Multi-objective parallel optimization of train energy-saving curves considering different passenger loads

This study investigates the optimization of train trajectories between stations under variable passenger loads to enhance the energy efficiency of inter-station travel. First, a bi-objective optimization model is formulated to simultaneously minimize inter-station running time and energy consumption. The model incorporates passenger load variations and is constructed using a time-step discretization approach integrated within a working regime sequence. Second, a solution framework is developed by integrating a multi-objective optimization algorithm with a parallel computing architecture to significantly improve computational efficiency. Finally, a case study is conducted using operational data from the Beijing Yizhuang Line. Simulation results demonstrate significant improvements: the optimized trajectories achieve substantial energy savings ranging from 25.0% to 37.8% compared to actual operational data, highlighting the model’s practical effectiveness in reducing operational costs and environmental impact. Furthermore, the parallel computing architecture achieves an 18-fold average reduction in computational time, demonstrating its critical role in making computationally intensive multi-scenario optimization tasks feasible for practical implementation. Additionally, the optimization process yields a three-dimensional Pareto surface that elucidates the trade-offs among the passenger numbers, inter-station running time, and energy consumption.