Multi-objective train trajectory design based on dynamic programming

The optimization of train trajectory plays a critical role in the improvement of operational performance of trains and has received intensive attention in recent years. However, the accurate calculation of operational cost of trains, such as time and energy, needs the establishment of corresponding effective formulas, which has not been investigated sufficiently in the existing literature. This paper studies an optimal control problem of train trajectory design and a new modeling approach which provides accurate formulas as for the calculation of time and energy are provided. By using this method, the optimization problem can be transformed into a multi-stage decision process, and hence can be resolved by the famous dynamic programming. Finally, the simulation results demonstrate the effectiveness of the proposed method in obtaining the optimal trajectory of a real subway line with the minimum cost of time and energy, as well as reaching a relative high level of riding comfort.