# Differential Evolution in Waveform Design for Wireless Power Transfer
## 4 Results
### Convergence Plots  
The assessment of the derived results so far has exhibited that among the tested EAs, no one stands out for yielding superior solutions. The next step for the evaluation of their performance is to check which one of them converges within a lower number of function evaluations. This can be achieved by examining the convergence plots of the algorithms in each one of the cases. These plots are generated by processing the already obtained data and depict the mean fitness value over 50 runs as a function of objective function evaluations (Figures 6-9). By observing the convergence plots for all channels and waveforms, we could say that CoDE algorithm converges slightly faster or at least equally fast in most of the cases compared to the other competitors. It seems that the adaptive nature of CODE makes it suitable for different problems. An exception is detected in Channel 1 for \(B=100\) MHz and \(T_{o}=40\) ns. The superiority of CoDE's convergence speed is more apparent for a larger number of sub-carriers (\(N=16\), \(N=32\)). On the other hand, Jaya performs satisfactorily for \(N=4\) and \(N=8\), yet poorly for \(N=16\) and \(N=32\), probably due to its greedy vector generation strategy. Finally, DE and L-SHADE demonstrate quite similar behavior, as they require a larger number of function evaluations for convergence than CODE and Jaya for \(N=4\) and \(N=8\), while they converge faster than Jaya and slower than CoDE for \(N=16\) or \(N=32\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Ch. No. ** & \(\mathbf{T_{o}}\) **(ns)** & \(\mathbf{N}\) & **DE** & **CODE** & **L-SHADE** & **Jaya** & **SCP-QCLP** \\ \hline
1 & 20 & 2 & 2.07835\(\times\)\(10^{-9}\) & 2.07835\(\times\)\(10^{-9}\) & 2.07835\(\times\)\(10^{-9}\) & 2.07835\(\times\)\(10^{-9}\) & 2.07835\(\times\)\(10^{-9}\) & 2.07835\(\times\)\(10^{-9}\) \\ \hline
1 & 40 & 4 & 1.11555\(\times\)\(10^{-8}\) & 1.05200\(\times\)\(10^{-8}\) & 1.12385\(\times\)\(10^{-8}\) & 1.12385\(\times\)\(10^{-8}\) & 1.12360\(\times\)\(10^{-8}\) \\ \hline
1 & 80 & 8 & 1.27505\(\times\)\(10^{-8}\) & 1.29655\(\times\)\(10^{-8}\) & 1.29655\(\times\)\(10^{-8}\) & 1.29655\(\times\)\(10^{-8}\) & 1.29655\(\times\)\(10^{-8}\) & 1.29614\(\times\)\(10^{-8}\) \\ \hline
1 & 160 & 16 & 2.21499\(\times\)\(10^{-8}\) & 2.21555\(\times\)\(10^{-8}\) & 2.21555\(\times\)\(10^{-8}\) & 2.21518\(\times\)\(10^{-8}\) & 2.21524\(\times\)\(10^{-8}\) \\ \hline
1 & 320 & 32 & 6.32045\(\times\)\(10^{-8}\) & 6.62450\(\times\)\(10^{-8}\) & 6.62450\(\times\)\(10^{-8}\) & 6.58989\(\times\)\(10^{-8}\) & 6.62428\(\times\)\(10^{-8}\) \\ \hline
2 & 20 & 2 & 1.20617\(\times\)\(10^{-8}\) & 1.20617\(\times\)\(10^{-8}\) & 1.20617\(\times\)\(10^{-8}\) & 1.20617\(\times\)\(10^{-8}\) & 1.20617\(\times\)\(10^{-8}\) \\ \hline
2 & 40 & 4 & 1.38367\(\times\)\(10^{-8}\) & 1.37849\(\times\)\(10^{-8}\) & 1.38367\(\times\)\(10^{-8}\) & 1.38367\(\times\)\(10^{-8}\) & 1.38289\(\times\)\(10^{-8}\) \\ \hline
2 & 80 & 8 & 1.96683\(\times\)\(10^{-8}\) & 1.96685\(\times\)\(10^{-8}\) & 1.96685\(\times\)\(10^{-8}\) & 1.96685\(\times\)\(10^{-8}\) & 1.96655\(\times\)\(10^{-8}\) \\ \hline
2 & 160 & 16 & 4.20886\(\times\)\(10^{-8}\) & 4.20886\(\times\)\(10^{-8}\) & 4.20886\(\times\)\(10^{-8}\) & 4.20763\(\times\)\(10^{-8}\) & 4.20882\(\times\)\(10^{-8}\) \\ \hline
2 & 320 & 32 & 1.75929\(\times\)\(10^{-7}\) & 1.76295\(\times\)\(10^{-7}\) & 1.76295\(\times\)\(10^{-7}\) & 1.75450\(\times\)\(10^{-7}\) & 1.76295\(\times\)\(10^{-7}\) \\ \hline
3 & 20 & 2 & 3.29902\(\times\)\(10^{-8}\) & 3.29904\(\times\)\(10^{-8}\) & 3.29904\(\times\)\(10^{-8}\) & 3.29903\(\times\)\(10^{-8}\) & 3.29903\(\times\)\(10^{-8}\) \\ \hline
3 & 40 & 4  
Figure 6: Convergence plots for propagation channel 1, B = 100 MHz and (**a**) T = 40 ns, N = 4, (**b**) T = 80 ns, N = 8, (**c**) T = 160 ns, N = 16, (**d**) T = 320 ns, N = 32. Figure 7: Convergence plots for propagation channel 2, B = 100 MHz and (**a**) T = 40 ns, N = 4, (**b**) T = 80 ns, N = 8, (**c**) T = 160 ns, N = 16, (**d**) T = 320 ns, N = 32.