## 3 Results and Discussion
### Analysis of the Impact of the Number of Evaluations
\begin{table}
\begin{tabular}{r r r r r r r} \hline \multirow{2}{*}{**Evaluations \(E_{\_}{\_}{p}\)**} & \multicolumn{2}{c}{**ABC**} & \multicolumn{2}{c}{**FWA**} & \multicolumn{2}{c}{**PSO**} \\  & **Average** & **St. Dev.** & **Average** & **St. Dev.** & **Average** & **St. Dev.** \\ \hline
25 & 0.0764 & 0.0045 & 0.0738 & 0.0039 & 0.0790 & 0.0004 \\
50 & 0.0786 & 0.0012 & 0.0766 & 0.0020 & 0.0795 & 0.0001 \\
75 & 0.0791 & 0.0005 & 0.0772 & 0.0017 & 0.0795 & 0.0001 \\
100 & 0.0793 & 0.0004 & 0.0769 & 0.0024 & 0.0795 & \(<\)0.0001 \\
150 & 0.0794 & 0.0002 & 0.0773 & 0.0013 & 0.0795 & \(<\)0.0001 \\
200 & 0.0795 & 0.0001 & 0.0776 & 0.0011 & 0.0795 & \(<\)0.0001 \\
300 & 0.0795 & 0.0001 & 0.0779 & 0.0008 & 0.0795 & \(<\)0.0001 \\
400 & 0.0795 & \(<\)0.0001 & 0.0781 & 0.0008 & 0.0795 & \(<\)0.0001 \\
500 & 0.0795 & 0.0001 & 0.0783 & 0.0007 & 0.0795 & \(<\)0.0001 \\
600 & 0.0795 & 0.0001 & 0.0784 & 0.0008 & 0.0795 & \(<\)0.0001 \\
700 & 0.0795 & \(<\)0.0001 & 0.0783 & 0.0006 & 0.0795 & \(<\)0.0001 \\
800 & 0.0795 & \(<\)0.0001 & 0.0786 & 0.0005 & 0.0795 & \(<\)0.0001 \\
900 & 0.0795 & 0.0001 & 0.0785 & 0.0005 & 0.0795 & \(<\)0.0001 \\
1000 & 0.0795 & \(<\)0.0001 & 0.0786 & 0.0006 & 0.0795 & \(<\)0.0001 \\ \hline \end{tabular}
\end{table} 
Table 5: Coverage averages and standard deviations of the different algorithms for each number of evaluations for three-dimensional Environment 1. In both cases, the post hoc analysis with a Bonferroni adjustment led to the same conclusions as for the two-dimensional placement. The full results of the pairwise post hoc comparisons for the factor _Algorithm_ can be found in Table 6.
* The interaction between the factors _Algorithm_\(*\)_Number of evaluations_ is statistically significant: \[F(26,1218)=7.787,p<0.001.\]  
Although the statistical analysis showed that 50 evaluations per independent variable achieved a coverage value that was not significantly different from that achieved with more evaluations, the statistically significant interaction between the factors prompted us to perform a post hoc analysis of all factors. This post hoc analysis showed that PSO performs better than ABC only for \(E_{v}=50\) for two-dimensional environments and for \(E_{v}=25\) evaluations for three-dimensional environments, while there is no statistically significant difference for a higher number of evaluations. Both algorithms outperform FWA up to \(E_{v}=150\) for two-dimensional environments and \(E_{v}=400\) for three-dimensional environments, after which there is no statistically significant difference between the pairs of algorithms. This difference can be seen in Figure 2.  
As can be seen in Figure 3, the computation time increases linearly with the number of evaluations \(E_{v}\). The computation time for ABC and PSO overlaps, while it increases faster for FWA. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{2}{c}{**Mean Difference**} & \multicolumn{1}{c}{**SE**} & \multicolumn{1}{c}{\(\mathbf{t}\)} & \(\boldsymbol{p_{bonf}}\) \\ \hline ABC & FWA & \(0.002\) & \(7.942\times 10^{-5}\) & \(20.204\) & \(<\)\(0.001\) \\  & PSO & \(-3.135\times 10^{-4}\) & \(7.942\times 10^{-5}\) & \(-3.948\) & \(<\)\(0.001\) \\ FWA & PSO & \(-0.002\) & \(7.942\times 10^{-5}\) & \(-24.152\) & \(<\)\(0.001\) \\ \hline \end{tabular}
\end{table} 
Table 6: Post hoc comparison for _Algorithm_ for three-dimensional Environment 1 with factor _Number of evaluations._  
Figure 2: _Cont._  
Figure 3: Cont. Figure 2: Coverage value \(C\) for each of the algorithms based on the number of evaluations \(E_{v}\) for Environment 1.