## 2 Related Work  
The concept of beam hopping was first proposed in NASA's project ACTS [7], which realizes beam hopping by switching the feed source through a switch. In 2007, the multi-beam satellite system Spaceway3 developed by Hughes Networks was equipped with a beam hopping module, which was the first instance of beam hopping being applied to an actual system and greatly improved system capacity and spectrum utilization through flexible radio resource assignment. Since then, many companies have scrambled to apply beam hopping technology to their high-throughput satellite systems, such as the Wideband Global Satellite (WGS) and Advanced Extremely High Frequency (AEHF) projects in the United States and the Wideband Internetworking Engineering Test and Demonstration Satellite (WINDS) system in Japan. Ref. [8] investigated the advantages of beam hopping and showed the performance and capacity improvement over non-hopped systems. Scholars have also proposed a new generation of high-throughput satellite communication system architecture based on beam hopping, and the hopping pattern design is jointly optimized by a convex optimization algorithm [9; 10; 11]. [PERSON]'s team also sorted out the existing algorithms for satellite beam hopping resource allocation, and verified the good applicability of beam hopping in high-throughput systems [12]. However, the existing beam hopping research mainly focuses on GEO satellites. Due to the limited on-board resources and mobility of LEO satellites, the BH design scheme for GEO satellite systems cannot be directly applied to LEO satellite systems. Some scholars have explored the adaptive improvement scheme of BH technology in the LEO satellite communication scenario. In [13], [PERSON] introduced the concept of beam hopping into the LEO satellite system for the first time, and analyzed the effectiveness of the proposed iterative algorithm through system indicators such as throughput and delay. [PERSON] proposed a satellite zoning coverage model and designed a clustering beam allocation method for the uneven traffic distribution in LEO satellite coverage area [14]. [PERSON] proposed a greedy algorithm in the LEO system to allocate frequency and power to the beam, and evaluate the algorithm in terms of throughput and demand satisfaction rate [15]. References [16; 17; 18; 19] constructed preliminary model of resource allocation with the goal of throughput or delay. However, the above studies only consider the resource allocation of single or some certain dimensions, which lacks the consideration of multi-dimensional resource allocation and does not propose a complete multi-objective optimization model. To address this issue, some scholars systematically study the joint allocation of multi-dimensional resources with the goal of maximizing throughput and minimizing transmission delay [20; 21]. Recently, graph-based deep learning optimization, which can guarantee high performance with low complexity, has received great attention and has been applied in communication networks [22]. Deep learning methods can capture the spatial information hidden in the network topology and work well for high dynamic scenes, thus providing new ideas for satellite traffic prediction [23] and resource allocation [24; 25; 26]. For example, Ref. [27]applied deep reinforcement learning in a beam-hopping problem to decide the illumination pattern and bandwidth allocation and achieve superior performance; however, the problem scale is small. Ref. [28] has a relatively large scale, but only focuses on cell selection. In addition to certain limitations in problem scale and resource dimension, the above studies also ignore some inherent problems. The existing work often only consider the constraints of total on-board bandwidth and power, ignoring the coupling relationship between them when considering interference in practical scenarios. On the one hand, many studies only limit co-channel interference (CCI) through physical isolation, which prevents adjacent hotspots from being served simultaneously.