We discuss the general requirements for the solution of the problem given in the 1st ACT Global Trajectory Optimization Competition. We introduce some novel numerical methods used for multiple gravity-assist and low-thrust trajectory optimization, and in particular an original method to compute interplanetary conic trajectories and a novel continuation technique for low-thrust trajectory optimization. The application of these methods to the competition problem is discussed. The final trajectory has an objective function value of J=1364042.86kgkm2/s2. It includes five swingbys in the inner Solar system and three thrusting arcs. An optimal direct Earth–asteroid trajectory is presented as a post-competition result.