## 4 Computational Experiments
### The Second Set of Experiments
DILA can find all the best solutions for two families and five families. ILS_DP + PR can also find all the best solutions for two families. The results in Tables 10 and 11 also indicate that the DILA performs better than the other heuristics regardless of the values of due-date ranges and setup-time ranges. The DILA can find all the best solutions when the setup-time range is [11; 20]. The average RDI produced by ILS_DP + PR is 0.94 when the setup range is [51; 100]. The average RDI value is very close to the value (0.63) generated by DILA. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Paired Differences**} \\ \cline{3-8}  & \multirow{2}{*}{**Mean**} & \multicolumn{2}{c}{**Std.**} & \multicolumn{2}{c}{**Std. Error**} & \multicolumn{2}{c}{**95\% Confidence Interval**} & \multirow{2}{*}{**t**} & \multirow{2}{*}{**df**} & \multirow{2}{*}{**Sig. (2-Tailed)**} \\  & & \multicolumn{2}{c}{**Deviation**} & \multicolumn{2}{c}{**Mean**} & & & & \\ \cline{5-8}  & & & & \multicolumn{2}{c}{**Lower**} & & & \\ \hline Pair 1 & HGA\(-\)DILA & 17.66 & 38.02 & 1.00 & 15.70 & 19.63 & 17.63 & 1439 & 0.00 \\ Pair 2 & ILS\_BASIC\(-\)DILA & 3.04 & 15.70 & 0.41 & 2.23 & 3.85 & 7.35 & 1439 & 0.00 \\ Pair 3 & ILS\_DP\(-\)DILA & 2.06 & 12.77 & 0.34 & 1.40 & 2.72 & 6.14 & 1439 & 0.00 \\ Pair 4 & ILS\_DP + PR\(-\)DILA & 1.20 & 11.22 & 0.30 & 0.62 & 1.78 & 4.07 & 1439 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Paired \(t\)-test for HGA, ILS_BASIC, ILS_DP, and ILS_DP + PR, and DILA heuristics. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **HGA** & **ILS\_BASIC** & **ILS\_DP** & **ILS\_DP + PR** \\ \hline Number of improved solutions & 258 & 113 & 105 & 68 \\ Number of equal solutions & 1181 & 1325 & 1333 & 1368 \\ Number of inferior solutions & 1 & 2 & 2 & 4 \\ Number of all solutions & 1440 & 1440 & 1440 & 1440 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of comparing DILA with reference heuristics. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(n\times F\) & **HGA** & **ILS\_BASIC** & **ILS\_DP** & **ILS\_DP + PR** & **DILA** \\ \hline \(60\times 2\) & 0.83/119 & 0.00/120 & 0.00/120 & 0.00/120 & 0.00/120 \\ \(60\times 3\) & 0.83/119 & 0.00/120 & 0.00/120 & 0.00/120 & 0.00/120 \\ \(60\times 4\) & 5.00/114 & 0.00/120 & 0.83/119 & 0.00/120 & 0.00/120 \\ \(60\times 5\) & 6.67/112 & 1.25/118 & 0.40/119 & 0.06/119 & 0.00/120 \\ \(80\times 2\) & 5.00/114 & 1.67/118 & 1.25/118 & 0.00/120 & 0.00/120 \\ \(80\times 3\) & 12.26/105 & 1.67/118 & 1.83/117 & 0.00/120 & 0.83/119 \\ \(80\times 4\) & 24.87/89 & 3.87/110 & 5.47/111 & 2.21/114 & 0.83/119 \\ \(80\times 5\) & 30.53/83 & 3.36/109 & 2.88/111 & 5.22/111 & 0.00/120 \\ \(100\times 2\) & 17.37/99 & 5.24/112 & 0.55/115 & 0.00/120 & 0.00/120 \\ \(100\times 3\) & 31.68/81 & 7.11/97 & 3.25/101 & 2.41/111 & 0.28/119 \\ \(100\times 4\) & 39.81/72 & 7.77/94 & 6.28/93 & 3.45/106 & 1.67/118 \\ \(100\times 5\) & 40.72/71 & 8.15/88 & 5.65/87 & 4.70/91 & 0.00/120 \\ \hline Average & 17.96/1178 & 3.34/1324 & 2.37/1331 & 1.50/1372 & 0.30/1435 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Relative deviation index (RDI) and number of best solutions (NBS) of the HGA, ILS_BASIC, ILS_DP, and ILS_DP + PR, and DILA heuristics.