Optimization of Train Timetable for Intercity Railway Based on Coordinated Operation of Multi-periodic Trains

To ensure regularity of train arrival and departure times at stations operating with strict train periodicity and timing schedules, a novel methodology for coordinated operation of multi-periodic trains is proposed. The proposed method aims to ensure a better fit for the time distribution of passenger demands in the intercity railway system and is further compared with the existing aperiodic and single periodic train operation patterns to analyze their characteristic differences. On this basis, an optimisation model aimed at minimising the total travel times of all periodical operating trains is built to solve the train scheduling problem; this involves the coordinated operation of multi-periodic trains with identical time interval constraints for each period type of trains and all safety intervals. An algorithm based on Lagrangian relaxation framework is designed and combined with the gradient method by relaxing the complex constraints via Lagrangian multiples. The proposed model is implemented numerically for Beijing-Tianjin intercity railway using its operating timetable for four periodical operating trains with intervals of 17 min, 34 min, 34 min, and 35 min. The analysis shows that their objective values differ from the optimised lower boundary by 2.55%.