## 4 Computational Evaluation and Results  
This section presents the computational evaluation of the proposed antenna, by means of several simulations using the CRO-SL and CST software. In the first experiment carried out, we consider the highest two frequency bands (\(f_{2}\) and \(f_{3}\), associated with LTE and 5G mobile communication  
Figure 2: Hybridization of the CST simulation software with the Coral Reefs Optimization with Substrate Layer (CRO-SL) for optimized the parameters of the proposed antenna. systems). In this case, the CRO-SL algorithm is able to obtain a good solution for the problem, within 50 generations, as can be in the S\({}_{11}\) antenna parameter obtained (Figure 3), with peaks under \(-10\) dBs in both frequency bands considered. The best solution (antenna) obtained by the CRO-SL is shown in Figure 4 (front and bottom view). In this case, the fitness evolution followed by the CRO-SL is shown in Figure 5. The CRO-SL performance depends on how the different substrates operate for this problem. Figure 6 shows the percentage of best solutions and the number of solutions got into the reef for the different substrates. This is a good indication of the best substrates for this specific optimization problem. In this case, the GM substrate is the most active  
The design of the antenna with the CRO-SL considering the three frequency bands for LTE and 5G has been carried out using the solution for the two frequencies shown above as initial point. In order to do this, we include the best solution for the two-frequencies case into the initial population of the CRO-SL, completing it with randomly-generated solutions and a number of variations of the two-frequencies case obtained by mutation of the best solution. With this, the evolution of the CRO-SL towards a high-quality antenna, able to respond in the three frequency bands considered was really fast. Figure 7 shows the S\({}_{11}\) antenna parameter obtained by the CRO-SL. Note that the solution obtained is extremely good. In Figure 7a, it is possible to visualize three peaks under \(-25\) dBs in the three frequency bands, with a peak under \(-45\) dB in the 5G frequency centered in 3.5 GHz, and good bandwidth associated with all the frequencies considered. In the same way, the results represented in Figure 7b confirm the good performance of the optimized antenna. Please note that the markers on Figure 7b show the center frequency for each service, but not the exact resonant frequency. To further evaluate the performance of the CRO-SL algorithm, the optimization problem with three bands has been also tackled with an Evolutionary Algorithm. The initial parameters of the EA are the same as the CRO (population size and number of iterations) in order to be fully comparable. Table 3 shows the comparison between the CRO-SL algorithms and an Evolutionary algorithm. This table shows the best objective function obtained by each compared algorithm (CRO-5 SL optimizing two bands, CRO-5 SL optimizing three bands, and EA optimizing three bands). It can be seen that the CRO reach a better solution than the EA even when it is optimizing  
Figure 5: Evolution of the CRO-SL fitness (Equation (2)) in two frequency bands antenna optimization process. Figure 6: CRO-SL substrate performance metrics for the two-frequencies antenna optimization. (**a**) Best substrate for larvae generation; (**b**) best substrate for getting larvae into the reef. Figure 7: Reflection coefficient of the proposed antenna optimized for f\({}_{1}\), f\({}_{2}\) and f\({}_{3}\) frequency bands. (**a**) Reflection coefficient in dB; (**b**) reflection coefficient in Smith Chart. Figure 8 shows the final antenna layout obtained with the CRO-SL algorithm when the three frequency bands are considered. As can be seen after a comparison with the two-frequency bands case, the obtained antenna for the three frequency band shows a more reduced Circle R characteristic, with a wider U_T.