This work utilizes a particle swarm optimizer (PSO) for initial orbit determination for a chief and deputy scenario in the circular restricted three-body problem (CR3BP). The PSO is used to minimize the difference between actual and estimated observations and knowledge of the chief's position with known CR3BP dynamics to determine the deputy's initial state. Convergence is achieved through limiting particle starting positions to feasible positions based on the known chief position, and sensor constraints. Parallel and GPU processing methods are used to improve computation time and provide an accurate initial state estimate for a variety of cislunar orbit geometries.