This dissertation describes a hybrid optimization algorithm that is able to determine optimal trajectories for many complex mission analysis and design orbital mechanics problems. This new algorithm will be used to determine optimal trajectories for a variety of mission design problems, including asteroid rendezvous, multiple gravity-assist (MGA), multiple gravity-assist with deep-space maneuvers (MGA-DSM), and low-thrust trajectory missions. The research described here was conducted at the Asteroid Deflection Research Center (ADRC) at Iowa State University.