Simultaneous periodic and aperiodic train timetabling and routing under flexible track utilisation policy

Train timetabling and train platforming are problems of crucial importance when scheduling high-speed trains. This study puts forward a flexible track utilisation policy by investigating the internal structure of the station, which aims to incorporate train platforming into the timetabling optimisation of periodic and aperiodic trains, establishing an integrated optimisation mode of simultaneous periodic and aperiodic train timetabling and routing. However, considering the non-deterministic polynomial-time hard (NP-hard) nature of this model, a discrete space–time network is constructed to reformulate the timetabling and routing optimisation model of periodic and aperiodic trains. And an equivalent multi-objective mixed-integer programming model is yielded based on the space–time network. On this basis, an efficient Lagrangian relaxation decomposition algorithm is designed for solving it. Finally, the effectiveness of the model and algorithm is verified using a series of simple experiments and a real-world case study derived from Beijing-Shanghai high-speed railway.