A fast multi-objective optimization design method for emergency libration point orbits transfer between the Sun-Earth and the Earth-Moon systems

This paper considers the emergency trajectory design mission of libration point orbit transfer between the Sun-Earth system and the Earth-Moon system. In order to balance the two indexes of transfer time and fuel consumption, Halo orbits and their invariant manifolds in the circular restricted three body problem (CRTBP) are combined with low thrust in the bicircular restricted four body problem (BRFBP) to design the transfer trajectories. A fast multi-objective optimization method based on surrogate model which is greatly needed especially for emergency transfer missions is proposed to overcome the low-efficacy of original evolutionary multi-objective optimization methods. The advantages of the Sun-Earth manifolds, the Earth-Moon manifolds and the optimal control method are fully considered. In the part of numerical simulations, several simple problems with analytical solutions are first employed to validate the proposed fast optimization algorithm, then the proposed method is compared with NSGA-II for the same multi-objective transfer problem. Numerical results show that the fast optimization method chooses the expected samples and has a much higher efficiency than direct multi-objective optimization. The significance of the Sun-Earth manifolds and the Earth-Moon manifolds are considered. Several cases show the complicated relationship between transfer time and fuel consumption.