An energy-efficient train trajectory describing the motion of a single train can be used as an input to a driver guidance system or to an automatic train control system. The solution for the best trajectory is subject to certain operational, geographic, and physical constraints. There are two types of strategies commonly applied to obtain the energy-efficient trajectory. One is to allow the train to coast, thus using its available time margin to save energy. The other one is to control the speed dynamically while maintaining the required journey time. This paper proposes a distance-based train trajectory searching model, upon which three optimization algorithms are applied to search for the optimum train speed trajectory. Instead of searching for a detailed complicated control input for the train traction system, this model tries to obtain the speed level at each preset position along the journey. Three commonly adopted algorithms are extensively studied in a comparative style. It is found that the ant colony optimization (ACO) algorithm obtains better balance between stability and the quality of the results, in comparison with the genetic algorithm (GA). For offline applications, the additional computational effort required by dynamic programming (DP) is outweighed by the quality of the solution. It is recommended that multiple algorithms should be used to identify the optimum single-train trajectory and to improve the robustness of searched results.

中文翻译：

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单列轨迹优化

描述单列列车运动的节能列车轨迹可用作驾驶员引导系统或自动列车控制系统的输入。最佳轨迹的解决方案受某些操作、地理和物理限制。有两种类型的策略通常用于获得节能轨迹。一种是允许列车滑行，从而利用其可用的时间余量来节省能源。另一种是动态控制速度，同时保持所需的行驶时间。本文提出了一种基于距离的列车轨迹搜索模型，在此模型上应用三种优化算法来搜索最优列车速度轨迹。而不是为列车牵引系统寻找详细复杂的控制输入，该模型试图获取沿途每个预设位置的速度水平。以比较的方式广泛研究了三种常用的算法。结果表明，与遗传算法（GA）相比，蚁群优化（ACO）算法在稳定性和结果质量之间取得了更好的平衡。对于离线应用程序，解决方案的质量超过了动态规划 (DP) 所需的额外计算工作量。建议使用多种算法来识别最优单列列车轨迹并提高搜索结果的鲁棒性。结果表明，与遗传算法（GA）相比，蚁群优化（ACO）算法在稳定性和结果质量之间取得了更好的平衡。对于离线应用程序，解决方案的质量超过了动态规划 (DP) 所需的额外计算工作量。建议采用多种算法来识别最优单列列车轨迹，提高搜索结果的鲁棒性。结果表明，与遗传算法（GA）相比，蚁群优化（ACO）算法在稳定性和结果质量之间取得了更好的平衡。对于离线应用程序，解决方案的质量超过了动态规划 (DP) 所需的额外计算工作量。建议采用多种算法来识别最优单列列车轨迹，提高搜索结果的鲁棒性。