# Hybrid Arctic Puffin Algorithm for Solving Design Optimization Problems
## 10 Conclusions  
The Hybrid Arctic Puffin Optimization with JADE (APO-JADE) algorithm, developed in this study, marks a significant advancement in the field of engineering optimization. By \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Optimizer** & **Mean** & **Std** & **Min** & **Max** & **Time** & **Rank** \\ \hline APO-JADE & 0.534044 & 0.008255 & 0.525769 & 0.546293 & 0.346536 & 1 \\ GWO & 0.536622 & 0.008531 & 0.526281 & 0.546226 & 0.314501 & 2 \\ SMA & 0.537747 & 0.001538 & 0.537059 & 0.540499 & 0.495669 & 3 \\ WSO & 0.538528 & 0.009277 & 0.53 & 0.550827 & 0.265397 & 4 \\ WOA & 0.543474 & 0.012613 & 0.53 & 0.56027 & 0.317191 & 5 \\ COOT & 0.549901 & 0.009018 & 0.537059 & 0.560148 & 0.326915 & 6 \\ ChOA & 0.55487 & 0.047682 & 0.530858 & 0.640035 & 0.592802 & 7 \\ MVO & 0.556714 & 0.009149 & 0.543846 & 0.569722 & 0.311267 & 8 \\ CSA & 0.575204 & 0.044916 & 0.537059 & 0.626842 & 0.311805 & 9 \\ HGS & 0.632534 & 0.134272 & 0.537059 & 0.831176 & 0.323582 & 10 \\ SCA & 0.728357 & 0.085562 & 0.626873 & 0.850079 & 0.309534 & 11 \\ OOA & 0.91252 & 0.127154 & 0.774379 & 1.106128 & 0.597909 & 12 \\ MFO & 0.959623 & 0.632534 & 0.600415 & 2.087053 & 0.294518 & 13 \\ BWO & \(2\times 10^{19}\) & \(4.47\times 10^{19}\) & 0.868333 & \(1\times 10^{20}\) & 0.400448 & 14 \\ DBO & \(3.6\times 10^{20}\) & \(4.93\times 10^{20}\) & 0.668876 & \(9\times 10^{20}\) & 0.341972 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistical results of planetary gear train design optimization problem. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Optimizer** & **BestF** & **x1** & **x2** & **x3** & **x4** & **x5** & **x6** & **x7** \\ \hline APO-JADE & 0.525769 & 35.4056 & 26.09467 & 24.50622 & 24.49569 & 22.16595 & 87.27599 & 0.552916 \\ GWO & 0.526281 & 37.08876 & 22.04243 & 19.60519 & 24.06343 & 24.83011 & 86.85415 & 0.56138 \\ SMA & 0.537059 & 51.89215 & 31.39729 & 13.51 & 16.81067 & 13.73118 & 62.34633 & 3.35882 \\ WSO & 0.53 & 46.92745 & 28.58478 & 23.84963 & 27.74762 & 29.71729 & 99.81658 & 1.411459 \\ WOA & 0.53 & 38.56415 & 28.43977 & 24.66321 & 24.89985 & 24.16159 & 91.37937 & 0.855906 \\ COOT & 0.537059 & 23.58742 & 14.1981 & 13.71687 & 16.68069 & 13.70893 & 61.84528 & 0.539953 \\ ChOA & 0.530858 & 48.29306 & 31.82713 & 27.43576 & 28.66665 & 23.84089 & 105.0577 & 1.600849 \\ MVO & 0.543846 & 49.22918 & 25.86212 & 19.25218 & 25.73422 & 21.99729 & 94.81407 & 0.810171 \\ CSA & 0.537059 & 21.18168 & 13.80307 & 16.30397 & 17.26642 & 16.06311 & 61.69202 & 1.4666052 \\ HGS & 0.537059 & 39.33023 & 22.72602 & 13.51 & 16.51 & 13.51 & 62.28936 & 0.9005 \\ SCA & 0.626873 & 16.51 & 13.51 & 25.04317 & 23.41888 & 13.51 & 80.32202 & 0.766665 \\ OOA & 0.774379 & 34.26634 & 24.48169 & 24.44834 & 26.08502 & 22.86613 & 79.74747 & 1.188417 \\ MFO & 0.600415 & 28.44194 & 16.78863 & 13.51 & 16.51 & 13.51403 & 58.92139 & 0.51 \\ BWO & 0.868333 & 16.51 & 13.89767 & 13.51 & 16.99064 & 13.51 & 65.36427 & 0.51 \\ DBO & 0.668876 & 26.09791 & 15.68695 & 13.51 & 16.51 & 13.51 & 55.76995 & 0.553839 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of planetary gear train design optimization problem. combining the unique exploration strategies of the Arctic Puffin Optimization (APO) with the adaptive and evolutionary characteristics of the JADE algorithm, APO-JADE addresses critical limitations found in traditional optimization methods. Our extensive testing on benchmark functions demonstrates that APO-JADE significantly outperforms existing algorithms in terms of convergence speed, accuracy, and computational efficiency. Moreover, when applied to real-world engineering problems, APO-JADE consistently delivered superior solutions, highlighting its ability to effectively navigate and optimize complex, multimodal design spaces. This capability is crucial for engineering applications where design parameters are hainterdependent and optimal solutions are difficult to delineate using standard methodsgibly.