## 5 Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **D** & **P** & **SaNSDE-1-6** & **DE-1** & **DE-3** & **NSDE** & **PSO** \\ \hline
1 & 3 & 10 & 10.1 & 17.6 & 19.2 & 12.9 & 51.5 \\
2 & 5 & 11 & 18.7 & 30.2 & 33 & 26.4 & 127.3 \\
3 & 5 & 12 & 22.3 & 28.7 & 43.3 & 32.9 & 437.2 \\
4 & 6 & 12 & 22.5 & 35.4 & 37.4 & 33.2 & 468.6 \\
5 & 7 & 13 & 17.7 & 29.3 The results in Table 6 show that the top four algorithms are SaNSDE-1-6, NSDE, DE-1 and DE-3. For small test cases, including Case 1 through Case 11, the fitness function values obtained using SaNSDE-1-6, NSDE, DE-1 and DE-3 are the same. However, as the problem size grows, the average fitness function values obtained via SaNSDE-1-6 are significantly better than those obtained via NSDE, DE-1 and DE-3. For Case 12, the average fitness function value obtained via SaNSDE-1-6 is better than those obtained by NSDE, DE-1 and DE-3. The differences between the average fitness function value obtained via SaNSDE-1-6 and those obtained via NSDE, DE-1 and DE-3 are about 0.1674% to 0.73959%. For Case 12, the average fitness function value obtained via SaNSDE-1-6 is better than those obtained via NSDE, DE-1 and DE-3. For Case 13, the differences between the average fitness function values obtained via SaNSDE-1-6 and those obtained via NSDE, DE-1 and DE-3 are about 4.00326% to 7.9796%. For Case 14, the differences between the average fitness function value obtained via SaNSDE-1-6 and those obtained via NSDE, DE-1 and DE-3 are about 3.1171% to 46.403%. In short, SaNSDE-1-6 outperforms NSDE, DE-1 and DE-3 in terms of scalability. To compare performance clearly, please refer to the bar chart shown in Figure 10 for the average fitness function values of Case 1 through Case 14. In terms of convergence rate (the number of generations to find the best solutions), the results in Table 7 indicate that the average numbers of iterations for SaNSDE-1-6 to find the best solutions are significantly less than those for NSDE, DE-1 and DE-3 to find the best solutions for most test cases (with some exception). This indicates that SaNSDE-1-6 outperforms NSDE, DE-1 and DE-3 in convergence rate. To compare the convergence rate clearly, please refer to the bar chart shown in Figure 11 for the average number of generations of Case 1 through Case 10 and please refer to the bar chart shown in Figure 12 for the average number of generations of Case 11 through Case 14. Figure 10: Average fitness function values for \(r_{D}=r_{P}=r=0.1\) with POP = 50. Figure 11: Average number of generations for Case 1 through Case 10 with \(r_{D}=r_{P}=r=0.1\) and POP = 50. Figure 12: Average number of generations for Case 11 through Case 14 with \(r_{D}=r_{P}=r=0.1\) and POP = 50. Figure 16: Convergence curves for a run of Case 13 for \(r_{D}=r_{P}=r=0.1\) with POP = 50. Figure 15: Convergence curves for a run of Case 12 for \(r_{D}=r_{P}=r=0.1\) with POP = 50. The results presented above are based on comparison of average number of generations. The results in Table 8 indicate that the average computation time for SaNSDE-1-6 to find the best solutions is significantly less than that for PSO to find the best solutions for Case 1 through Case 10 and is greater than those of NSDE, DE-1 and DE-3 for Case 1 through Case 10. This indicates that SaNSDE-1-6 outperforms PSO in terms of computation time for Case 1 through Case 10 and NSDE, DE-1 and DE-3 outperform SaNSDE-1-6 in terms of computation time for Case 1 through Case 10. For Case 11 and Case 12, SaNSDE-1-6 outperforms PSO, NSDE, DE-1 and DE-3 in terms of computation time. For Case 13 through Case 14, PSO, NSDE, DE-1 and DE-3 outperform SaNSDE-1-6 in terms of computation time. As the experiments to compare the different algorithms were done on the same platform as the one used in [13], which was an old laptop delivered in 2019 with Intel(R) Core(TM) i7 CPU, base clock speed of 2.6 GHz and16 GB of onboard memory, the computation times of SaNSDE-1-6 are much longer for Case 12, Case 13 and Case 14.