###### Abstract  
The new Automatic Train Operation (ATO) system over the standard European Rail Traffic Management System (ERTMS) will specify the requirements that an automatic train driving system must fulfil in order to be interoperable. The driving is defined by target times located along the journey that are received from the trackside system. Then, the on-board equipment drives the train with the objective of meeting all of the target times. The use of eco-driving methods to calculate the train driving is necessary, as one of the main goals of modern train driving systems is to increase the energy efficiency. This paper presents a simulation-based optimisation algorithm to solve the eco-driving problem constrained by multiple target times. This problem aims to minimize the energy consumption subject to a commercial running time, as the classical eco-driving problem, and also to meet intermediate target times during the journey between stations to enable automatic traffic regulation, especially at junctions. The algorithm proposed combines a Differential Evolution procedure to generate possible solutions with a detailed train simulation model to evaluate them. The use of this algorithm makes possible to find accurate speed profiles that meet the requirements of multiple time objectives. The proposed Differential Evolution algorithm is capable of finding the feasible speed profile with the minimum energy consumption, obtaining a 7.7% of energy variation in the case of a journey with one intermediate target time and 3.1% in the case of two intermediate targets. ATO over ERTMS; differential evolution; eco-driving; energy efficiency; railway operation; train simulation 2020 10 7705 29 October 2020 29 October 2  
there is a single vendor that provides the signalling system and the automatic control in an urban line. On the other hand, mainlines are characterised by having multiple companies providing signalling equipment in different track sections. These differences are some of the reasons why the ATO implementation in mainline systems is still under development. In view of these difficulties, interoperability arises as the keystone in the development of ATO for long distance travels. In terms of interoperability, there is much work done thanks to the European Railway Traffic Management System (ERTMS). ERTMS was born as part of a project undertaken by the European Commission to develop the specification of a standardised signalling system [2]. The aim of this system is to ensure interoperability of European trains and to improve safety, capacity and economic effectiveness. The ERTMS is composed of two main subsystems: European Train Control System (ETCS) and the Global System for Mobile Communications-Railways (GSM-R). ETCS is in charge of the control and safety of the traffic while GSM-R is in charge of communications. ERTMS is a successful system, which is implemented in many European railway lines and continues its expansion reaching countries from other continents. The following levels can be found in ETCS specifications:  
* Level 0: this level is used when an ETCS equipped train runs on non-ETCS route. The on-board equipment monitors the maximum train speed and the driver has to observe the lineside signals. * Level National Train Control (NTC): this level is meant for trains equipped with ETCS running on lines equipped with national Automatic Train Protection (ATP) systems instead of ERTMS. At this level, the train needs Specific Transmission Modules (STM) to interact with the national system and the ETCS system is used as an interface of the national ATP with the driver. * Level 1: this level makes use of Eurobalises or Euroloops to perform a spot transmission of data from the track to the train. Eurobalises send the lineside signals aspect and the movement authority to the on-board train equipment. Using this information, the on-board computer calculates and monitors continuously the maximum speed and braking curves that the train must observe.