In spite of bulk literature about the tuning of TMD, the effectiveness of TMD in reducing the seismic response of engineering structures is still in a row. This paper deals with the optimum tuning parameters of a passive TMD and simulated on MATLAB with a ten-story numerical shear building. A weighted multi-objective optimization method based on computer experiment consisting of coupled with central composite design(CCD) central composite design and response surface methodology(RSM) was applied to find out the optimum tuning parameters of TMD. After the optimization, the so-conceived TMD turns out to be optimal with respect to the specific seismic event, hence allowing for an optimum reduction in seismic response. The method was employed on above structure by assuming first the El Centro seismic input as a sort of benchmark excitation, and then additional recent strong-motion earthquakes. It is found that the RSM based weighted multi-objective optimized damper improves frequency responses and root mean square displacements of the structure without TMD by 31.6% and 82.3% under El Centro earthquake, respectively, and has an equal or higher performance than the conventionally designed dampers with respect to frequency responses and root mean square displacements and when applied to earthquakes.