## 5 Results and Discussions
### Numerical Analysis on Benchmark Functions  
#### 5.3.1 Numerical Results for SET-1  
Each of the 23 problems was solved by all the stated algorithms, and experimental results such as mean value (_mean_), standard deviation (_SD_), median value (_med_) and worst (_worst_) of the best-so-far solution in the last iteration are reported. The obtained results are presented in Table 2. The outcomes, namely the mean and standard deviation values, are averaged over the number of program runs, which was equal to 30, and the best results are shown in bold type in Table 2.  
Figure 1: Fuzzy terms for all 6 outputs. ==ERROR: No output for this page== \begin{table} \
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \(f\) & \multicolumn{2}{c}{**PSO**} & **WPS** & **FSS** & **CSA** & **FEA** & **RA** & **FFA-a** & **CSA-a** & **BA-a** & **CORBA-f** & **CORBA-fs** & **CORBA-SHA** \\ \hline  & best & 1.638\(-\)24 & 8.63E\(-\)08 & 0.000161 & 6.56E\(-\)08 & 0.000599 & 6.67E\(-\)10 & 0.000273 & 4.90E\(-\)08 & 4.75E\(-\)13 & **0** & 0** & **0** \\  & worst & 3.51E\(-\)24 & 3.69E\(-\)06 & 0.000403 & 1.70E\(-\)07 & 0.002639 & 4.44E\(-\)06 & 0.000723 & 1.50E\(-\)07 & 3.99E\(-\)06 & 2.81E\(-\)15 & 6.47E\(-\)16 & **1.05E\(-\)22** \\  & mean & 8.60E\(-\)24 & 8.42E\(-\)07 & 0.00026 & 1.07E\(-\)07 & 0.000995 & 1.10E\(-\)06 & 0.000678 & 1.05E\(-\)07 & 9.46E\(-\)07 & 1.88E\(-\)16 & 2.16E\(-\)17 & **3.35E\(-\)22** \\  & sd & 1.06E\(-\)23 & 9.00E\(-\)07 & 9.64E\(-\)05 & 3.02E\(-\)08 & 0.00055 & 1.15E\(-\)06 & 0.000405 & 2.64E\(-\)08 & 1.11E\(-\)06 & 7.02E\(-\)16 & 1.16E\(-\)16 & **0** \\ \hline  & best & 0.009514 & 0.213847 & 7.40168 & 0.001712 & 11.4098 & 0.080951 & 10.7438 & 0.000126 & 0.088981 & 0.044043 & **7.54E\(-\)24** & 1.25E\(-\)11 \\  & worst & 0.17305 & 0.330575 & 8.46311 & 0.010075 & 20.0667 & 0.089954 & 16.0295 & **0.001501** & 0.09981 & 0.199479 & 1.702 & 0.015126 \\  & mean & 0.082827 & 0.259768 & 7.99109 & 0.001586 & 15.6137 & 0.0893 & 1.3452 & **0.000679** & 0.092172 & 0.09937 & 0.063924 & 0.001354 \\  & sd & 0.001129 & 0.043318 & 0.393871 & 0.00263 & 3.020 & **0.000287** & 1.96209 & 0.000373 & 0.000273 & 0.001352 & 0.008703 & 0.003631 \\ \hline  & best & 1.45E\(-\)17 & 1.70E\(-\)15 & 0.000484 & 7.54E\(-\)05 & 0.001073 & 0.00773 & 3.83E\(-\)05 & 0.000231 & 0.62E\(-\)17 & **0** \\  & worst & 6.91E\(-\)16 & 3.77E\(-\)05 & 0.000354 & 0.000293 & 0.009237 & 0.009179 & 0.05193 & 0.000246 & 0.007369 & 1.39E\(-\)11 & **4.25E\(-\)13** & **5.67E\(-\)10** \\  & mean & 1.65E\(-\)16 & 2.6E\(-\)06 & 0.000599 & 0.000193 & 0.05747 & 0.002502 & 0.024586 & 0.00163 & 0.003161 & 7.51E\(-\)13 & 1.54E\(-\)14 & **1.98E\(-\)10** \\  & sd & 1.72\end{tabular}\end{table} 
+++  
Additionally, in Table 6 the results of the comparison between COBRA-SHA and the other mentioned algorithms according to the Mann-Whitney statistical test with significance level \(p=0.01\) are presented. The same notations as in Table 3 are used in Table 6. The results of the Mann-Whitney statistical test are presented in Figures 4 and 5. In addition, all the stated algorithms were compared with the proposed modification COBRA-SHA according to the Friedman statistical test. The obtained results are demonstrated in Figures 6 and 7. The following notations were used in Figures 6 and 7: COBRA-fas was denoted as \"C-FAS\" and for COBRA-SHA the notation \"C-SHA\" was used. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \(D\) & **PSO** & **WPS** & **FSS** & **CSA** & **FFA** & **BA** & **FFA-a** & **CSA-a** & **BA-a** & **COBRA-f** & **COBRA-fas** \\ \hline \multirow{3}{*}{\(10\)} & \(+\) & 8 & 9 & 9 & 9 & 9 & 7 & 9 & 8 & 7 & 5 & 2 \\  & \(=\) & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 1 & 2 & 4 & 5 \\  & \(-\) & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 \\ \hline \multirow{3}{*}{\(30\)} & \(+\) & 8 & 9 & 9 & 8 & 9 & 8 & 9 & 8 & 8 & 6 & 4 \\  & \(=\) & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 3 & 2 \\  & \(-\) & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 3 \\ \hline Total & 14 & 18 & 18 & 17 & 18 & 15 & 18 & 16 & 15 & 11 & 1 \\ \hline \hline \end{tabular}
\end{table}