## 5 Results
### Performance of Three PSO-Based Algorithms and Seven DE-Based Algorithms
The average fitness function values obtained by PSO outperformed those of the CLPSO and CenPSO algorithms for all other cases (Case 2 through Case 10) when the population size was 30. By comparing the average fitness function values obtained by applying the PSO algorithm and the DE-7(NSDE) algorithm, we found that the average fitness function values obtained by the DE-7(NSDE) algorithm were equal to those of the PSO algorithm for Case 1 and Case 2. Moreover, the fitness function values obtained by the DE-7(NSDE) algorithm were greater than those of the PSO algorithm for all other cases (Case 3 through Case 10). This indicated that the performance of the DE-7(NSDE) algorithm was either as good as the PSO algorithm or better than the PSO algorithm for all test cases when the population size was 30. When the population size was 30, the average fitness function values obtained by applying the six DE algorithm variations are listed in Table 13. The average fitness function values obtained by the DE-1 algorithm and the DE-3 algorithm were the same as those obtained by the NSDE algorithm for all test cases. Although the average fitness function values of the DE-2, DE-4, DE-5, and DE-6 algorithms were not as good as those of the NSDE algorithm for all test cases, the average fitness function values obtained by these four DE algorithms were close to those of the NSDE algorithm for most test cases, with some exceptions. The DE-4 and DE-5 algorithms performed poorly in Case 10. In short, the performance of the DE-7(NSDE) algorithm was the same as that of the DE-1 algorithm and the DE-3 algor \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Case** & **D** & **P** & **DE-1** & **DE-2** & **DE-3** & **DE-4** & **DE-5** & **DE-6** \\ \hline
1 & 3 & 10 & 32.998 & 32.998 & 32.998 & 32.4747 & 32.998 & 32.998 \\
2 & 5 & 11 & 63.615 & 50.8922 & 63.615 & 63.615 & 63.615 & 61.9928 \\
3 & 5 & 12 & 41.715 & 41.715 & 41.715 & 41.715 & 41.715 & 41.715 \\
4 & 6 & 12 & 51.11 & 50.9085 & 51.11 & 51.11 & 50.141 & 50.9085 \\
5 & 7 & 13 & 30.063 & 26.1379 & 30.063 & 30.063 & 28.4254 & 30.063 \\
6 & 8 & 14 & 72.328 & 68.6614 & 72.328 & 72.328 & 72.328 \\
7 & 9 & 15 & 89.03 & 86.9898 & 89.03 & 85.323 & 86.213 & 89.03 \\
8 & 10 & 16 & 54.02 & 53.7046 & 54.02 & 53.2235 & 52.0531 & 52.1271 \\
9 & 11 & 17 & 74.05 & 65.5666 & 74.05 & 74.05 & 69.4864 & 72.6228 \\
10 & 12 & 18 & 50.0623 & 47.1623 & 50.9 & 40.9119 & 38.3571 & 49.5823 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Fitness function values for six discrete DE algorithms with population size \(NP=30\); \(r_{D}=r_{P}=0.1\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **D** & **P** & **PSO** & **CLPSO** & **CenPSO** & **DE-7** \\  & & & & & & **(NSDE)** \\ \hline
1 & 3 & 10 & 32.998 & 32.998 & 32.998 & 32.998 \\
2 & 5 & 11 & 63.615 & 57.1262 & 60.3706 & 63.615 \\
3 & 5 & 12 & 41.2892 & 38.1928 & 36.6922 & 41.715 \\
4 & 6 & 12 & 50.9085 & 50.9085 & 47.9958 & 51.11 \\
5 & 7 & 13 & 28.4254 & 21.9635 & 25.482 & 30.063 \\
6 & 8 & 14 & 70.2629 & 67.0561 & 62.0001 & 72.328 \\
7 & 9 & 15 & 80.8106 & 67.7562 & 69.6551 & 89.03 \\
8 & 10 & 16 & 44.0023 & 27.1189 & 26.1877 & 54.02 \\
9 & 11 & 17 & 49.356 & 41.6211 & 37.5057 & 74.05 \\
10 & 12 & 18 & 32.8349 & 15.6644 & 9.361 & 50.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Fitness function values for discrete PSO, CLPSO, CenPSO, and DE-7 (NSDE) algorithms with \(NP=30\); \(r_{D}=r_{P}=0.1\). performances of the DE-1, DE-3, and DE-7(NSDE) algorithms were either as good as or better than those of the DE-2, DE-4, DE-5, and DE-6 algorithms for all test cases when the population size was 30. Based on the analysis above, we found that the DE-1, DE-3, and DE-7(NSDE) algorithms either performed as well as or better than the three variants of the PSO algorithm and the other three DE-based algorithms when the population size was 30. Figure 4 shows the bar chart based on the results listed in Tables 12 and 13.