The growing demand for resilient and cost-effective structural systems in seismic regions has led to significant advances in performance-based seismic design (PBSD). Conventional design methodologies typically rely on deterministic hazard levels and prescriptive code requirements, which may not adequately capture the inherent uncertainty of earthquake ground motions and their probabilistic characteristics. Consequently, performance-based optimization frameworks that explicitly consider different levels of seismic hazard, structural performance objectives, and cost-effectiveness have gained increasing attention. In this study, an advanced performance-based optimal design (PBOD) methodology is developed and applied to special steel moment-resisting frames (SMRFs). The optimization framework employs the Center of Mass (CMO) metaheuristic algorithm as the core search strategy. Furthermore, probabilistic seismic hazard coefficients derived for Iran are incorporated into the optimization constraints to ensure realistic evaluation of seismic demand and structural performance.
The primary objective of this research is to obtain optimal structural designs that achieve satisfactory seismic performance while minimizing structural weight and material cost. To this end, two representative SMRFs—a three-story frame and a six-story frame—are considered as case studies. The optimization problem is formulated in terms of minimizing the total weight of the frame subject to performance constraints. These constraints include interstory drift ratios, global stability requirements, and collapse prevention limits defined by the PBSD framework. In order to capture the probabilistic nature of seismic demand, hazard coefficients corresponding to exceedance probabilities of 0.25, 0.30, and 0.40 are applied. These values are consistent with hazard curves obtained from the probabilistic seismic hazard analysis (PSHA) of Iran, ensuring that the designs are relevant to realistic seismic environments.
The optimization process is carried out using the CoM metaheuristic algorithm. This relatively new algorithm is inspired by the physical concept of the center of mass in mechanics, where the balance of forces leads to equilibrium at a central point. In the computational analogy, candidate solutions are treated as interacting entities in a search space, whose collective behavior tends toward the “center of mass” of optimality. This approach enables the algorithm to efficiently balance exploration and exploitation, avoiding premature convergence while ensuring global search capability. The CoM algorithm is coupled with pushover analysis in the optimization loop, providing nonlinear performance assessment at each iteration. By integrating structural analysis results into the optimization framework, the algorithm adaptively guides the search toward designs that satisfy seismic performance objectives while reducing overall material usage.
To further validate the structural performance of the optimized frames, Incremental Dynamic Analysis (IDA) is conducted. This technique provides detailed information about collapse capacity, fragility characteristics, and seismic demand-to-capacity relationships. Fragility curves are developed for the optimized frames to evaluate their probability of exceeding different damage states under increasing ground motion intensities. This comprehensive evaluation ensures that the optimized solutions are not only efficient in terms of weight reduction but also reliable under severe seismic events.
The results of the optimization process reveal important insights. First, designs obtained with lower hazard coefficients (e.g., 0.25) tend to be significantly more economical, as the imposed seismic demand is lower and the structural members are sized more efficiently. However, such designs may exhibit reduced robustness when subjected to extreme ground motions. In contrast, designs corresponding to higher hazard coefficients (e.g., 0.40) display greater redundancy and improved collapse resistance, albeit at the cost of higher structural weight and material usage. Thus, a trade-off emerges between economy and resilience.
The IDA results demonstrate that frames optimized under higher hazard coefficients achieve superior collapse capacities and exhibit lower fragility under increasing seismic demands. Specifically, the six-story frame designed with a hazard coefficient of 0.40 showed markedly reduced probability of collapse at high intensity levels compared to its counterpart designed with 0.25. However, the latter design achieved approximately 15% reduction in weight, illustrating the potential economic advantage of designs optimized under less conservative hazard levels.
Another key finding relates to interstory drift control. The results indicate that as hazard coefficients increase, drift constraints become more sensitive and dominate the optimization process. This highlights the importance of displacement-based performance objectives in PBSD frameworks. The study confirms that frames designed under higher hazard levels are better able to control drift, reducing the likelihood of non-structural damage and ensuring improved functional recovery after earthquakes.
Overall, this research demonstrates the effectiveness of combining the CMO metaheuristic algorithm with performance-based seismic design principles. The methodology successfully integrates nonlinear structural analysis, probabilistic hazard considerations, and advanced optimization to produce designs that balance economy and safety. Importantly, the study provides a practical framework that can be adapted for other structural systems and seismic regions, offering engineers a powerful tool for resilient design.
In conclusion, the findings emphasize that performance-based optimization using the CMO algorithm offers a rational and systematic approach to the seismic design of SMRFs. By explicitly incorporating probabilistic hazard levels, the method allows decision-makers to evaluate the trade-offs between cost efficiency and structural safety. The dual use of pushover and incremental dynamic analyses ensures comprehensive assessment of both serviceability and collapse prevention performance objectives. The study not only highlights the applicability of metaheuristic optimization algorithms in structural engineering but also provides valuable insights into the role of probabilistic hazard coefficients in shaping optimal design outcomes. Future research may extend this methodology to multi-objective optimization frameworks, integrating additional criteria such as life-cycle cost, repairability, and sustainability, thereby contributing to the development of truly resilient and sustainable seismic design practices.