The aim of this thesis is to investigate the effect of using viscoelastic dampers in seismic retrofitting of weak steel structures and reducing the life cycle cost of the building, while taking the effect of the random parameters, including the type of accelerogram, excitation frequency and ambient temperature, in to account. For this purpose, a three-parameter fractional derivative Kelvin model is used, being capable of realistic modeling of the damper’s behavior and including the effect of temperature and frequency. In order to calculate the response of the structure, UMRHA method has been used. The natural frequencies and mode shapes have been calculated using the continuation method. After modal decomposition of the structure, the response of each SDF system has been calculated by means of Newmark method. Also, the ductility demand parameter has been used according to ASCE 7-10 to account for nonlinear behavior of the structure. Then, a weak steel structure is modeled with viscoelastic dampers mounted on it, and a life cycle cost analysis is performed, taking in to account the effects of random parameters, assuming two kinds of behavior for the structure: linear and nonlinear. In the section attributed to the assumption of nonlinear behavior, the results are illustrated in the form of IDA curves, fragility curves and life cycle cost of the building for 6 different retrofitting scenarios. The results demonstrate the impact of utilizing viscoelastic dampers for reducing structural response and failure cost. Additionally, comparison of the results of the 6 distinct scenarios, shows that increasing the retrofitting cost does not necessarily lead to decreasing the failure cost. This proves the importance of maintaining an optimal design. In the section attributed to the assumption of linear behavior, after presenting IDA and fragility curves, it is attempted to maintain an optimal design by means of genetic algorithm, with the objective of minimizing the life cycle cost of the structure, while enhancing structural performance. Afterwards, the results are compared for optimal and non-optimal scenarios, which emphasizes the superiority of the optimal design.