Structural optimization for performance-based seismic design (PBSD) in earthquake engineering aims at finding optimum design variables corresponding to a minimum objective function with constraints on performance requirements. In this study, an efficient methodology, consisting of two computational strategies, is presented for performance-based optimum seismic design (PBOSD) of steel moment frames. In the first strategy, a modified firefly algorithm (MFA) is proposed to efficiently find PBOSD at the performance levels. Because that for computing the structural responses at the performance levels a nonlinear static pushover analysis must be conducted, the overall computational time of optimization process is extremely large. In the second strategy, to reduce the computational burden, a new neural network model termed as wavelet cascade-forward back-propagation (WCFBP) is proposed to effectively predict the results of nonlinear pushover analysis during the optimization process. To illustrate the effectiveness of the proposed methodology, 3, 6 and 12 storey planar steel moment resisting frames are optimized for various performance levels. The results demonstrate the effectiveness of the proposed soft computing-based methodology for PBOSD of steel structures spending low computational cost. 
Performance-based optimum seismic design of steel structures by a modified firefly algorithm and a new neural network