The overspeed protection, smooth driving, punctuality, and energy efficiency of freight trains largely depend on their trajectory optimization. This paper proposes a multi-objective optimization model, which maximizes the weighted sum of energy efficiency, punctuality, and driving smoothness. Model constraints systematically cover many practical conditions, including varying line resistance, overspeed protection, discrete neutral zones, and nonlinear traction and electric braking characteristics. Electric braking and pneumatic braking are distinguished in the freight train model, and the utilization of feedback braking energy is also considered. By nonlinear approximation, the proposed multi-objective optimization model is solved by the quadratic programming (QP) algorithm, and optimized trajectories are obtained. Numerical simulation demonstrates the correctness and effectiveness of the proposed method. Comparisons with two actual trials show that the energy efficiency and driving smoothness of the proposed method are better than that of the drivers’ operation with the same journey time. In addition, the algorithm has a short computation time, which has the potential to be integrated for on-board devices such as the driver advisory system (DAS).

货运列车的超速保护，平稳行驶，准时和能效在很大程度上取决于其轨迹的优化。本文提出了一个多目标优化模型，该模型使能量效率，守时性和行驶平稳性的加权总和最大化。模型约束系统地涵盖了许多实际条件，包括变化的线路电阻，超速保护，离散的中性区以及非线性牵引力和电动制动特性。货运模型中区分了电动制动和气动制动，并考虑了反馈制动能量的利用。通过非线性逼近，通过二次规划（QP）算法求解所提出的多目标优化模型，并获得了优化的轨迹。数值仿真表明了该方法的正确性和有效性。与两个实际试验的比较表明，所提方法的能量效率和行驶平稳性均优于相同行驶时间下驾驶员的操作效率。此外，该算法的计算时间很短，有可能集成到诸如驾驶员咨询系统（DAS）之类的车载设备上。