The design of spacecraft trajectories for missions visiting multiple celestial bodies is here framed as a multi-objective bilevel optimization problem. A comparative study is performed to assess the performance of different Beam Search algorithms at tackling the combinatorial problem of finding the ideal sequence of bodies. Special focus is placed on the development of a new hybridization between Beam Search and the Population-based Ant Colony Optimization algorithm. An experimental evaluation shows all algorithms achieving exceptional performance on a hard benchmark problem. It is found that a properly tuned deterministic Beam Search always outperforms the remaining variants. Beam P-ACO, however, demonstrates lower parameter sensitivity, while offering superior worst-case performance. Being an anytime algorithm, it is then found to be the preferable choice for certain practical applications.
 This paper describes the methodologies used to tackle the problem of the 5th Global Trajectory Optimization Competition within the team composed by the Advanced Concepts Team of the European Space Agency and theGlobal Optimization Laboratory of the University of Florence. The method pursued is powered by two innovative approaches: a linearized model of the ‘self fly-by’ aiding a first broad tree search of chemical propulsion options and the use of global optimization techniques (Monotonic Basin Hopping, in this case) applied directly to the low-thrust trajectory model. The space close to our planet is getting more and more polluted. Orbiting debris are posing an increasing threat to operational orbits and the cascading effect, known as Kessler syndrome, may result in a future where the risk of orbiting our planet at some altitudes will be unacceptable. Many argue that the debris density at the Low Earth Orbit (LEO) has already reached a level sufficient to trigger such a cascading effect. An obvious consequence is that we may soon have to actively clean space from debris. Such a space mission will involve a complex combinatorial decision as to choose which debris to remove and in what order. In this paper, we find that this part of the design of an active debris removal mission (ADR) can be mapped into increasingly complex variants to the classic Travelling Salesman Problem (TSP) and that they can be solved by the Inver-over algorithm improving the current state-of-the-art in ADR mission design. We define static and dynamic cases, according to whether we consider the debris orbits as fixed in time or subject to orbital perturbations. We are able, for the first time, to select optimally objects from debris clouds of considerable size: hundreds debris pieces considered while previous works stopped at tens.