The passenger demand of urban rail transit (URT) lines often present asymmetric tidal time-varying characteristics. To match the demand fluctuation, the train operational plan (TOP) generally has asymmetric bi-directional frequency/headway setting and imbalanced circulation, leading to high operation cost. This paper incorporates circulation balance into TOP optimization to balance the bi-directional arrival, departure, circulation, and resource utilization, and reduce the overall operation cost. Based on time-varying section demand and predetermined service level, bi-directional stepped maximum headway functions are collaboratively constructed, and then the circulation process is described by the trip flow circulation network that is formulated as a cost-oriented integer linear programming model. Using the optimized frequency setting, the final TOP is obtained by a two-stage approach to successively solve the schedule and rolling stock circulations at terminals. The case study based on an URT line in Shenzhen indicates that the proposed approach can not only ensure the required service level for travel demand, but also improve the efficiency of circulation and utilization, and effectively reduce the overall operation cost. The proposed approach provides an effective technique to keep balanced, stable and sustainable operation for URT lines.

Daily line planning in the operation stage should satisfy the fluctuating travel demand on different days and ensure the operation stability. In this paper, we propose an approach of daily line planning optimization for high-speed railway (HSR) lines to trade off the system costs and operation stability. The line plan is optimized by adjusting the reference line plan based on the baseline plan. A bi-level programming model is constructed based on Stackelberg game theory to describe the interaction and conflicts between railway companies and passengers. We propose the thought of “trigger decision, space-time coupling and joint iteration” to solve the model under the framework of the Simulated Annealing Algorithm (SAA). The case study on the Beijing–Shanghai HSR Line demonstrates that the adjusted line plan can not only optimize the system costs but also ensure the operation stability. It can provide sufficient transit capacity to satisfy the travel requirements of passengers and present the obvious advantage of operation cost reduction.

Stop planning is aimed to provide proper services for passenger demand, but diverse stop patterns lead to differences in stop density and travel speeds, impacting the utilization of line capacity. This paper incorporates capacity utilization into stop planning in the strategic line planning stage to trade off the matching between supply and demand and the stop distribution balance among trains. A bi-level programming model is established to formulate the Stackelberg game relation between supply and demand, where the stop distribution imbalance and the passenger travel inefficiency are measured. An adaptive hybrid solving algorithm combined with Genetic Algorithm and Simulated Annealing Algorithm is proposed, with several adaptive operations according to the problem characteristics and optimization degree to improve searching efficiency. A case study on the local network of Beijing–Shanghai High-speed Railway Line demonstrates that the proposed approach can not only mitigate the stop distribution imbalance, but also improve the travel efficiency of passengers, indicating that it can benefit the simultaneous improvement of capacity utilization and service level.

It is particularly important to develop efficient air–rail intermodal path planning methods for making full use of the advantages of air–rail intermodal networks and providing passengers with richer and more reasonable travel options. A Time-Expanded Graph (TEG) is used to model the timetable information of public transportation providing a theoretical basis for public transportation path planning. However, if the TEG includes a large amount of data such as train stations, airports, train and air schedules, the network scale will become very large, making path planning extremely time-consuming. This study proposes an XGBoost-based heuristic path planning algorithm (XGB-HPPA) for large scale air–rail intermodal networks, which use the XGBoost model to predict transfer stations before path planning, and quickly eliminate unreasonable transfer edges by adding a heuristic factor, reducing the network scale, thus accelerating the computation speed. Comparative results indicate that XGB-HPPA can markedly enhance computational speed within large-scale networks, while obtaining as many valid solutions as possible and approximating the optimal solution.