## 3 Results
This synergy improves the fidelity and computational efficiency of the optimization process. COMSOL's advanced meshing capabilities generate high-quality finite element meshes that accurately represent the intricate details of the imported design domain. Its powerful FEM solver then facilitates precise simulations of structural behavior under various loading conditions. Figure 2: The design domain for a pillar. In Figure 4, the computer modeling for topology optimization is presented, with a pillar simulated for two cases; the first case is with central mass (as shown in Figure 4a) and the second case is with mass on the far side of the pillar as shown in Figure 4b). Topology optimization endeavors to minimize the volume of the design while concurrently improving the structure dynamic stability addressing the reduction in the natural frequency. The Young moduli of elasticity and mass are standardized to unity, with a Poisson ratio set at 0.3 to maintain consistency across analyses. The results are depicted in Figure 5. Topology optimization gave a result of an elongated hollow pillar. In the three-dimensional perspective (a), the pillar exhibits distinct vertical and horizontal striations, oriented along the \(z\)-axis. The cross-sectional profile (b) provides a detailed view of the internal structure. From the frontal view (c), the pillar reveals a symmetrical narrowing towards the bottom, maintaining alignment with the \(z\)-axis. The rear view (d) highlights a concentric circular design centered on the \(z\)-axis. The top view (e) emphasizes the striated texture and the tapering shape towards each end. Finally, the side view (f) within a bounding box illustrates the uniform width of the pillar and its tapered ends, providing a comprehensive understanding of the structure's geometry. Figure 4: Topology optimization designs of central mass shown from multiple perspectives: (**a**) isometric projection of the design, (**b**) middle-section view, (**c**) front view, (**d**) rear view, (**e**) top view, and (**f**) side view. Figure 3: The computer vision-based design domain includes the following configurations: (**a**) a pillar with a central mass, and (**b**) a pillar with an eccentric mass, where the center of gravity is positioned on the left side of the top surface. Our investigation reveals a significant reduction in the volume of the design domain, a central goal in our comprehensive optimization framework. Notably, this volume reduction demonstrates a clear spatial pattern, with the most pronounced decreases occurring towards the central region of the design domain and gradually tapering towards the periphery near the structural constraints. This deliberate spatial distribution of volume reduction is strategically designed to enhance the stability of the resulting structure while also optimizing the utilization of materials. This approach, rooted in optimization principles, parallels strategies seen in civil engineering where minimizing weight often involves incorporating hollow structures within solid frameworks. Figure 5 illustrates the convergence pattern of our optimization algorithm across multiple iterations. The \(x\)-axis tracks the iteration count, while the \(y\)-axis represents the value of the eigen frequency. Initially, the objective function value starts near 1, indicating suboptimal conditions at the outset. As iterations progress, there is a sharp decline in the objective function value, signaling rapid convergence towards an optimal solution. By around the 50 th iteration, the curve begins to plateau, approaching a value close to zero, indicating diminishing returns from subsequent iterations. This plateau suggests that the algorithm has effectively maximized the objective function and is nearing its optimal value. The steep initial descent followed by the leveling off underscores the efficiency and stability of the algorithm in achieving optimization. Such behavior is highly desirable in optimization techniques, showcasing both computational efficiency and robustness in achieving convergence.