The genetic algorithms (GAs) have been recently used in many design problems including an orbit design and trajectory optimization problems due to their global search capability and the robust characteristics. Furthermore, the GAs do not require convenient analytical representations of the problem any more. For this reason, the GAs can provide good solutions to the orbital dynamics design problem, especially a local coverage problem of Low Earth Orbit (LEO), which is difficult to formulate and handle the problem since an orbit propagation and local coverage analysis should be performed at the same time. This paper presents the possibility to using a genetic algorithm as a computational approach to finding the temporary target orbit in order to reduce the average revisit time of current mission orbit over a particular target site during the specified days. Through a comprehensive simulation study, the possibility of using a genetic algorithm to apply this kind of a temporary reconnaissance mission using a single LEO spacecraft is successfully demonstrated.