## 5 Results and Discussion
### Performance Evaluation Using Three-Objective Benchmarks  
The nonparametric Wilcoxon signed rank test is carried out by following the procedure in [44] to confirm that the results are different. In Table 5, the sum of all better ranks and the sum of all worse ranks are represented by R+ and R\(-\), respectively. In order to confirm the rejection of the null hypothesis, the significance level (\(\alpha\)) and the \(p\)-values are calculated. Consequently, due to the \(p\)-value being less than 1, the null hypothesis is rejected. The second experiment is done over the benchmarks reported in [15]. The proposed hybrid method is compared to evolutionary programming, hybrid GA (HGA), GA, NSGA-II-WA, and ensemble systems. Table 6 illustrates the obtained results and shows that the proposed method outperforms its competitors. \begin{table}
\begin{tabular}{c c c} \hline
**CCR** & **Spacing** & **Hypervolume** \\ \hline
1 & 35.65 & 0.91823 \\ \hline
2 & 28.90 & 0.883519 \\ \hline
3 & 31.26 & 0.940621 \\ \hline \end{tabular}
\end{table} 
Table 4: Spacing and Hypervolume of obtained PF. Figure 8: Extracted PF for CCR = 3. \begin{table}
\begin{tabular}{c c c c c} \hline
**Method** & **R+** & **R\(-\)** & \(\alpha\)** & \(p\)**Value** \\ \hline FA & 78 & 25 & 0.05 & 0.002364 \\ \hline MGA & 62 & 18 & 0.01 & 0.000231 \\ \hline BGA & 81 & 12 & 0.01 & 0.000843 \\ \hline NSGA-II-WA & 71 & 25 & 0.01 & 0.091024 \\ \hline Ensemble System & 61 & 28 & 0.05 & 0.115243 \\ \hline Hybrid Method & 56 & 32 & 0.06 & 0.325524 \\ \hline \end{tabular}
\end{table} 
Table 5: [PERSON] signed test results. In addition, Table 7 confirms the rejection of the null hypothesis and the significant differences between the results. The next evaluation is carried out based on the benchmarks and results reported in [12]. The proposed hybrid method is compared to EP, GA, NSGA-II-WA, and a system to solve a three-objective multi-processor scheduling problem, where the objectives are makespan, mean flow time, and reliability. Table 8 represents the results gained by three methods. Table 8 indicates that the proposed hybrid method performs better than GA and EP. Also, Figure 9 represents the extracted Pareto-Front consisting of 73 solutions by the proposed hybrid method. Table 8's values were chosen at random from the Pareto front. The derived Pareto-front has spacing and hypervolume values of 18.32 and 0.78921, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Objective** & **Method** & **Makespan** & **Reliability Index** \\ \hline \multirow{6}{*}{Best \
\begin{tabular}{} \end{tabular} } & GA & 584 & 14.88 \\ \cline{2-4}  & EP & 594 & 15.77 \\ \cline{2-4}  & HGA & 562 & 13.37 \\ \cline{2-4}  & NSGA-II-WA & 511 & 11.23 \\ \cline{2-4}  & Ensemble System & **471.23** & **8.85** \\ \cline{2-4}  & Hybrid Method & 468.92 & 8.73 \\ \hline \multirow{6}{*}{Best
\begin{tabular}{} \end{tabular} } & GA & 961 & 6.64 \\ \cline{2-4}  & EP & 964 & 7.19 \\ \cline{2-4}  & HGA & 1243 & 4.35 \\ \cline{2-4}  & NSGA-II-WA & 680.37 & 4.03 \\ \cline{2-4}  & Ensemble System & 661.43 & 3.62 \\ \cline{2-4}  & Hybrid Method & **648.25** & **3.62** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Obtained objective values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **R+** & **R\(-\)** & \(\mathbf{\alpha}\) & \(\mathbf{p}\)-Value** \\ \hline GA & 62 & 19 & 0.035 & 0.002938 \\ \hline EP & 49 & 28 & 0.042 & 0.007328 \\ \hline HGA & 32 & 21 & 0.032 & 0.006401 \\ \hline NSGA-II-WA & 41 & 32 & 0.041 & 0.008324 \\ \hline Ensemble System & 44 & 29 & 0.052 & 0.019232 \\ \hline Hybrid Method & 36 & 27 & 0.057 & 0.029351 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: [PERSON] signed test results. Figure 9: Pareto Front found by developed hybrid method. The authors of [11] compared their suggested MFA approach to NSGAII using the test graph shown in Figure 2 on four CPUs. They evaluated the problem objectives to be makespan, mean flow time, and reliability.