As the hardware capabilities of unmanned battlefield robots, such as Micro Aerial Vehicles (MAVs) and Unmanned Ground Vehicles (UGVs), increases, so to must the intelligence of the software controlling them. Genetic Algorithms (GAs) and Genetic Programming (GP) have proven effective in preliminary MAV and UGV simulations for evolving simple tracking and surveillance behaviors. However, the reactive approach that most robotic GAs provide falls short of demonstrating a comprehensive range of intelligence. If for instance, an object becomes occluded from a robot's view, GAs usually must evolve to considerable complexity before they can effectively handle such situations. In this paper, we suggest an approach whereby we augment the GA with a neural network predictor as one of its inputs. The robot's task consists of following another moving object and maintaining a certain distance. The neural network system is trained with the behavior of the robot's intended target, and feeds this as an input to the GA. We present simulation results of how well this method achieves its task, as well as suggestions for adapting these techniques for implementation on advanced mobile cluster computers.