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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.