## 5 Results
### Performance of Three PSO-Based Algorithms and Seven DE-Based Algorithms
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, they were close to those of the NSDE algorithm for most test cases, with the exception of Case 10. The DE-4 and DE-5 algorithms performed poorly for Case 10. In short, the performances of the NSDE, DE-1, and DE-3 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 50. 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 \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **D** & **P** & **PSO** & **CLPSO** & **CenPSO** &
\begin{tabular}{c} **DE-7** \\ **(NSDE)** \\ \end{tabular} \\ \hline
1 & 3 & 10 & 32.998 & 32.998 & 32.998 & 32.998 \\
2 & 5 & 11 & 63.615 & 63.615 & 58.7484 & 63.615 \\
3 & 5 & 12 & 41.2892 & 40.2464 & 40.0118 & 41.715 \\
4 & 6 & 12 & 51.11 & 49.2425 & 50.707 & 51.11 \\
5 & 7 & 13 & 30.063 & 27.3001 & 26.7878 & 30.063 \\
6 & 8 & 14 & 69.9483 & 65.5762 & 68.2854 & 72.328 \\
7 & 9 & 15 & 80.5986 & 76.1522 & 75.207 & 89.03 \\
8 & 10 & 16 & 46.8013 & 34.9718 & 34.544 & 54.02 \\
9 & 11 & 17 & 55.9356 & 40.201 & 51.2736 & 74.05 \\
10 & 12 & 18 & 31.1131 & 19.7403 & 20.5417 & 50.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Fitness function values for discrete PSO, CLPSO, CenPSO, and DE-7 (NSDE) algorithms with \(NP=50\); \(r_{D}=r_{P}=0.1\). algorithms. The DE-7 (NSDE) algorithm was more efficient than the three variants of the PSO algorithm. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **D** & **P** & **PSO** & **CLPSO** & **ConPSO** &
\begin{tabular}{c} **DE-7** \\ **(NSDE)** \\ \end{tabular} \\ \hline
1 & 3 & 10 & 51.5 & 117.3 & 146.6 & 12.9 \\
2 & 5 & 11 & 127.3 & 399.3 & 355 & 26.4 \\
3 & 5 & 12 & 437.2 & 316.6 & 540.7 & 32.9 \\
4 & 6 & 12 & 468.6 & 541.4 & 514.6 & 33.2 \\
5 & 7 & 13 & 347.1 & 219.9 & 319.3 & 24.8 \\
6 & 8 & 14 & 416.4 & 431.1 & 559.3 & 41.9 \\
7 & 9 & 15 & 366.4 & 499.8 & 363.6 & 61.3 \\
8 & 10 & 16 & 609.5 & 438.9 & 502.1 & 48.6 \\
9 & 11 & 17 & 611.5 & 487.6 & 422.8 & 67 \\
10 & 12 & 18 & 521.5 & 455.6 & 513.6 & 63.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 20: Average number of generations for discrete PSO, CLPSO, CenPSO, and DE-7 (NSDE) algorithms with _NP_ = 50; \(r_{D}=r_{P}=0.1\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Ranking** \\ \hline
**PSO** & 6.65 \\
**CLPSO** & 8.75 \\
**CenPSO** & 9.05 \\
**NSDE** & 3.2 \\
**DE-1** & 6.4 \\
**DE-3** & 3.2 \\
**DE-4** & 3.2 \\
**DE-5** & 4.65 \\
**DE-5** & 5.15 \\
**DE-6** & 4.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 19: Average rankings of the ten algorithms obtained by [PERSON] test for _NP_ = 50. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Ranking** \\ \hline
**PSO** & 6.65 \\
**CLPSO** & 8.75 \\
**CenPSO** & 9.05 \\
**NSDE** & 3.2 \\
**DE-1** & 6.4 \\
**DE-3** & 3.2 \\
**DE-4** & 3.2 \\
**DE-4** & 4.65 \\
**DE-5** & 5.15 \\
**DE-6** & 4.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Average rankings of the ten algorithms obtained by [PERSON] test for _NP_ = 50. By comparing Table 20 with Table 21, it can be seen that the average number of generations required to find the best solutions for the six DE-based algorithms was much smaller than that of the PSO, CLPSO, and CenPSO algorithms. The six DE-based algorithms were more efficient than the three variants of the PSO algorithm when the population size was 50. Based on the comparison above, the seven DE-based algorithms were more efficient than the PSO, CLPSO, and CenPSO algorithms when the population size was 50. The above analysis of the POP = 30 and POP = 50 experimental results indicated that the DE-1, DE-3, and DE-7 (NSDE) algorithms were either as good as or outperformed all the other algorithms for the test cases in terms of the average fitness function values.