Multi-Layer LEO Constellation Optimization Based on D-NSDE Algorithm

Low-Earth-orbit (LEO) satellites have unique advantages in communication, navigation, and remote sensing due to their low orbit, strong landing signal strength, and low launch cost. However, the optimization of the design of LEO constellations to obtain the optimal configuration to meet different missions faces great challenges. Traditional multi-objective optimization algorithms often struggle with designing constellations involving composite functions due to various constraints, which can result in premature termination and local optimality issues. This paper introduces a dynamic parameter-based non-dominated sorting differential evolution (D-NSDE) algorithm to obtian better solutions, which is capable of dynamically adjusting the boundary of feasible solutions and modifying operators according to the iteration process to mitigate these constraints. Additionally, we model a composite LEO constellation with multiple layers, constructing 2-/3-/4-layer configurations, and we include constraints from the third-generation BeiDou Navigation Satellite System (BDS-3) navigation constellations. Subsequently, we employ the D-NSDE algorithm to solve the corresponding multi-objective optimization problems and derive the optimal solution set. The results demonstrate that D-NSDE can generate complete and multi-level solution sets under diverse constraint conditions, with 75% of D-NSDE algorithm optimization solutions being able to achieve seamless positioning for 95% of global coverage. Furthermore, the PDOP median values are 5.12/4.23/2.97 without BDS-3 navigation constraints and 1.38/1.44/1.51 with BDS-3 navigation constraints. Additionally, simulation experiments conducted on standard function test sets confirm that the solution sets produced by the D-NSDE algorithm exhibit favorable distribution and convergence performance better than the Non-dominated Sorting Genetic Algorithm (NSGA)-III.