## 5 Experiments and Results
### Robustness Evaluation  
We evaluated the optimisation process in terms of accuracy and reliability in the previous section. Now, we also want to address the robustness of HEAs solutions. Having been initially fitted to one particular scenario, now they are tested on a new set of 30 unseen scenarios per case study. To do this, we run the corresponding ARGoS simulations using the calculated swarm configuration and collected data from the formation achieved by the swarm. Table 7 shows the evaluation of the formation through the obtained fitness values, the distance between UAVs (D\({}_{\text{UAV}}\)), and the distance to the rogue drone at the centre (D\({}_{\text{RD}}\)) for all the scenarios in which a successful formation was achieved. It can be seen that the measured D\({}_{\text{RD}}\) was always closer to the desired \(D_{CENTRE}\), i.e., 3 m for 3, 5, and 10 UAVs; 4 m for 15 UAVs; and 5 m for 30 UAVs. The distance between UAVs (D\({}_{\text{UAV}}\)) showed little \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**\# UAVs**} & \multicolumn{4}{c}{**Fitness**} & \multicolumn{4}{c}{**Time (minutes)**} & \multirow{2}{*}{**Converged**} \\ \cline{2-2} \cline{4-7}  & **Mean** & & & & & & & \\ \hline
3 & 2.804 & 0.625 & 1.217 & 13.570 & 0.781 & 15.332 & **100.0\%** \\
5 & 6.770 & 8.245 & 3.833 & 29.429 & 2.185 & 32.924 & 96.7\% \\
10 & 6.033 & 0.370 & 5.348 & 85.214 & 10.352 & 115.564 & **100.0\%** \\
15 & 26.699 & 19.390 & 8.055 & 157.386 & 42.317 & 225.209 & 60.0\% \\
30 & 10.356 & 0.887 & 9.419 & 1188.376 & 91.172 & 1449.161 & **100.0\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results from the optimisation of one new, unseen scenario for each case study. Best values are in bold. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**\# UAVs**} & \multirow{2}{*}{**ARGoS**} & \multirow{2}{*}{**gp\_lin**} & \multirow{2}{*}{**gp\_sexp**} & \multirow{2}{*}{**gp\_nn**} & \multirow{2}{*}{**gp\_m32**} & \multirow{2}{*}{**gp\_m52**} & \multirow{2}{*}{**ann**} & \multirow{2}{*}{**Speed-Up**} \\ \hline
3 & 6.601 & 0.190 & 0.190 & 0.190 & 0.191 & 0.190 & 0.122 & 54.1 \\
5 & 10.169 & 0.191 & 0.191 & 0.195 & 0.190 & 0.191 & **0.124** & 82.0 \\
10 & 24.342 & 0.190 & 0.190 & 0.188 & 0.190 & 0.190 & **0.124** & 196.3 \\
15 & 83.414 & 0.191 & 0.191 & 0.191 & 0.190 & 0.189 & **0.125** & 667.3 \\
30 & 446.939 & 0.189 & 0.194 & 0.193 & 0.191 & 0.192 & **0.124** & 3604.3 \\ \hline
**Mean:** & 114.293 & 0.190 & 0.191 & 0.191 & 0.190 & 0.190 & **0.124** & 920.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average computing times in seconds for the six predictors compared with the corresponding ARGoS simulations (30 testing scenarios). Best values are in bold. variations, representing equally spaced UAVs in the formation, except for the most difficult case, i.e., 30 UAVs, although the variation is still lower than 13%. We have observed that for swarms of 10, 15, and 30 UAVs, there were some formation attempts that failed: 9, 13, and 10. Observing more than 50% successful formations is a good result, as the HEA has optimised only one particular scenario, in contrast to the 30 tested in this section. An increase in the robustness can be easily achieved by optimising not just one but several scenarios in parallel and using the average fitness values obtained to evaluate each swarm configuration, as has been previously observed in [7; 24]. Finally, we present in Figure 7 the final positions achieved by the UAV swarm in all the working formations. Although it is not easy to appreciate how the UAVs are arranged in a virtual sphere, this figure complements the data reported in Table 7, where each colour corresponds to a different scenario. Moreover, each sphere radius is in accordance with the desired distance to the centre, i.e., 3 m for 3, 5, and 10 UAVs; 4 m for 15 UAVs; and 5 m for 30 UAVs.