An energy-efficient train trajectory corresponds to the speed profile of a train between two stations that minimizes energy consumption while respecting the scheduled arrival time and operational constraints such as speed limits. Determining this trajectory is a well-known problem in the operations research and transport literature, but has so far been studied without accounting for stochastic variables like weather conditions or train load that in reality vary in each journey. These variables have an impact on the train resistance, which in turn affects the energy consumption. In this paper, we focus on wind variability and propose a train resistance equation that accounts for the impact of wind speed and direction explicitly on the train motion. Based on this equation, we compute the energy-efficient speed profile that exploits the knowledge of wind available before train departure, i.e., wind measurements and forecasts. Specifically, we: (i) construct a distance-speed network that relies on a new non-linear discretization of speed values and embeds the physical train motion relations updated with the wind data, and (ii) compute the energy-efficient trajectory by combining a line-search framework with a dynamic programming shortest path algorithm. Extensive numerical experiments reveal that our “wind-aware” train trajectories present different shape and reduce energy consumption compared to traditional speed profiles computed regardless of any wind information.

节能火车的轨迹与两个站点之间火车的速度曲线相对应，该轨迹在考虑到计划到达时间和诸如速度限制之类的操作约束的同时，将能耗降至最低。确定这一轨迹是运筹学和运输文献中的一个众所周知的问题，但是到目前为止，在研究中并未考虑随机变量，例如天气条件或火车负荷，而这些随机变量实际上在每次旅程中都会发生变化。这些变量会影响列车阻力，进而影响能耗。在本文中，我们关注风的可变性，并提出了一个列车阻力方程，该方程明确考虑了风速和风向对列车运动的影响。根据此等式，我们计算能量效率的速度曲线，该曲线利用了火车出发前可用的风的知识，即风的测量和预报。具体而言，我们：（i）构造一个基于速​​度值的新非线性离散化的距离-速度网络，并嵌入以风数据更新的物理火车运动关系，并且（ii）通过组合计算能效轨迹具有动态规划最短路径算法的线搜索框架。大量的数值实验表明，与计算出的任何风信息无关的传统速度曲线相比，我们的“风意识”火车轨迹呈现出不同的形状并降低了能耗。（i）建立一个基于速​​度值的新非线性离散化的距离-速度网络，并嵌入以风数据更新的物理火车运动关系，以及（ii）通过组合线搜索来计算能效轨迹动态编程最短路径算法的框架。大量的数值实验表明，与计算出的任何风信息无关的传统速度曲线相比，我们的“风意识”火车轨迹呈现出不同的形状并降低了能耗。（i）构建一个依赖于速度值的新非线性离散化的距离-速度网络，并嵌入以风数据更新的物理火车运动关系，并且（ii）通过组合线搜索来计算能效轨迹动态编程最短路径算法的框架。大量的数值实验表明，与计算出的任何风信息无关的传统速度曲线相比，我们的“风意识”火车轨迹呈现出不同的形状并降低了能耗。