## 4 Results and Discussion
### Performance Evaluation  
Taking into account the simulation scenario and the hyper-parameters presented, the following section focuses on presenting and analyzing the results obtained from the simulations. It is worth mentioning that in [18], MSCPSO was used to optimized the parameters of a \(4\times 4\) antenna array using PSO, and the results of the unknown positions were interpolated. However, the latter was evaluated using different restrictions compared to the ones in this manuscript. In particular, the authors in [18] restricted the position of the vehicle in the road, but this restriction was discarded in our manuscript since for safety applications, every possible position is important. New results for MSCPSO were hence computed in this manuscript. Initially, the results for the average power received in each of the four roads (P1, P2, P3, and P4) are exposed in Table 4. These powers are expressed in dBm. As can be seen, by using beamforming with any of the algorithms outperformed using an isotropic antenna. The values showed that the performance of the GA and MSCPSO was similar in the vertical roads (P3 and P4), but the GA outperformed MSCPSO significantly in the horizontal roads (P1 and P2). On the other hand, NEAT outperformed both algorithms considerably for all four roads. While the GA and MSCPSO use the interpolation of known positions to generate the output, NEAT trains a neural network that can output the values \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Antenna** & **P1 (dBm)** & **P2 (dBm)** & **P3 (dBm)** & **P4 (dBm)** \\ \hline Isotropic antenna & \(-112.82\) & \(-112.82\) & \(-114.16\) & \(-124.60\) \\ Beamforming with MSCPSO & \(-105.22\) & \(-105.82\) & \(-105.07\) & \(-110.07\) \\ Beamforming with GA [17] & \(-89.36\) & \(-89.30\) & \(-108.55\) & \(-109.03\) \\ Beamforming with NEAT & \(-74.24\) & \(-74.30\) & \(-96.35\) & \(-95.89\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Received power in each road for the isotropic antenna case and beamforming for different algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Parameter** & **Value** \\ \hline \multirow{6}{*}{GA} & Individuals & 500 \\  & Generations & 150 \\  & \(dx\) & 1 m \\  & \(dy\) & 1 m \\  & \(\sigma_{\Phi}^{2}\) & 10.0 \\  & \(\sigma_{\Phi}^{2}\) & 0.5 \\  & Crossover probability & 0.8 \\  & Mutation probability & 0.3 \\ \hline \multirow{6}{*}{NEAT} & Population size & 150 \\  & Generations & 300 \\  & Activation function & sigmoid \\  & Input nodes & 2 \\  & Output nodes & 32 \\  & Probability to add connection & 0.7 \\  & Probability to delete & 0.3 \\  & connection & \\  & Probability to add node & 0.4 \\  & Probability to delete node & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters used for the evaluated algorithms. for any position. This has proven to make NEAT a flexible algorithm that can learn to generalize in various and complex learning tasks. Another interesting result was the percentage (%) of the positions in which each of the algorithms outperformed the isotropic antenna in each of the four roads. The results were computed by sampling \(10^{4}\) positions in order to obtain representative outcomes and comparing the received power for the isotropic antenna and beamforming with each of the algorithms. The results presented in Table 5 show that all of the presented algorithms using beamforming outperformed the isotropic antenna in most scenarios. Even though Table 4 seems to indicate that the performances of the GA and MSCPSO were similar for two of the roads (P3 and P4), Table 5 shows that the GA was superior compared to MSCPSO in all scenarios. This observation seems to indicate that even though, on average, the performance was similar for both algorithms, MSCPSO tended to have much more extreme values when compared to the GA. Table 5 also shows that NEAT outperformed the isotropic antenna in all simulation scenarios.