## 3 Method
### Procedures of AOQPIO
]\), the same to \(V_{i}\) Calculate fitness values of different pigeon individuals with cost function, using the real coordinate transformed by the position value in solution space according to Equation (27);
9 Set \(X_{pi}=X_{i}\), \(X_{g}=\text{argmin}[calculate\_fitness(X_{pi})]\); /*Map and compass operations with quantum-behavior*/
10 for\(N_{c}=1\):\(N_{c1\text{max}}\)
11 Generate parameter \(\varphi\), \(\varepsilon\), \(m\);
12 Update parameter \(R\) according to Equations (22) and (23);
13 Sum the \(X_{pi}(i)\) for each \(i\);
14 Calculate m_best according to Equation (15);
15 for\(i=1\):\(N_{p}\)
16 Calculate \(P_{i}\) according to Equation (14);
17 Update \(V_{i}\) according to Equation (11);
18 Update \(X_{i}\) with quantum-behavior according to Equation (10);
19 new_fitness = calculate_fitness (\(X_{i}(N_{c})\));
20
21 If new_fitness < Fitness(\(i\)) then Fitness(\(i\)) = new_fitness; \(X_{pi}\)=\(X_{i}\);
22 endif
23\(X_{g}=\text{argmin}[calculate\_fitness(X_{pi}(N_{c}))]\);
24 endfor
25 endfor
26 /*Landmark operator*/
27 for\(N_{c}=N_{c1\text{max}}+1\):\(N_{c2\text{max}}\)
28 Rank all the available pigeon individuals according to their fitness values;
29 Update the population of pigeon \(N_{p}\) according to Equation (24);
30 Calculate the center of the pigeons \(X_{c}(N_{c})\) according to Equation (18);
31 for\(i=1\):\(N_{p}\)
32 Update \(X_{i}\) according to Equation (26);
33 Evaluate \(X_{i}\), and update \(X_{pi}\) and \(X_{g}\) according to line (16)-(20);
34 endfor
35 endfor
36 /*Output*/
37\(X_{g}\) is output as the global optimal of the fitness function
38 Transform the best solution result into the coordinate of point in real flying space according to Equation (27)
```

**Algorithm 2**AOQPIO Based path planner. ## 4 Results and Discussion

To validate the efficiency of AOQPIO algorithm on UAV path planning problem, the optimization results in 3D environment are presented. The 3D environment containing a complex undulating terrain as shown in Figure 2, can also be found in [42]:

\[z(x,y)=\bigg{|}\sin(x/5+1)+\sin(y/5)+\cos\bigg{(}\alpha*\sqrt{x^{2}+y^{2}}\bigg{)} +\sin(\beta*\sqrt{x^{2}+y^{2}})\bigg{|}, \tag{24}\]

where \(\alpha\), \(\beta\) are constant parameters, and \(z\) represents the altitude of a certain point. Compared with existing swarm-intelligence algorithms, i.e., PIO, QPIO, PSO, we utilized path distance, cost, and altitude variations to evaluate the performance of above algorithms. All of the experiments were conducted by MATLAB 2014a on a PC with 2.4 GHz CPU. The corresponding parameters used in the algorithms are presented in following Table 1.

To verify the generalization ability of the proposed algorithm in different environments, experiments, which were utilized by the mentioned algorithms, were carried out in three maps with different threat sources. The corresponding parameters of the threat sources in the three maps are provided as supplementary in the enclosure. The start coordinates of the planning mission were (18,20,2) and the target coordinates were (90,105,2). Apparently, the planning results calculated by AOQPIO, indicated with a green line in Figures 2(a), 3(a) and 4(a), are smoother than the results of other algorithms. Convergence curves of the cost values in the three scenarios are displayed in Figures 7-8. According to the altitude value in Figures 2(b), 3(b) and 4(b), most of the waypoints generated by our algorithm are lower than those of other algorithms. Further, according to the convergence results of cost function value, our algorithm has the ability of converging more stably and quickly when compared with other three algorithms.