## 5 Results
A comparison is presented for the proposed **GD + GR** method (MT and ST) and an improved EA (MT and ST). The four first graphs use LAPD as the wake aggregation method, and the fifth one uses LAVD. Red segments and crosses are the medians and outliers, respectively. Figure 7: Fitness evolution for the proposed algorithm, compared to the evolution of an EA. In magenta, the power deficit \(\mathbb{E}[\delta P]=\overline{\delta P}\) evolution using LAPD, which is the real fitness used in the EA. In green, the same evolution using LAVD. The second figure represents the \(\mathbb{E}[P]=\overline{P}=\text{AEP}/T\) of the obtained solution after executing the algorithms. Again, the proposed algorithm shows a better performance than EAs. However, using LAPD instead of LAVD can deteriorate the performance of other algorithms (an EA in this case). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{4}{c}{**LAPD**} & \multicolumn{2}{c}{**LAVD**} \\ \hline \multirow{2}{*}{Comp. Time} & \multicolumn{2}{c}{GD + GR} & \multicolumn{2}{c}{EA} & EA \\ \cline{2-6}  & MT & ST & MT & ST & MT \\ \hline \multirow{2}{*}{Anholt} & 24.78 s & 50.94 s & 477.27 s & 407.20 s & 5168.5 s \\  & (1.90 s) & (8.78 s) & (132.96 s) & (124.44 s) & (194.51 s) \\ \hline \multirow{2}{*}{Horns Rev 1} & 13.44 s & 39.83 s & 243.56 s & 218.48 s & 3375.1 s \\  & (7.73 s) & (24.83s) & (48.62 s) & (50.18 s) & (22.24 s) \\ \hline \multicolumn{6}{c}{**LAPD**} & \multicolumn{2}{c}{**LAVD**} \\ \hline \(\mathbb{E}[P]\) (LAVD used for final solution) & \multicolumn{2}{c}{GD + GR} & EA & EA \\ \cline{2-6}  & MT & ST & MT & ST & MT \\ \hline \multirow{2}{*}{Anholt} & 192.20 MW & 192.20 MW & 189.48 MW & 189.57 MW & 190.55 MW \\  & (0.10 MW) & (0.10 MW) & (0.09 MW) & (0.19 MW) & (0.3803 MW) \\ \hline \multirow{2}{*}{Horns Rev 1} & 70.26 MW & 70.23 MW & 68.94 MW & 68.78 MW & 69.66 MW \\  & (0.10 MW) & (0.09 MW) & (0.09 MW) & (0.12 MW) & (0.23 MW) \\ \hline \multicolumn{6}{c}{With the conditions of Table A1 \(\mathbb{E}[P]_{Anholt}=192.0\,\text{MW}\) and \(\mathbb{E}[P]_{HR1}=69.6\,\text{MW}\)} \\ \hline \multirow{2}{*}{\(\frac{\mathbb{E}[P]_{\text{LAPD}}}{\mathbb{E}[P]_{\text{LAVD}}}\)} & GD + GR & \multicolumn{2}{c}{EA} & EA \\ \cline{2-6}  & MT & ST & MT & ST & MT \\ \hline \multirow{2}{*}{Anholt} & 0.9499 & 0.9499 & 0.9518 & 0.9514 & 0.9317 \\  & (0.0005) & (0.0005) & (0.0009) & (0.0009) & (0.0081) \\ \hline \multirow{2}{*}{Horns Rev 1} & 0.9636 & 0.9640 & 0.9642 & 0.9639 & 0.9043 \\  & (0.0007) & (0.0009) & (0.0008) & (0.0010) & (0.0187) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison of the proposed GD + GR algorithm, an EA one (both using LAPD for the \(\overline{\delta P}\) estimation), and an EA algorithm using LAVD for the \(\overline{\delta P}\) estimation. The computation time is presented in the upper table and the obtained power is in the central one. The lower table displays the ratio between the value of \(\delta P\) obtained using the aggregations LAPD y LAVD. For each data the mean value of 10 launches is displayed together with the standard deviation in brackets. Input data from Table A1. Figure 9: AEP of the solutions found for the test beds with data from Anholt **(left)** and Horns Rev 1 **(right)**. MT and ST refer, respectively, to parallel CPU processing and a single thread. A comparison is presented for the proposed **GD + GR** method (MT and ST) and an improved EA (MT and ST). The four first graphs use LAPD as wake aggregation method, and the fifth one uses LAVD. Red segments and crosses are the medians and outliers, respectively. These results confirm the two main contributions:  
* LAPD can be used as the objective function during the search process, since during the optimization of the power deficit (calculated by means of LAPD), the power deficit (calculated by means of LAVD) is also minimized. Using LAPD, the computation time is substantially reduced. * The proposed method based on GD together with GR substantially improves the solution obtained with an EA.