Robust multi-objective optimization framework for performance-based seismic design of steel frame with energy dissipation system

Modern seismic codes ensure life safety, but code-compliant buildings can still suffer significant economic losses from earthquake-induced damage, even during moderate events. Performance-Based Seismic Design (PBSD) has been developed to mitigate the impact of disproportionate financial losses. However, optimizing seismic retrofits involves complex trade-offs and requires explicit consideration of design robustness against uncertainties. This study introduces a novel Robust Multi-objective Optimization framework for Performance-Based Seismic Design (RMO-PBSD). This framework addresses the inherent conflict between three key objectives: economic efficiency, post-earthquake repair costs, and design robustness. Economic efficiency is quantified by the cost of fluid viscous dampers (FVDs), a common retrofit measure. Repair costs are estimated using the FEMA P-58 methodology, while robustness is quantified by the variability of structural response under seismic uncertainty. The core contribution lies in integrating these three metrics (FVD cost, repair cost, and a robustness measure) into an integrated optimization process using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The framework’s applicability and effectiveness are demonstrated through a case study of a 4-story steel moment-resisting frame retrofitted with FVDs, modeled in OpenSees. Seismic demand uncertainty is rigorously quantified using a series of ground motion records. Optimization results reveal a clear Pareto front, generally showing that higher FVD costs lead to lower repair costs and more robust designs (i.e., less sensitive to ground motion variability), although the robustness measure displays a non-linear relationship with the cost metrics. By analyzing designs along the Pareto front, the framework facilitates informed decision-making, identifying optimal, cost-effective FVD configurations that significantly enhance seismic performance while explicitly managing performance variability. This work provides a practical tool for achieving resilient and economically efficient seismic retrofits.