Non-Grid-Mesh Topology Design for MegaLEO Constellations: An Algorithm Based on NSGA-III

The rapid deployment of Low Earth Orbit (LEO) satellites, driven by technological advancements and cost reductions, has led to the emergence of mega-constellations for satellite-based Internet services. Among them, the networking problem has become a significant area of research. Specifically, breaking away from the traditional Grid-Mesh + topology schemes has been a focal point. Although some related studies have been conducted, there are still three major challenges in optimizing the topology of laser inter-satellite links: the lack of theoretical derivation for satellite visibility, the need for comprehensive modeling goals, and the absence of network simulation verification. To address these challenges, we introduce the theory of visibility analysis of laser terminals in real scenarios and propose a theoretical model of topologically feasible solutions for integer linear programming. Furthermore, a mathematical model is developed that considers time delay, hop count, and link load as optimization objectives. The Many-objective Non-Grid-Mesh Topology Optimization (M-NGTO) algorithm, based on Non-dominated Sorting Genetic Algorithm III (NSGA-III), is then designed to effectively optimize the topology. The optimized Non-Grid-Mesh topology is validated through packet-level simulations on the Hypatia platform. Additionally, consistency analysis is performed to establish agreement between theory and simulation results. The results of simulations conducted on two megaLEO satellite Internet constellations, GW and Starlink, demonstrate that the performance of the Non-Grid-Mesh topology in the above three optimization objectives is approximately 39.11% better than the average of the Grid-Mesh + topology, confirming the effectiveness of the M-NGTO algorithm. The findings have significant implications for enhancing the communication performance and load balancing of satellite Internet systems.