In this thesis, a new method to approximate the cost function of Low-Thrust, Multiple-Gravity-Assist interplanetary trajectories using a Machine Learning surrogate is proposed. This method speeds up the optimization process without fine tuning of the surrogate parameters for every individual case. The computational cost of obtaining training data was identified as the main limitation when using Machine Learning methods for this purpose. Therefore, the surrogate was built with an Online Sequential Extreme Learning Machine Multi-Agent System (OS-ELM-MAS) due to its theoretical good performance when the training data is limited. A high-fidelity global optimization problem was implemented, and a method to include the surrogate during the optimization process was designed. This method does not require specialized optimization algorithms. The parameters that control the interaction between the surrogate and the optimization process were identified and a procedure to obtain the best values was designed and applied. The final results show that the use of the surrogate improves the optimization results when evaluations of the cost function are computationally expensive. However, the values of the parameters that control the interaction between the surrogate and the optimization algorithm had to be carefully selected. The search for a general procedure to obtain these parameters without repeated tests is proposed for future research. Several applications to new optimization problems of the method developed in the thesis are also proposed for future research.