This Master's thesis aims to compute optimised orbital transfers in the Earth-Moon system using a hybrid optimisation framework combining a Genetic Algorithm, for global solution search, and Sequential Quadratic Programming, for local refinement. The following topics are analysed at a theoretical level: the main operational and future missions in the cislunar environment, in order to provide a broad overview of the explored space scenario; the fundamental astrodynamics needed to understand the physical mechanisms of the problem; and the state of the art of the optimisation algorithms used to fully exploit their capabilities. The optimised trajectories are referenced to the NRHO of a similar-Lunar Gateway mission and to circular orbits around the Earth and the Moon.