## 3 Solving Method  
The MAEOSSP investigated in this study involves determining the execution resources and time windows for each task under temporal and capacity constraints to optimize the objective function. Given the finite nature of satellite resources, tasks exhibit competitive relationships where scheduling sequences critically influence objective values. To mitigate complexity, the problem is decomposed into three interdependent decisions: task sequence determination, resource allocation, and execution time window determination. Once the task sequence is established, the subsequent focus narrows to identifying appropriate resources and temporal windows for individual tasks. As a promising approach, deep reinforcement learning (DRL) demonstrates balanced capabilities in decision quality and efficiency and has shown good sequential decision-making abilities, motivating our proposed DRL-based algorithm for task sequence determination. DRL updates model parameters through agent-environment interactions, with the MDP framework serving as its foundational model, comprising states, actions, state transitions, and reward mechanisms. Establishing an MDP enables the precise specification of agent-environment interactions, which we systematically formalize in this section. The state vector, representing environmental characteristics, is the input to the deep neural network. To enhance feature representation, state elements are categorized into static and dynamic elements based on their value variability during iterations. Actions, the network's output, constitute the agent's decision space. While environmental state transitions must jointly determine task sequences, resource allocations, and temporal windows, the deep network primarily generates sequence decisions. This necessitates complementary mechanisms for resource and execution time determination. Considering computational efficiency, heuristic methods are employed. Given that tasks with visible time windows form satellite-specific sets, different satellites correspond to sets with different tasks due to distinct orbital parameters. To preserve resource diversity during the whole scheduling process, a maximum residual capacity (MRC) rule is proposed. An MRC rule indicates that a feasible satellite with maximum residual capacity is allocated to the determined task. This mechanism ensures that the observation system maintains resource diversity without premature depletion due to storage capacity constraints. Following previous studies [26; 30; 42; 48], the beginning execution time of the determined task is set to the earliest of its feasible time windows in the determined satellite, i.e., the Earliest Start Time (EST) rule. State transitions occur through the interplay of current states, DRL-generated task sequences, and heuristic-based resource allocations, with the agent receiving immediate reward feedback. The agent optimizes its policy by maximizing cumulative rewards representing long-term returns. Upon completing the scheduling process, the total return of the whole scheduling process is obtained. However, determining the contributions of individual step decisions to final returns remains challenging. As each decision schedules one task, task profit has naturally served as the immediate reward feedback in previous studies [42; 47; 48]. Nevertheless, task execution simultaneously consumes finite resources, significantly impacting long-term returns. In this study, resources are categorized into temporal resources and storage capacity resources. Temporal resources involve complex factors such as durations, visible time windows, and transition time, making them difficult to simply characterize. Furthermore, since task execution timing is determined by the EST (Earliest Start Time) heuristic, temporal attributes are partially accounted for in the scheduling process. Consequently, a reward function combining task profit and storage consumption ratios is proposed.