Assessment of Objective Functions in the Optimization of Tuned Liquid Dampers for Seismic Retrofit of Vertically Irregular Steel Frames

Steel moment-resisting frames exhibiting vertical geometric irregularities, particularly those with setback configurations, experience increased seismic demands due to stiffness discontinuities and complex dynamic interactions. These conditions present significant challenges for conventional vibration control strategies. This study introduces a performance-based optimization framework that utilizes the Circle-Inspired Optimization Algorithm (CIOA) to enhance the design of tuned liquid dampers (TLDs) in irregular steel structures. Structural responses are simulated in OpenSees, with a rheological model based on the Housner method employed to accurately capture fluid–structure interaction. Seismic performance is evaluated using a suite of real subduction-type ground motions, selected to represent the seismic hazard level of Armenia, Colombia, in accordance with the Conditional Scenario Spectra (CSS) methodology and the National Seismic Risk Model for Colombia. The optimization process considers the mean response across multiple ground-motion records to ensure robustness against seismic variability. Multiple time-domain objective functions are examined, including peak interstory drift, maximum displacement, and peak acceleration. The results indicate that objective functions related to interstory drift and displacement provide the most effective, stable, and consistent reductions in seismic demand across all scenarios, while acceleration-based objectives display greater sensitivity to record-to-record variability. These outcomes underscore the importance of objective function selection in determining both optimization stability and control effectiveness. The CIOA demonstrates rapid convergence, numerical robustness, and reliable performance, confirming its suitability as a computationally efficient and resilient optimization tool for the design of passive control systems in irregular steel structures exposed to high seismic hazard.