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An important factor in the design and implementation of structural control strategies is the number and placement of actuators. By employing optimally-located actuators, the effectiveness of control system increases, while with an optimal number of actuators, an acceptable level of performance can be achieved with fewer actuators. The method proposed in this paper, simultaneously determines the number and location of actuators, installed in a building, in an optimal sense. In particular, a genetic algorithm which minimizes a suitably defined structural damage index is introduced and applied to a well-known nonlinear model of a 20-story benchmark building. It is shown in the paper that an equal damage protection, compared to the work of other researchers, can be achieved with fewer numbers of optimally placed actuators. This result can be important from economic point of view. However, the attempt to minimize one performance index has negative effect on the others. To cope with this problem to some extent, the proposed genetic methodology has been modified to be applied in a multi-objective optimization problem.