determined by the conversion of operating conditions between stations and the force changes under the premise of ensuring safe and on-time train operation. A single-train energy consumption calculation combinatorial optimization model with the dual control objectives of reducing passengers' average waiting time as well as train traction energy consumption is established. The energy saving control strategy of a single train is investigated by ARMA-Radial Basis Function Neural Network (ARMA-RBFNN) and Genetic Algorithm (GA). Next, the queuing theory is introduced to analyze the variation in passenger waiting time for multiple trains at different arrival intervals. A Deep Reinforcement Learning (DRL) algorithm is designed to obtain the correlation among passenger waiting time, arrival interval and train stopping time. The optimization objective is to minimize the multi-train traction energy consumption and the average passenger waiting time while considering conditions such as train operating safety interval, speed limit, multiple operating state and single train energy-saving models, etc. Then, a multi-train cooperative energy-saving control model is proposed based on the Dragonfly Algorithm (DA). Finally, a case study of Beijing Metro Line 4 is conducted to illustrate the effectiveness of the proposed method. The results demonstrate that the total traction energy consumption and passenger waiting time are reduced by 3.1% and 5 s, respectively, compared with the method of independently optimizing the single-train control strategy. The findings can aid in the development of energy-saving strategies and also provide a basis for energy-saving operation control of multiple trains. urban rail transit; multi-train energy saving control; dual control objectives; collaborative optimization; deep reinforcement learning; dragonfly algorithm +
Footnote †: journal: Applied Sciences  
in 2017 to 9192.62 km in 2021 Q3 [1,2]. The average annual growth rate is about 19.16% [2]. With the increase in the operating mileage, the energy consumption of the URT systems has drawn more attention. In 2020, the annual energy consumption of the URT systems was about 172.4 billion kWh [3]. Among them, traction energy consumption accounted for 8.4 billion kwh or 48.7% [3]. From the perspective of environmental protection and operational cost reduction, it is necessary to study how to reduce the energy consumption in URT systems. Therefore, it is of great importance to reduce energy consumption by optimizing the multi-train operating conditions and statuses. As a result, the reduction in traction energy and the improvement of multi-train operating control strategies are two effective measures to save energy in URT systems. Regarding single-train energy-saving operating control strategies, most studies focus on the line condition, train operating speed and condition conversion point. [PERSON], [PERSON] and [PERSON] [4] calculated the critical switching points and key speeds so as to obtain an optimal and feasible solution for train energy saving. [PERSON], [PERSON] and [PERSON] [5] presented a single-train trajectory optimization to obtain minimum energy consumption with maximum regenerated energy. [PERSON] et al. [6,7] proposed a method to obtain an energy-efficient driving strategy for a train's journey on an undulating track with steep grades. [PERSON] et al. [8] proposed an energy-saving operation optimization model of a single train based on time discretization. [PERSON] et al.