"The rising population of space debris poses a collision hazard to active satellites functioning in their orbits around the Earth. Often these satellites are required to perform orbital maneuvers to avoid high-energy collision with space debris. In addition to maintaining a safe proximity from the approaching debris during the time of closest approach, it is crucial to ensure that the satellite must then be brought back to its nominal orbit. This requires execution of additional orbital maneuvers and optimizing these maneuvers is important so that the impact on the mission life is minimal. Therefore, a framework of minimum-fuel orbital maneuvers in the context of finding an optimal trajectory considering both collision avoidance and orbit re-entry is desired. Most of the previous research work was focused only on optimization of orbital maneuver for collision avoidance. In this study, trajectory optimization for both maneuver processes is attempted using an evolutionary algorithm for which two methods: three-impulse method and two-impulse method, are developed and investigated. The three-impulse method is established as a two-stage maneuver process. In the first maneuver stage, a small impulse is applied to alter the course of the satellite in order to avoid the predicted collision. The second stage involves a bi-impulse maneuver that will take the satellite back to its nominal orbit after bypassing the obstacle. This bi-impulsive maneuver is estimated using the solutions of the well-known Lambert's problem. The design of the two-impulse method, on the other hand, is more straightforward which involves determining the optimal transfer orbit by just solving the Lambert's problem while the constraints are satisfied to an acceptable level. The proposed methods are tested for a high-risk collision predicted in a Low Earth Orbit while the test involves accurate numerical propagation taking into account the Earth zonal harmonics and the attraction from other bodies (Sun and Moon). The numerical simulations demonstrate that the conjunction could be mitigated satisfying the minimum-fuel objective and the satellite-safety constraints." --