Identifying homoclinic and heteroclinic intersections of manifolds associated with libration point periodic orbits has proven to be an effective design methodology for generating low-energy trajectory solutions in the restricted three-body problem. The method of intersection identification upon Poincaré surfaces of section has been previously automated by the authors; this paper extends that work by incorporating the algorithm into an automated global optimization framework. The second half of this paper then focuses on the important issue of making the automated detection process numerically efficient; otherwise runtime performance of the global optimizer could be excessive. We accomplish this by using graphics processing units (GPU) and CUDA programming. We discuss run-time performance, implementation improvements, and demonstrate the aforementioned capabilities on a variant of the Hiten mission.