In this paper an effective method has been proposed for designing optimal multiple tuned mass dampers (MTMDs) to mitigate the seismic response of structures based on defining an optimization problem which considers the parameters of tuned mass dampers (TMDs) as variables and minimization of maximum structural response as an objective function while a number of constraints have been applied on TMDs response and parameters. The genetic algorithm (GA) has been used successfully for solving the optimization problem. For illustration, for a ten-story linear shear frame subjected to a filtered white noise excitation optimal MTMDs have been designed. The results have shown the simplicity and convergence behavior of the method. It has also been concluded that the performance of MTMDs depends on TMDs mass ratio, TMDs configuration and design criteria where increasing the TMDs mass ratio has improved monotonously the performance of MTMDs especially for the domain of smaller values of the mass ratio, while for this case study the number of TMDs has not been more effective. Testing the optimal MTMDs under near-field and far-field earthquakes shows that the performance of MTMDs has been influenced by input excitation. The capability of the method in considering the effect of higher modes has been shown.

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