In this study, the multi-objective optimization and decision-making for optimal positions of actuators and consensus adaptive dynamic programming (CADP) are investigated to mitigate the vibration of large flexible space structures (LFSS). The optimization of the actuator positions maintains a balance between maximizing actuation efficiency and maximizing input voltage decoupling. Meanwhile, the CADP control method accelerates the attenuation of vibration when agents collaborate in the designed communication topology network. First, the electromechanical coupled dynamic model of the LFSS is built by the finite element method. Subsequently, the multi-objective optimization criteria are proposed, which maximize the actuation efficiency and decoupling of control inputs. Moreover, the multi-objective optimization and decision-making, which is based on the non-dominated sorting differential evolutionary algorithm (NSDE) and technique for order preference by similarity to ideal solution (TOPSIS), respectively, are performed to rapidly find the optimal position of actuators. In addition, the CADP control algorithm is designed and its stability is proven. Finally, for harmonic excitation under multi-frequency superposition, simulation comparisons based on the CADP and adaptive dynamic programming (ADP) are performed. Simulation results verify the effectiveness of the proposed optimization criterion of actuators and the CADP algorithm for vibration mitigation of LFSS.