New Insights in Topology-Based Cost Optimization of Braced Structures Using Bilinear Fuzzy-Genetic Algorithm: Effect of Foundation Uplift Force

Real-world structural problems are complex, requiring accurate simulation with a well-defined objective function and detailed constraints to avoid unrealistic models that lead to unacceptable solutions. One of the key factors in optimizing braced structures is the foundation’s effect and uplift forces under lateral loads. In this study, the size and topology optimization of braced structures was implemented to achieve optimal arrangements of braces. Structures with different bracing types [X, V, Λ, and Λ with zipper column (₼)] are first optimized for minimum structural weight and then for a minimum-cost objective that explicitly includes uplift-dependent foundation expenses. To tackle the multicriteria design optimization of this detailed problem, an efficient and robust fuzzy-genetic algorithm utilizing a bilinear membership function was employed. The optimum results for different bracing types were compared, and the effect of stories and span numbers was investigated. Results demonstrated that foundation-considered cost-optimized configurations, while sometimes exhibiting slightly higher structural weights, consistently achieved improved structural performance through foundation uplift mitigation and reduced interstory drifts and maximum displacements. The average reduction was approximately 15% compared with weight-optimized designs. Thus, these configurations were proved to be more efficient across key performance metrics and so economically advantageous. This integrated approach yields more practical and economical solutions by effectively balancing structural performance with uplift-related foundation requirements.