Optimization of High-speed Railway Train Timetabling

This research article presents a study focused on optimizing train timetables for high-speed railways using a directed space-time network. The study introduces incompatible arc sets to consolidate constraints such as minimum headway time and train overtaking into mutually exclusive arc segment constraints, thereby forming an integer programming model. The model is processed using the Lagrangian relaxation method, enhanced by fuzzy theory, and incorporates an improved subgradient optimization algorithm. The objective is to eliminate potential conflicts in the allocation of transportation resources among different train operation lines. A case study on the Beijing-Shanghai high-speed railway is conducted, optimizing the timetables for 82 train lines. The computational performance of both the standard and fuzzy subgradient algorithms is compared, revealing that the enhanced algorithm significantly improves the quality of the optimal solution while ensuring computational accuracy. The findings indicate a reduction in the dual gap value, demonstrating the effectiveness of the refined Lagrangian relaxation algorithm in generating higher-quality train timetables.