Global Optimization and Space Pruning for Spacecraft Trajectory Design

Abstract

problems highlighting their common nature. We then present the detailed definition of two popular typologies, the Multiple Gravity Assist (MGA) and the Multiple Gravity Assist with single Deep Space Manouver (MGA-1DSM). Later we describe in detail the instantiation of four particular problems proposing them as a test set to benchmark the performances of different algorithms and pruning solutions. We take inspiration from real interplanetary trajectories such as Cassini, Rosetta, and the proposed TandEM mission, considering a large search space in terms of possible launch windows and transfer times, but also from rather academic cases such as that of the First Global Trajectory Optimisation Competition (GTOC). We test four popular heuristic paradigms on these problems (differential evolution, particle swarm optimization, simulated annealing with adaptive neighborhood, and genetic algorithm) and note their poor performances both in terms of reliability and solution quality, arguing for the need to use more sophisticated approaches, for example, pruning methods, to allow finding better trajectories. We then introduce the cluster pruning method for the MGA-1DSM problem and we apply it, in combination with the simulated annealing with adaptive neighborhood algorithm, to the TandEM test problem finding a large number of good solutions and a new putative global optima. Many of the results reported here would not have been possible without the great passion and competence of Tamas Vinko, Marco del Rey Zapatero, and Marek Rucinski, all researching, at different times, different global trajectory optimization aspects. The author also wishes to acknowledge Massimiliano Vasile who, while a research fellow with the Advanced Concepts Team at the European Space Agency, conceived the Ariadna studies on Advanced Global Optimization Tools for Mission Analysis and Design, which ignited the spark of this now incredibly rich research topic.