Self-adaptive uniform differential evolution for optimizing the initial integral point of the Earth-Moon low-energy transfer

Low-energy transfer trajectory is of growing interest in the space community. It is important to choose 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 main contributions of this study are two areas: (a) designing the optimization model and using evolutionary algorithms to optimize the initial condition and (b) developing effective algorithms for this problem. In this article, an improved differential evolution (DE) algorithm, named adaptive uniform design differential evolution (AUDE), is proposed to solve the Earth-Moon low-energy transfer optimization problem. It incorporates the uniform design technology and the self-adaptive parameter control method into standard DE to accelerate its convergence speed and improve the stability and calculation accuracy. To verify the performance of AUDE, the Earth-Moon low-energy transfer optimization problem and 15 benchmark functions with diverse complexities are employed. The experiment results indicate that the authors' approach is able to find the better one, or at least comparably, in terms of the quality and stability of the final solutions than the other three algorithms. Moreover, it proves that the application of DE algorithm in the Earth-Moon low-energy transfer optimization problem is effective.