###### Abstract
The on-board equipment will need algorithms to calculate the train speed profile and, as energy efficiency is one of the main goals of ATO over ERTMS, these algorithms have to be designed using eco-driving principles. The eco-driving design algorithms have to find the speed profiles that minimise the energy consumption fulfilling a target running time given by the timetable. Typically, the commercial timetables are not those associated with the minimum running time (flat-out driving), but they include time margins to be able to recover delays when necessary and thus can be fulfilled running at a lower speed. This is also important in high speed lines, where both the speed and the punctuality define the quality of the train service. If the train is delayed the driving is fast enough to recover the delay but, when the train is not delayed, the time margin can be used to save energy (instead of arriving at the station in advance). ATO over ERTMS requirements establish that the way in which the speed profile must be calculated will depend on the timetable information. The time information that is sent to the on-board equipment could be the nominal timetable, or a timetable generated by complex algorithms for traffic regulation purposes. Timetable information is provided by means of timing points. A timing point includes the following information:  
* Type of point: departure, passing, or arrival. * Position of the point. * Time assigned. The departure timing point is the departure time from the station associated to the commercial timetable. The arrival timing point is the arrival time at the next station according to the commercial timetable. These two points are the classical requirements in timetabling problems. The ATO over ERTMS system includes a new type of time reference at intermediate points between stops at the stations. At the intermediate timing points, a passing time is imposed that is not published to passengers in the commercial timetable. The purpose of these passing times is operative for the railway administrator, for example, to guarantee a specific passing order of two consecutive trains when they converge at a point in the line (imposing first the high-speed service and second the long distance service). When the train receives the information, the on-board ATO equipment generates the speed profile that the train must follow to comply with the timing points. By this way, the interoperability of train is ensured. Each train is responsible of generating its own speed profile following its own driving commands to meet the target times. The method to obtain the speed profile could vary depending on the exploitation and the manufacturer of the ATO equipment. For instance, a set of speed profiles can be offline calculated and stored in the ATO on board memory when a set of possible timetables that never change are defined in a railway line. Other possibility is to generate online the speed profile if the target times could change freely depending on traffic conditions. In any case, the use of eco-driving methods is the key stone to maximise the energy efficiency of the train operation while fulfilling the time objectives. Other measures can be applied to improve the energy efficiency of the train such as the increase of traction chain yield [15], the reduction of aerodynamic running resistance [16], or the improvement of energy usage of auxiliary systems [17]. However, compared with eco-driving, these measures require high investments during the train design while eco-driving is a short-term action that can be applied in existing trains. This paper presents the ATO over ERTMS eco-driving optimisation problem as well as a Nature Inspired algorithm proposed to solve it. The algorithm proposed in this paper is based on Differential Evolution (DE) framework, and it is combined with a detailed simulation model to guarantee the accuracy of the solutions obtained. DE algorithms are simple, can be implemented straightforward, flexible to combine with any simulation model, and the parameters to be tuned are very few.