Optimizing routing, convoy formation, and timetabling for virtual coupling trains in mixed freight railway networks via logic-based Benders decomposition

Virtual coupling is an emerging platoon control paradigm that facilitates dynamic coupling and decoupling of trains, enhancing the efficiency and flexibility of freight railway transportation. This study addresses the integrated optimization of train routing, convoy formation, and timetabling for virtual coupling train scheduling in multi-directional networks. We propose an integer linear programming model based on big-M and cumulative flow methods to maximize transport capacity and minimize operation costs. To handle large-scale instances, we propose an Enhanced Branch-Relax-Check Benders algorithm based on logic-based Benders decomposition. Numerical experiments demonstrate that virtual coupling significantly enhances capacity, achieving a 57% increase in single-track networks and approximately 25% in double- and mixed-track networks. Convoy length and track availability at critical stations significantly impact overall transportation performance.