In this paper, a semi-active control method for seismically excited nonlinear benchmark buildings equipped with controllable fluid viscous dampers is presented and evaluated. A Fuzzy Logic Controller (FLC) is designed to alter the damping coefficient of controllable viscous dampers during an earthquake. A Genetic Algorithm (GA) is employed to find optimum fuzzy controller rules, as well as adjusting the membership functions to minimize the overall damage index. This combination of a Genetic algorithm and a Fuzzy Logic Controller (GFLC) is also used to minimize the peak value of the top story displacement response, in order to verify the effectiveness of minimizing displacement on the damage index. The effectiveness of the FLC is verified and illustrated using the simulated response of 3-story and 20-story full-scale nonlinear benchmark buildings excited by several historical earthquake records, through a computer simulation on MATLAB. For comparison, a Linear Quadratic Gaussian (LQG) active controller is designed to minimize the peak value of the top story displacement response. Moreover, the results of a study that has used Self-Organizing Fuzzy Logic Controllers (SOFLC) with active actuators are used. The results demonstrate that the GFLCs are quite effective in overall damage reduction for a wide range of motions, compared with the SOFLC and LQG controllers.