## 3 The Algorithm
### SaNSDE Algorithm
The standard deviation of the fitness function values obtained by the proposed algorithm is smaller than those of the other algorithms compared in this study with only a few exceptions. This indicates that the variation in the fitness function values obtained by the proposed algorithm is smaller than those of other algorithms, and the fitness function values are clustered tightly around the mean of the fitness function values. Therefore, this shows that the proposed algorithm is more robust than the compared algorithms in this study. The standard deviation of the fitness function values obtained by the proposed algorithm and all the algorithms compared in this study are listed in Tables 15 and 16 for \(NP=30\) and \(LP=1000\). Again, the standard deviation of the fitness function values obtained by the proposed algorithm is smaller than those of the other algorithms compared in this study with only a few exceptions. In particular, the standard deviation of the fitness function values obtained by the proposed algorithm is smaller than those of all the compared DE algorithms in this study. Therefore, this shows that the proposed algorithm is more robust than the compared algorithms in this study. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Case** & **I** & **K** & **SaNSDE** & **NSDE** & **PSO** \\ \hline
1 & 4 & 3 & 0 & 2.5298 & 0 \\
2 & 5 & 5 & 0 & 0 & 0 \\
3 & 5 & 5 & 0 & 5.1639 & 3.1622 \\
4 & 10 & 10 & 6.7461 & 17.519 & 0 \\
5 & 10 & 10 & 12.2495 & 27.4067 & 41.1472 \\
6 & 10 & 20 & 16.0752 & 22.0254 & 351,447 \\
7 & 20 & 20 & 85.9152 & 81.2595 & 88.2892 \\
8 & 30 & 10 & 12.9653 & 45.785 & 230.4394 \\
9 & 30 & 20 & 37.4189 & 43.6379 & 131.5278 \\
10 & 40 & 10 & 19.3301 & 66.71 & 96.3574 \\ \hline \end{tabular}
\end{table} 
Table 13: Standard deviation of fitness function values for discrete SaNSDE, NSDE and PSO with population size \(NP=10\) and \(LP=1000\). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Case** & **I** & **K** & **DE1** & **DE2** & **DE3** & **DE4** & **DE5** & **DE6** \\ \hline
1 & 4 & 3 & 1.8973 & 1.8973 & 1.8973 & 1.8973 & 0 & 0 \\
2 & 5 & 5 & 0 & 0 & 2.4152 & 5.3758 & 1.5811 & 5.3758 \\
3 & 5 & 5 & 5.3758 & 9.3903 & 5.1639 & 15.6005 & 6.168 & 4.2163 \\
4 & 10 & 10 & 20.7379 & 5.0596 & 0 & 6.7461 & 17.519 & 6.7461 \\
5 & 10 & 10 & 12.0483 & 116.9596 & 46.3209 & 158.0998 & 150.3754 & 89.9087 \\
6 & 10 & 20 & 93.9822 & 183.4416 & 33.4099 & 245.0483 & 183.8067 & 182.9856 \\
7 & 20 & 20 & 322.4046 & 591.8342 & 477.0795 & 572.9579 & 599.2337 & 309.0789 \\
8 & 30 & 10 & 57.7062 & 312.8212 & 52.0465 & 284.4938 & 203.4308 & 222.3413 \\
9 & 30 & 20 & 52.1204 & 103.5533 & 55.656 & 63.2463 & 76.2017 & 95.0312 \\
10 & 40 & 10 & 36.1963 & 187.0451 & 140.7144 & 114.6247 & 254.3267 & 241.3109 \\ \hline \end{tabular}
\end{table} 
Table 14: Standard deviation of fitness function values for DE1, DE2, DE3, DE4, DE5 and DE6 with \(NP=10\) and \(LP=1000\). The standard deviation of the fitness function values obtained by the proposed algorithm and all the algorithms compared in this study are listed in Tables 17 and 18 for \(NP=50\) and \(LP=1000\). Again, the standard deviation of the fitness function values obtained by the proposed algorithm is smaller than those of the other algorithms compared in this study with only a few exceptions. In particular, the standard deviation of the fitness function values obtained by the proposed algorithm is smaller than those of all DE algorithms. Therefore, this shows that the proposed algorithm is more robust than the other algorithms compared in this study.