Temporal and spatial imbalances in passenger demand pose significant challenges for urban rail transit (URT) systems, which must balance minimizing operational costs with maintaining service quality. This study develops a mixed-integer programming (MIP) model that simultaneously optimizes train timetabling, formation planning, and unit circulation to better align with passenger demand, explicitly accounting for dynamic capacity at turnaround stations. To efficiently solve this complex problem, a multi-strategy adaptive optimization (MSAO) algorithm is introduced, featuring five searching strategies (altering service frequency, routes, departure interval/headway, train formation types, and train unit connections), and three repairing strategies (restoring the infeasibility in train unit circulations, timetables, and storage-track capacity). Real-world data from Chongqing URT Line 5 is used to validate the model's performance, yielding near-optimal solutions for small instances (within 2.82% of the optimum) in under 10 seconds. Large-scale experiments further demonstrate a 64.27% improvement in the normalized objective through flexible operations, outperforming benchmark algorithms by 5.4–6.8%.
Hu, X., Jiang, S., Huang, P., D'Ariano, A., Cao, M., Peng, Q. (2026). Integrated optimization of train timetables, formations, and unit connections with multiple operational strategies in urban rail transit systems. COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, 42 [10.1016/j.cacaie.2026.100025].
Integrated optimization of train timetables, formations, and unit connections with multiple operational strategies in urban rail transit systems
D'Ariano A.;
2026-01-01
Abstract
Temporal and spatial imbalances in passenger demand pose significant challenges for urban rail transit (URT) systems, which must balance minimizing operational costs with maintaining service quality. This study develops a mixed-integer programming (MIP) model that simultaneously optimizes train timetabling, formation planning, and unit circulation to better align with passenger demand, explicitly accounting for dynamic capacity at turnaround stations. To efficiently solve this complex problem, a multi-strategy adaptive optimization (MSAO) algorithm is introduced, featuring five searching strategies (altering service frequency, routes, departure interval/headway, train formation types, and train unit connections), and three repairing strategies (restoring the infeasibility in train unit circulations, timetables, and storage-track capacity). Real-world data from Chongqing URT Line 5 is used to validate the model's performance, yielding near-optimal solutions for small instances (within 2.82% of the optimum) in under 10 seconds. Large-scale experiments further demonstrate a 64.27% improvement in the normalized objective through flexible operations, outperforming benchmark algorithms by 5.4–6.8%.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
