###### Abstract
To obtain high-quality scheduling solutions quickly, some scholars have employed reinforcement learning methods [21; 22; 23; 24; 25]. [PERSON] et al. [21] proposed a general reinforcement learning-based approach that can efficiently handle unknown data and generate good solutions in a short time. [PERSON] et al. [22] addressed the multi-objective AEOS scheduling problem. [PERSON] et al. [23] proposed neural networks with an 'encoder-decoder' structure that significantly reduce the inference time. [PERSON] et al. [24] presented a two-phase neural combinatorial optimization method with reinforcement learning for AEOS scheduling. [PERSON] et al. [25] proposed a non-iterative heuristic construction neural network method, which demonstrated excellent performance. On the other hand, a series of articles addressed the time-dependent transition time constraint of AEOS scheduling. [PERSON] et al. [26] presented an adaptive large neighborhood search algorithm for scheduling an observation  
Figure 1: (**a**) CEOSs where the VTW is equivalent to the OTW; (**b**) AEOS where the VTW is usually longer than the OTW. task for a single AEOS. The proposed method in [26] was extended to cases with multiple AEOSs [27]. [PERSON] et al. [28; 29] presented the concept of minimal transition time and based on this idea, an effective local search algorithm was developed. Most of the centralized schedule plans are generated on the ground and are uploaded to the satellite, thus neglecting dynamic and unpredictable events, such as the arrival of new task or the required change of users. To overcome those problems, the onboard distributed AEOS scheduling approaches have received increasing attention [30]. In a distributed framework, an AEOS creates a local schedule after exchanging information with neighbor satellites via inter-satellite links (ISLs). Then, the global schedule result can be obtained by integrating all these local schedules using coordination and communication mechanisms. Specifically, [PERSON] and [PERSON] [31] proposed a market-based method to allocate observation tasks to a set of satellites, though the satellites were managed by different mission centers. [PERSON] et al. [32] proposed an extended contract net protocol (ECNP) to solve dynamic task assignments for multiple satellites. [PERSON] et al. [30] developed an online schedule for distributed AEOS systems according to the idea of the well-known consensus-based bundle algorithm (CBBA). Herein, CBBA selects tasks using the auction approach and the conflict is resolved by the consensus procedure [33]. Conflict-free assignment can be achieved in the CBBA by iterating between the bundle construction phase and the conflict resolution phase. The performance impact (PI) algorithm is another important distributed task allocation approach [34; 35]. It aims to directly optimize the overall objective using the same two-phase architecture as the CBBA by introducing a key concept called the _significance_ of a task to measure its contribution to the global objective value. In other words, the PI algorithm considers not only the cost of a task assignment but also the impact of that assignment on the overall objective. Compared with the CBBA, the PI can solve more time-critical task allocation problems and find a task assignment with a lower time cost. Although the time-dependent transition time constraint is important for realistic AEOS observation scheduling, there is no distributed scheduling method taking it into consideration. On the other hand, as far as we know, implementation of the PI algorithm for AEOS observation scheduling has not been reported. Inspired by these points, this paper intends to propose a PI-based distributed scheduling method (PIDSM) for solving the problem of time-dependent observation scheduling in the AEOS constellation. To facilitate our understanding, we propose a mathematical model of the considered problem. The global fitness (or objective) function is designed to not only maximize the profit sum but also account for system load balancing.