## 5 Experimental Simulation Analysis
### Analysis of Results  
The path planning of the UAV needs to bypass the threat area from the coordinates of the starting point and fly to the coordinates of the target point. Considering the randomness of the heuristic algorithm, every tested algorithm was independently executed 30 times, and the experimental results were used to evaluate and compare its performance. For the comfort of comparison, Figures 4-7 exhibit the top view and fitness function value curves of the optimal UAV paths generated by using the PSO algorithm, the VAINDIWPSO algorithm, and the IC-VAINDIWPSO algorithm in 30 independent runs, respectively. To visualize the differences between the tested algorithms, Table 5 shows the data results of the three algorithm runs. According to Figures 4-6, all three algorithms can generate feasible paths that meet the necessities of path length, threat, turn angle, climb/dive angle, and altitude. However, the PSO algorithm is susceptible to falling into the local optimum and cannot locate an optimal solution. The VAINDIWPSO algorithm introduces improved nonlinear dynamic \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Algorithm** & **Inertia Weight** & \(\mathbf{\omega}\)**(1)** & \(\mathbf{\omega}_{\text{max}}\) & \(\mathbf{\omega}_{\text{min}}\) & \(\mathbf{\omega}_{\text{damp}}\) \\ \hline PSO algorithm & \(\omega(k+1)=\omega(k)*\omega_{\text{damp}}\) & 1 & - & - & 0.98 \\ VAINDIWPSO algorithm & \(\omega(k+1)=(\omega(k)-\omega_{\text{min}})\times(\frac{\omega_{\text{min}}}{ \omega_{\text{min}}})\frac{12^{2}}{\text{max}^{2}}+R(k)\) & 1 & 0.9 & 0.4 & - \\ IC-VAINDIWPSO algorithm & \(\omega(k+1)=(\omega(k)-\omega_{\text{min}})\times(\frac{\omega_{\text{min}}}{ \omega_{\text{max}}})\frac{12^{2}}{\text{max}^{2}}+R(k)\) & 1 & 0.9 & 0.4 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The inertia weight formula and parameters of the three algorithms. Figure 4: Top view of the path generated by the PSO algorithm. Figure 3: 3D terrain environment. inertia weight and interferes with the velocity, the convergence algebra is decreased by 44.3%, the fitness function value is additionally reduced, and a better path than the PSO algorithm is obtained. The IC-VAINDIWPSO algorithm, which introduces chaos theory and adaptively adjusts the velocity, can precisely acquire near-optimal solutions. The iterative convergence of the PSO algorithm is very slow. So the number of iterations is chosen to be 1000, and the number of iterations of the VAINDIWPSO algorithm and the IC-VAINDIWPSO algorithm is chosen to be 500 times. The IC-VAINDIWPSO algorithm performs a chaotic initialization operation. So 1000 particles are generated in the course of initialization. Then 500 particles with low fitness function values are chosen as the initial population, and the initial population of the other two algorithms is also additionally chosen as 500. According to the combination of Table 5 and Figure 7, it can be seen precisely and intuitively that the iterative convergence times of the VAINDIWPSO algorithm are smaller than those of the PSO algorithm, and the average fitness value is additionally decreased a lot, which indicates that the VAINDIWPSO algorithm has relatively proper performance. However, the number of iterative convergences is nonetheless large. Therefore, we introduced chaos theory and adaptively adjusted the velocity to structure the IC-VAINDIWPSO algorithm. The iteration convergence times of the IC-VAINDIWPSO algorithm are 20, the initialization running time is 0.644 s, and the average fitness value is 5575.7793. Compared with the preceding two algorithms, the iterative convergence times of the IC-VAINDIWPSO algorithm are a whole lot smaller than the other two algorithms, and the average fitness is additionally the lowest. The IC-VAINDIWPSO initialization r  
Figure 5: Top view of the path generated by the VAINDIWPSO algorithm. Figure 6: Top view of the path generated by the IC-VAINDIWPSO algorithm. Additionally noticeably reduced, which is shorter than the PSO algorithm.