A gradient-based evolutionary optimization methodology is presented for finding the optimal design of both the added dampers and their supporting members to minimize an objective function of a linear multi-storey structure subjected to the critical ground acceleration. The objective function is taken as the sum of the stochastic interstorey drifts. A frequency-dependent viscoelastic damper and the supporting member are treated as a vibration control device. Due to the added stiffness by the supplemental viscoelastic damper, the variable critical excitation needs to be updated simultaneously within the evolutionary phase of the optimal damper placement. Two different models of the entire damper unit are investigated. The first model is a detailed model referred to as "the 3N model" where the relative displacement in each component (i.e., the spring and the dashpot) of the damper unit is defined. The second model is a simpler model referred to as "the N model" where the entire damper unit is converted into an equivalent frequency-dependent Kelvin-Voigt model. Numerical analyses for 3 and 10-storey building models are conducted to investigate the characters of the optimal design using these models and to examine the validity of the proposed technique.