Halo-to-halo Cost Optimal Transfer Based on CMA-ES

A method is developed to implement the cost-optimal transfer between two halo orbits of the same family. The problem is recast as a three-body Lambert's problem (TBLP), which is solved efficiently and reliably by a revised version of the algorithm initially proposed by Sukhanov and Prado. Six scalar optimization parameters are selected by analyzing the design variables of the problem and the characteristics of the iterated algorithm for solving the TBLP. The searching range of each optimization parameter is provided for speeding up the convergence of the evolution process. The performance index is the sum of velocity discontinuities at both ends of the two-impulse transfer orbit, and the cost-optimal result is obtained by using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which saves approximately 16% fuel as compared with the relevant work.