## 5 Results
In terms of convergence rate (the number of generations to find the best solutions), the results in Table 4 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 exceptions). This indicates that SaNSDE-1-6 outperforms NSDE, DE-1 and DE-3 in terms of convergence rate. To compare the convergence rate clearly, please refer to the bar chart shown in Figure 3 for the average number of generations of Case 1 through Case 10 and please refer to the bar chart shown in Figure 4 for the average number of generations of Case 11 through Case 14. Figure 2: Average fitness function values for \(r_{D}\) = \(r_{p}\) = 0.1 with POP = 30. Figure 4: Average number of generations for Case 11 through Case 14 with \(r_{D}=r_{P}=r=0.1\) and POP = 30. Figure 3: Average number of generations for Case 1 through Case 10 with \(r_{D}=r_{P}=r=0.1\) and POP = 30. Figure 8: Convergence curves for a run of Case 13 for \(r_{D}=r_{p}=r=0.1\) with POP = 30. Figure 7: Convergence curves for a run of Case 12 for \(r_{D}=r_{p}=r=0.1\) with POP = 30. The results presented above are based on a comparison of the average number of generations. For the comparison of computation time, the results in Table 5 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 9 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 9 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, SaNSDE-1-6 outperforms PSO, NSDE, DE-1 and DE-3 in terms of computation time. For bigger cases, Case 12 through Case 14, PSO, NSDE, DE-1 and DE-3 outperform SaNSDE-1-6 in terms of computation time. As the experiments 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, to compare different algorithms, the computation times of SaNSDE-1-6 are much longer for Case 12, Case 13 and Case 14. Obviously, a more powerful computer or a server class computer is required to apply the SaNSDE-1-6 algorithm. Experiments based on the parameters in Table 2 for \(NP=50\) were performed. The results were summarized in Tables 6 and 7 for \(NP=50\). Table 6 shows the average fitness function values and Table 7 shows the average number of iterations to find the best solutions. Figure 9: Convergence curves for a run of Case 14 for \(r_{D}=r_{p}=r=0.1\) with POP = 30. \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 & 32.998 & 32.998 & 32.998 & 32.998 & 32.998 \\
2 & 5 & 11 & 63.615 & 63.615 & 63.615 & 63.615 & 63.615 \\
3 & 5 & 12 & 41.715 & 41.715 & 41.715 & 41.715 & 41.2892 \\
4 & 6 & 12 & 51.11 & 51.11 & 51.11 & 51.11 & 51.11 \\
5 & 7 & 13 & 30.063 & 30.063 & 30.063 & 30.063 & 30.063 \\
6 & 8 & 14 & 72.328 & 72.328 & 72.328 & 72.328 & 69.9483 \\
7 & 9 & 15 & 89.03 & 89.03 & 89.03 & 89.03 & 80.5986 \\
8 & 10 & 16 & 54.02 & 54.02 & 54.02 & 54.02 & 46.8013 \\
9 & 11 & 17 & 74.05 & 74.05 & 74.05 & 74.05 & 55.9356 \\
10 & 12 & 18 & 50.9 & 50.9 & 50.9 & 50.9 & 31.1131 \\
11 & 20 & 20 & 112.906 & 112.906 & 112.906 & 112.906 & 104.4808 \\
12 & 30 & 30 & 202.15 & 201.8116 & 200.6549 & 201.8116 & 145.0514 \\
13 & 40 & 40 & 202.4952 & 194.0284 & 190.4004 & 185.9914 & \(-\)1.2835 \\
14 & 50 & 50 & 192.343 & 190.4874 & 157.1781 & 162.1984 & \(-\)3.6674 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Fitness function values for discrete SaNSDE-1-6,DE-1, DE-3, NSDE and PSO algorithms with \(NP=50\); \(r_{D}=r_{P}=0.1\).