As urban mobility demands continue to grow, integrating diverse rail transit modes, alleviating congestion at transfer hubs, and enhancing passenger transfer efficiency have become pressing challenges in both practice and research. This study addresses the coordination between feeder systems (e.g., high-speed rail) and collector systems (e.g., metro) within urban rail networks, leveraging the flexibility enabled by emerging virtual coupling technologies at the tactical planning level. We propose a large-scale mixed-integer linear programming (MILP) model that jointly optimizes train platooning strategies, including rolling stock allocation, coupling/decoupling operations, and timetable decisions. To efficiently solve this complex problem, we develop a tailored constraint-generation algorithm that decomposes the MILP into a relaxed master problem (for train operations) and a series of linear subproblems (for passenger flow feasibility), iteratively adding violated constraints to the master. Our methodological contributions are twofold. First, we prove that feasibility checking of the subproblems can be conducted analytically rather than via linear programming (LP) solving, significantly improving computational efficiency. Second, we show that the generated cuts are provably stronger than classical Benders feasibility cuts. In addition, we introduce several acceleration techniques, including valid inequalities and structure-based cut refinement, to further enhance algorithmic performance. Finally, we validate our approach using real-world operational data from the Beijing rail network. The results show that our algorithm consistently outperforms commercial solvers in both solution quality and computational time. Compared to the current operational plan in Beijing, which involves fixed train formations and uncoordinated timetables, our method reduces both rolling stock operating costs and passenger transfer delay times by over 30%.
Chai, S., Yin, J., D'Ariano, A., Zhang, J., Tang, T., Yang, L. (2026). Train platoon optimization for coordinating feeder and collector lines in urban rail networks. TRANSPORTATION RESEARCH PART B-METHODOLOGICAL, 212 [10.1016/j.trb.2026.103543].
Train platoon optimization for coordinating feeder and collector lines in urban rail networks
D'Ariano, Andrea;
2026-01-01
Abstract
As urban mobility demands continue to grow, integrating diverse rail transit modes, alleviating congestion at transfer hubs, and enhancing passenger transfer efficiency have become pressing challenges in both practice and research. This study addresses the coordination between feeder systems (e.g., high-speed rail) and collector systems (e.g., metro) within urban rail networks, leveraging the flexibility enabled by emerging virtual coupling technologies at the tactical planning level. We propose a large-scale mixed-integer linear programming (MILP) model that jointly optimizes train platooning strategies, including rolling stock allocation, coupling/decoupling operations, and timetable decisions. To efficiently solve this complex problem, we develop a tailored constraint-generation algorithm that decomposes the MILP into a relaxed master problem (for train operations) and a series of linear subproblems (for passenger flow feasibility), iteratively adding violated constraints to the master. Our methodological contributions are twofold. First, we prove that feasibility checking of the subproblems can be conducted analytically rather than via linear programming (LP) solving, significantly improving computational efficiency. Second, we show that the generated cuts are provably stronger than classical Benders feasibility cuts. In addition, we introduce several acceleration techniques, including valid inequalities and structure-based cut refinement, to further enhance algorithmic performance. Finally, we validate our approach using real-world operational data from the Beijing rail network. The results show that our algorithm consistently outperforms commercial solvers in both solution quality and computational time. Compared to the current operational plan in Beijing, which involves fixed train formations and uncoordinated timetables, our method reduces both rolling stock operating costs and passenger transfer delay times by over 30%.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
