The optimal seismic retrofitting of NPP(Nuclear Power Plant) cabinet structures that contain seismic category 1 relays was studied in this paper. During earthquake event, the failure modes of relays are not appeared in form of structural failure, but are appeared in form of contact chatter of relay. Therefore, the retrofitting of cabinet has to be aimed at the reducing of the structural response, such as acceleration. In this study, the optimal characteristic values of dampers were searched by ${mu}$-GA (micro-Genetic Algorithm) scheme for several installation patterns. To keep accuracy and efficiency of analysis, the structural models of cabinet were considered as a frame structure. The responses of structure were obtained inform of acceleration response spectra derived from the results of nonlinear time history analysis including damping nonlinearity. The objective function of the optimum procedure was constructed based on the maximum ratio of maximum spectral value and target GERS (General Equipment Ruggedness Spectra). The results show the good improvements of fitness for adequate retrofitting pattern. Especially, the improvements of fitness were remarkable when the values of damping exponents are low.