## 4 Simulation Experiment of IABCBAS Algorithm Path Planning Application
### Comparison Experiment of Three-Dimensional Environment Simulation  
In this section, 3D path planning experiments are conducted on maps constructed from 3D elevation data to derive more comprehensive empirical conclusions and verify the adaptability of the proposed algorithm to real complex environments in 3D path planning. The comparison algorithms remain SSA, ACO3, and BAS3. For experimental data processing, the values in the simulation coordinates are multiplied by ten to convert them to real environment values. The experiment is repeated 30 times, and the average value of each index calculated by each algorithm is recorded to eliminate the interference of random errors. The experimental results are shown in Table 5.  
The results of optimal 3D path planning among different algorithms in the two environments are illustrated in Figure 10. The convergence comparison of different algorithms in these environments is presented in Figure 11. As can be seen from Figures 10 and 11, when path planning in a 3D unimodal simple environment map, the SSA converges to the optimal solution around the 56 th iteration, and the optimal path length is 74.1, which is 32.64% more than the proposed algorithm. The BAS3 and ACO algorithms converge to the optimal solution around the 50 th and 48 th generation, with optimal paths of 67.6 and 64.2, which are 18.73% and 13.57% longer than that of our method. The optimal paths are 67.6 and 64.2, respectively, which are 18.73% and 13.57% more than that of our method. Compared with the SSA, both algorithms exhibit fewer turns; however, their ability to traverse ascending and descending obstacles is weaker. The proposed IABCBAS algorithm converges to the optimal solution at the 42 nd iteration, with a shorter planned path, superior obstacle-traversing capability, and the smoothest and most rational path in this environment.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Environments** & **Method** & \begin{tabular}{c} **Average Path** \\ **Length (m)** \\ \end{tabular} & \begin{tabular}{c} **Average Number** \\ **of Turns** \\ \end{tabular} & \
\begin{tabular}{c} **Average Number** \\ **of Iterations** \\ \end{tabular} &
\begin{tabular}{c} **Average Planning** \\ **Time (s)** \\ \end{tabular} \\ \hline \multirow{4}{*}{\(20\times 20\) 2D simple environment} & SSA & 34.8 & 16.3 & 28.5 & 15.58 \\  & BAS3 & 31.4 & 13.2 & 21.2 & 11.59 \\  & ACO3 & 29.7 & 12.5 & 19.7 & 10.77 \\  & IABCBAS & 26.2 & 9.8 & 11.1 & 6.07 \\ \hline \multirow{4}{*}{\(30\times 30\) 2D complex environment} & SSA & 62.6 & 23.1 & 49.3 & 39.28 \\  & BAS3 & 52.9 & 17.4 & 41.8 & 33.31 \\  & ACO3 & 50.5 & 16.6 & 39.4 & 31.39 \\ \cline{1-1}  & IABCBAS & 44.3 & 12.4 & 30.6 & 24.38 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of average performance of four algorithms in two-dimensional environments.  
As presented in Table 7, our algorithm traverses the fewest grid squares in the simulation map and exhibits the optimal number of turns. The actual path distance is 92.6 m, which is 14.29%, 25.00%, and 35.71% shorter than those of the ACO3 (98.5 m), BAS3 (102.7 m), and SSA (108.3 m) algorithms, respectively. The planning time is 32.34 s, which is 16.14%, 24.86%, 31.14%, and 58.53% shorter than those of the four comparative algorithms, respectively. The proposed IABCBAS algorithm exhibits high efficiency in path planning for mobile target vehicles in real-world environments.