The mitigation of the dynamic response of buildings and structures to earthquakes is onernof the fundamental aims within the design of vibration control devices. In this sense, TunedrnMass Damper (TMD) devices are generally conceived as useful and efficient means forrnthe control of the dynamic response of structures and constructions, especially whenrnconsidering ideal dynamic excitations. However, their optimum tuning and relevantrnperformance in effectively reducing the seismic response of civil structures is currently anrnopen topic, mostly due to the intrinsic nature of the passive device and the uncertainty andrnunpredictability of the earthquake event.rnThe present paper deals with determining of the optimum parameters of TMD to minimizerndynamic response of a single and multi-storied building system. To optimize dynamicrnparameters of the TMD system for minimum top deflection of the structure, a MinmaxrnOptimization Simulation analysis is used in a MATLAB environment. Analytical formulasrnand graphical charts are also developed to determine the optimal parameters of TMD.rnThree three-dimensional building models are modeled using SAP2000 to validate thernoptimum values of design variables and to examine the optimum installation location ofrnTMD in elevation under seismic excitation. It is well recognized that the performance ofrna TMD is sensitive to the slight deviation of frequency ratio between the TMD and thernstructure.rnKeywords: TUNED MASS DAMPER, OPTIMUM PARAMETERS, MINMAXrnOPTIMIZATION.