###### Abstract  
Designing routing algorithms for Low Earth Orbit (LEO) satellite networks poses a significant challenge due to their high dynamics, frequent link failures, and unevenly distributed traffic. Existing studies predominantly focus on shortest-path solutions, which compute minimum-delay paths using global topology information but often neglect the impact of traffic load on routing performance and struggle to adapt to rapid link-state variations. In this regard, we propose a Multi-Agent Reinforcement Learning-Based Joint Routing (MARL-JR) algorithm, which integrates centralized and distributed routing algorithms. MARL-JR combines the accuracy of centralized methods with the responsiveness of distributed approaches in handling dynamic disruptions. In MARL-JR, ground stations initialize Q-tables and upload them to satellites, reducing onboard computational overhead while enhancing routing performance. Compared to traditional centralized algorithms, MARL-JR achieves faster link-state awareness and adaptation; compared to distributed algorithms, it delivers superior initial performance due to optimized pre-training. Experimental results demonstrate that MARL-JR outperforms both Q-Routing (QR) and DR-BM algorithms in average delay, packet loss rate, and load-balancing efficiency. satellite network; low earth orbit; reinforcement learning; distributed routing 2025 15 4664 1225 15 46  
Table 1 summarizes the orbital types, advantages/disadvantages, and transmission delays of these three satellite categories. Due to significant advantages, like less signal propagation delay, path loss, and cost-effective deployment [2], LEO satellites can enable comprehensive global wireless communication. Therefore, LEO satellite communication has emerged as a critical area of focus in modern communication research. However, unlike terrestrial networks and Geostationary Earth Orbit (GEO) satellite networks, LEO satellite constellations face challenges such as dynamic network topologies because of rapid satellite movement [3], heterogeneous communication demands across diverse coverage regions, instability in inter-satellite links, and constrained onboard computational resources. Consequently, traditional ground-based routing algorithms are not directly applicable to LEO satellite networks. To address these challenges, novel routing algorithms must be developed to enhance network throughput, optimize load distribution, and ensure low-latency data delivery. Satellite routing algorithms, as a core and critical technology in satellite networks, have been extensively studied in the literature. However, addressing the challenge of rapidly time-varying satellite topology remains a primary issue that requires immediate resolution. To tackle this problem, researchers have proposed innovative approaches, such as virtual topology and virtual node strategy. Among these, [PERSON] [4] introduced the Dynamic Virtual Topology Routing (DV-DVTR) algorithm. As illustrated in Figure 1, the virtual topology strategy method partitions the constellation's operational timeline into fixed-duration epochs. Within each time slot, topological changes in the satellite network are masked, resulting in a fixed network topology throughout the slot duration. This enables topology-dependent routing computation that significantly reduces algorithmic complexity. In addition to time interval-based partitioning, the snapshot approach [5] is another representative virtual topology scheme. Whenever an inter-satellite link is temporarily disconnected or reconnected, a new snapshot distinct from the previous one is generated, and the satellite topology within each snapshot remains unchanged.