## 3 The Algorithm
### SaNSDE Algorithm
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **I** & **K** & **SaNSDE (\(NP\) = 10)** & **SaNSDE (\(NP\) = 30)** & **SaNSDE (\(NP\) = 50)** \\ \hline
1 & 4 & 3 & 321/17.8 & 321/6 & 321/6.2 \\
2 & 5 & 5 & 42/133 & 42/10.1 & 42/4.3 \\
3 & 5 & 5 & 55/1731.8 & 55/37 & 55/74 \\
4 & 10 & 10 & 539/70.9 & 542.2/13.9 & 542.2/11.3 \\
5 & 10 & 10 & 715.08/5327.1 & 721.56/1551.2 & 724.02/1794.6 \\
6 & 10 & 20 & 1717/5140.6 & 1728.4/2322.6 & 1730.5/2311.2 \\
7 & 20 & 20 & 1557.9/4860.4 & 1598.3/1268.3 & 1576.6/1088.1 \\
8 & 30 & 10 & 726.9/3750.3 & 731/558.9 & 731/279.2 \\
9 & 30 & 20 & 768.8/2453.2 & 802/519.9 & 802/375.9 \\
10 & 40 & 10 & 780.1/3175.5 & 797/1379.6 & 797/663.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Average fitness values and average number of generations for SaNSDE with algorithmic parameter \(NP\) = 10, 30 and 50. Figure 13: The average fitness function values obtained by SaNSDE with \(NP\) = 10, 30 and 50 for Case 1, Case 2, Case 3, Case 4 and Case 5.

obtained by setting \(NP\) = 10. The difference between the maximum and the minimum average fitness values is \((542.2-539)/539\) = 0.5936%. For Case 5, the maximum average fitness value is 724.02, which is obtained by setting \(NP\) = 50, and the minimum average fitness value is 715.08, which is obtained by setting \(NP\) = 10. The difference between the maximum and the minimum average fitness values is \((724.02-715.08)/715.08=1.2502\%\). For Case 6, the maximum average fitness value is 1730.5, which is obtained by setting \(NP\) = 50, and the minimum average fitness value is 1717, which is obtained by setting \(NP\) = 10. The difference between the maximum and the minimum average fitness values is \((1730.5-1717)/1717\) = 0.7862%. For Case 7, the maximum average fitness value is 1598.3, which is obtained by setting \(NP\) = 30, and the minimum average fitness value is 1557.9, which is obtained by setting \(NP\) = 10. The difference between the maximum and the minimum average fitness values is \((1598.3-1557.9)/1557.9=2.5932\%\). For Case 8, the maximum average fitness value is 731, which is obtained by setting \(NP\) = 30 or \(NP\) = 50, and the minimum average fitness value is 726.9, which is obtained by setting \(NP\) = 10. The difference between the maximum and the minimum average fitness values is \((731-726.9)/726.9=0.5640\%\). For Case 9, the maximum average fitness value is 802, which is obtained by setting \(NP\) = 30 or \(NP\) = 50, and the minimum average fitness value is 768.8, which is obtained by setting \(NP\) = 10. The difference between the maximum and the minimum average fitness values is \((802-768.8)/768.8=4.3184\%\). For Case 10, the maximum average fitness value is 797, which is obtained by setting \(NP\) = 30 or \(NP\) = 50, and the minimum average fitness value is 780.1, which is obtained by setting \(NP\) = 10. The difference between the maximum and the minimum average fitness values is \((797-780.1)/780.1=2.1663\%\). The above results show that the difference between the maximum average fitness value and the minimum average fitness value is less than 2% for most test cases, with the exceptions of Case 7, Case 9 and Case 10. The difference between the maximum average fitness value and the minimum average fitness value is less than 4.5% for Case 7, Case 9 and Case 10. The results of the experiments show that the proposed algorithm is not sensitive to population size. Figure 14: The average fitness function values obtained by SaNSDE with \(NP\) = 10, 30 and 50 for Case 6, Case 7, Case 8, Case 9 and Case 10. ### Statistical Significance of the Results

To illustrate the benefits and statistical significance of the results obtained by the proposed algorithm, let us take the setting with \(LP=1000\) as an example. 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 13 and 14 for \(NP=10\) and \(LP=1000\).