## 5 Simulation Results
### Cluster Performance for Static Networks
#### 5.2.2 Performance Evaluation  
In this part, we verify whether the clustering algorithm can meet the three goals defined in the structured clustering problem through the following performance indicator: cluster count, the average number of clusters for UAVs in the same group, and the total inter-cluster communication correlation. In addition, we add the load balance indicator, defined as the ratio of UAV numbers in the smallest cluster to the average UAV numbers in all clusters:  
\[LB=\min_{k\in\mathcal{K}}n_{k}\bigg{/}\bigg{(}\frac{N}{K}\bigg{)} \tag{14}\]  
In a given task area, the larger the swarm size, the more difficult to partition the UAV swarm. We compare the clustering effects under different sizes of the UAV swarm. The number of UAVs in each task group is in \([1,3]\). The scale of the UAV swarm varies between 25, 50, 75, and 100. Figure 6 displays the cluster numbers under different swarm sizes. The number of clusters in our algorithm is slightly higher than the COG algorithm and significantly less than the CMPOG algorithm. The clustering load balance of each algorithm is exhibited in Figure 7. Although our algorithm has slightly more clusters, the number of UAVs for each cluster is more balanced, which avoids the generation of small clusters. Figure 5: The number of iterations under different scales of the UAV swarm for our algorithm and the comparison algorithms. Figure 6: The number of clusters for the final clustering structure under different scales of the UAV swarm. Figure 8 shows the average number of corresponding clusters for UAVs belonging to the same task group. When the swarm size is 25 and 50, both our algorithm and the comparison algorithm can divide the UAVs in the same task group into one identical cluster. When the swarm size increases, the UAVs are distributed too densely, and occasionally the UAVs of the same task group are divided into different clusters. Compared with the COG and CMPOG algorithms, there are fewer UAVs belonging to the same task group divided into different clusters in our algorithm. The total inter-cluster communication link correlation is indicated in Figure 9. Our algorithm has the smallest total inter-cluster communication link correlation compared with the comparison algorithm under different swarm sizes. Additionally, our algorithm has more advantages in terms of the total inter-cluster communication link correlation with the increased swarm size. Figure 8: The average number of clusters corresponding to one group under different scales of the UAV swarm. Figure 7: The clustering load balance for the UAV swarms with different scales. Figure 9: The total inter-cluster communication link correlation for the UAV swarm with different numbers of UAVs. Next, we compare the clustering performance under different group numbers of the UAV swarm. The number of UAVs is fixed as \(N=50\), while the group number is set as \(5,10,15,20\), and \(30\). The group size will be smaller when more groups are in the swarm. Figure 10 displays the cluster numbers under different numbers of groups. The clustering load balance of each algorithm is shown in Figure 11. Our algorithm divides the swarm into fewer clusters and has the best load balance. In addition, Figure 11 illustrates that load balance increases when the group numbers reduce (i.e., each task group contains more UAVs). As UAVs belonging to the same group tend to be divided into the same cluster, each cluster may contain only one task group when the group numbers are small. Thus, the number of UAVs in each cluster is more balanced. Our algorithm also has better load balance than COG and CMPOG. Figure 12 exhibits the average number of corresponding clusters for UAVs belonging to the same task group under different group counts. When there are more groups, UAVs in the same task group may appear in different clusters. However, only one group is assigned to different clusters on average when the group count is \(30\).