## 2 System Model  
According to the dynamic characteristics of low-orbit satellite network topology, in this paper, we design the GNN-DRL algorithm, which is based on the following assumptions:  
1. According to the interval of \(t_{0}\), the time is divided into \(n\) time periods (\(t_{1},t_{2},t_{3}\ldots t_{n}\)), and the physical topology of the constellation remains unchanged in the time period between two adjacent moments;
2. It is assumed that the propagation delay between the two satellites in different orbits is almost the same as that in the same orbit. Authors of studies in the literature [14] believe that the selection of the location and number of ground stations is a key issue for low-orbit satellite networks, which directly affects their construction. It is mentioned that one of the criteria for determining the location of ground stations is the number of satellites (e.g., \(m\)) that a ground station can connect to. So, for the algorithm model designed in this paper, the ground station will also be an important factor to be considered. The agent of the algorithm proposed in this paper is placed on the ground station, which is responsible for sending the final execution action (routing final decision) to \(m\) satellites. The network composed by m satellites that is managed by each ground station is called the regional network in this paper. Different regional networks are connected by selecting an inter-satellite link with stable (as in, the same orbital plane) and small load between regional networks to form the final LEO satellite network. Firstly, the problem of dynamic topological changes in low-orbit satellite networks has two parts: topological changes caused by satellite node movement and topological changes caused by satellite state or link changes. Then, solving the routing problem of topological changes caused by the movement of satellite nodes is equivalent to solving the routing problem of a fixed topology at different times (\(t_{1},t_{2},t_{3}\ldots t_{n}\)) through the above assumptions. In the time period in which the topology is unchanged, the routing problem with link state and satellite node state changes is equivalent to a routing problem of a hierarchical network with a fixed topology, but link state and node state may change through the strategy of network classification according to the ground station. In order to make the problem easier to solve, hierarchical networks with the characteristics of fixed topology but possible changes in link state and node state are considered as equivalent to NSFNET networks with the same characteristics. The LEO satellite network can be represented as a graph \(G=(\mathrm{V},\mathrm{E})\) during \(t_{0}\) period, where V and E denote the set of LEO satellite nodes and edges between them. Then the routing problem of the LEO satellite network can be defined as follows: given \(G=(\mathrm{V},\mathrm{E})\), the source node \(src\), the destination node \(dst\) and the traffic flow demand \(bw\), find a set of paths in order to forward the data from the source to the destination. And when the inter-satellite link changes, E will show the changes in the links. The goal is to minimize the network end-to-end delay while increasing the network throughput, whether the network topology is changing or not. It is found that its future state only depends on the current state by analyzing the LEO satellite network routing problem, which is a typical [PERSON] decision process. Therefore, all node states can be directly input into DRL to seek the maximum reward to find the optimal path. But DRL cannot learn topological information when dealing with routing optimization problem. Once one or more nodes fail for some reason, the network topology will change. The routing algorithms based on DRL do not work well when the network topology changes. This is because DRL algorithms mainly focus on the state information of individual network nodes and ignore the impact of selecting the routing for the individual node on the whole network topology.