This thesis addresses the issue of low-energy transfers between low Earth orbit (LEO) and near rectilinear halo orbits (NRHO) within the Earth–Moon system. The focus is on supporting the Lunar Gateway within NASA’s Artemis program. The cislunar domain is presented as an ideal environment for testing technologies, establishing logistics hubs, and enabling future Mars missions. Trajectory optimization is constrained by the Kourou launch site in French Guiana as the departure point, which has strict altitude and inclination constraints. These limitations significantly impact the feasibility of different trajectories. The optimization process employs a combination of two approaches. First, a Genetic Algorithm (GA) scans the solution space to identify promising trajectories.