## 3 Results
### GPP Parameter Selection  
The proposed GPP method utilises several parameters which need to be defined by the user prior to the execution of the algorithm. In order to select the parameters configuration which allows to produce the best path in terms of ME, O2E, and PL, a sensitivity analysis was conducted. Such investigation was performed on the data relative to the first geographical area, represented in Figure 4a. Afterwards, the selected parameters configuration was validated on the other two areas considered in this work, which significantly differ from Area 1 for dimension, shape and covariance map of the GP. The parameters involved in the analysis are the gene mutation rate \(q\), the chromosome mutation rate \(z\), the tuning parameter for the utility function \(\beta\), and the crossover method. Varying the values of these parameters, several possible combinations are obtained. Then, 40 offline executions of the GPP algorithm were computed for each set of parameters, calculating the metrics ME, PL, and O2E for each generated path. Finally, the configuration providing the best result in terms of mean and standard deviation of the considered metrics was selected. The resulting values for the parameters considered in the sensitivity analysis are reported in Table 1 together with, for the sake of completeness, a summary for all the other parameters adopted for the offline tests reported in the comparative analysis in Section 2.2. Parameters in the table are divided according to the phase of the algorithm they affect and a brief description of each of them is provided. Furthermore, the \"Single-Point\" method (details in Appendix A.3) resulted to be the crossover methods which provides the best routes, among the implemented ones. It must be stressed that the values \(d_{min}\) and \(d_{max}\) are chosen according to the size of Area 1, thus for the other target areas these values have been scaled by the ratio between the size of the target area and the size of Area 1, which result to be 1.6 and 2.45, respectively, for Area 2 and Area 3. Thus, the values for \(d_{min}\) and \(d_{max}\) are 0.32 m and 1.28 m for Area 2, while for Area 3 they are 0.49 m and 1.96 m. It is worth noticing that limits in the manoeuvrability could occur if the vehicle moves at the same speed and \(d_{min}\) decreases. Therefore, if a target area presents some peculiarity or the AUV has different manoeuvrability capabilities (or a different speed), the parameter \(d_{min}\) may differ from the one presented in Table 1. Moreover, the parameter \(\sigma_{\alpha}\) have been set considering the manoeuvrability capabilities of the AUV utilised for the collection of the images exploited to train the GP, which is a SPARUS II AUV [39] of property of the University of the Balearic Islands (UIB). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Description** & **Value** \\ \hline \multicolumn{3}{c}{_Global initialisation_} \\ \hline \(n\) & \# of chromosomes in the initial population & 200 \\ \(m\) & \# of genes per chromosome & 40 \\ \(\sigma_{\alpha}\) & Std. Dev. of the Gaussian distribution of \(\alpha\) & 20\({}^{\circ}\) \\ \(d_{min}\) & Lower bound of the uniform distribution of d & 0.2 m \\ \(d_{max}\) & Higher bound of the uniform distribution of d & 0.8 m \\ \hline \multicolumn{3}{c}{_Genetic operations_} \\ \hline \(k\) & \# of chromosomes maintained after the “Ranking” phase & 10 \\ \(q\) & Gene mutation rate & 5\% \\ \(z\) & Chromosome mutation rate & 40\% \\ \(t_{max}\) & Duration limit of the iterative phase & 15 s \\ \hline \multicolumn{3}{c}{_Utility function_} \\ \hline \(\beta\) & Tuning parameter for the trade-off in the utility function & 0.95 \\ \hline \multicolumn{3}{c}{_Consistency check_} \\ \hline \(C_{g}\) & Attempts limit to generate \(\alpha\) from the Gaussian distributions & 10 \\ \(C_{u}\) & Attempts limit to generate \(\alpha\) from the uniform distribution & 15 \\ \(C_{n}\) & \# of genes to delete to exit from inconsistent conditions & 5 \\ \hline \hline \end{tabular}
\end{table}