## 3 Utilized Design Optimization Algorithms
### Grey Wolf Optimizer (GWO)
Table 6 reports the optimized mounts' position and orientation where the engine mounts at these positions and orientations largely contribute towards minimizing transmitted forces and isolating mechanical vibrations considering shaking loads only. Likewise, Tables 7-9 report the optimal design variables, optimized objective function, and mount stiffness along each axis for the 12-DOF model when considering the combined shaking loads and road forces for various optimization strategies. Table 10 reports the optimized mounts' position and orientation considering combined loads. It is worth noting that because the goal function values are directly proportional to the design variables, the lower objective function values indicate a better overall isolation system. Lower damping and stiffness values, on the other hand, will aid in accomplishing this goal. The amount of damping and stiffness of a vehicle has a direct impact on its handling and maneuverability. High damping and stiffness rates can result in low vibration transmission at low frequencies, resulting in poor performance at higher frequencies. Low damping and stiffness rates, on the other hand, will result in low noise but significant vibration transmission. Finding the best damping and stiffness parameters for the engine mounts can assist in reducing vibration transmission without sacrificing handling and agility. The GWO method, as shown in Tables 3 and 7, delivers the lowest values of the objective function, i.e., transmitted loads. The related values of the improved design variables, such as mount stiffness, position, and orientation, are shown in Tables 3 and 6 when only shaking loads are considered and in Tables 7 and 10 when combined loading is considered. Figure 14: SQP-optimized mode shapes 7–12 (12-DOF model–combined loading). After around 100 iterations, GWO converged to the global optimum solution, which was significantly less than the 1000 iterations chosen as the stopping condition. This demonstrates that GWO had a fast convergence rate for this particular application PMS, which means less computing time and expense, as well as optimum outcomes with limited computational resources. The outcomes of the PMS application demonstrate GWO's exploration ability. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Opt. Algorithm** & **Load Trans. (lb.)** & **Number of Iterations** & \multicolumn{2}{c}{**Optimized Mount Stiffness (lb./in)**} \\ \hline  & & & \(\mathbf{K_{x}}\) & \(\mathbf{K_{y}}\) & \(\mathbf{K_{z}}\) \\ \hline GWO & 92.9407 & 100 & 100 & 100 & 500 \\ GA & 288.0116 & 200 & 1500.657 & 1500.657 & 500 \\ SQP & 434.3781 & 76 & 1264.616 & 1264.616 & 2135.474 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimized mounts’ stiffness (12-DOF model—combined loading). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Opt. Algorithm** & \multicolumn{5}{c}{**Natural Frequencies (HZ)**} \\ \hline GWO & 1.5034 & 8.4261 & 10.7094 & 15.4325 & 20.9817 & 36.4454 \\ (Un-Damped) & 41.4712 & 71.2310 & 103.2026 & 104.7980 & 200.5963 & 1271.338 \\ \hline GWO & 1.4179 & 8.4167 & 10.7086 & 15.3437 & 20.9767 & 36.3291 \\ (Damped) & 41.2907 & 70.7991 & 103.1668 & 104.7911 & 198.4041 & 1270.326 \\ \hline GA & 1.5205 & 9.8706 & 10.5851 & 12.2400 & 21.6985 & 31.4408 \\ (Un-Damped) & 37.3987 & 81.8021 & 103.0300 & 104.3988 & 200.5693 & 1271.372 \\ \hline GA & 1.4506 & 9.8058 & 10.5762 & 12.2377 & 21.6925 & 31.3493 \\ (Damped) & 37.2482 & 80.9966 & 102.9962 & 104.3956 & 198.378 & 1270.352 \\ \hline SQP & 1.426 & 8.9260 & 10.0566 & 11.3306 & 22.3357 & 36.9528 \\ (Damped) & 43.7704 & 79.2452 & 102.9955 & 104.4396 & 198.4062 & 1270.352 \\ \hline SQP & 1.5001 & 8.9318 & 10.1301 & 11.3319 & 22.3410 & 37.1080 \\ (Un-Damped) & 43.9998 & 79.9703 & 103.0294 & 104.4435 & 200.5984 & 1271.371 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Optimization results of natural frequencies (12-DOF model—combined loading).