A life-cycle cost-based optimization framework for seismic design of structures using FEMA P-58 and the SAR algorithm

This study presents a life-cycle cost-based optimization framework for the seismic design of structures, developed within the second generation of the Performance-Based Earthquake Engineering (PBEE-2) methodology. The design problem was formulated as a single-objective optimization to minimize life-cycle cost. To reduce the high computational demand of nonlinear analyses required for seismic loss estimation, an approximate loss estimation method was developed based on the story-based method and FEMA P-58. Additionally, a new constraint-handling method was presented, which reduces computational cost by more than 80 % compared with the conventional penalty function method. It requires no parameter tuning and can be implemented with any optimization algorithm. The framework’s effectiveness was demonstrated through the optimal design of a three-dimensional five-story steel moment-resisting frame, with direct comparisons to a conventional design approach. The results reveal that these optimized structures not only achieved approximately 20 % reductions in both structural weight and expected seismic loss, but also showed lower probabilities of collapse. These designs also exhibited increased stiffness, strength, and ductility. The performance of several metaheuristic algorithms was compared for solving the optimization problem, and among the studied algorithms, the SAR algorithm demonstrated superior performance, providing more effective optimization results. The effect of member grouping on the optimal design was also investigated. Overall, the proposed framework provides a practical and computationally efficient tool for life-cycle cost optimization within PBEE-2.