Abstract:

With the continuous expansion of urban rail transit networks, system energy consumption has been increasing, while passengers’ demands for travel efficiency and service equality are also growing. To balance energy saving and service quality, this study proposes an energy-efficient timetable optimization model for urban rail transit considering travel speed equality under time-varying passenger flow, aiming to achieve coordinated optimization between energy consumption and service equality. The model takes traction energy minimization as its primary objective and introduces equality constraints in the optimization process to balance energy efficiency and service uniformity from the passenger perspective. Service equality is evaluated by the average travel speed differences among origin–destination (OD) pairs (including the passenger entering stations and waiting before platform), using the mean absolute deviation (MAD) as a quantitative indicator. A smaller MAD value indicates a higher level of equality in service. To reconcile the trade-off between energy saving and travel efficiency, the total passenger travel time is constrained, and the passenger loading process follows the first-come, first-served principle to represent dynamic demand variations. Considering the nonlinear and complex constraints of the model, an adaptive particle swarm optimization algorithm is designed to solve it. The algorithm incorporates a penalty function and rule-based feasibility mechanism to ensure fast convergence and computational efficiency. A case study based on the Beijing Changping Line is conducted under multiple scenarios with different total travel time and equality constraints. The results indicate that appropriately relaxing total travel time can significantly reduce traction energy consumption and improve equality. When the total travel time increases by 10%, energy consumption decreases by more than 10%, and the equality indicator improves by about 35%. Even when total travel time remains unchanged, energy consumption decreases by around 3.7%, and equality improves by 20%. The findings demonstrate that the proposed model and algorithm can achieve energy-efficient operation and improved service equality without compromising travel efficiency, providing an effective theoretical and technical reference for energy-saving scheduling and equitable operation in urban rail transit systems.

Key words: urban rail transit, time-dependent passenger flow, average travel speed, energy-efficient train timetable, particle swarm optimization