## Appendix E Performance Metrics of the CHT Behavior
### Ranks Achieved by the Friedman Test  
The ranks obtained by the Friedman test for the three study cases are shown in Table A19.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multirow{2}{*}{**CHT**} & \multirow{2}{*}{**Study Case 1**} & \multicolumn{2}{c}{**Ranks**} \\  & & & **Study Case 2** & **Study Case 3** \\ \hline DER1B & FR & 2.5 & 1.8 & 2 \\ DER1B & SR & 2.5 & 2.7 & 3.1 \\ DER1B & eC & 2.5 & 3.1 & 3.3 \\ DER1B & PF & 2.5 & 2.4 & 1.6 \\ \hline Statistic & & \(\mathit{Inf}\) & 15 & 24 \\ \(p\)-value & & \(\mathit{Inf}\) & \(1.63\times 10^{-3}\) & \(2.23\times 10^{-5}\) \\ \hline DER1E & FR & 2.5 & 2.3 & 3 \\ DER1E & SR & 2.5 & 2.6 & 4 \\ DER1E & eC & 2.5 & 3.4 & 1 \\ DER1E & PF & 2.5 & 1.7 & 2 \\ \hline Statistic & & \(\mathit{Inf}\) & 28 & \(\mathit{Inf}\) \\ \(p\)-value & & \(\mathit{Inf}\) & \(3.56\times 10^{-6}\) & \(\mathit{Inf}\) \\ \hline DEB1B & FR & 2.5 & 2.7 & 2.6 \\ DEB1B & SR & 2.5 & 1 & 2.3 \\ DEB1B & eC & 2.5 & 2.9 & 2.7 \\ DEB1B & PF & 2.5 & 3.4 & 2.4 \\ \hline Statistic & & \(\mathit{Inf}\) & 48 & 1.5 \\ \(p\)-value & & \(\mathit{Inf}\) & \(1.71\times 10^{-10}\) & \(6.82\times 10^{-1}\) \\ \hline DEB1E & FR & 2.5 & 2.2 & 3 \\ DEB1E & SR & 2.5 & 2.5 & 4 \\ DEB1E & eC & 2.5 & 3.1 & 1 \\ DEB1E & PF & 2.5 & 2.2 & 2 \\ \hline Statistic & & \(\mathit{Inf}\) & 11 & \(\mathit{Inf}\) \\ \(p\)-value & & \(\mathit{Inf}\) & \(1.19\times 10^{-2}\) & \(\mathit{Inf}\) \\ \hline DECR & FR & 2.5 & 1.8 & 3 \\ DECR & SR & 2.5 & 2.8 & 1.8 \\ DECR & eC & 2.5 & 3.2 & 1.2 \\ DECR & PF & 2.5 & 2.1 & 4 \\ \hline Statistic & & \(\mathit{Inf}\) & 23 & 84 \\ \(p\)-value & & \(\mathit{Inf}\) & \(4.94\times 10^{-5}\) & \(5.29\times 10^{-18}\) \\ \hline DECB & FR & 2.5 & 2 & 2 \\ DECB & SR & 2.5 & 2.8 & 3 \\ DECB & eC & 2.5 & 3 & 1 \\ DECB & PF & 2.5 & 2.3 & 4 \\ \hline Statistic & & \(\mathit{Inf}\) & 11 & \(\mathit{Inf}\) \\ \(p\)-value & & \(\mathit{Inf}\) & \(1.38\times 10^{-2}\) & \(\mathit{Inf}\) \\ \hline DER1B & FR & 2.5 & 1.8 & 2.2 \\ DER1B & SR & 2.5 & 2.4 & 1 \\ DER1B & eC & 2.5 & 3.5 & 2.8 \\ DER1B & PF & 2.5 & 2.2 & 4 \\ \hline Statistic & & \(\mathit{Inf}\) & 29 & 84 \\ \(p\)-value & & \(\mathit{Inf}\) & \(2.14\times 10^{-6}\) & \(5.29\times 10^{-18}\) \\ \hline DER1E & FR & 2.5 & 2.2 & 2 \\ DER1E & SR & 2.5 & 2.5 & 3 \\ DER1E & eC & 2.5 & 3 & 1 \\ DER1E & PF & 2.5 & 2.3 & 4 \\ \hline Statistic & & \(\mathit{Inf}\) & 7.8 & \(\mathit{Inf}\) \\ \(p\)-value & & \(\mathit{Inf}\) & \(5.04\times 10^{-2}\) & \(\mathit{Inf}\) \\ \hline GA & FR & 2.5 & 2 & 2.1 \\ GA & SR & 2.5 & 2.2 & 1.2 \\ GA & eC & 2.5 & 3.2 & 2.7 \\ GA & PF & 2.5 & 2.6 & 4 \\ \hline Statistic & & \(\mathit{Inf}\) & 16 & \(\mathit{Inf}\) \\ \(p\)-value & & \(\mathit{Inf}\) & \(9.78\times 10^{-4}\) & \(\mathit{Inf}\) \\ \hline PSO & FR & 2.5 & 2.3 & 3 \\ PSO & SR & 2.5 & 2.5 & 1.3 \\ PSO & eC & 2.5 & 2.7 & 2 \\ PSO & PF & 2.5 & 3.8 \\ \hline Statistic & & \(\mathit{Inf}\) & 1.6 & 70 \\ \(p\)-value & & \(\mathit{Inf}\) & \(6.60\times 10^{-1}\) & \(4.71\times 10^{-15}\) \\ \hline \hline \end{tabular}
\end{table}
Table 19: Ranks and \(p\)-value obtained by the Friedman test for the EVALS metric. A \(p\)-value less than 0.05 indicates that at least two groups of values for each algorithm are different.  
Appendix E.6.2. Multiple Comparison Friedman Test  
The collected data from the thirty executions of the four CHTs per each one of the ten metaheuristic algorithms are used to make the multiple comparison Friedman test with the post-hoc correction method. Holm correction is used in this analysis. This test is presented in Table A20.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Algorithms** & **Study Case 1** & \multicolumn{3}{c}{**Study Case 2**} & \multicolumn{3}{c}{**Study Case 3**} \\
**Alg. A + CHT vs. Alg B + CHT** & _p-Value_ & **z** & **Win** & _p-Value_ & **z** & **Win** & _p-Value_ & **z** & **Win** \\