# Optimization Model of Express-Local Train Schedules Under Cross-Line Operation of Suburban Railway
###### Abstract  
Cross-line operation and express-local train coordination are both crucial for enhancing the efficiency of multi-level urban rail transit systems. Most studies address suburban railway operations in isolation, overlooking coordination and inducing supply-demand mismatches that weaken system efficiency. This study addresses the joint optimization of cross-line operation and express-local scheduling by proposing a novel train timetable model. The model determines train service plans and departure times to minimize total system cost, including train operating and passenger travel costs. A space-time network represents integrated train-passenger interactions, and an extended adaptive large neighborhood search (E-ALNS) algorithm is developed to solve the model efficiently. Numerical experiments verify the effectiveness of the proposed approach. The E-ALNS achieves near-optimal solutions with less than 4% deviation from Gurobi. Comparative analysis shows that the proposed hybrid operation mode reduces total passenger travel cost by 6% and improves the cost efficiency ratio by 13% compared to independent operations. Sensitivity analyses further confirm the model's robustness to variations in transfer walking time, passenger penalties, and waiting thresholds. This study provides a practical and scalable framework for optimizing train timetables in complex cross-line transit systems, offering insights for enhancing system coordination and passenger service quality. 23 May  
Suburban railway commonly adopts express-local train organization in its operations. Under a cross-line operation framework, the integration of express-local services can improve the alignment between service supply and demand, thus reducing overall travel time and enhancing system responsiveness. However, such integration also substantially increases the complexity of timetable design and train service planning. As a result, there is a growing need for scientifically sound methods that can optimize train timetables in the combined context of cross-line operation and express-local coordination to ensure operational feasibility and improve overall system efficiency. Despite growing interest in suburban railway planning, most existing studies focus on optimizing train schedules under isolated operation modes, such as either cross-line service or express-local coordination alone. Few have explored the joint optimization of these two dimensions within an integrated framework. This lack of synergy limits the capacity of current models to cope with real-world complexities and provide coordinated solutions for multi-tier transit systems. To fill this gap, this study proposes a train timetable optimization model that jointly determines train service plans and departure times under a hybrid operation framework. A space-time network is constructed to capture interactions between trains and passenger flows, and an extended adaptive large neighborhood search (E-ALNS) algorithm is developed to solve the model efficiently. The proposed approach is evaluated through numerical experiments and sensitivity analyses, aiming to verify its performance and provide insights for the design of effective suburban-urban integrated rail operations. Figure 1 presents the overall research flow of this study. The process begins with the identification of practical challenges and literature gaps in suburban railway scheduling, particularly under the combined context of cross-line operation and express-local service coordination. This is followed by the formulation of a timetable optimization model based on a space-time network, including an objective function and operational constraints. To solve the model, an extended adaptive large neighborhood search (E-ALNS) algorithm is designed with tailored destruction and repair operators. The algorithm is iteratively applied and refined to enhance solution quality. Computational experiments are then conducted, involving comparative analysis of different operation modes and sensitivity analyses on key parameters.