## 6 Simulation Results and Discussion
### Numerical Results
In general, the proposed tSSO without \(c_{r}\) has a more satisfying performance in all aspect of measures. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(\mathbf{N_{\mathrm{med}}}\)} & \multicolumn{1}{c}{**Alg**} & \multicolumn{1}{c}{**Avg (\(\mathbf{N_{\mathrm{a}}}\))**} & \multicolumn{1}{c}{**Std (\(\mathbf{N_{\mathrm{a}}}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{N_{\mathrm{b}}}\))**} & \multicolumn{1}{c}{**Sd (\(\mathbf{N_{\mathrm{b}}}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{G}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{G}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{G}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{G}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{G}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{G}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{G}\))**} & \multicolumn{1}{c}{**Avg (\(\mathbf{G}\))**} \\ \hline S0 & ISSO & 48.34 & 2.22 & 0.012 & 0.109 & 0.565  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(N_{\rm red}\)} & \multicolumn{1}{c}{**Alg**} & \multicolumn{1}{c}{**Avg (N\({}_{\rm N}\))**} & \multicolumn{1}{c}{**Std (N\({}_{\rm N}\))**} & \multicolumn{1}{c}{**Avg (N\({}_{\rm N}\))**} & \multicolumn{1}{c}{**Std (N\({}_{\rm N}\))**} & \multicolumn{1}{c}{**Avg (ICD)**} & \multicolumn{1}{c}{**Avg (GSD)**} & \multicolumn{1}{c}{**Std (GD)**} & \multicolumn{1}{c}{**Avg (GD)**} & \multicolumn{1}{c}{**Avg (GD)**} & \multicolumn{1}{c}{**Avg (TD)**} & \multicolumn{1}{c}{**Std (TD)**} & \multicolumn{1}{c}{**Avg (Fb)**} & \multicolumn{1}{c}{**Sd (Fb)**} & \multicolumn{1}{c}{**Avg (Fb)**} & \multicolumn{1}{c}{**Sd (Fb)**} & \multicolumn{1}{c}{**Avg (Fb)**} & \multicolumn{1}{c}{**Sd (Fb)**} \\ \hline
50 & tSSO\({}_{\rm 2}\) & 24.72 & 4.177 & 0 & 0 & 20.001 & 2.216 & 109.497 & 7.657 & 4.3751 & 0.7871 & 3  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\(N_{\rm red}\)} & \multicolumn{1}{c}{Alg} & \multicolumn{1}{c}{Avg (N\({}_{\rm N}\))} & \multicolumn{1}{c}{Std (N\({}_{\rm N}\))} & \multicolumn{1}{c}{Avg (N\({}_{\rm N}\))} & \multicolumn{1}{c}{Std (N\({}_{\rm N}\))} & \multicolumn{1}{c}{Avg (ICD)} & \multicolumn{1}{c}{Std (ICD)} & \multicolumn{1}{c}{Avg (GPI)} & \multicolumn{1}{c}{Std (STD)} & \multicolumn{1}{c}{Avg (T)} & \multicolumn{1}{c}{Std (T)} & \multicolumn{1}{c}{Avg (F)} & \multicolumn{1}{c}{Std (F)} & \multicolumn{1}{c}{Avg (F)} & \multicolumn{1}{c}{Std (F)} & \multicolumn{1}{c}{Avg (F)} & \multicolumn{1}{c}{Std (F)} \\ \hline
50 & ESNO & 27,174 & 4,135 & 0 & 0 & 784,62 & 96,656 & 4480.39 & 365,757 & 8,4167 & 1,529 & 96,628.83 & 771,782 & 143,665.5  
In addition, the histogram graphs for the average and standard deviations of the results of two-objective values, i.e., the energy consumption values and the makspan values, for three different-sized benchmark problems by the proposed tSSO and the compared MOPSO, MOSSO, and NSGA-II algorithms are further drawn, as shown in the following Figures 1-12, in order to obtain more results and discussion to validate the performance of the proposed model and to have a comparison at a glance. The best results among tSSO\({}_{0}\) to tSSO\({}_{8}\) are taken as the solution of tSSO and plotted in Figures 1-12. Figure 4: Std of the makspan for small-size benchmark. Figure 5: Average of the energy consumption for medium-size benchmark. Figure 3: Average of the makspan for small-size benchmark. Figure 8: Std of the makspan for medium-size benchmark. Figure 6: Std of the energy consumption for medium-size benchmark. Figure 7: Average of the makspan for medium-size benchmark. Figure 11: Average of the makspan for large-size benchmark. Figure 9: Average of the energy consumption for large-size benchmark.