## 1 Introduction  
Solving scheduling problems by intelligent optimization algorithms has been utilized in many industrial and engineering applications [1]. Earth observation satellites (EOSs) are primary platforms for acquiring spatial image information. They are widely used in disaster relief, emergency monitoring, and other fields due to their broad observation coverage and absence of national boundaries [2]. Conventional non-agile Earth observation satellites have only one roll angle, which aligns the observation time window with the visible time window (VTW). In recent years, there has been a significant increase in demand for observation, leading to the deployment of a large number of agile Earth observation satellites. As shown in Figure 1, compared with ordinary non-agile ground observation satellites, agile dispatching satellites have three rolling angles [3], namely, roll angle, pitch angle, and yaw angle. This capability allows the satellite to observe the ground target before it is directly overhead by adjusting the pitch angle. Consequently, the observation time window for the mission is narrower than the visible time window. Yet, the duration of observation is extended and is not limited to the period when the satellite is overhead but instead spans throughout the observable period. The use of agile Earth observation satellites greatly enhances observation capabilities. As the observation window expands, scheduling becomes more challenging. Therefore, selecting a reasonable start time for tasks is necessary while determining the visible time window. Additionally, a certain transition time is required between two consecutive observation tasks of a satellite, which depends on the satellite's attitude angles during observation. Non-agile satellites have only a single side-sway angle, determined by the target's geographic location, making the required transition time fixed. Agile satellites, however, involve roll, pitch, and yaw angles, with the pitch angle determined by the observation time point. Consequently, the transition time during the imaging process of agile satellites is no longer a fixed value but varies with time. This time-dependency characteristic of agile satellites imposes higher demands on algorithm performance. Due to its complexity properties, the AEOS task scheduling has been proven to be an NP-hard problem [4]. The objective is to maximize observation benefits by reasonably allocating tasks, considering both constraints handling and task requirements. Current approaches to solving agile satellite scheduling mainly involve heuristic algorithms, meta-heuristic algorithms, and machine learning algorithms. Heuristic algorithms demonstrate exemplary performance in small-scale instances [5; 6]. Still, as the problem scales up, the algorithm design becomes more challenging, often leading to locally optimal solutions and failing to produce high-quality scheduling solutions [2; 7]. [PERSON] et al. initially provided a comprehensive overview of the AEOS problem and proposed various heuristic algorithms to address it [8]. [PERSON] and [PERSON] further employed tabu search algorithms to solve the AEOS problem, albeit only considering single-orbit optimization issues [9]. Metaheuristic algorithms enhance the ability to escape local optima by guiding heuristic algorithms with meta-knowledge during the solving process. [PERSON] et al. proposed an algebraic method based on repeated permutations, designing a discrete operator for the differential evolution algorithm, and successfully applied it to the job shop scheduling problem [10]. [PERSON] et al. introduced an iterative greedy algorithm for solving the blocking flow shop scheduling problem. They generated an initial solution using a heuristic method and designed two local search algorithms, utilizing an iterative jumping probability to determine which neighborhood structure to adopt for guiding the search [11]. [PERSON] et al.