## 6 Numerical Simulation and Analysis
### MUCS Based on CPIO Algorithm  
The region \(R\) consists of \(50\times 50\) cells, the center of every cell is the allowed waypoint. And the setting of the coordinate system of \(R\) is consistent with Figure 9a. The starting positions, i.e, the locations of starting airports, and orientations of the four UAVs are as follows. \(UAV_{1}\): [(1, 20), 2] where (1, 20) is the position, and 2 is the orientation, \(UAV_{2}\): [(20, 50), 4], \(UAV_{3}\): [(27, 1), 0], \(UAV_{4}\): [(50, 26), 6]. No-fly zones: \(5\leq x\leq 20\), \(30\leq y\leq 40\) and \(30\leq x\leq 40\), \(5\leq y\leq 15\). Known region: \(30\leq x\leq 45\), \(20\leq y\leq 28\), where \(P_{e}^{m,n}(k)=0\), \(\chi_{e}^{m,n}(k)=0\). Generating 5 randomly distributed targets shown in pink stars in each key region: \(5\leq x\leq 24\), \(10\leq y\leq 25\) and \(25\leq x\leq 45\), \(30\leq y\leq 35\), where \(P_{e}^{m,n}(k)=0.9\), \(\chi_{e}^{m,n}(k)=0.9\). Other cells are non-key regions, where \(P_{e}^{m,n}(k)=0.5\), \(\chi_{e}^{m,n}(k)=0.5\). The other simulation parameters are listed in Table 1.  
Figure 5: Cause for the remaining range. **Scenario 1:** Search for the best \(N_{p}\)  
The advantages of \(N_{p}\)SAP are discussed in Section 3.1. If \(N_{p}\) is relatively large, the benefits of \(N_{p}\)SAP will be limited or even negligible. In contrast, the number of alternative paths will increase exponentially. Figure 6 shows the simulation results and error analysis with different values of \(N_{p}\). In Figure 6a, the running time \(T_{a}\) of the personal computer increases with the increase of \(N_{p}\). When \(N_{p}=7\) and the time steps of the search is 100, the computation time is \(T_{a}=121.7\) s. Combined with the actual search process, it do not meet the requirements of the real-time search task. Figure 6b shows that if \(N_{p}=1\) or \(2\), the average fitness value, average rewards for the search process, decreases gradually in the later stages of the search, this is because one or two time steps in advance cannot effectively avoid obstacles or continue to search within the key region. When \(N_{p}=4\), UAV has enough time to make obstacle avoidance and continue to search in the key regions. However, the increase of \(N_{p}\) will not significantly improve the rewards. In Figure 6c, when \(N_{p}\leq 4\), the number of targets found out is less instead. When \(N_{p}=5\) to \(7\), the number of targets found out are the same. Based on the above analysis, we choose \(N_{p}=5\) as the best prediction steps. Figure 7 shows the search trajectories of four UAVs when \(N_{p}=5\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Description** & **Value** \\ \hline \(P_{P}^{m,n}(k)\) & Detection probability of the UAV sensor to the goal. & 0.9 \\ \(P_{P}^{m,n}(k)\) & False alarm rate. & 0.1 \\ \(\omega_{1},\omega_{2},\omega_{3},\omega_{4}\) & Weight factor of fitness function \(J_{1}\). & 0.3, 0.3, 0.3, 0.1 \\ \(M\) & Number of UAVs (subgroups). & 4 \\ \(C_{1}\) & Initial number of pigeons in every subgroup. & 40 \\ \(R_{p}\) & Coefficient of the map and compass operator. & 0.5 \\ \(N_{c1},N_{c2}\) & Number of iterations of Operation 1 and Operation 2 in the CPIO algorithm. & 25, 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters in MUCS. Figure 6: Error analysis for different values of \(N_{p}\): (**a**) Running time; (**b**) Average fitness value; (**c**) Number of targets found. **Scenario 2:** Searching performance of CPIO  
To demonstrate the effectiveness of CPIO, comparative experiments are conducted with identical initial conditions. The searching performance of CPIO is compared to the basic PIO, particle swarm optimization (PSO), and GA. In Figure 8a, The convergence speed of the CPIO algorithm is faster than the basic PIO, PSO and GA. And the standard deviations of 100 experiments are also the smallest. Figure 8b shows that when the searching time step is 100, the average number of targets found out by CPIO is 9.6, which is more than the other three algorithms.