Integrating Bayesian Optimization and Combinatorial Optimization for LEO Satellite Constellation Design
摘要
We study the problem of selecting optimal design parameters for Low-Earth-Orbit (LEO) satellite constellations, where the performance of a design is determined by the maximum Satellite–Ground Link (SGL) duration it enables. The design space spans altitude, inclination, plane count, satellites per plane, and phasing, rendering a full mathematical programming model intractable. We propose a two-layer optimization framework: Bayesian Optimization (BO) explores the constellation design space, while each candidate design is evaluated by solving a large Satellite–Ground Link Scheduling Problem (SGLSP). The SGLSP is solved using PINCH, our fast primal heuristic based on LP-relaxation-guided fixing and clustering. PINCH produces high-quality schedules significantly faster than Gurobi, one of the most advanced commercial mixed-integer linear programming solvers. This acceleration allows BO to evaluate constellation designs for 40 ground stations within hours, making large-scale exploration of the design space computationally feasible. The framework scales to large instances and offers a practical approach for complex space-system design problems with combinatorial structure. Moreover, by modifying the weights in the cost–quality trade-off, the same computational pipeline can be steered toward different design priorities (e.g., longer SGL duration, lower deployment cost, or reduced latency), enabling users to obtain constellation configurations that match their specific requirements and preferences.