High-Speed Railway Train Diagram Optimization Model and Algorithm Considering Station Throat Capacity Constraints

In response to the issues of insufficient throat capacity at high-speed railway stations. This paper proposes a train scheduling model that considers the balance of capacity utilization and has the ability to optimize the train diagram under large-scale traffic flow. Considering the ability to use exclusive constraints, this model is a 0-1 planning model which is based on the cumulative flow theory, with the objective of minimizing total travel time of trains. Comparing with other models, this model has tighter constraints and can compress the decision space. In order to solve the large-scale example, this paper proposes a Lagrangian relaxation algorithm. This method decomposes the difficult problem into sub-problems that are easy to solve. Through examples, we prove that the proposed method improves the quality of the solution by 2.83%, and the upper and lower bound gap can be optimized to 24%.