A Novel Cooperative Approach for Energy-Efficient Train Operation: Time Allocation and Trajectory Optimization to Minimize Power Fluctuations: Train Optimization Using Grouped Knapsack Dynamic Programming and a Two-Layer Optimization Approach

In the context of maintaining a constant total running time for the entire line, current strategies for running time allocation fail to achieve optimal total energy consumption. Furthermore, in the case of coordinated multi-train operations, existing methods do not fully account for real-time power fluctuations from the grid, nor do they maximize the utilization of regenerative energy. To address these issues, this paper proposes a comprehensive framework for optimizing train running time allocation and operational strategies. First, an offline database is established using the Pareto curve for each interstation, and a specialized grouped knapsack dynamic programming algorithm is employed to allocate running times with the goal of minimizing overall traction energy consumption. Next, an improved fourstage strategy for single-train operation is developed, and a twolayer optimization approach is applied. This approach considers the real-time power demand of other trains to optimize the operational strategies for departing trains, thereby maximizing regenerative braking energy utilization and minimizing power fluctuations. Finally, simulation experiments are conducted using the timetable and configuration of Wuxi Metro Line 1. The results demonstrate the energy-saving effectiveness of the proposed method for entire line operations, significantly reducing real-time power consumption.