## 6 Results and Discussion
### Solutions Quality
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multicolumn{3}{c}{**Optimum**} & \multirow{2}{*}{**GGA**} & \multicolumn{3}{c}{**CPLA**} & \multicolumn{3}{c}{**ACO-TS**} & \multicolumn{3}{c}{**MOGA**} & \multicolumn{3}{c}{**BCO-SHI**} \\  & \multicolumn{3}{c}{**KDMSS**} & & & & & & & & & & \\ \cline{2-11}  & **NV** & **Cost** & **NV** & **RE** & **NV** & **RE** & **NV** & **RE** & **NV** & **RE** \\ \hline C101 & 10 & 827.3 & 10 & 0.0111 (1) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) \\ C102 & 10 & 827.3 & 10 & 0.1100 (1) & 10 & 0.1982 (3.0) & 10 & 0.1982 (3.0) & 10 & 0.8872 (5.0) & 10 & 0.1982 (3.0) \\ C103 & 10 & 826.3 & 10 & 0.1141 (1) & 10 & 0.2130 (2.5) & 10 & 0.2130 (2.5) & 10 & \(-\)(5) & 10 & 1.1388 (4.0) \\ C104 & 10 & 822.9 & 10 & 0.1310 (1) & 10 & 0.2285 (2.0) & 10 & 0.3208 (3.0) & 10 & \(-\)(5) & 10 & 7.5538 (4.0) \\ C105 & 10 & 827.3 & 10 & 0.0001 (1) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) \\ C106 & 10 & 827.3 & 10 & 0.0023 (1) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) \\ C107 & 10 & 827.3 & 10 & 0.0704 (1) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) & 10 & 0.1982 (3.5) \\ C108 & 10 & 827.3 & 10 & 0.0002 (1) & 10 & 0.1982 (3.0) & 10 & 0.1982 (3.0) & 10 & 0.1982 (3.0) & 10 & 0.5355 (5.0) \\ C109 & 10 & 827.3 & 10 & 0.0451 (1) & 10 & 0.1982 (3.0) & 10 & 0.1982 (3.0) & 10 & 0.1982 (3.0) & 10 & 1.6149 (5.0) \\ \hline \multicolumn{2}{c}{Average ranking} & \multicolumn{3}{c}{1} & \multicolumn{3}{c}{3.06} & \multicolumn{3}{c}{3.17} & \multicolumn{3}{c}{3.89} & \multicolumn{3}{c}{3.89} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the experimental results with nine Solomon benchmark problems. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multicolumn{3}{c}{**Best Results**} & \multicolumn{3}{c}{**GGA**} & \multicolumn{3}{c}{**LC03**} & \multicolumn{3}{c}{**HM4**} \\ \cline{2-10}  & **NV** & **Cost** & **Method** & **NV** & **RE** & **NV** & **RE** & **NV** & **RE** \\ \hline C1\_10\_1 & 100 & 42,478.95 & HM4 & 100 & 0.0000 (2) & 100 & 0.0000 (2) & 100 & 0.000 (2) \\ \hline C1\_10\_2 & 90 & 42,222.96 & CAINIAO & 90 & 0.0571 (1) & 93 & 5.1592 (2) & 93 & 5.2975 (3) \\ \hline C1\_10\_3 & 90 & 40,101.36 & Q & 90 & 0.0000 (1) & 90 & 9.4338 (2) & 90 & 14.2066 (3) \\ \hline C1\  
significance level of 5%, the null hypothesis is rejected. Next, the Bergmann-Hommel post-hoc test is applied to find all the possible hypotheses that cannot be rejected. In Table 8 is shown both the average rank (AR) of the results yielded by each method and the \(p\)-values computed by comparing the average accuracies achieved by the GGA versus those obtained by the other methods. The \(p\)-values highlighted with bold numbers indicate that the null hypothesis is rejected for this pair of methods since they show different performance. Unadjusted \(p\)-values are calculated with the average ranks of the two methods being compared, as is described by [PERSON] [66]. These values are used by the Bergmann-Hommel post-hoc test to compute the corresponding adjusted \(p\)-values. Table 8 shows that the GGA has a better performance than the other methods since it has the lowest average rank (1), and its results are statistically different than the others. Figure 12 shows a graph where the nodes represent the compared methods and the edges joining two nodes indicates that the performance of these methods does not present significant differences. The values shown in the edges are the \(p\)-values computed by the Bergmann-Hommel post-hoc test. This figure is based on that obtained using the _scramp_ library. Finally, the Friedman statistics computed by analyzing the results produced by these three methods with 10 problems is 9.8, and the corresponding \(p\)-value is 0.007447, therefore the null hypothesis is rejected.