## 6 Experimental Results
### Factorial Experiment  
To assess the best parameterisation of QLHH-II, an analysis of the sensitivity to its three parameters has been conducted. To this end, four values have been considered for each parameter. The size of the mini-batch can be 16, 32, 48 or 64; the learning rate can be 0.01, 0.05, 0.1 or 0.2; and the embedding dimension can be 8, 16, 24 or 32. The objective is to learn a heuristic for each possible combination. The training is identical to the stability experiment, i.e., on 50 instances from the class (\(20\times 20/10\)) (with a \(20\times 20\) grid graph as an environment and 10 UAVs) with 10 epochs. After the training, the generated heuristic for each parameterisation is executed on 30 instances from the same class. These instances are the same for every heuristic generated. A distribution of 30 solutions is thus obtained and  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Name** & **Notation** & **Value** \\ \hline maximal distance of communication & \(D^{com}\) & 4 \\ \hline exploration rate & \(\epsilon\) & 0.05 \\ \hline discount factor & \(\gamma\) & 0.9 \\ \hline size of movement frame & \(\tau\) & 10 \\ \hline \hline \multicolumn{3}{c}{**Factorial experiment**} \\ \hline \hline learning rate & \(\alpha\) \\ \hline embedding dimension & \(p\) \\ \hline mini-batch size & \(|\mathcal{B}|\) \\ \hline \hline \multicolumn{3}{c}{**Stability experiment**} \\ \hline \hline number of epochs & 10 \\ \hline number of instances & 50 \\ \hline grid width & 20 \\ \hline grid height & 20 \\ \hline number of UAVs & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental parameters used for training QLHH-II.  
the non-dominated solutions are retained so that the Pareto fronts are compared with the three multi-objective metrics presented in Section 5.1.2. The results are depicted in Table 2.  
For each column of Table 2, i.e., for each metric, values are normalised and a colour gradient is used to enhance the quality of a parameterisation according to metrics (the more red the better). By looking at the table, it can be noted that the model is very sensitive to parameterisation. This is shown by the high disparity of values. Among parameters, the size of the batch \(|\mathcal{B}|\) seems to have an impact independently from other parameters. Among the range of values, the bigger is \(|\mathcal{B}|\), the better the results in general. The size of the batch has an impact on the IGD. Selecting fewer elements for the gradient descent indeed enhances the exploration. It is not obvious to analyse the impact of the other two parameters independently according to Table 2. The embedding dimension \(p\) has a direct impact on the size of the searching space (the higher \(p\), the wider the searching space). For a certain learning rate \(\alpha\), the model would struggle to converge with a lower searching space, i.e., a lower \(p\). It is thus relevant to admit that the lower is \(p\), the lower should be \(\alpha\). Among the best five parameterisations, the convergence is observed and at the end, the selected paramterisation is the following: \(|\mathcal{B}|=48\); \(\alpha=0.2\); \(p=32\).