New Heuristic Algorithm Based on the Lagrangian Relaxation for a Real-World High-Speed Railway Timetabling Problem

High-speed railway (HSR) systems have been developing rapidly in China and other countries throughout the past decade; as a result, efficiently operating these large-scale systems has presented new challenges to the railway industry. A high-quality train timetable should satisfy transportation demands with the best possible benefit. This study presents a scheduling model for double-track HSR lines based on a train service plan for timetable optimization. First, we construct a space-time network and assign each resource a usage cost at every discrete instant of time to maximize the total profit of a train timetable as a whole. Second, we propose a heuristic method based on the Lagrangian relaxation algorithm to solve the model by updating the resource usage costs according to the conflicts caused by trains in each iteration. Finally, we consider the Beijing-Shanghai HSR line as a real-world application of the methodology. In each of the four cases tested, we obtain an approximate optimal solution with a duality gap of less than 8% within 120 s. The results show that the proposed model and heuristic offer an efficient and promising means of addressing HSR timetable problems.