The increased interest in satellite formations and deep space exploration drives the need to better understand and explore relative trajectories at the collinear libration points. This paper presents a preliminary study in applying a genetic algorithm to search for relative trajectories in the vicinity of the collinear libration points using the nonlinear equations of motion of the circular restricted three-body problem. Preliminary results identify a relative trajectory about a chief spacecraft located at the Earth-Moon L2 libration point. The approach presented may also reveal trajectories not predicted by analytic approximations, and is a focus of continued efforts by the authors. This initial effort provides for future development of the genetic algorithm's fitness function to accommodate proximity constraints and the inclusion of multiple deputy spacecraft, with an ultimate goal of developing an efficient trajectory design tool given mission objectives for a formation/swarm near a collinear libration point.