A differential evolution-based optimization tool for interplanetary transfer trajectory design

The extremely sensitive and highly nonlinear search space of interplanetary transfer trajectory design bring about big challenges on global optimization. As a representative, the current known best solution of the global trajectory optimization problem (GTOP) designed by the European space agency (ESA) is very hard to be found. To deal with this difficulty, a powerful differential evolution-based optimization tool named \textbf{CO}operative \textbf{D}ifferential \textbf{E}volution (CODE) is proposed in this paper. CODE employs a two-stage evolutionary process, which concentrates on learning global structure in the earlier process, and tends to self-adaptively learn the structures of different local spaces. Besides, considering the spatial distribution of global optimum on different problems and the gradient information on different variables, a multiple boundary check technique has been employed. Also, Covariance Matrix Adaptation Evolutionary Strategies (CMA-ES) is used as a local optimizer. The previous studies have shown that a specific swarm intelligent optimization algorithm usually can solve only one or two GTOP problems. However, the experimental test results show that CODE can find the current known best solutions of Cassini1 and Sagas directly, and the cooperation with CMA-ES can solve Cassini2, GTOC1, Messenger (reduced) and Rosetta. For the most complicated Messenger (full) problem, even though CODE cannot find the current known best solution, the found best solution with objective function equaling to 3.38 km/s is still a level that other swarm intelligent algorithms cannot easily reach.