The use of low-thrust propulsion for interplanetary missions requires the implementation of new methods for the preliminary design of their trajectories. This thesis proposes a method using the Monotonic Basin Hopping global optimization algorithm to find feasible trajectories with optimum use of the mass of fuel for the case in which the trajectory is modeled using the Sims-Flanagan transcription method. Due to the large computational time required to find the global optimum, Artificial Neural Networks have been used to predict the objective value and feasibility terms of the local minimum. Therefore, the procedure to set up a working regression Artificial Neural Network is studied as well as its transferability to predict values outside the trained limits and for different missions. In addition to this, the use of pre-training is analyzed to improve the performance of the network without increasing the size of the training database.