Trajectory Planning of Train Platoons in Urban Rail Networks: A Mixed Integer Linear Programming Approach

With the application of virtual coupling technology (VCT) in railways, the concept of train platoons - where multiple train units operate with extremely short inter-unit distances - has gained significant research attention. A key challenge in this context is the optimal design of train platoon trajectories to ensure both efficiency and safety, given the highly nonlinear characteristics of railway systems (e.g., track resistance, safety constraints for train following). To address this, this paper develops a mixed-integer linear programming (MILP) model based on a time-indexed formulation to generate trajectories for two groups of train units merging at a bottleneck zone. The model also incorporates binary variables to determine the optimal merging order and enforces safety constraints through a set of nonlinear conditions tailored for a moving block system. To facilitate tractable optimization, we propose linearization techniques to transform nonlinear terms into linear expressions. Case studies using real-world data from the Beijing Metro Yizhuang Line demonstrate the effectiveness and applicability of the proposed approach.