## 3 Experiment and Application
### Engineering Application: Multi-UAVs Cooperative Path Planning  
At present, the research methods used for path planning can be divided into the following categories: methods based on graph theory, methods based on potential field, search algorithms based on heuristic information, and algorithms based on swarm intelligence optimization. The results show that the swarm intelligence algorithm has obvious advantages in processing high-dimensional and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Functions** & **APO Versus GWO** & **APO Versus WOA** & **APO Versus PSO** & **APO Versus DE** \\ \hline \(f_{1}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{2}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{3}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{4}\) & 0.0039 & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{5}\) & 6.6392 \(\times 10^{-4}\) & 0.1156 & 8.4661 \(\times 10^{-6}\) & 0.0018 \\ \hline \(f_{6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 5.7517 \(\times 10^{-6}\) & 1.6046 \(\times 10^{-4}\) \\ \hline \(f_{7}\) & 2.4118 \(\times 10^{-4}\) & 1.6046 \(\times 10^{-4}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{8}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{9}\) & 1.7224 \(\times 10^{-6}\) & 1 & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{10}\) & 1.6521 \(\times 10^{-6}\) & 0.0623 & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{11}\) & 0.5000 & 0.1250 & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{12}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 0.0132 & 5.2165 \(\times 10^{-6}\) \\ \hline \(f_{13}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 2.1266 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{14}\) & 0.5440 & 0.0519 & 0.2059 & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{15}\) & 0.0859 & 4.1955 \(\times 10^{-4}\) & 0.0028 & 0.0859 \\ \hline \(f_{16}\) & 1.0570 \(\times 10^{-6}\) & 0.0786 & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{17}\) & 8.9443 \(\times 10^{-6}\) & 6.9838 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{18}\) & 1.9209 \(\times 10^{-6}\) & 1.4936 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{19}\) & 0.8936 & 0.5577 & 1.7344 \(\times 10^{-6}\) & 1.7344 \(\times 10^{-6}\) \\ \hline \(f_{20}\) & 0.5038 & 0.2134 & 0.0285 & 0.8130 \\ \hline \(f_{21}\) & 0.0013 & 1.8910 \(\times 10^{-4}\) & 0.0449 & 0.0018 \\ \hline \(f_{22}\) & 0.0300 & 1.7344 \(\times 10^{-6}\) & 0.6435 & 3.1123 \(\times 10^{-5}\) \\ \hline \(f_{23}\) & 0.0350 & 5.2165 \(\times 10^{-6}\) & 0.0571 & 0.0350 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The results of Wilcoxon signed ranks test based on the solution for each benchmark with 30 independently runs.  
multi-constraint challenges. The novel proposed APO can then be used to solve the problem on multi-UAVs cooperative path planning to further verify the algorithm's effectiveness. In this part, we will cite the model in reference [71] and the algorithms involved to verify algorithm performance.