This thesis focuses on optimizing escape trajectories from the Lagrangian point of the Earth-Moon system in a higher fidelity model using electric propulsion. Lagrangian points represent specific locations in space where objects placed there tend to remain stationary. At Lagrangian points, the gravitational attraction exerted by two massive bodies exactly balances the centripetal force necessary for a smaller object to move with them. These points are useful for spacecraft to minimize the amount of fuel consumption required to maintain their position. Therefore, the exploitation of these points has become of great interest for the future space missions. In fact, among many uses, it also allows a gateway to Deep Space exploration.