## 6 Experimental Results
### Stability
#### 6.3.2 Testing  
For both WO and the generated heuristics, each UAV has a deterministic behaviour so they are not stochastic as are heuristics \(\Phi\) and \(\Phi\)-K. However, since UAVs move asynchronously, two executions on the same instance may provide two different solutions, which makes these two heuristics non-deterministic. Thus, all heuristics have been executed 30 times per instance, resulting in 30 solutions per instance. These distributions are compared according to their Pareto front using the three MO metrics defined in Section 5.1. A Wilcoxon signed-rank test is then used to assess the statistical significance of the results. The results of the latter test are displayed in three tables, one per MO metric (HV in Table 3, IGD in Table 4 and \(\Delta\) in Table 5). For each table, a cell in dark blue means that the heuristic generated by QLHH-II outperforms the specific heuristic (column name) for the specific instance class (row name) with a 95% confidence. A light-blue cell means that the heuristic generated by QLHH-II provides better results on average but without statistical confidence. According to the HV metric, the heuristic generated by QLHH-II outperforms all pheromone-based heuristics. However, for most of the instance classes, the WO heuristic provides better results with 95% confidence. This is an unexpected result when looking at its results in terms of IGD and \(\Delta\) metrics. It indeed clearly appears that the generated heuristic outperforms WO for every instance class according to IGD and \(\Delta\). While these metrics, respectively, measure the convergence and the diversity of the front, the results in terms of HV values are not similarly competitive with respect to WO. This behaviour can be visualised in Figure 10, which displays the non-dominated solutions for two different instances. It can be observed that, despite a clear lack of diversity in the front of WO, its lowermost point is very distant from the other solutions (including the dominated ones), which in turn drastically increases the value of HV. In terms of IGD, the heuristic generated by QLHH-II outperforms all other heuristics as presented in Table 4. It means that the non-dominated solutions provided by the generated heuristic are closer to the optimal front than other heuristics. This result is particularly good since the front provided by the generated heuristic has more points than other ones for most instances (see Figure 10). This diversity in the Pareto fronts obtained with the QLHH-II generated heuristic is confirmed by the results according to the Spread metric (\(\Delta\)) presented in Table 5. QLHH-II obtained fronts are, in the majority of cases, more diverse than the state-of-the-art heuristics. For some class, heuristic \(\Phi\)-K, however, provides more diverse fronts, but with a 95% confidence only for the class (\(20\times 20/5\)). Figure 9: Evolution of the front during the training according to HV, IGD and \(\Delta\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \multicolumn{1}{c}{**Instance Class**} & \multicolumn{1}{c}{**Heuristic**} & \multicolumn{1}{c}{**Heuristic**} & \multicolumn{1}{c}{**} & \multicolumn{1 Overall, except for some specific cases, the heuristic generated by QLHH-II outperforms the state-of-the-art heuristics according to the three MO metrics. By observing the fronts obtained with different heuristics (see Figure 10, for example), several aspects can be pointed out. First, in terms of convergence of the Pareto front, all of the pheromone-based heuristics are completely outperformed by the generated heuristic. Most of the solutions provided by heuristics \(\Phi\) and \(\Phi\)-K are dominated by solutions from the front of the generated heuristic. Another point is that the WO heuristic provides the best coverage results for every instance. However, it does not seem to consider the connectivity aspect of the swarm while that heuristic has been designed to balance the CCUS3O objectives.