Improving Global Optimization Methods for Low-Thrust Trajectories

Optimization of spacecraft trajectories is an interesting area of research, where a lot of development takes place: in the past years, an optimizer called OPTIDUS was implemented at the chair of Astrodynamics at Delft Univierstiy. This tool is able to do optimization of spacecraft trajectories (and other problems) using an evolutionary algorithm. However, there are other optimization algorithms available which (according to literature) also perform well on trajectory optimizations. These are Particle Swarm Optimization (PSO) and Differential Evolution (DE). For this thesis, a new version of OPTIDUS has been implemented, which not only supports evolutionary algorithms, but also several variants of differential evolution and particle swarm optimization. These algorithms are also implemented in a way that can exploit the availability of multiple processing cores in a computer, which can give a very good improvement in the runtime of optimizations. Also, a local optimizer using Powell's quadratically convergent method has been implemented. This new version of OPTIDUS is benchmarked against several PSO implementations, and it is found that performance on several (mathematical) testing functions is comparable to existing implementations. However, it is not possible to appoint DE or PSO as the best algorithm in general, as that is problem dependent. The software is also applied to improve the optimization of a Solar polar sailing mission. By comparing the number of function evaluations and the best fitness value found for a family of optimizers (several variants of PPO and DE and an EA), it is found that DE gives the best results, giving an reduction in mission cost almost 4% compared to the original result found using an EA. The use of a local optimizer on this best result is able to improve it even further by another 0.15%. Finally, this software is used to find a solution to the GTOC3 problem, where the goal is to find a low-thrust trajectory for a spacecraft to rendezvous with several asteroids. The hard part of this mission are the rendezvous constraints: upon arrival at an asteroid, the location and velocity of the spacecraft relative to the asteroids have very low margins, making a very large part of the solution space infeasible. For that reason, an augmented objective function which takes these violations into account is used. Both an augmentive function in the form of a weighted sum (of violations) and a multi-objective function are considered. The multi-objective variants gives better results, but is not compatible with the local optimizer, Powell's method. Only the first part of the mission, from Earth to the first asteroid, is optimized. Using DE, a solution is found, which almost satisfies the constraints, but not completely. By applying Powell's method to this solution, the constraint violations are further reduced, but still a small violation of the position remains. It is found that doing global optimization using DE can generate solutions with quite large constraint violations, but that subsequent application of a local optimizer can reduce those violations, while not changing the solution considerably. How the solution of this first leg compares to solutions by other teams is not known, as the per-leg results have not been published.Astrodynamics and Satellite SystemsAerospace Engineerin