## 5 Computational Framework and Result
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & & & & \multicolumn{2}{c}{**Exact**} & \multicolumn{2}{c}{**Traditional Method**} & \multicolumn{2}{c}{**Method (THB)**} & \multicolumn{2}{c}{**Proposed Methods**} & \\ \cline{4-13}
**No** & **Job** & \(m\) & **NT** & & & \multicolumn{2}{c}{**DE**} & \multicolumn{2}{c}{**CU**} & \multicolumn{2}{c}{**VaNSAS**} & \multicolumn{2}{c}{**SDR**} & \multicolumn{2}{c}{**TTM**} & \multicolumn{2}{c}{**MF**} \\ \cline{4-13}  & & & & & & & & & & & & & & & \\ \cline{4-13}  & & & & & & & & & & & & & & & & \\ \hline M-1 & 40 & 5 & 3 & 18,227 & 16,381 & 163 & 18,728 & 936 & 15,794 & 157 & 17,719 & 708 & 17,653 & 529 & 17,756 & 532 \\ \hline M-2 & 40 & 4 & 4 & 18,385 & 17,288 & 518 & 21,193 & 2119 & 15,992 & 159 & 17,578 & 703 & 17,233 & 861 & 17,481 & 874 \\ \hline M-3 & 40 & 4 & 2 & 19,371 & 16,872 & 337 & 22,371 & 1118 & 16,014 & 320 & 17,722 & 886 & 17,235 & 689 & 17,443 & 697 \\ \hline M -4 & 45 & 4 & 4 & 19,184 & 16,880 & 506 & 20,883 & 1670 & 16,598 & 497 & 16,957 & 847 & 17,182 & 687 & 17,084 & 512 \\ \hline M -5 & 45 & 3 & 2 & 21,827 & 17,998 & 179 & 21,059 & 1263 & 17,550 & 526 & 18,018 & 720 & 18,242 & 912 & 18,115 & 905 \\ \hline M -6 & 45 & 3 & 5 & 21,284 & 17,094 & 170 & 22,014 & 1761 & 16,881 & 506 & 17,225 & 689 & 17,188 & 687 & 17,269 & 518 \\ \hline M -7 & 45 & 5 & 4 & 21,189 & 16,995 & 339 & 20,913 & 2091 & 16,774 & 335 & 17,281 & 518 & 17,192 & 515 & 17,007 & 680 \\ \hline M -8 & 45 & 5 & 2 & 21,087 & 18,047 & 180 & 22,387 & 2238 & 17,559 & 351 & 18,817 & 564 & 19,110 & 764 & 18,349 & 733 \\ \hline M -9 & 50 & 5 & 4 & 24,871 & 20,122 & 402 & 25,881 & 2329 & 19,563 & 195 & 21,883 & 656 & 22,915 & 1145 & 23,120 & 924 \\ \hline M -10 & 50 & 5 & 3 & 24,483 & 23,287 & 232 & 24,879 & 2239 & 22,397 & 223 & 23,589 & 1179 & 23,117 & 924 & 22,996 & 689 \\ \hline M -11 & 50 & 3 & 5 & 25,598 & 24,448 & 733 & 26,712 & 2404 & 22,014 & 220 & 24,421 & 732 & 24,388 & 731 & 24,817 & 1240 \\ \hline M-12 & 52 & 4 & 6 & 26,515 & 24,481 & 734 & 26,818 & 1340 & 22,456 & 673 & 25,817 & 1032 & 25,985 & 1039 & 25,671 & 1026 \\ \hline \multicolumn{13}{c}{\% Improved from best objective} & \multicolumn{2}{c}{14.59} & \multicolumn{2}{c}{4.37} & \multicolumn{2}{c}{19.55} & \multicolumn{2}{c}{11.19} & \multicolumn{2}{c}{11.04} & \multicolumn{2}{c}{11.24} \\ \multicolumn{13}{c}{} & \multicolumn{2}{c}{found by Lingo} & \multicolumn{2}{c}{} & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistical test of small test instances. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **DE** & **CU** & **VaNSAS** & **SDR** & **TTM** & **MF** \\ \hline Lingo & 0.000 & 0.006 & 0.000 & 0.001 & 0.000 & 0.001 \\ \hline DE & & 0.000 & 0.002 & 0.006 & 0.030 & 0.039 \\ \hline CU & & & 0.000 & 0.000 & 0.000 & 0.000 \\ \hline VaNSAS & & & & 0.000 & 0.000 & 0.000 \\ \hline SDR & & & & & 0.777 & 0.962 \\ \hline TTM & & & & & & & 0.767 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Computation results of medium-sized test instances. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & **DE** & **CU** & **VaNSAS** & **SDR** & **TTM** & **MF** \\ \hline Lingo & 0.000 & 0.006 & 0.000 & 0.001 & 0.000 & 0.001 \\ \hline DE & & 0.000 & 0.002 & 0.006 & 0.030 & 0.039 \\ \hline CU & & & 0.000 & 0.000 & 0.000 & 0.000 \\ \hline VaNSAS & & & & 0.000 & 0.001 & 0.001 \\ \hline SDR & & & & & 0.777 & 0.962 \\ \hline TTM & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Statistical test of objective function for medium-sized problem. Computation results in Tables 9-11 show that VaNAS performed much better than the other proposed and traditional methods did, and its performance was not significantly different from that of the exact method, while that of others significantly differed from that of the exact method.