Obtaining efficient speed profiles for metro trains is a multi-objective optimisation problem where energy consumption and travel time must be balanced. Automatic Train Operation (ATO) systems may handle a great number of possible speed profiles; hence optimisation algorithms are required to find efficient ones in a timely manner. This paper aims to assess the performance of a particular meta-heuristic optimisation algorithm, a variation of the traditional Ant Colony (ACO) modified to deal with multi-objective problems with continuous variables: MOACOr. This algorithm is used to obtain efficient speed profiles in up to 32 interstation sections in the metro network of Valencia (Spain), and the convergence and diversity of these solution sets is evaluated through metrics such as Inverse Generational Distance (GD) and Normalised Hypervolume (NH). The results are then compared to those obtained with a conventional genetic algorithm (NSGA-II), including a statistical analysis to identify significant differences. It has been found that MOACOr shows a better performance than NSGA-II in terms of convergence, regularity and diversity of the solution. These results indicate that MOACOr is a good alternative to the widely used genetic algorithm and could be a better tool for rail operation managers trying to improve energy efficiency.

中文翻译：

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多目标蚁群优化以获得有效的地铁速度曲线

获得地铁列车的有效速度曲线是一个多目标优化问题，其中必须平衡能源消耗和行驶时间。自动列车运行 (ATO) 系统可以处理大量可能的速度曲线；因此需要优化算法来及时找到有效的算法。本文旨在评估一种特定元启发式优化算法的性能，该算法是对传统蚁群 (ACO) 进行修改以处理具有连续变量的多目标问题的变体：MOACOr。该算法用于获得瓦伦西亚（西班牙）地铁网络中多达 32 个站间路段的高效速度剖面，并通过反代距离 (GD) 和归一化超容量 (Normalized Hypervolume) 等指标评估这些解决方案集的收敛性和多样性。 NH)。然后将结果与使用传统遗传算法 (NSGA-II) 获得的结果进行比较，包括用于识别显着差异的统计分析。已经发现MOACOr在解的收敛性、规律性和多样性方面表现出比NSGA-II更好的性能。这些结果表明，MOACOr 是广泛使用的遗传算法的一个很好的替代方案，并且可能是铁路运营管理人员试图提高能源效率的更好工具。