## 5 D MMAEO for Engineering Application Problems
### Results and Analysis of DMMAEO on Engineering Application Problems
\begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Best** & **Ave.** & **Worst** & **Std.** \\ \hline EO & 8.412698 & 100.6675 & 167.4727 & 79.30246 \\ PSO & 8.412698 & 128.08544 & 230.0218 & 84.22322 \\ GWO & 8.412698 & 129.60275 & 215.5009 & 73.23548 \\ HHO & 8.422038 & 276.9406 & 653.4973 & 121.4145 \\ SMA & 8.412698 & 110.9658 & 181.5428 & 75.01844 \\ MPSO & 8.412698 & 78.45850 & 167.4727 & 79.70457 \\ MELGWO & 8.412698 & 91.12391 & 167.4727 & 80.27315 \\ LWMEO & 8.412698 & 45.048660 & 167.4728 & 67.24763 \\ SASS & 8.412698 & 24.341897 & 167.4727 & 47.71793 \\ DMMAEO & **8.412698** & **11.59390** & **167.4727** & **22.49449** \\ \hline \end{tabular}
\end{table} 
Table 20: Results for compared algorithms across reinforced concrete beam design (EA6). \begin{table}
\begin{tabular}{c c c c} \hline
**Algorithm** & **Best** & **Ave.** & **Worst** & **Std.** \\ \hline EO & 359.2080 & 359.8164 & 362.2500 & 1.229154 \\ PSO & 359.2080 & 360.5407 & 362.6340 & 1.586392 \\ GWO & 359.2080 & 360.3118 & 362.6502 & 1.426005 \\ HHO & 359.2080 & 361.10553 & 373.4700 & 3.028778 \\ SMA & 359.2080 & 359.8932 & 362.6340 & 1.384313 \\ MPSO & 359.2080 & 359.4696 & 362.6340 & 0.897198 \\ MELGWO & 359.2080 & 359.7776 & 362.6340 & 1.229518 \\ LWMEO & 359.2080 & 359.3307 & 362.2500 & 0.596149 \\ SASS & 359.2080 & 359.2222 & 362.6340 & 0.614986 \\ DMMAEO & **359.2080** & **359.2080** & **359.2080** & **3.5838 \(\times\) 10\({}^{-6}\)** \\ \hline \end{tabular}
\end{table} 
Table 21: Results for compared algorithms across UGV multi-target path planning (EA7). DMMAEO outperforms the compared algorithms in terms of minimizing the fabrication cost of the pressure vessel based on the results from Table 17. As per the results of the tubular column design (EA4) from Table 18, the DMMAEO exhibits a superior performance compared to the other algorithms in designing a uniform column of the tubular section to carry a compressive load at minimum cost. Regarding the piston lever design (EA5), the DMMAEO achieves the strongest performance in minimizing the oil volume when the lever of the piston is lifted up from 0\({}^{\circ}\) to 45\({}^{\circ}\) compared to the other algorithms based on the results from Table 19. Regarding the reinforced concrete beam design (EA6), the DMMAEO outperforms the compared algorithms in terms of minimizing the total cost of the structure based on the results from Table 20. As per the results of UGV multi-target path planning problem (EA7) in Figure 11 and Table 21, the compared algorithms generate feasible paths in different types and the DMMAEO performs better in obtaining the shortest path compared to other algorithms. Therefore, the DMMAEO outperforms other compared algorithms and obtains the top rank in all seven engineering application problems. These results mean that the DMMAEO is superior to other compared algorithms and exhibits the most competitive overall performance within the compared algorithms for addressing engineering application problems. Based on the aforementioned results, it can be seen that the DMMAEO efficiently solves the engineering application problem by constructing dynamic multi-population mutation architecture. In the UGV multi-target path planning problem (EA7) especially, the dynamic multi-population mutation architecture in the DMMAEO could effectively deal with the problems caused by various obstacles, multi-stage optimization, and numerous local optima through enhancing population diversity and search ability, which makes the DMMAEO more suitable for the UGV multi-target path planning problem. To summarize, the results and analysis mentioned above indicate that the proposed DMMAEO has practicability and competitiveness in solving engineering application problems.