Due to fundamental limitations on terrestrial quantum links, satellites have received considerable attention for their potential as entanglement generation sources in a global quantum internet. In this work, we focus on the problem of designing a constellation of satellites for such a quantum network. We find satellite inclination angles and satellite cluster allocations to achieve maximal entanglement generation rates to fixed sets of globally distributed ground stations. Exploring two black-box optimization frameworks: a Bayesian Optimization (BO) approach and a Genetic Algorithm (GA) approach, we find comparable results, indicating their effectiveness for this optimization task. While GA and BO often perform remarkably similar, BO often converges more efficiently, while later growth noted in GAs is indicative of less susceptibility towards local maxima. In either case, they offer substantial improvements over naive approaches that maximize coverage with respect to ground station placement.

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