## 6 Conclusions  
The new ATO over ERTMS system will permit the automatic driving imposing interoperability requirements. In addition, the standard will include energy efficiency requirements for the driving. This paper presents the eco-driving problem defined by the specification of the new system. This eco-driving problem aims to minimise the energy consumption fulfilling the commercial arrival time to the next station. Furthermore, it is subject to new constraints compared with the classical eco-driving problem because of the intermediate target times imposed by the timing points during the journey. The DE algorithm, a Nature Inspired algorithm, combined with a detailed simulation model, has been proposed to solve this eco-driving problem. This algorithm has been widely applied in the field of constraint optimisation. Besides, a fitness function has been defined to handle the new constraints in the problem. The use of this algorithm makes it possible to find speed profiles that meet the requirements of multiple target times. This is an improvement in numerical eco-driving approaches given that the typical numerical methods proposed in literature cannot be easily adapted to solve this complex problem. The use of a detailed simulation model allows the algorithm to obtain solutions with great accuracy taking into account any detail of the complex railway operation. The performance of the DE algorithm has been compared with the GA. Both algorithms have been tested in two case studies where one and two intermediate timing points have been taken into account beside the arrival target time. The results have shown that the GA does not find feasible solutions. Contrary, the proposed DE algorithm has demonstrated its capability to find speed profiles that meet all the target times. Apart from finding feasible solutions, it finds the one with the minimum energy consumption. This task is not trivial since important energy variations have been obtained among feasible solutions. Thus, it has been observed: 7.7% of energy variation in the case of one intermediate timing point and 3.1% in the case of two intermediate timing points. The presence of more constraints reduces the feasible region making more similar the speed profiles that meet all the target times. For this reason, the energy differences observed in the case of two intermediate timing points are smaller compared with the case of one intermediate point. The time tolerance allowed to meet the target times influences the performance of the algorithm and the energy consumption of the optimal solution. The greater the tolerance the greater the feasible region and the easier to find valid speed profiles. Furthermore, the energy consumption of the solution obtained is lower as greater is the tolerance. The impact of the target times on the energy consumption has also been shown. Important energy consumption variations have been obtained modifying the nominal timing points. For this reason, the minimum energy consumption on the train operation can be achieved not only obtaining the best speed profile for a given timetable, but also choosing properly the best possible target times (thus, designing an optimal timetable). The proposed method can be used in real-life applications to forecast the efficient speed profile of train in a journey with intermediate time targets and to offline pre-calculate efficient driving in trains controlled by ATO over ERTMS systems when the timetable is known before the journey. The execution time required by the algorithm to perform the optimisation is around 6 min. This time is adequate for an offline application. However, this calculation time is excessive to be applied online at the on-board train equipment. In the online application, the timing points can change during the journey, so quick response times are required in the speed profile calculation. For this reason, future work is needed to improve the calculation speed of the algorithm.