In this simulation study, the operational GNSS satellites of Global Positioning System (GPS), Galileo, GLONASS, and BDS, which are currently in service, are used to transmit signals for GNSS Reflectometry (GNSS-R) measurement. LEO constellations composed of 8, 16 and 24 satellites and with two different patterns, the 2D-lattice flower constellation (2D-LFC) and the 3D-lattice flower constellation (3D-LFC), are designed considering the trade-off among three objectives, namely the visited coverage (<i>V C</i>), the revisited coverage (<i>RC</i>) and the total cost of the constellation. Two multi-objective evolution-ary algorithms (MOEAs), the non-dominated sorting genetic algorithm II (NSGA-II) and the multi-objective evolutionary algorithm based on decomposition (MOEA/D), are applied to solve this multi-objective optimization problem (MOP). The optimal constellations meeting the best trade-off for the three objectives are picked out, and the distributions of the reflected points observed by them are presented and compared. It is found that NSGA-II generally performs better with respect to the convergence and the diversity of the Pareto solutions. The optimal trade-off constellations are generally with inclinations of around 67° to 77° and orbital altitudes of nearly 1000 km. For certain number of satellites, the latitudinal and longitudinal distributions of the number of the reflected points observed by the optimal 2D-LFC and 3D-LFC are highly similar to each other. Moreover, with the resolution of 0.25°×0.25°, the VCs of the optimal 8-satellite and 16-satellite 3D-LFCs reach 58.30% and 79.59%, respectively, and the optimal 24-satellite 2D-LFC and 3D-LFC can achieve an average revisit time of about 11.0 h and 10.2 h, respectively.
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