A new computational framework is developed for the design and retroÿt of building structures by considering aseismic design as a complex adaptive process. For the initial phase of the development within this framework, genetic algorithms are employed for the discrete optimization of passively damped structural systems. The passive elements may include metallic plate dampers, viscous uid dampers and viscoelastic solid dampers. The primary objective is to determine robust designs, including both the non-linearity of the structural system and the uncertainty of the seismic environment. Within the present paper, this computational design approach is applied to a series of model problems, involving sizing and placement of passive dampers for energy dissipation. In order to facilitate our investigations and provide a baseline for further study, we introduce several simpliÿcations for these initial examples. In particular, we employ deterministic lumped parameter structural models, memoryless ÿtness function deÿnitions and hypothetical seismic environments. Despite these restrictions, some interesting results are obtained from the simulations and we are able to gain an understanding of the potential for the proposed evolutionary aseismic design methodology.