In this paper, we address multi-objective space mission design problems. We argue that it makes sense from the practical point of view to consider ill addition to the 'optimal' trajectories (in the Pareto sense) also approximate or nearly optimal solutions since this can lead to a significant larger variety for the decision maker. For this we suggest a novel MOEA which is a modification of the well-known NSGA-II algorithm equipped with a recently proposed archiving strategy which aims for the storage of the set of approximate, solution of a given MOP. Using this algorithm we will examine several space missions and demonstrate the benefit of the novel approach.