This paper investigates the multi-objective optimization of active control systems for vibration control of three-dimensional (3D) high-rise buildings under a variety of earthquake excitations. To this end, a novel multi-objective genetic algorithm is developed through the integration of the best features of a non-dominated sorting II (NS2) genetic algorithm (GA) and an implicit redundant representation (IRR) GA. The proposed NS2-IRR GA finds not only minimum distributions of both actuators and sensors within structures, but also minimum dynamic responses of 3D structures. Linear quadratic Gaussian controllers, hydraulic actuators and accelerometers are used for implementation of active control systems within the 3D buildings. To demonstrate the effectiveness of the proposed NS2-IRR GA, two 3D building models are investigated using finite element methods, including low- and high-rise buildings. It is shown that the proposed NS2-IRR GA is effective in finding not only optimal locations and numbers of both actuators and sensors in 3D buildings, but also minimum responses of the 3D buildings. The simulation also shows that the control performances of the proposed approach significantly enhance those of the engineering judgment oriented benchmark layout, which is validated by comparisons of each performance using the same number of actuators.
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