## 4 Creation of Two-Head Self-Adaptive Metaheuristic Algorithms
In particular, \(SaNSDE(2,4)\) significantly outperforms \(DE\) (\(2\)) and \(DE\) (\(4\)) for larger cases, Case 12, Case 13 and Case 14. The results show that the saying is valid for \(SaNSDE(2,4)\). Figure 4: Comparison of \(SaNSDE(1,4)\) with \(DE\) (\(1\)) and \(DE\) (\(4\)). \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Test Case**} & \multirow{2}{*}{
\begin{tabular}{c} **Participant** \\ **(D/P)** \\ \end{tabular} } & \multirow{2}{*}{_SaNSDE(2,3)_} & \multirow{2}{*}{_DE(2)_} & \multirow{2}{*}{_DE(3)_} \\ \hline
1 & 4/10 & 32.998/6.8 & 32.998/16.7 & 32.998/19.8 \\ \hline
2 & 5/11 & 63.615/17.3 & 50.8922/108.5 & 63.615/36.9 \\ \hline
3 & 5/12 & 41.715/19.5 & 41.715/26 & 41.715/47.6 \\ \hline
4 & 6/12 & 51.11/18.2222 & 50.9085/28.3 & 51.11/50.3 \\ \hline
5 & 7/13 & 30.063/14.4 & 26.1379/48.5 & 30.063/44.1 \\ \hline
6 & 8/14 & 73.328/17.1 & 68.6614/274 & 72.328/67.8 \\ \hline
7 & 9/15 & 89.03/33 & 86.9898/82.9 & 89.03/135 \\ \hline
8 & 10/16 & 54.02/35 & 53.7046/77.2 & 54.02/78.6 \\ \hline
9 & 11/17 & 74.05/39.8 & 65.5666/103.3 & 74.05/65 \\ \hline
10 & 12/18 & 50.9/143.4 & 47.1623/121.1 & 50.9/146.3 \\ \hline
11 & 20/20 & 112.906/103.8 & 104.6357/14,180.2 & 112.906/817.1 \\ \hline
12 & 30/30 & 202.15/1618.1 & 172.4707/9605.8 & 200.1078/16,065.1 \\ \hline
13 & 40/40 & 202.1562/26,276 & 161.4642/7370.7 & 179.4224/27,574.4 \\ \hline
14 & 50/50 & 195.4592/19,867.1 & 135.1454/19,995.4 & 171.1756/22,745.3 \\ \hline \end{tabular}
\end{table} 
Table 9: The results (average fitness values and average number of generations) obtained by applying \(SaNSDE(2,3)\), \(DE\) (\(2\)) and \(DE\) (\(3\)) to the test cases. The results of Experiment 6 obtained by applying the two-head self-adaptive algorithm \(SaNSDE(3,4)\), \(DE\) (3) and \(DE\) (4) to the test cases are summarized in Table 11. Figure 7 shows the results in a bar chart. The results show that the performance of \(SaNSDE(3,4)\) is either better than or the same as that of \(DE\) (3). The results show that the performance of \(SaNSDE(3,4)\) is either better than or the same as that of \(DE\) (4). In particular, \(SaNSDE(3,4)\) significantly outperforms \(DE\) (3) and \(DE\) (4) for larger cases, Case 12, Case 13 and Case 14. The results show that the saying is valid for \(SaNSDE(3,4)\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test Case**} & **Participant** & \multirow{2}{*}{_SaNSDE(2,4)_} & \multirow{2}{*}{_DE(2)_} & \multirow{2}{*}{_DE(4)_} \\  & **(D/P)** & & & \\ \hline
1 & 4/10 & 32.998/12.5 & 32.998/16.7 & 32.4747/11.9 \\ \hline
2 & 5/11 & 63.615/36,8 & 50.8922/108.5 & 63.615/91.3 \\ \hline
3 & 5/12 & 41.715/37.9 & 41.715/26 & 41.715/33.9 \\ \hline
4 & 6/12 & 51.11/17.4444 & 50.9085/28.3 & 51.11/34.3 \\ \hline
5 & 7/13 & 30.063/24.6 & 26.1379/48.5 & 30.063/32.7 \\ \hline
6 & 8/14 & 73.328/29.9 & 68.6614/274 & 72.328/40.3 \\ \hline
7 & 9/15 & 89.03/35.7 & 86.9898/82.9 & 85.323/144.8 \\ \hline
8 & 10/16 & 54.02/40.3 & 53.7046/77.2 & 53.2235/101.1 \\ \hline
9 & 11/17 & 74.05/34.8 & 65.5666/103.3 & 73.1033/80.1 \\ \hline
10 & 12/18 & 50.9/70 & 47.1623/121.1 & 40.9119/229.7 \\ \hline
11 & 20/20 & 112.906/105.9 & 104.6357/14,180.2 & 112.1708/7149.9 \\ \hline
12 & 30/30 & 202.15/1702.5 & 172.4707/9605.8 & 188.1118/7445.2 \\ \hline
13 & 40/40 & 203.7134/3753.8888 & 161.4642/7370.7 & 194.7417/9897 \\ \hline
14 & 50/50 & 195.305/13,134.6 & 135.1454/19,995.4 & 161.954/14,146.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The results (average fitness values and average number of generations) obtained by applying \(SaNSDE(2,4)\), \(DE\) (2) and \(DE\) (4) to the test cases. Figure 5: Comparison of \(SaNSDE(2,3)\) with \(DE\) (2) and \(DE\) (3). Table 12 shows the average fitness values and average number of generations for \(SaNSDE(1,2),SaNSDE(1,3),SaNSDE(1,4),SaNSDE(2,3),SaNSDE(2,4)\) and \(SaNSDE(3,4)\). Figure 8 shows the results in a bar chart. Note that these two-head algorithms generate the same average fitness values for all test cases with the exception of Case 13 and Case 14.