## 5 Computational Results
In addition, the ARPD for each instance, totally 150, is recorded to make statistical analyses. The computational results are given in Table 3. The first observation from Table 3 that the IG_RIS and DABC_RCT algorithms are not competitive to the DABC*_RCT and VBIH variants. Especially, even though the fast fitness calculation is employed in the IG_RIS algorithm, which is known as one of the best algorithms in the scheduling literature, it could not be able to generate competitive results. In fact, its local search is based on only the insertion neighborhood, which is very effective for the makespan criterion. However, the results in Table 3 indicate that the swap neighborhood should be used in algorithms designed for the total flowtime criterion. The second observation is the performance of the DABC*_RCT algorithm, which is quite competitive to the VBIH variants. The overall ARPD is decreased from 0.593 percent to 0.376 percent due to the use of the PFT_NEH(x) heuristic as a solution in the initial population. It indicates that the proposed PFT_NEH(x) heuristic was so effective on the results of the DABC*_RCT algorithm. Amongst the VBIH variants, the first four variants were able to generate results ranging from 0.303 percent to 0.285 percent. As can be seen from Table 3, especially, the larger instances with sizes 500 \(\times\) 20, 500 \(\times\) 5 and 500 \(\times\) 10 were further improved by the first four variants of the VBIH algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**n \(\times\) m** & **IG\_RIS** & **DABC\_RCT** & **IVLS** & **DABC\({}^{*}\_\)RCT** & **VBHH1** & **VBHH2** & **VBHH3** & **VBHH4** & **VBHH5** & **VBHH6** \\ \hline
20 \(\times\) 5 & 0.049 & 0.004 & 0.068 & 0.006 & 0.001 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 \\
20 \(\times\) 10 & 0.016 & 0.021 & 0.151 & 0.031 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 \\
20 \(\times\) 20 & 0.010 & 0.015 & 0.032 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 \\
50 \(\times\) 5 & 0.901 & 0.788 & 0.713 & 0.490 & 0.418 & 0.354 & 0.346 & 0.376 & 0.296 & 0.325 \\
50 \(\times\) 10 & 0.819 & 0.752 & 0.916 & 0.752 & 0.562 & 0.455 & 0.457 & 0.424 & 0.463 & 0.502 \\
50 \(\times\) 20 & 0.521 & 0.561 & 0.652 & 0.490 & 0.318 & 0.378 & 0.316 & 0.355 & 0.330 & 0.321 \\
100 \(\times\) 1 & 1.555 & 1.135 & 1.133 & 0.937 & 0.650 & 0.764 & 0.709 & 0.650 & 0.696 & 0.714 \\
100 \(\times\) 10 & 1.639 & 1.301 & 1.358 & 1.285 & 1.070 & 1.179 & 1.126 & 1.098 & 1.112 & 1.118 \\
100 \(\times\) 20 & 1.147 & 1.279 & 0.927 & 0.983 & 0.759 & 0.833 & 0.799 & 0.903 & 0.796 & 0.750 \\
200 \(\times\) 10 & 0.633 & 0.559 & 0.236 & 0.312 & 0.427 & 0.243 & 0.357 & 0.293 & 0.297 & 0.308 \\
200 \(\times\) 20 & 0.337 & 0.581 & 0.193 & 0.201 & 0.146 & 0.227 & 0.211 & 0.255 & 0.430 & 0.421 \\
500 \(\times\) 20 & 0.429 & 0.426 & \(-0.381\) & \(-0.274\) & \(-0.353\) & \(-0.374\) & \(-0.395\) & \(-0.303\) & \(-0.192\) & \(-0.185\) \\
200 \(\times\) 5 & 0.854 & 0.470 & 0.373 & 0.358 & 0.392 & 0.325 & 0.341 & 0.372 & 0.388 & 0.401 \\
500 \(\times\) 5 & 0.259 & 0.397 & \(-0.014\) & \(-0.022\) & 0.150 & \(-0.012\) & \(-0.053\) & \(-0.042\) & 0.299 & 0.369 \\
500 \(\times\) 10 & 0.234 & 0.607 & \(-0.033\) & 0.092 & 0.000 & \(-0.031\) & 0.035 & \(-0.046\) & 0.174 & 0.282 \\ \hline Average & 0.583 & 0.593 & 0.422 & 0.376 & 0.303 & **0.289** & **0.285** & **0.289** & 0.339 & 0.355 \\ \hline \hline \end{tabular} Bold: better results  
\end{table} 
Table 3: Average relative percentage deviations for algorithms compared. In order to see the statistical difference between algorithms, we provide the interval plot of the algorithms compared in Figure 12. Since the 95% confidence intervals of DABC*_RCT and VBIH variants do not overlap, we can conclude that the DABC*_RCT and the VBIH variants generated results, which are statistically significant to those results generated by the IG_RIS and DABC_RCT algorithms. When we look at the confidence intervals of the DABC*_RCT and VBIH variants, there are overlaps between the algorithms.