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Space missions have traditionally been controlled by operators from a mission control center. Given the increasing number of satellites for some space missions, generating a command list for multiple satellites can be time-consuming and inefficient. Developing multi-satellite, onboard mission scheduling & planning techniques is, therefore, a key research field for future space mission operations. In this paper, an improved Genetic Algorithm (GA) using a new mutation strategy is proposed as a mission scheduling algorithm. This new mutation strategy, called Hybrid Dynamic Mutation (HDM), combines the advantages of both dynamic mutation strategy and adaptive mutation strategy, overcoming weaknesses such as early convergence and long computing time, which helps standard GA to be more efficient and accurate in dealing with complex missions. HDM-GA shows excellent performance in solving both unconstrained and constrained test functions. The experiments of using HDM-GA to simulate a multi-satellite, mission scheduling problem demonstrates that both the computation time and success rate mission requirements can be met. The results of a comparative test between HDM-GA and three other mutation strategies also show that HDM has outstanding performance in terms of speed and reliability. [ABSTRACT FROM AUTHOR]