## 1 Introduction
### Literature Review  
Optimized mission planning in satellite operations has attracted significant scholarly attention, leading to a variety of research methodologies. While traditional mathematical models often rely on Mixed-Integer Linear Programming (MILP) [15] and make use of established solvers like Gurobi, CPLEX, and Xpress, they also explore algorithms such as Branch-and-Bound (BB) [16] and Dynamic Programming (DP) [17]. These approaches have been tailored to suit different satellite configurations, including both agile [18] and non-agile types [19], as well as to interact with ground stations [20]. In addition to MILP-based studies, meta-heuristic methods like Genetic Algorithms (GAs) [21; 22; 23], Ant Colony Optimization (ACO) [24], and Particle Swarm Optimization (PSO) [25] have gained traction for complex scenarios, especially those requiring rapid response, such as natural disasters [26]. With the rise of Artificial Intelligence (AI), the field has seen a paradigm shift toward utilizing machine learning algorithms. Deep Reinforcement Learning (DRL) [27; 28; 29], in particular, is carving a niche for itself, offering enhanced capabilities in autonomous mission planning and a wide range of applications from online scheduling [30] to Agile Earth Observation Satellite (AEOS) planning [31]. In recent advancements, [PERSON] and [PERSON] [32] explored the optimization of sequential target imaging scheduling for agile satellites using neural network function approximators to model transition times, enhancing the efficiency of MIP formulations. Similarly, [PERSON] et al. 's patent [33] on Earth Observation Constellation Methodology & Applications presented a method for deploying a constellation of satellites capable of capturing high-resolution planetary images in a week or less, emphasizing simplicity in  
Figure 1: Observation comparison between single target and multi-targets. satellite control for effective imaging. Further, [PERSON] and [PERSON] [34] demonstrated the application of Semi-Markov Decision Processes (SMDPs) for optimizing satellite imaging plans across 1000 locations, leveraging forward search and Monte Carlo tree search to outperform traditional methods. [PERSON] et al. [35] addressed the scheduling and task assignment for satellite clusters, utilizing the QUadratically constrainEd program Solver Technology (QUEST) based on the CPLEX problem solver, showcasing its superiority over established heuristics such as MYopic Planning-based Image aCquisition heuristic (MYPICC) and Genetic Algorithm-based collecTion scHedulER (GATHER). In addition, the research landscape for satellite mission planning has evolved to address the distinctive challenges presented by satellite clusters. Recent studies have taken steps to optimize mission planning for satellite constellation, acknowledging their rising significance in space missions. [PERSON] et al. [36] introduced the Mission Planning System (MPS), developed by Surrey Satellite Technology Ltd (SSTL), as a tool for planning Electro-Optical (EO) imaging tasks for small clusters of satellites. Moreover, [PERSON] et al. [37] extended optimization techniques to satellite swarms, specifically for onboard scheduling via a Hybrid Dynamic Mutation Genetic Algorithm (HDMGA). [PERSON] and [PERSON] [38] tackled the problem of scheduling and assigning imaging missions and emergency tasks for clusters of up to five satellites with varying target priorities, ranging from 25 to 200. [PERSON] [39], on the other hand, utilized weighted-sums optimization algorithms to optimize mission planning for cubesat clusters. Furthermore, addressing the increasing challenge of orbital debris monitoring, [PERSON] et al. [40] introduced Networked Instrument Coordinator for Observations on debris (NICO), a scheduling system that utilizes genetic algorithms for efficient debris observation. This innovation showcases the expanded applicability of scheduling methodologies from traditional Earth observation to the critical areas of space safety and debris monitoring.