Abstract: The 4D flight trajectory of a space probe is globally optimized by a combinatorial algorithm of trajectory optimization based on a two-body model of low-thrust space exploration. The combinatorial optimization method consists of dynamic programming, static parameter optimization and conjugate gradient algorithms based on optimal control theory. Dynamic programming and static parameter optimization algorithms are employed to globally optimize the launch and return time windows，and obtain approximate solutions of optimal trajectories, while the conjugate gradient algorithm (solving two-point boundary value problems) is used to optimize the exact 4D flight trajectory based on the approximate solutions obtained. The launch and return time windows as well as the 4D flight trajectories between the Earth and the asteroid are globally optimized based on a great deal of numerical optimization simulations. The numerical simulation results show that the combinatorial optimization algorithm is a general method for 4D global flight trajectory optimization. This algorithm may be widely used in engineering problems on global optimization of dynamic and static parameters.

Key words: flight trajectories, global optimization, combinatorial optimization algorithm, low-thrust, time window, simulation