Multi-Objective Trajectory Optimization for Freight Trains Based on Quadratic Programming

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).