## 3 The Algorithm
### SaNSDE Algorithm
The number of best solutions found by the SaNSDE algorithm, the NSDE algorithm, the PSO algorithm, DE1 algorithm, DE2 algorithm, DE3 algorithm, DE4 algorithm, DE5 algorithm and DE6 algorithm are 7, 3, 4, 5, 1, 4, 2, 2 and 1, respectively. Therefore, in terms of the number of best solutions found, the SaNSDE algorithm outperforms the other algorithms. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **1** & **K** & **DE1** & **DE2** & **DE3** & **DE4** & **DES** & **DE6** \\ \hline
1 & 4 & 3 & 321/7.7 & 321/138.8 & 321/178 & 321/1107.2 & 321/325.3 & 321/551 \\
2 & 5 & 5 & 42/9.7 & 41.5/526.4 & 42/743.2 & 42/1925.5 & 42/27.8 & 415/9.9 \\
3 & 5 & 5 & 54/133 & 47.5/4147.6 & 49.9/1808.3 & 44.9/1367.2 & 44.3/1920.8 & 45.7/495.9 \\
4 & 10 & 10 & 542.2/342.3 & 540.6/41.6 & 530.1/2907.3 & 535.6/6976 & 539.5/63.5 & 540.6/78.7 \\
5 & 10 & 10 & 715.36/3430.6 & 627.7/3291.1 & 727.83/3778.6 & 648.7/2632.6 & 635.83/4070.5 & 587.12/3588.4 \\
6 & 10 & 20 & 1734.1/3210.3 & 1726.6/2628.1 & 1693/5468.9 & 1711.7/4546.3 & 1701.5/2996.4 & 1626.9/4184.7 \\
7 & 20 & 20 & 1646.1/4503.7 & 1300.7/3689.6 & 1328.9/7119.39 & 1382/4348.7 & 1279.3/2512.1 & 161.2 \\
8 & 30 & 10 & 720.8/460.1 & 541.9/1235.6 & 723.1/2999.5 & 714.6/3235 & 644.4/1370.3 & 714.4/2184.7 \\
9 & 30 & 20 & 777.7/622.8 & 745.4/2565.8 & 802/707.8 & 774.9/879.5 & 756.4/529.3 & 770.2/1279.8 \\
10 & 40 & 10 & 787.9/976 & 722.1/902 & 774.3/3339.9 & 771.8/3505.2 & 635.1/1247.5 & 664.6/2989.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Average fitness function values for DE1, DE2, DS2, DE4, DE5 and DE6 with \(NP=50\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **1** & **K** & **SaNSDE** & **NSDE** & **PSO** \\ \hline
1 & 4 & 3 & 321/6.2 & 320.4/23.9 & 321/8.2 \\
2 & 5 & 5 & 42/4.3 & 41/61.7 & 42/14.9 \\
3 & 5 & 5 & 55/74 & 52/119.2 & 55/1371 \\
4 & 10 & 10 & 542.2/11.3 & 542.2/25.5 & 542.2/34.6 \\
5 & 10 & 10 & 724.02/1794.6 & 612.07/156.6 & 494.62/6664.5 \\
6 & 10 & 20 & 1730.5/2311.2 & 1637/6304.8 & 1381.1/5476.9 \\
7 & 20 & 20 & 1576.6/1088.1 & 1203.9/4685.2 & 359.7/5671.6 \\
8 & 30 & 10 & 731/2792.2 & 731/2092.8 & 586.2/3114.5 \\
9 & 30 & 20 & 802/375.9 & 802/240.3 & 495.9/5033.8 \\
10 & 40 & 10 & 797/663.4 & 797/2420.8 & 357.1/4258.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Fitness function values for discrete NSDE, NSDE and PSO with population size \(NP=50\). Figure 9: Average fitness function values for discrete SaNSDE (\(LP=1000\)), NSDE and PSO with \(NP=50\). ### Influence of the LP Parameter on the Performance/Efficiency

The learning period parameter of the SaNSDE algorithm proposed in Section 3.2 may have an influence on its performance and efficiency. An important issue to study is whether the learning period parameter \(LP\) has a significant influence on performance and efficiency. To understand the effects of the learning period parameter, we perform three series of experiments by setting the learning period parameter, \(LP\), to 10, 1000 and 2000, respectively, and then analyzing the outcomes by comparing performance and efficiency. The results of the series of experiments are based on the same set of test cases. The results are summarized in Table 11. The average fitness function values in Table 10 are shown in the bar charts of Figures 11 and 12, respectively. Figure 11: The average fitness function values obtained by SaNSDE with \(LP\) = 10, 1000 and 2000 for Case 1, Case 2, Case 3, Case 4 and Case 5. Figure 10: Average fitness function values for SaNSDE (\(LP\) = 1000), DE1, DE2, DE3, DE4, DE5 and DE6 with \(NP\) = 50. According to Table 11, the average fitness values are the same for Case 1 through Case 4, Case 9 and Case 10 regardless of whether the learning period parameter \(LP\) is set to 10, 1000 or 2000. This indicates that the proposed SaNSDE algorithm is not sensitive to the learning period parameter \(LP\) for Case 1 through Case 4, Case 9 and Case 10. For Case 5, the average fitness values depend on the values of \(LP\).