Train scheduling optimization, as a core issue in urban rail transit transportation organization, is crucial for enhancing the operational efficiency and service quality of rail transit systems. To systematically review the research progress in this field and promote its further development, this study conducts a comprehensive survey of relevant literature from both domestic and international sources. From the perspective of mathematical modeling, the paper summarizes the core elements of train scheduling optimization, including objective functions and constraints, from both the line-level and network-level perspectives. Furthermore, a detailed review of solution methods is presented, categorizing the approaches into heuristic algorithms and exact algorithms. Finally, the paper identifies existing research gaps and proposes future directions, including the need for improved modeling of dynamic passenger flow and behavior patterns, optimization of operations under network interconnection scenarios, exploration of multi-strategy operational models, and the integration of intelligent optimization algorithms, to further advance research on train scheduling optimization in urban rail transit.

This study investigates a flexible marshalling mode to address the pronounced temporal-spatial imbalance of passenger flows in urban rail transit, achieve a more precise matching between supply (capacity) and demand (ridership), and thereby reduce operating costs. A comprehensive analysis is conducted on the current state of research on flexible marshalling, its passenger-flow adaptability, and engineering implementation requirements; using Qingdao Metro Line 5 as a case, the study further structures the online coupling/decoupling workflow and examines train operation routing design, fleet allocation strategy, track layout requirements, capacity evaluation, and life-cycle operational economic benefits. Results show that online coupling/decoupling is best located within the track arrangement zones of turnback terminals and junction stations, and that configuring terminals with paired turnback sidings increases turnback capacity. Additional capital expenditures attributable to the flexible mechanical marshalling mode are dominated by rolling stock and signalling systems, which together account for approximately 90%; it is therefore recommended that civil works reserve the necessary interfaces (e.g., for track layout adjustments and platform screen doors) during initial construction. Compared with an all-6-car fixed formation baseline, a mixed operation pattern comprising conventional 6-car fixed formations and 3+3 flexible coupled sets yields superior cost effectiveness through notable reductions in traction energy consumption and maintenance costs; nevertheless, current deployment remains constrained by limited system capacity, higher marginal equipment investment, and increased operational management complexity, all requiring further optimization. The findings provide a technical and organizational reference for designing train operation schemes on comparable urban rail lines.

Ningbo's urban rail transit system faces the challenge of making more efficient use of limited corridor resources, prompting a study on express-local operation technology for Line 6 to enhance operational efficiency. The technical and economic rationale for adopting an express-local operation pattern on Line 6 was evaluated by examining technical principles, travel demand and operating schemes, selection of overtaking stations and track layouts, and time efficiency and economic benefits. Results indicate that adopting the express-local operation pattern on Line 6 meets the planned goal of a “30-minute travel circle covering Ningbo's six districts,” confers clear competitive and economic advantages, reduces travel time by about 6 minutes per trip for commuter express trains and 12 minutes for super-express trains, and generates an estimated annual social value of approximately 48.2 million yuan from passenger time savings.

To address the challenge of accurate fine-granularity passenger flow prediction and decision support in urban rail transit, the study analyzes spatiotemporal passenger flow patterns and influencing factors using automatic fare collection (AFC) data, and employs a support vector regression (SVR) model whose parameters are optimized by a particle swarm optimization (PSO) algorithm. Using October 2021 data from Beijing Metro Line 4 at a 15 min aggregation interval, weather, time period, and date type were used as input variables; model accuracy was evaluated via mean squared error (MSE), mean absolute error (MAE), coefficient of determination (R²), and relative accuracy, together with comparative model experiments. The results demonstrate that the proposed model effectively captures the spatiotemporal characteristics of rail transit passenger flow and achieves high prediction accuracy, with a mean squared error of 0.0164 and a coefficient of determination of 0.93. Additionally, a positive correlation is observed between the volume of rail transit passenger flow and error values of different model predictions. The study enhances understanding of the distribution and evolution of urban rail transit passenger flows and supports optimization of operations organization, scheduling strategies, and network planning.

To address multi-factor subway line passenger volume forecasting needs, 12 influential features are selected (time, weather, network scale, urban development, holidays, and events) via feature mining and correlation analysis, and—targeting the difficulty of XGBoost hyperparameter tuning—a hyperparameter optimization approach based on the Zebra Optimization Algorithm (ZOA) is proposed. An XGBoost-ZOA integrated forecasting model is developed, a cross-validation scheme tailored for time-series prediction is designed, and a case study is conducted using Xi'an Metro data. The ZOA-optimized model achieves a MAPE of 3.85% on the Line 1 test set; compared with representative intelligent optimization algorithms, it yields the best performance, confirming the algorithm's superiority. Across nine lines, the XGBoost-ZOA model attains an average MAPE of 5.18%, with the maximum error below 7%, and the predicted and actual curves show a high degree of agreement. Compared with SARIMA and LSTM, the MAPE decreases by 17.8% and 21.9%, and the RMSE decreases by 10.8% and 13.6%, respectively. Finally, using feature importance, the nine lines were grouped into three categories: trend-driven, holiday/activity-driven, and multi-factor balanced passenger flows. Lines dominated by holidays/activities exhibit larger prediction errors, whereas those governed by periodic trends show smaller errors, confirming the model's interpretability and practical utility.

Accurate, comprehensive assessment of the spatiotemporal alignment between supplied capacity and dynamic, multidimensional passenger demand is essential for deploying capacity more effectively and alleviating load imbalances across the network. This study evaluates capacity-demand matching in urban rail transit from two dimensions—transport capacity supply and passenger service quality—by incorporating not only capacity utilization but also key passenger-oriented indicators (e.g., waiting time, crowding). A three-tier (station-segment-line) evaluation framework is established, and a composite assessment model is developed that integrates combined weighting (AHP-entropy) with the TOPSIS ideal-solution approach to quantify overall line-level performance. An empirical case using operational data from a Beijing Metro line verifies the model's accuracy and practicality and yields targeted optimization recommendations.

To address the issues of reduced network transport capacity and increased operational safety risks caused by large-scale passenger stranding when unidirectional service interruptions occur on urban rail transit lines, a train rescheduling model based on virtual coupling technology is constructed, and the optimization model is utilized to characterize the train rescheduling process under virtual coupling technology. A hybrid two-layer simulated annealing-genetic algorithm is employed to solve the problem. Finally, taking a case of unidirectional disruption in a city's subway line as an example, the feasibility and effectiveness of the proposed strategy are verified. The results demonstrate that compared with the traditional reverse operation strategy, the reverse operation strategy under virtual coupling technology reduces passenger total waiting time by 16.4%, passenger waiting time at stations by 14.1%, and significantly decreases the number of stranded passengers. Moreover, the flexibility and efficiency of train operation adjustments are substantially enhanced. The findings provide a modeling and optimization approach for train rescheduling under similar operational disruption scenarios.

With the background of transit-oriented development (TOD), urban underground complex structure is often joint constructed with a subway tunnel. However, the running trains in tunnel can also induce vibration responses of the underground complex, which may have negative effect on the functional use of the structure. To address this issue, a three-dimensional nonlinear soil-structure finite element model of the “Galaxy One Mile” underground complex in Changchun was developed and coupled with a vehicle-track dynamic sub-model to perform time-history analyses under subway train loading. Time history analyses on the vibration of the large underground complex were conducted, under the subway train load. After the effectiveness of the modelling method was verified through the in-situ measurement results, the interlayer and transversal vibration responses of the underground complex were acquired. Results show that train-induced vibrations propagate upward along walls and columns and then spread and attenuate horizontally through each floor slab, the columns and adjacent zones with the smallest horizontal distance to the track centerline exhibit the largest vibration responses on each floor; whereas in regions far from the vibration source, slab responses become more critical. The findings provide a reference for the development and design of underground space.

To address the technical challenges of the synchronous close-proximity construction during the shield tunneling of Line 1 of the Dongguan Rail Transit in Guangdong Province, an analysis was conducted on the impact of the construction sequence of the shield tunnel and the intermediate ventilation shaft. A construction plan was proposed that would minimize impact and maximize economic benefits. Based on the actual site conditions, three construction plans were put forward: (1) involves constructing the ventilation shaft after the shield has passed through, (2) involves the shield passing through after the construction of the shaft's base slab is completed, (3) involves the shield passing through after the main construction of the shaft is completed. Through numerical simulation, the impact of different construction schemes on surface vertical displacement, wall-top horizontal displacement, wall-top vertical displacement, and support axial force was analyzed. From the perspective of impact and economic benefits, the optimal construction plan has been determined. Finally, the impact of the selected scheme and the reliability of numerical simulation were verified through field monitoring data. The research results indicate that the surface settlement and structural deformation are minimal after the main construction of the air shaft is completed and the shield machine passes through, although the construction period is longer. After the completion of the air shaft base slab construction, the construction period for the shield machine to pass through again and for the air shaft construction to be carried out after the shield machine passes through are similar, but the surface settlement and structural deformation are smaller after the shield machine passes through again following the completion of the air shaft base slab construction. This option also has higher economic benefits and is the preferred construction plan. The results of on-site monitoring indicate that all monitoring data are within the controlled range, the selected construction plan is safe and feasible, and the impact of construction is minimal. The measured data were in good agreement with the numerical results, validating the reliability of the theoretical conclusions. The findings provide valuable reference for similar engineering projects.

In order to evaluate the safety impact of shield tunneling under close range on existing bridge pile foundations, this article focuses on a practical project and studies the influence of shield tunneling on the deformation of the lower structure of the bridge, the disturbance degree of a single pile, and the bearing capacity of the pile foundation in the vicinity of the bridge pile foundation area, especially when operating within a range of 3.0 meters from the pile foundation and crossing directly below it. The study adopts a combination of on-site monitoring and numerical simulation to systematically analyze the response characteristics of pile foundations during shield tunneling construction, and evaluates their impact in different zones based on the degree of disturbance. The results show that: ① When the shield tunneling machine excavates in the moderately weathered limestone layer with a horizontal clearance of 0 m, the induced single pile stress disturbance is significant, and the impact level is “strong impact”; ② When tunneling in strongly weathered limestone layers, due to insufficient residual bearing capacity of the pile foundation, the impact level within a horizontal distance of 3.0 m and a vertical range of 1.0~3.0 m is classified as “strong impact”; ③ When the rock embedding depth of the pile foundation is 1.0, 2.0, and 4.0 meters, significant single pile stress disturbances occur, and the impact level is also “strong influence”. The research conclusion can provide theoretical basis and engineering reference for the safety assessment and construction risk control of the interaction between shield tunnels and bridge pile foundations in similar projects.