Due to the increasing interest of the aerospace industry and the scientific community in missions targeting halo orbits, a specific family of periodic solutions within the circular restricted three-body problem, it is highly desirable to find ways to reduce the cost of transfers between these orbits. To achieve this, depending on the mission characteristics, one could opt for reducing the required propellant mass or the time of flight. As such, with two objectives to be minimized, an ideal implementation for a mission designer would provide a Pareto front of feasible transfers instead of the single trajectory commonly obtained with conventional methods. Moreover, the necessary propellant mass can be minimized even further by means of electric low-thrust propulsion due to the significantly larger exhaust velocities. Therefore, the purpose of this research is to develop, implement, and study a suitable approach to obtain a collection of low-thrust transfers between halo orbits optimized in terms of both propellant mass and time of flight.

The approach employs an optimal control indirect method as thrust law which, combined with a heuristic optimizer based on differential evolution, can find a wide variety of trajectories that minimize the aforementioned objectives within the circular restricted three-body problem. Heuristic optimization is employed to remove the dependency of the solution on the provided initial guess and find trajectories in the region of the global minima. To satisfy the demanding boundary conditions characteristic of indirect methods, these constraints are included as a third objective for the optimizer to minimize as well. Due to the tolerance allowed on the constraints, the trajectories are subsequently refined with direct collocation methods. Then, they can be transitioned to a high-fidelity model, taking advantage of the versatility of direct methods. Furthermore, the implementation allows for the inclusion of invariant manifold phases arising from the departure and target orbits to obtain a wider set of Pareto-optimal solutions.

To assess the suitability of the proposed procedure, a specific transfer between two halo orbits around different Lagrange points of the Earth-Moon system was optimized. The results consisted of 100 Pareto-optimal transfers spanning more than 60 days, offering significant mission design freedom. Moreover, the Pareto front outperforms the trajectory found in the literature for a comparable use case by 30\% in all objectives. Next, an optimized trajectory was first successfully verified with the mission analysis software ASTOS and then refined with direct collocation. The refined trajectory exhibited negligible changes in performance, rendering the trajectories obtained with this approach as promising initial guesses for further optimization with direct collocation methods. Moreover, several major perturbations not included in the simplified dynamic system were also corrected with direct collocation. The next steps include: accounting for the eccentricity of the Moon's orbit to fully transition the trajectories to a high-fidelity model, assessing the optimization quality with different use cases, and implementing transfers between different periodic solutions and dynamic systems, such as the Sun-Earth system.