Learning-based model predictive control for train timetabling and rolling stock circulation planning with flexible train composition on Y-type metro lines

To better satisfy the uneven spatiotemporal distribution of passenger demand on the Y-type metro line, the concept of flexible train composition is explored, where the train compositions can be changed flexibly at a joint station and terminal stations connected to depots. A mixed-integer nonlinear programming model is developed to jointly optimize train timetables, rolling stock circulation plans, and flexible train compositions on a Y-type metro line. Using standard linearization techniques, the model is reformulated as a mixed-integer linear programming (MILP) model with an objective that balances operating cost and passenger service quality. To incorporate short-term demand variations and support real-time operations, the integrated MILP is embedded into a Model Predictive Control (MPC) framework, which updates timetabling decisions dynamically based on demand forecasts. However, solving the resulting MPC-based MILP in real time is computationally challenging due to the large number of binary decision variables. To overcome this limitation, we propose a learning-based optimization framework that integrates offline learning with online mixed-integer optimization. The learning module is trained offline on historical MPC solutions and is designed to selectively predict a subset of high-impact binary decisions, including train composition and routing choices, thereby reducing the combinatorial complexity of the online optimization problem. The predicted decisions are then fixed in an online MILP to optimize the remaining variables while preserving feasibility and consistency across rolling horizons. In addition, a feasibility-efficiency balancing strategy is introduced through selective decision prediction and feasibility-aware penalized training, which reduces infeasible learning outputs. Numerical experiments based on real-world operational data from Guangzhou Metro Line 14 show that the proposed learning-based MPC framework achieves real-time timetabling, while maintaining solution quality comparable to a full MPC-based optimization benchmark, with only a marginal loss in feasibility. Computational results demonstrate the effectiveness of integrating learning and MPC for real-time timetable optimization.