Space trajectory design: Analysis of a real-world many-objective optimization problem

Unlike most of the scalability studies on many-objective optimization problems found in the literature, in this paper we present a scalability study adopting a real-world optimization problem. The problem employed is a trajectory design optimization problem in which the objectives where varied from three to six objectives. Likewise, we evaluate the performance of the Chebyshev preference relation, which is a recently proposed technique designed for dealing with many-objective optimization problems. In this study we find that the hardness of the trajectory optimization problem, as observed in benchmark problems, increases with the addition of objective functions. Additionally, for this problem, the proportion of nondominated solutions in a random population quickly increases with the number of objectives. We also find that the Chebyshev relation has a better scalability than the standard Pareto dominance with respect to the dimension of the objective space.