## 5 Results and Discussion
### Performance Evaluation Using Three-Objective Benchmarks
Table 9 illustrates the results obtained by the developed hybrid methods: MFA, NSGAII, NSGA-II-WA, and Ensemble System. It can be seen that the proposed method outperforms MFA and NSGAII. The Pareto front extracted by the proposed hybrid method is represented in Figure 10. In addition, the derived Pareto-front has spacing and hypervolume values of 42.12 and 0.96547, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Objective** & **Method** & **Makespan** & **Reliability Index** & **Flow Time** \\ \hline \multirow{6}{*}{Best} & GA & 416 & 372.75 & 7.18 \\ \cline{2-5}  & EP & 419 & 368.5 & 7.02 \\ \cline{2-5}  & NSGA-II-WA & 412 & 325.43 & 6.85 \\ \cline{2-5}  & Ensemble System & 404.10 & 303.59 & 5.18 \\ \cline{2-5}  & Hybrid Method & **398.45** & **301.34** & **4.41** \\ \hline \multirow{6}{*}{Best} & GA & 603 & 280.75 & 5.6 \\ \cline{2-5}  & EP & 632 & 292 & 5.6 \\ \cline{2-5}  & NSGA-II-WA & 511.60 & 308.16 & 4.23 \\ \cline{2-5}  & Ensemble System & 483.88 & 266.06 & 3.81 \\ \cline{2-5}  & Hybrid Method & **461.02** & **242.16** & **3.11** \\ \hline \multirow{6}{*}{Best Average} & GA & 810 & 281.25 & 3.07 \\ \cline{2-5}  & EP & 818 & 284.55 & 3.10 \\ \cline{2-5}  & NSGA-II-WA & 659.63 & 308.41 & 3.49 \\ \cline{2-5}  & Ensemble System & 502.76 & 276.34 & 2.83 \\ \cline{2-5}  & Hybrid Method & **502.76** & **258.55** & **2.62** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Obtained objective values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Objective** & **Method** & **Makespan** & **Reliability Index** & **Flow Time** \\ \hline \multirow{6}{*}{Best} & NSGAII & 62 & 25 & 53 \\ \cline{2-5}  & MFA & 59 & 25 & 51 \\ \cline{2-5}  & NSGA-II-WA & 54 & 25 & 51 \\ \cline{2-5}  & Ensemble System & 52 & 21 & 53 \\ \cline{2-5}  & Hybrid Method & **50** & **22** & **51** \\ \hline \multirow{6}{*}{Best} & NSGAII & 65 & 24 & 49 \\ \cline{2-5}  & MFA & 61 & 24 & 50 \\ \cline{1-1} \cline{2-5}  & NSGA-II-WA & 61 & 24 & 49 \\ \cline{1-1} \cline{2-5}  & Ensemble System & 59 & 19 & 46 \\ \cline{1-1} \cline{2-5}  & Hybrid Method & **60** & **18** & **47** \\ \hline \multirow{6}{*}{Best Average} & NSGAII & 65 & 24 & 49 \\ \cline{1-1} \cline{2-5}  & MFA & 61 & 24 & 50 \\ \cline{1-1} \cline{2-5}  & NSGA-II-WA & 59 & 24 & 47 \\ \cline{1-1} \cline{2-5}  & Ensemble System & 59 & 21 & 43 \\ \cline{1-1} \cline{2-5}  & Hybrid Method & **58** & **21** & **41** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Obtained objective values. The results of the final assessment are provided in [17]. The HEFT [34] and CPGA algorithms [35] were contrasted with the recommended technique, HEFT-NSGA [17]. Findings are presented on the Fast Fourier Transformation and Gaussian Elimination graphs [54; 55; 56]. The FFT graph is shown in Figure 11. Schedule Length Ratio (SLR), another comparative parameter taken into account in [19], is computed as follows:  
\[SLR=\frac{\mathit{Makespan}}{\sum_{v_{j}\in CP_{\min}}\min(cost(v_{j}))} \tag{10}\]  
where \(\mathit{CP}\) stands for the graph's critical path, which is focused on minimizing computing costs. The minimal computing costs of tasks on the critical path are added up to form _SLR_. The best algorithm is one that has the lowest _SLR_. The reliability values for the proposed hybrid technique over the Gaussian Elimination graph on four processors are shown in Figure 12 for the HEFT, CPGA, HEFT-NSGA, and HEFT-NSGA algorithms. Figure 13 shows the Makespan, SLR, and reliability values for HEFT, CPGS, and HEFT-NSGA methods and depicts hybrid methods over the FFT graph. Figure 11: FFT Graph. Figure 10: Pareto Front extracted by proposed hybrid method. Figure 12: Makespan (**a**), SLR (**b**) and Reliability index (**c**) of CPGA, HEFT, HEFT-NSGA and proposed Hybrid method for Gaussian Elimination Graph.