# 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  
#### 4.2.1 Simulation Results in Scenario 1  
Firstly, we set \(P_{m}=1\) and compared the results of MPPWPA with different \(Num\). Since the dimension of the solution space was low, the exact solution of the problem could be obtained using the exhaustive method in 756 s, and the minimum value of the objective function was 28.71. The results of several heuristic algorithms involved in the experiment are shown in Figure 16 and the statistics for the results are shown in Table 4 where the best results are marked in boldface. For four basic algorithms, it is clearly shown that WPA performed better than PSO both in terms of accuracy and convergence speed, performed better than the GA in terms of accuracy, but performed worse than the GA in terms of convergence speed, and the WPA performed worse than the ABC both in terms of accuracy and convergence speed. As an improvement of the WPA, the MPPWPA was improved in terms of both accuracy and convergence speed. For the task assignment problem with an eight-dimensional solution space, when \(Num\) ranged from 2 to 8, the optimization performance gradually improved, but the performance did not continue to improve when \(Num\) was 16. In addition, we found that the larger the \(Num\) was, the more stable the convergence value would be. The results indicated that increasing the number of sub-populations is conductive to exploiting the optimal solution and decreasing the convergence time. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Scenario 1** & **Scenario 2** & **Scenario 3** \\ \hline \(l_{\text{max}}\) & 200 & 400 & 1000 \\ \hline \(N\) & 160 & 160 & 160 \\ \hline \(step_{a}\) & 2 & 2 & 2 \\ \hline \(step_{b}\) & 4 & 14 & 70 \\ \hline \(step_{c}\) & 1 & 1 & 1 \\ \hline \(T_{\text{max}}\) & 10 & 10 & 10 \\ \hline \(d_{near}\) & 2 & 14 & 70 \\ \hline \(\alpha\) & 4 & 4 & 4 \\ \hline \(\beta\) & 5 & 5 & 5 \\ \hline \(h_{\text{min}}\) & 1 & 1 & 1 \\ \hline \(h_{\text{max}}\) & 5 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of WPA in three scenarios. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Meaning** & **Values** \\ \hline \(Num\) & The number of mass sub-populations & 2, 4, 8, 16 \\ \hline \(P_{m}\) & Probability of migration & 1, 0.8, 0.6, 0.4, 0.2, 0 \\ \hline \(\tau\) & Mutation ratio & 20\% \\ \hline \(\Delta I\) & Interval of redundancy removal & 2 iterations in scenario 15 \\  & Interval of redundancy removal & iterations in scenario 25 \\  & & iterations in scenario 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Control parameters of MPPWPA. Then, we compared the influence of different \(P_{m}\) values on the optimization performance. The results are shown in Figure 17 and the statistics for the results are shown in Tables 5 and 6. When \(Num\) was 2, 4 or 8, a larger migration probability was useful to fully search the solution space to obtain the optimal value. Interestingly, when \(Num=16\), a stable optimal value could be obtained without population migration and it could be obtained faster with a small \(P_{m}\) or a large \(P_{m}\). Population migration with medium frequency may have degraded the optimization performance. This indicated that the quadratic optimization of elite-mass population distribution was an invisible population migration. It also suggested that population migration was not always beneficial to the development of sub-populations. In particular, when the population size was very small (10 individuals when \(Num=16\)), the adverse effects of population migration may not have been eliminated by iteration.