The purpose of this thesis is to analyze a low-energy transfer, a route capable of taking advantage of the Weak Stability Boundary region in order to travel from LEO to lunar orbit with minimal deltaV. The challenge in finding such a transfer lies in identifying the initial conditions to be used for trajectory propagation. The main methodology considered is based on an optimization of design variables through a genetic algorithm(GA). Before that, it has been attempted the application of a single shooting method which, unfortunately, has proved to be too constrained by the initial conditions provided, causing considerable difficulty in achieving the desired convergence.