# Multi-Population Parallel Wolf Pack Algorithm for Task Assignment of UAV Swarm
## 4 Experiments of Task Assignment for UAV Swarm Using MPPWPA
### The Results and Analyses of Simulation Experiments
#### 4.2.2 Simulation Results in Scenario 2  
We set \(P_{m}=0.8\) and compared the results of MPPWPA with different \(Num\) values. When the dimension of the solution space in scenario 2 was enlarged to 30, the exhaustive method failed. The results of heuristic algorithms involved in the experiment are shown in Figure 18 and the statistics for the results are shown in Table 7. The WPA clearly performed better than the PSO and GA and had a faster convergence speed compared to ABC. The proposed MPPWPA had obvious advantages both in terms of accuracy and convergence speed, compared with the four basic algorithms. For the task assignment problem with eight-dimensional solution space, the MPPWPA improved the optimization performance both in terms of accuracy and convergence speed. When \(Num\) ranged from 2 to 8, the optimization performance gradually improved, while the convergence speed declined when \(Num\) reached 16. This was because frequent population migration caused great disturbances to small-size sub-populations; it improved the exploitation but reduced the exploration. As shown in Figure 18, the MPPWPA had an excellent convergence speed in the early stage of iteration. This means that it could obtain better values in a short time compared with PSO,  
Then, we compared the influence of different \(P_{m}\) on the optimization performance. The results are shown in Figure 19 and the statistics for the results are shown in Tables 8 and 9. Compared with the results in scenario 1, population migration was necessary to improve the convergence speed and accuracy for the task assignment problem with 30-dimensional solution space. When \(Num=2\) and \(Num=4\), the convergence trends under different \(P_{m}\) were basically the same and there was no significant difference in optimization performance. When \(Num=8\), excluding 0 and 1, a large \(P_{m}\) contributed to ensuring accuracy, while a small \(P_{m}\) contributed to a shortening of convergence time. When \(Num=16\), the algorithm preferred a small \(P_{m}\), but not 0. Compared with the WPA, the MPPWPA could obtain a better solution regardless of the value of \(P_{m}\), which shows that the MPPWPA was robust to \(P_{m}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{\(Num\)} & \multicolumn{2}{c}{**Objective Function Value (m)**} & \multicolumn{2}{c}{**Convergence Time**} \\ \cline{3-6}  & & **Ave.** & **Std.** & **Ave.** & **Std.** \\ \hline PSO & - & 511.8 & 37 & 174.73 & 47.78 \\ GA & - & 330.86 & 30.36 & 21.87 & 4.25 \\ ABC & - & 269.78 & 5.8 & 170.73 & 42.86 \\ WPA & - & 266.3 & 19.48 & 158.83 & 49.29 \\  & 2 & 252.6 & 15.1 & 109.2 & 47.0 \\ MPPWPA & 4 & 257.1 & 19.3 & 72.1 & 24.2 \\
8 & **250.6** & 13.6 & **63.7** & 22.5 \\
16 & 257.2 & 13.5 & 64.9 & 12.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Objective function value and convergence time with different \(Num\) in scenario 2. Figure 19: Average objective function values with different \(Num\) and \(P_{m}\) in scenario 2: (**a**) \(Num=2\); (**b**) \(Num=4\); (**c**) \(Num=8\); (**d**) \(Num=16\). In terms of convergence performance, the algorithm with 16 mass sub-populations performed better, as it could obtain a stable best solution in a shorter time, while the algorithm with two mass sub-populations needed more time to obtain a best solution. In terms of convergence trend, the algorithm with eight mass sub-populations performed better because it converged faster in the early stage, and thus, was found to be suitable for application requirements where a solution is needed in a specified short time such as 10 s or 20 s.  
From Figure 19d, we can see that the optimization performance of the algorithm with 16 mass sub-populations was poor when \(P_{m}=0\), which was different from the performance in scenario 1. The reason is that the optimization abilities of the sub-populations with small sizes are insufficient when the solution space is 30-dimensional; thus population migration is needed to improve the exploration of the solution space.