  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 COoperative Differential Evolution
(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.
