An Integrated Optimization Framework for Energy-Efficient Timetabling Considering Rolling Stock Circulation in Urban Rail Transit

Timetable optimization is a crucial strategy for reducing energy consumption in urban rail transit. However, existing research often narrowly focused on energy reduction while neglecting fundamental operational requirements such as rolling stock circulation and fixed first/last train schedules, limiting the practical applicability of the resulting optimization schemes. This study proposes a mixed-integer nonlinear programming model to jointly determine departure headways, section running levels, and rolling stock circulation plans, with the objectives of minimizing net energy consumption and depot entry/exit operations. To support the solution of this model, an optimization framework comprising two modules is developed: (1) an energy precomputation module that decouples redundant energy computations across discrete time intervals from the core optimization process; (2) a hybrid solution module that combines an adaptive large neighborhood search algorithm with the Gurobi solver to efficiently solve the large-scale integrated model. A series of real-world case studies based on Fuzhou Metro Line 5 in China demonstrated the effectiveness of the proposed framework. Compared with the current timetable, the optimized timetable reduced traction energy consumption and net energy consumption by 6.12 % and 10.20 %, respectively, with a 61.32 % increase in the amount of utilized regenerative braking energy. The number of depot entry/exit operations was reduced from 20 to 19, while maintaining the required rolling stock units unchanged. Results demonstrated that the proposed optimization framework can enhance energy efficiency and operational feasibility in urban rail transit by minimizing overall operational costs, encompassing electrical energy consumption and rolling stock circulation costs.