en Optimal design Optimal design پژوهشي Research <span style="font-size:11.5pt"><span new="" roman="" style="font-family:" times="">The dual steel system comprising moment-resisting frames integrated with steel shear walls represents an advanced seismic-resistant solution in structural engineering. This system synergistically combines the high ductility and energy dissipation capacity of steel frames with the substantial lateral stiffness and strength provided by steel shear walls. Proper design of such systems requires precise determination of the optimal location, thickness, and mechanical properties of the shear walls parameters that critically govern seismic performance, structural safety, material efficiency, and construction cost. To achieve an optimal balance between performance and economy, the problem is formulated as a constrained optimization task. This study employs the recently developed Puma Optimizer (PO) and introduces a novel enhanced variant, termed the Upgraded Puma Optimizer (U-PO). The key novelty of this work lies in the integration of L&eacute;vy flight distribution into the PO framework, replacing conventional Brownian motion to significantly strengthen the exploration&ndash;exploitation balance, global search capability, and convergence speed. This modification enables more effective handling of complex, high-dimensional structural optimization problems. The performance of the proposed U-PO is rigorously evaluated through the optimal design of three benchmark steel frames (1-, 10-, and 20-story) equipped with shear walls. The primary objective is to minimize the total structural weight while satisfying strength, serviceability, and seismic design requirements according to relevant building codes. Decision variables include frame member cross-sections as well as the location and thickness of shear walls. Comparative results against several established metaheuristic algorithms (HHO, AOA, and GWO) demonstrate the superiority of the U-PO, confirming that the incorporation of L&eacute;vy flights leads to markedly improved convergence behavior and solution quality. The U-PO consistently yields superior designs featuring notable reductions in structural weight through more efficient sizing and strategic placement of steel shear walls.</span></span>&nbsp; Steel shear walls, Metaheuristic optimization, Puma Optimizer, Lévy flight, Structural weight minimization 375 403 http://ijoce.iust.ac.ir/browse.php?a_code=A-10-6619-2&slc_lang=en&sid=1 R. Sepehri rezasepehri135@gmail.com 180031947532846003394 180031947532846003394 No Department of Civil Engineering, Mah.C., Islamic Azad University, Mahabad, Iran H. Azizian hadi.azizian@iau.ac.ir 180031947532846003395 180031947532846003395 Yes Department of Civil Engineering, Mah.C., Islamic Azad University, Mahabad, Iran R. Sojoudizadeh Reza.Sojoudizadeh@iau.ac.ir 180031947532846003396 180031947532846003396 No Department of Civil Engineering, Mah.C., Islamic Azad University, Mahabad, Iran S. Salehian sasan.salehian@iau.ac.ir 180031947532846003397 180031947532846003397 No Department of Civil Engineering, Mah.C., Islamic Azad University, Mahabad, Iran