Trajectory Optimization for High-Speed Trains via a Mixed Integer Linear Programming Approach

This paper proposes a trajectory optimization approach for high-speed trains to reduce traction energy consumption and increase riding comfort. Besides, the proposed approach can also achieve energy-saving effects by optimizing the operation time between stations. First, an optimization model is developed by defining the objective function as a trade-off function of the traction energy consumption and riding comfort. In addition to constraints in the classic optimal train control model, three new factors-the discrete throttle settings, neutral zones, and sectionalized tunnel resistance-are considered. Then, the model is discretized and turned into a multi-step decision optimization problem. All the nonlinear constraints are approximated using piecewise affine (PWA) functions, and the trajectory optimization problem is turned into a mixed integer linear programming (MILP) problem which can be solved by existing solvers CPLEX and YALMIP. Finally, some case studies with real-world data sets are conducted to present the effectiveness of the proposed approach. The simulation results are compared with the practical running data of trains, which shows that the proposed model and the optimization approach save energy and improve the riding comfort.