## 5 Results
\begin{table}
\begin{tabular}{c l l} \hline \hline
**Algorithm** & **Parameters for Case 1 through Case 10** & **Parameters for Case 11 through Case 14** \\ \hline
**SaNSDE-1-6** & POP = 30, Gen = 1000, & POP = 50, Gen = 50,000, \\  & LP = 1000 & LP = 1000 \\ \hline \multirow{3}{*}{**DE-1**} & POP = 30, Gen = 1000, & POP = 50, Gen = 50,000, \\  & CR = 0.5 & \(CR\) = 0.5 & \(F\): a value arbitrarily selected from uniform (0, 2) \\ \hline \multirow{3}{*}{**DE-3**} & POP = 30, Gen = 1000, & POP = 50, Gen = 50,000, \\  & CR = 0.5 & \(CR\) = 0.5 & \(CR\) = 0.5 \\  & CR = 0.5 & \(F\): a value arbitrarily selected from uniform (0, 2) \\ \hline \multirow{3}{*}{**NSDE**} & POP = 30, Gen = 1000, & POP = 50, Gen = 50,000, \\  & CR = 0.5, & \(F\): a value arbitrarily selected from uniform (0, 2) \\ \hline \multirow{3}{*}{**NSDE**} & POP = 30, Gen = 1000, & POP = 50, Gen = 50,000, \\  & CR = 0.5, & \(CR\) = 0.5, \\  & \(F_{i}\) = 0.5\(r_{1}\) + 0.5, where \(r_{1}\) is a & \(F_{i}\) = 0.5\(r_{1}\) + 0.5, where \(r_{1}\) is a \\  & random value with Gaussian distribution \(N(0,1)\). & random value with Gaussian distribution \(N(0,1)\). \\ \hline \multirow{3}{*}{**PSO**} & POP = 30, Gen = 1000, & POP = 50, Gen = 50,000, \\  & \(c_{1}\) = 0.4, \(c_{2}\) = 0.6, \(\omega\) = 0.4 & \(c_{1}\) = 0.4, \(c_{2}\) = 0.6, \(\omega\) = 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for different algorithms and test cases. \begin{table}
\begin{tabular}{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 & 41.2892 \\
4 & 6 & 12 & 51.11 & 51.11 & 51.11 & 51.11 & 50.9085 \\
5 & 7 & 13 & 30.063 & 30.063 & 30.063 & 30.063 & 28.4254 \\
6 & 8 & 14 & 72.328 & 72.328 & 72.328 & 72.328 & 70.2629 \\
7 & 9 & 15 & 89.03 & 89.03 & 89.03 & 89.03 & 80.8106 \\
8 & 10 & 16 & 54.02 & 54.02 & 54.02 & 54.02 & 44.0023 \\
9 & 11 & 17 & 74.05 & 74.05 & 74.05 & 49.356 \\
10 & 12 & 18 & 50.9 & 50.0623 & 50.9 & 50.9 & 32.8349 \\
11 & 20 & 20 & 112.906 & 112.906 & 112.906 & 112.906 & 97.7979 \\
12 & 30 & 30 & 202.15 & 196.9089 & 200.1078 & 200.7964 & 141.6005 \\
13 & 40 & 40 & 201.8256 & 190.1664 & 179.4244 & 186.6996 & \(-\)1.5081 \\
14 & 50 & 50 & 190.9436 & 137.1625 & 171.1756 & 161.3107 & \(-\)3.9598 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fitness function values for discrete SaNSDE-1-6,DE-1, DE-3, NSDE and PSO algorithms with _NP_ = 30; _r\({}_{D}\)_ = _r\({}_{P}\)_ = 0.1. The results in Table 3 show that the top four algorithms are SaNSDE-1-6, NSDE, DE-1 and DE-3. For small test cases, including Case 1 through Case 1, the fitness function values obtained using SaNSDE-1-6, NSDE, DE-1 and DE-3 are the same. However, as the problem size grows, the average fitness function values obtained using SaNSDE-1-6 are significantly better than those obtained using NSDE, DE-1 and DE-3. For Case 12, the average fitness function value obtained using SaNSDE-1-6 is better than those obtained using NSDE, DE-1 and DE-3. The differences between the average fitness function value obtained using SaNSDE-1-6 and those obtained using NSDE, DE-1 and DE-3 are about 1% to 2%. For Case 12, the average fitness function value obtained using SaNSDE-1-6 is better than those obtained using NSDE, DE-1 and DE-3. For Case 13, the differences between the average fitness function value obtained using SaNSDE-1-6 and those obtained using NSDE, DE-1 and DE-3 are about 5% to 10%. For Case 14, the differences between the average fitness function value obtained using SaNSDE-1-6 and those obtained using NSDE, DE-1 and DE-3 are about 10% to 28%. In short, SaNSDE-1-6 outperforms NSDE, DE-1 and DE-3 in terms of scalability. To compare performance clearly, please refer to the bar chart shown in Figure 2 for the average fitness function values of Case 1 through Case 14.