## 3 Results and Discussion
### Analysis of the Impact of the Number of Evaluations
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Evaluations \(E_{\mathrm{v}}\)**} & \multicolumn{2}{c}{**ABC**} & \multicolumn{2}{c}{**FWA**} & \multicolumn{2}{c}{**PSO**} \\  & **Average** & **St. Dev.** & **Average** & **St. Dev.** & **Average** & **St. Dev.** \\ \hline
25 & 0.1417 & 0.0026 & 0.1408 & 0.0034 & 0.1435 & 0.0012 \\
50 & 0.1432 & 0.0017 & 0.1417 & 0.0025 & 0.1443 & 0.0002 \\
75 & 0.1440 & 0.0007 & 0.1430 & 0.0011 & 0.1445 & \(<\)0.0001 \\
100 & 0.1442 & 0.0004 & 0.1430 & 0.0012 & 0.1445 & \(<\)0.0001 \\
150 & 0.1444 & 0.0002 & 0.1433 & 0.0011 & 0.1445 & \(<\)0.0001 \\
200 & 0.1444 & 0.0002 & 0.1437 & 0.0006 & 0.1445 & \(<\)0.0001 \\
300 & 0.1445 & 0.0001 & 0.1435 & 0.0006 & 0.1446 & \(<\)0.0001 \\
400 & 0.1445 & 0.0002 & 0.1436 & 0.0006 & 0.1446 & \(<\)0.0001 \\
500 & 0.1445 & \(<\)0.0001 & 0.1439 & 0.0005 & 0.1446 & \(<\)0.0001 \\
600 & 0.1445 & 0.0001 & 0.1437 & 0.0004 & 0.1446 & \(<\)0.0001 \\
700 & 0.1445 & 0.0002 & 0.1439 & 0.0004 & 0.1446 & \(<\)0.0001 \\
800 & 0.1445 & 0.0001 & 0.1442 & 0.0002 & 0.1446 & \(<\)0.0001 \\
900 & 0.1445 & 0.0002 & 0.1440 & 0.0004 & 0.1446 & \(<\)0.0001 \\
1000 & 0.1445 & 0.0001 & 0.1441 & 0.0003 & 0.1446 & \(<\)0.0001 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coverage averages and standard deviations of the different algorithms for each number of evaluations for two-dimensional Environment 1.  
in these tests. The full results of the pairwise post hoc comparisons can be found in Table 4.
* Mean coverage differed significantly between the _Number of evaluations_: \[F(13,1218)=47.555,\,p<0.001.\] A post hoc analysis with a Bonferroni adjustment confirmed a statistically significant difference in area coverage obtained with \(E_{\_}{\_}{p}=25\) and \(E_{\_}{\_}{p}=50\) evaluations compared to more. In most other cases, there is no statistically significant difference. * The interaction between the factors _Algorithm \(*\) Number of evaluations_ is statistically significant: \[F(26,1218)=5.446,\,p<0.001.\]  
Table 5 shows the descriptive statistics for using different numbers of evaluations \(E_{\_}{p}\) of the optimization for the sensor placement in the three-dimensional representation of Environment 1. This table shows the average and standard deviation of the coverage \(\mathcal{C}\) of all runs for each algorithm. We again performed a two-way \(3\times 14\) RM ANOVA, where _Algorithms_ (three instances) and _Number of evaluations_ (14 instances) were the within-subjects factors. The test yielded the following results:  
* The mean coverage differed significantly between the optimization _Algorithms_: \[F(2,1218)=335.709,\,p<0.001.\]
* Mean coverage differed significantly between the _Number of evaluations_: \[F(13,1218)=37.571,\,p<0.001.\] \begin{table}
\begin{tabular}{c c c c c c} \hline  & & **Mean Difference** & **SE** & **t** & \(\mathbf{p_{\_}{bonf}}\) \\ \hline ABC & FWA & \(8.408\times 10^{-4}\) & \(6.368\times 10^{-5}\) & \(13.203\) & \(<\)0.001 \\  & PSO & \(-3.064\times 10^{-4}\) & \(6.368\times 10^{-5}\) & \(-4.811\) & \(<\)0.001 \\ FWA & PSO & \(-0.001\) & \(6.368\times 10^{-5}\) & \(-18.014\) & \(<\)0.001 \\ \hline \end{tabular}
\end{table} 
Table 4: Post hoc comparison for _Algorithms_ for two-dimensional Environment 1 with factor _Number of evaluations_.