Optimization of the Earth-Moon low energy transfer with differential evolution based on uniform design

One of the important problems in the design of the Earth-Moon low energy transfer is to find the patch point of the unstable manifold of the Lyapunov orbit around Sun-Earth L2 and the stable manifold of the Lyapunov orbit around Earth-Moon L2. The traditional method is “trial and error”. It is extremely sensitive with the changes in the initial condition. In this paper, evolutionary algorithms are used to optimize the initial condition. An improved differential evolution algorithm is proposed to solve this problem. We incorporate the uniform design technology and the self-adaptive parameter control method into standard differential evolution to accelerate its convergence speed and improve the stability. The improvement algorithm is compared with three evolutionary algorithms. The experiment results indicate that our approach is able to find the better, or at least comparably, in terms of the quality and stability of the final solutions. Moreover, it proves the application of evolutionary algorithms in the Earth-Moon low energy transfer optimization problem is effective.