Parallel optimization method of train scheduling and shunting at complex high-speed railway stations

The train operations of large stations are critical in determining the efficiency of the railway network. Large high-speed railway stations often have more than two adjacent stations running in multiple directions and must address highly complex train operation patterns. To develop a more efficient operation plan than the existing route-based representations for modeling train conflicts, a more systematic track-based resource network (TRN) representation for a railway station that simulates fixed equipment is used in this paper. Based on this high-fidelity TRN, an improved operation scheduling model (OSM) is introduced for the integrated scheduling of train operations, including shunting operations. Besides, two approaches based on Lagrangian relaxation (LR) and the Alternating Direction Method of Multipliers (ADMM) are described in detail to address the operation scheduling problem (OSP) for stations, and an efficient heuristic rule-based algorithm is also designed to generate lower bound solutions. To improve the algorithm efficiency, we designed a parallelization strategy for the proposed approaches. Based on real-world case studies, the computing results demonstrate that the parallelized ADMM-based approach can always find high-quality feasible solutions for complex stations and generate conflict-free station operation plans with significantly improved efficiency.