Structural optimization has been shown to be an efficient and effective method to obtain the optimal design balancing competing objectives. However, literature on optimization of structures subject to random excitation is sparse. This study proposes a performance-based optimization approach for nonlinear structures subject to stochastic dynamic excitation. The optimization procedure is formulated as a multi objective problem considering various performance objectives. The excitation is modeled as a zero-mean filtered white noise and combined with the nonlinear equations of motion of the structure to create an augmented state space representation of the system. The optimization objectives are defined in terms of the variance of stationary structural responses, which are obtained via equivalent linearization. Thus, the stochastic optimization problem is converted into its deterministic counterpart. Numerical examples are provided to demonstrate the efficacy of the proposed approach. Three levels of seismic magnitudes, i.e., low-level, frequent earthquake, medium-intensity earthquake and high-intensity earth-quake, are investigated. For each seismic magnitude, two performance objectives are considered. The first performance objective considers serviceability, seeking to minimize floor acceleration response; and the second performance objective considers structural safety and seeks to minimize interstory drift response. The Pareto optimal fronts are calculated to illustrate the intrinsic tradeoffs between serviceability and safety of designs subject to all seismic magnitudes. (C) 2016 Elsevier Ltd. All rights reserved.