A New Train Timetable Optimization Model Using a Lagrangian Relaxation Guided Heuristic for a Real-World High-Speed Railway Line

Abstract

High-speed railway (HSR) systems have been developing rapidly in China and other countries throughout the past decade. A high-quality train timetable should satisfy transportation demands with the best possible benefit. This paper 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 (LR) 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. The results show that the proposed model and heuristic offer an efficient and promising means of addressing HSR timetable problems. h h O  , , where O is the set of segments,