## 3 Method
### Procedures of AOQPIO
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **AOQPIO** & **PIO** & **QPIO** & **PSO** \\ \hline \(N_{p}\) & 150 & 150 & 150 & 150 \\ \(D\) & 30 & 30 & 30 & 30 \\ \(N_{c1\max}\) & 150 & 150 & 150 & 200 \\ \(N_{c2\max}\) & 200 & 200 & 200 & — \\ \(w\) & 0.8 & — & — & — \\ \(s\) & 0.5 & — & — & — \\ \(a\) & 1 & — & — & — \\ \(b\) & 100 & — & — & — \\ \(q\) & 0.5 & — & 0.5 & — \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters used in experiments of different algorithms. Figure 2: The image of the 3D undulating terrain environment. Figure 4: (**a**) is the result of all algorithms and (**b**) is the result of optimal UAV altitude of the experiment carried out in map 2. Figure 3: (**a**) is the result of all algorithms and (**b**) is the result of optimal unmanned aerial vehicle (UAV) altitude of the experiment carried out in map 2. Figure 5: (**a**) is the result of the experiment and (**b**) is the result of optimal UAV altitude of the experiment carried out in map 3. Figure 6: The comparative curves of iteration of the algorithms of the experiment carried out in map 1. Figure 7: The comparative curves of iteration of the algorithms of the experiment carried out in map 2. The curve of the cost iteration in map 1 shows that our algorithm convergences at the eighth iteration and the convergence value is 73.8954, which is lower than the convergence value of other algorithms. Similar experiment results obtained on the above three test scenarios verify that the performance of AOQPIO is independent of changed battlefield environments that mainly mean different enemy threats. Clearly, the modifications provided in this paper had a positive effect on AOQPIO. To avoid the influence of random initial values, another 40 experiments in each map were carried out and the average values of path length, cost, and searching time were calculated. The statistical results are listed in Table 2. From the results in map 1, the path generated by AOQPIO is 5.9% lower than those of other algorithms, and cost decreases by at least 0.4% separately. Similar to the experiment carried out in map 1, our algorithm also has the best efficiency and can generate the shortest path in the experiments carried out in map 2 and map 3. Comprehensively comparing the statistical data of all algorithms on the three maps, AOQPIO still shows its superiority to other algorithms in terms of searching ability and efficiency. From the experiment results showed above, we can see that AOQPIO is significantly superior to other swarm-intelligence algorithms tested in this paper. The chaotic strategy indeed can improve the global search ability of the basic QPIO. Furthermore, the adaptive operator strategies help the AOQPIO to search more fully and carefully. With the adaptive compression factor, a smoother path can be generated by AOQPIO. In a word, the proposed AOQPIO has the advantage over the conventional QPIO, as well as PSO and PIO algorithms in terms of searching ability, stability, and robustness. ## 5 Conclusions

The AOQPIO algorithm for UAV path planning in 3D undulating terrain was proposed in this paper. Various improvements have been incorporated into conventional QPIO algorithms to ensure the convergence rate and avoid local optimum. By utilizing logistic mapping method, the introduced pigeon population initialization procedure improved the diversity of population and the ergodicity of