Partial Train Speed Trajectory Optimization Using Mixed-Integer Linear Programming

The inexorable increase in energy demand around the world has put the energy-saving technology in hot spot for railway transportation. Train speed trajectory optimization based on optimal control, coasting control, and collaborative control inside railway systems is a popular methodology to enhance energy efficiency. This paper studies a special and interesting problem, i.e., the partial train speed trajectory optimization problem, and proposes a complete mathematical model where a mixed-integer linear programming algorithm can be directly applied. During the transient operation process of a train, the speed of the train is often considered to be monotonically increasing and decreasing in normal conditions without extreme gradients. Given that, the proposed method can quickly locate the train speed profile under practical engineering constraints, and the objective function is either to maximize the regenerative braking energy or to minimize the traction energy. Such a method with a short computational time may become particularly interesting for online cases where a train is altering its speed in a fixed distance and time due to the operational requirement. The generated speed trajectory can be used to guide the train to control its speed or in a normal braking operation. The robustness and effectiveness of the method has been demonstrated through a number of detailed simulation results in this paper.