# Optimization Model of Express-Local Train Schedules Under Cross-Line Operation of Suburban Railway
## 2 Literature Review  
In recent years, extensive research has been conducted on the optimization of urban rail operation organization, focusing on multiple aspects, including multi-transfer coordination, express-local train services, and cross-line operations. These studies aim to improve the passenger travel experience and better match transport supply with dynamic demand. For instance, [PERSON] et al. [1] proposed a scheduling optimization method for large and  
Figure 1: The diagram of the Research flow diagram. small crossings based on passenger flow distribution to alleviate peak-hour congestion on specific segments. With the advancement of passenger flow data acquisition techniques, the research focus has gradually shifted from infrastructure constraints to passenger-oriented scheduling optimization. [PERSON] et al. [PERSON] et al. (2018) proposed a train service optimization model based on accurate demand inputs, expressing passenger travelling behavior through 0-1 integer planning and designing genetic algorithms to solve it. [PERSON] et al. [PERSON] et al. (2018) considered the time-varying passenger flow demand and constructed a train hopping scheme and schedule optimization model with the objective of reducing the waiting time of passengers. [PERSON] et al. [PERSON] et al. (2018) and [PERSON] et al. [PERSON] et al. (2018) constructed an optimization model for express-local train schedules from the perspective of fairness and crossing behavior. [PERSON] et al. [PERSON] et al. (2018) proposed a mixed integer planning model that minimizes the total waiting time while guaranteeing that all passengers reach their destinations, and verified through an arithmetic example that it was able to significantly improve synchronization as compared to the prevailing practice of using a fixed number of schedules and travel times. [PERSON] et al. [PERSON] et al. (2018) proposed an optimization model for train scheduling and operation, aiming to minimize operational costs and passenger waiting time, and solved it using a heuristic algorithm based on Lagrangian relaxation. Different from most existing studies that treat these two problems separately, this paper proposes an integrated approach for the train scheduling problem on a bi-directional urban metro line in order to minimize the operational costs and passenger waiting time. [PERSON] et al. [PERSON] et al. (2018) proposed an adaptive large neighborhood search algorithm to efficiently optimize train headways for non-periodic railway lines. [PERSON] et al. [PERSON] et al. (2018) proposed an integrated optimization model combining train stop plans and timetables under time-dependent passenger demand for commuter railways. The model, formulated as a mixed-integer nonlinear program, accounted for realistic factors such as no predefined schedules, variable train counts, and oversaturation. It aimed to minimize total passenger waiting time, stop-induced train delay, and train running time. An extended adaptive large neighborhood search (ALNS) algorithm was developed and validated through experiments and a real-world case, demonstrating improved scheduling efficiency and passenger service. [PERSON] et al. [PERSON] et al. (2018) proposed an optimization model that accounts for the effect of boarding and alighting passenger volumes on dwell times, aiming to minimize passenger dissatisfaction, and solved it using a heuristic algorithm. [PERSON] et al. [PERSON] et al. (2018) developed a real-time scheduling method that responds to dynamic passenger demand by adding temporary stops at key stations. Using a heuristic algorithm, they demonstrated in Dutch railway cases that demand-responsive adjustments can substantially reduce total passenger delays. [PERSON] et al. [PERSON] et al. (2018) proposed an optimization model for metro rescheduling under time-dependent and overcrowded passenger flow after a disruption. To ensure computational efficiency, the model was decomposed and solved using an iterative algorithm.