## 1 Introduction  
Earth observation satellites are important for scientific research, military reconnaissance, agricultural harvesting, and so on. With the increase of the space application scenarios, it is difficult for the in-orbit satellite resources to meet various requirements. Therefore, it is of great significance to rationally utilize limited satellite resources to obtain efficient observations. Space mission planning is a complex combinatorial optimization problem that solves the optimal satellite task planning sequence under the constraints of limited resources, time, and space. For the satellite observation planning problem, task clustering can enable a satellite to perform more tasks with fewer sensor opening times, as shown in Figure 1[1]. The yellow circle represents the task to be observed, and the red rectangle represents the clustering task that can perform the combined observation, where the maximum slewing ability needs to be considered. Through task clustering, several tasks can be combined at one observation activity, and the number of sensor slew times can be reduced. Meanwhile, task clustering makes it possible to accomplish some conflicting tasks at the same time [2]. Task clustering has gained more and more attention for Earth observation satellites and has been a research focus on the preprocessing field for satellite missions. [PERSON] al. [3] proposed a branch and bound algorithm for clique partition, contributing to the development of graphic theory. In 2013, [PERSON] [2] proposed a two-phase scheduling method that considers task clustering of Earth observation satellites. Further, a dynamic task clustering strategy was designed by [PERSON] in 2017 [4]. The problem was that he did not take into account the observation duration of the task, but observed the task in the whole visible time window, which would result in the satellite resources not being used effectively. [PERSON] [5] improved the classical clique partition algorithm to solve the imaging satellite task-clusteringproblem, but the adopted algorithm is relatively complex. [PERSON] and [PERSON] [6] adopted the task clustering based preprocessing method to improve the observation efficiency by combining potential targets. It was found that in the previous investigations and studies, few constraints were considered. Hence, many research achievements are difficult to translate into practical engineering solutions. In this paper, we consider practical constraints of the sensor, including the ground resolution, time window, observation duration, maximum observation time, slewing angle, and pitching angle, and propose an improved task clustering based on the approximate clique partition algorithm proposed by [PERSON] [7]. Moreover, for Earth observation satellite missions, the preprocessing based on the task clustering is the first step, and the main purpose is to improve the efficiency for task planning. Compared with task clustering, research for Earth observation task planning problems are progressing rapidly. The Earth observation task planning problem is an NP (Non-deterministic Polynomial)-hard problem, and most studies use either a heuristic algorithm or an intelligent optimization algorithm to solve it. [PERSON] et al. adopted the random search heuristic algorithm to solve the EO-1 (Earth Observing-1) system application [8]. [PERSON] et al. [9] compared the performance of various algorithms, such as the simulated annealing algorithm, hill climbing algorithm, and genetic algorithm, for the imaging scheduling problem of point targets. [PERSON] proposed a multi-objective binary-encoding differential evolution (MBDE) algorithm for observation satellite proactive scheduling [10]. [PERSON] et al. [11] proposed the optimal scheduling algorithm for satellite formation equipped with synthetic aperture radar (SAR) imaging equipment. The proposed optimal scheduling algorithm is based on a genetic algorithm (GA). The goal is to reduce the system response time.