The recent generation of Agile Earth Observation Satellite (AEOS) has emerged to be highly effective due to its increased attitude maneuvering capabilities. However, due to these increased degrees of freedom in maneuverability, the scheduling problem has become increasingly difficult than its non-agile predecessors. The AEOS scheduling problem consists of finding an optimal assignment of user-requested imaging tasks to the respective AEOSs in their orbits by satisfying the operational resource constraints in a specified time frame. Some of these tasks might require imaging the same area of interest (AOI) multiple times, while in some tasks, the AOIs are too large for the AEOS to image in a single attempt. Some tasks might even arise while the AEOSs are preoccupied with existing tasks. This thesis focuses on formulating the AEOS scheduling models where onboard energy and memory constraints while operating and the task specifications are diverse. A mixed-integer non-linear scheduling problem with a reward factor has been considered in order to handle multiple scan requirements for a task. Although initially, it is assumed that the AOIs are small, this work is extended to a three-stage optimization framework to handle the segmentation of large AOIs into smaller regions that can be imaged in a single scan. The uncertainty regarding scan failure is handled through a Markov Decision Process (MDP). These two proposed methods have significant benefits when tasks are available to schedule prior to the mission. However, they lack the flexibility to accommodate newly arrived tasks during the mission. When multiple new tasks arrive during the mission, predictive scheduling based on learning historical data of task arrivals is proposed, which can schedule tasks in an online manner faster than complete rescheduling and minimize disruption from the original schedule. Evolutionary optimization-based solution methodologies are proposed to solve these models and are validated with simulations. / Thesis / Doctor of Philosophy (PhD)