## 6 Results and Discussion
### Optimization and Computational Results  
Due to the stochastic and irreproducible nature of optimization algorithms, validating their performance is supposed to be via statistical analysis on the goodness of the found solutions of several trials. Thus, the suggested particle swarm optimization algorithm has been simulated 20 times with a maximum Number of Improvisations (iterations) \(NI=100\) and a Harmony Memory Size \(HMS=20\) while running on an Intel Core i5, 3.30 GHz CPU. Feasible solutions have been obtained in 80% of trials and in acceptable CPU calculation time. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Capture Chamber** & **Wells Turbine** & \multicolumn{2}{c}{**DFIG Generator**} \\ \hline \(w_{c}=4.5\) m & \(n=5\) & \(R_{s}=0.5968\)\(\Omega\) & \(P_{rated}=18.45\) kW \\ \(l_{c}=4.3\) m & \(b=0.21\) m & \(R_{r}=0.6258\)\(\Omega\) & \(V_{rated}=400\) V \\ \(\rho_{a}=1.19\) kg/m\({}^{3}\) & \(l=0.165\) m & \(L_{ss}=0.0003495\) H & \(f_{rated}=50\) Hz \\ \(\rho_{w}=1029\) kg/m\({}^{3}\) & \(r=0.375\) m & \(L_{rr}=0.324\) H & \(p=2\) \\  & \(a=0.4417\) m\({}^{2}\) & \(L_{m}=0.324\) H & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: OWC parameters from the NEREIDA wave power plant. Figure 10: Improvisation process in Self-adaptive Global-best Harmony Search (SGHS) algorithm. Figure 11 illustrates the box-and-whisker plot of the results of the optimization of all four variants of the Harmony Search algorithm (i.e., HS, IHS, GHS, SGHS) for Problem (18). The figure shows that the obtained solutions from all four algorithms are in the same region of the search space. From a statistical point of view, we focus on the average values which are 4.015, 3.575, 3.875, and 3.450 for HS, HIS, GHS and SGHS, respectively. However, in general, it is obvious that, in terms of average value (red line) and of minimum value (bottom whisker), among 20 trials of every algorithm the SGHS algorithm presents superiority over the previous variants. However, it is to be noted that the box of the IHS algorithm is the narrowest which is thanks to its pitch adjustment rules that favor exploitation and precision. On the other hand, the GHS show less favorable results with wider box, meaning dispersed solutions, this may be due to the lack of solution refinement via the \(BW\) parameter. The significant outcomes of the 20 trials using all four algorithms are detailed in Table 2. The SGHS algorithm is the best in terms of average value but not significantly better. SGHS has the lowest minimum, maximum, median and mean values and the HS algorithm has the lowest standard deviation. To further understand the behavior of the algorithms Figure 12 illustrates the most typical convergence curves of HS, IHS, GHS and SGHS along with the curves of previously tested algorithms--the Particle Swarm Optimization with decreasing inertia (PSO-In), the Fractional-Order Particle Swarm Optimization Memetic Algorithm (FPSOMA) and the Water \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Algorithm** & **Min** & **Max** & **Median** & **Mean** & **Standard Deviation** \\ \hline HS & 3.900 & 4.900 & 4.015 & 4.400 & 0.530 \\ IHS & 3.100 & 4.500 & 3.575 & 3.800 & 0.540 \\ GHS & 3.402 & 4.950 & 3.875 & 4.176 & 0.825 \\ SGHS & 2.874 & 4.300 & 3.450 & 3.587 & 0.697 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of optimization results from 20 trials of Problem (18). Figure 11: Box-and-whisker plot of the optimization results using HS, IHS, GHS and SGHS algorithms. From the convergence histories, it can be noticed that all algorithms successfully converge to the same region of the search space (between 3 and 4) but the optimal is from the SGHS algorithm. The other variants of the HS algorithm managed to enhance the exploration and exploitation capabilities but with different outcomes.