## 3 The Algorithm
### SaNSDE Algorithm
The maximum average fitness value is 727.66, which is obtained by setting \(LP\) = 2000, and the minimum average fitness value is 691.48, which is obtained by setting \(LP\) = 10. The difference between the maximum and the minimum average fitness values is (727.66 \(-\) 691.48)/691.48 = 5.2322%. For Case 6, the average fitness values depend on the values of \(LP\). The maximum average fitness value is 1743.7, which is obtained by setting \(LP\) = 2000, and the minimum average fitness value is 1685.8, which is obtained by setting \(LP\) = 10. The difference between the maximum and the minimum average fitness values is (1743.7 \(-\) 1685.8)/1685.8 = 3.4345%. For Case 7, the average fitness values depend on the values of \(LP\). The maximum average fitness value is 1629.2, which is obtained by setting \(LP\) = 2000, and the minimum average fitness value is 1334.1, which is obtained by setting \(LP\) = 10. The difference between the maximum and the minimum average fitness values is (1629.2 \(-\) 1334.1)/1334.1 = 22.1197%. For Case 8, the average fitness values depend on the values of \(LP\). The maximum average fitness value is 731, which is obtained by setting \(LP\) = 1000 or 2000, and the minimum average fitness value is 728.8, which is obtained by setting \(LP\) = 10. The difference between the maximum and the minimum average fitness values is (731 \(-\) 728.8)/728.8 = 0.3018%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **I** & **K** & **SaNSDE (\(LP\) = 10)** & **SaNSDE (\(LP\) = 1000)** & **SaNSDE (\(LP\) = 2000)** \\ \hline
1 & 4 & 3 & 321/11 & 321/6 & 321/7.6 \\
2 & 5 & 5 & 42/9.3 & 42/10.1 & 42/11.1 \\
3 & 5 & 5 & 55/74.7 & 55/37 & 55/47.9 \\
4 & 10 & 10 & 542.2/10 & 542.2/13.9 & 542.2/11.5 \\
5 & 10 & 10 & 691.48/5986.6 & 721.56/1551.2 & 727.66/1392.8 \\
6 & 10 & 20 & 1685.8/6989.9 & 1728.4/2322.6 & 1743.7/1163.9 \\
7 & 20 & 20 & 1334.1/7993.2 & 1598.3/1268.3 & 1629.2/1386.8 \\
8 & 30 & 10 & 728.8/1628.7 & 731/558.9 & 731/936.7 \\
9 & 30 & 20 & 802/591 & 802/519.9 & 802/1063.7 \\
10 & 40 & 10 & 797/3218.2 & 797/1379.6 & 797/2669.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Average fitness values and average number of generations for SaNSDE with algorithmic parameter \(LP\) = 10, 1000 and 2000. Figure 12: The average fitness function values obtained by SaNSDE with \(LP\) = 10, 1000 and 2000 for Case 6, Case 7, Case 8, Case 9 and Case 10. The above analysis indicates that the sensitivity to the average fitness values obtained by the proposed SaNSDE algorithm is less than 5% for most cases, with the exception of Case 7. Another observation of the results is that \(LP\) should be large enough to obtain better average fitness values. ### Influence of Population Size on Performance/Efficiency

To study the influence of population size on the performance of the SaNSDE algorithm proposed in Section 3.2, we perform three series of experiments for all test cases for \(NP\) = 10, 30 and 50. The results of these experiments are summarized in Table 12. The average fitness function values of Table 12 are shown in the bar charts of Figures 13 and 14, respectively. The results show that the average fitness values of Case 1, Case 2 and Case 3 are the same. For Case 4, Case 5, Case 6, Case 7, Case 8, Case 9 and Case 10, the differences between the average fitness values for \(NP\) = 10, 30 and 50 are small in terms of percentage based on the following analysis of the results. This indicates that the proposed SaNSDE algorithm is not sensitive to population size. For other test cases, although the average fitness values are not always the same, they are close. For Case 4, the maximum average fitness value is 542.2, which is obtained by setting \(NP\) = 30 or \(NP\) = 50, and the minimum average fitness value is 539, which is