Performance-based multi-objective optimal design of steel frame structures: Nonlinear dynamic procedure

The main problem in performance-based structures is the extremely high computational demand of time-history analyses. In this paper, an ecient framework is developed for solving the performance-based multi-objective optimal design problem considering the initial cost and the seismic damage cost of steel moment-frame structures. The Non-dominated Sorting Genetic Algorithm (NSGA-II) is employed as the optimization algorithm to search the Pareto optimal solutions. For improving the time eciency of the solution algorithm, the Generalized Regression Neural Network (GRNN) is utilized as the meta-model for tness approximation, and a specic evolution control scheme is developed. In this scheme, in order to determine which individuals should be evaluated using the original tness function and which by the meta-model, the Fuzzy C-Mean (FCM) clustering algorithm is used to choose the competent individuals rather than choosing the individuals randomly. Moreover, the computational burden of time history analyses is decreased through a particular wavelet analysis procedure. The constraints of the optimization problem are considered in accordance with the FEMA codes. The results obtained from numerical application of the proposed framework demonstrate its capabilities in solving the present multi-objective optimization problem.