Direct multiple shooting for computationally efficient train trajectory optimization

Energy efficient train control has been an active field of research for several decades, with Pontryagin's maximum principle and dynamic programming being the two most common approaches for the computation of optimal trajectories. In this paper, we detail how direct multiple shooting can be used in the same context and highlight its two main advantages: the flexibility in the problem formulation and the availability of computationally efficient open -source software. Using the proposed framework, which is made publicly available, we are able to solve particularly challenging train trajectory optimization problems within only a few seconds.