## 5 Computational Experiments
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Group** & **Instances** & **Size** & **SAOP** & **ILS** & **M-MMAS** & **PACO** & **HGA\_RMA** & **PSOVNS** & **NEGAVNS** & **RAMP** & **RDIS** \\ \hline
1 & ta001-ta010 & 20 \(\times\) 5 & 1.05 & 0.33 & 0.04 & 0.18 & 0.04 & 0.03 & 0.00 & 0.00 & 0.00 \\
2 & ta011-ta020 & 20 \(\times\) 10 & 2.60 & 0.52 & 0.07 & 0.24 & 0.02 & 0.02 & 0.01 & 0.03 & 0.03 \\
3 & ta021-ta030 & 20 \(\times\) 20 & 2.06 & 0.28 & 0.06 & 0.18 & 0.05 & 0.05 & 0.02 & 0.04 & 0.04 \\
4 & ta031-ta040 & 50 \(\times\) 5 & 0.34 & 0.18 & 0.02 & 0.05 & 0.00 & 0.00 & 0.00 & 0.01 \\
5 & ta041-ta050 & 50 \(\times\) 10 & 3.50 & 1.45 & 1.08 & 0.81 & 0.72 & 0.57 & 0.82 & 0.37 & 0.95 \\
6 & ta051-ta060 & 50 \(\times\) 20 & 4.66 & 2.05 & 1.93 & 1.41 & 0.99 & 1.36 & 1.08 & 0.61 & 1.88 \\
7 & ta061-ta070 & 100 \(\times\) 5 & 0.30 & 0.16 & 0.02 & 0.02 & 0.01 & 0.00 & 0.00 & 0.00 & 0.01 \\
8 & ta071-ta080 & 100 \(\times\) 10 & 1.34 & 0.64 & 0.39 & 0.29 & 0.16 & 0.18 & 0.14 & 0.06 & 0.38 \\
9 & ta081-ta090 & 100 \(\times\) 20 & 4.49 & 2.42 & 2.42 & 1.93 & 1.30 & 1.45 & 1.40 & 1.76 & 2.35 \\
10 & ta091-ta100 & 200 \(\times\) 10 & 0.94 & 0.50 & 0.30 & 0.23 & 0.14 & 0.18 & 0.16 & 0.15 & 0.32 \\
11 & ta101-ta110 & 200 \(\times\) 20 & 3.67 & 2.07 & 2.15 & 1.82 & 1.26 & 1.35 & 1.25 & 2.00 & 2.30 \\
12 & ta111-ta120 & 500 \(\times\) 20 & 2.20 & 1.20 & 1.02 & 0.85 & 0.69 & – & 0.71 & 1.20 & 1.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of average percent deviation with the best methods in the literature. Figure 8: So-far-Best solution versus iteration in the benchmark instances _ta001_ (**a**) and _ta012_ (**b**). Table 3 shows the comparison of the real and scaled maximum allowed running time for RDIS, NEGAVNS, PSOVNS, and HGA_RMA. The maximum allowed running time of the other approaches in Table 3 is equal to that of HGA_RMA, since they are re-implemented and compared in [48]. Furthermore, since only NEGAVNS and PSOVNS have reported the average time needed to reach their best solution, a comparison is presented in Table 4.  
In addition, based on the fact that NEGAVNS, RAMP, and RDIS, allow similar maximum allowed running time (ref. Table 3), statistical testing has been performed to further \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{PSOVNS} & \multicolumn{3}{c}{NEGAVNS} & \multicolumn{3}{c}{RDIS / RAMP} \\ \cline{3-10}
**Group** & **Instances** & **Size** & **Real** & **Scaled** & **Real** & **Scaled** & **Real** & **Scaled** \\ \hline
1 & ta001-ta010 & \(20\times 5\) & 13.5 & 17.145 & 2.2 & 2.4 & 0.0 & **0.0** \\
2 & ta011-ta020 & \(20\times 10\) & 26.3 & 33.401 & 12.2 & 13.3 & 0.3 & **0.3** \\
3 & ta021-ta030 & \(20\times 20\) & 69.3 & 88.011 & 29.2 & 31.8 & 13.5 & **13.5** \\
4 & ta031-ta040 & \(50\times 5\) & 2.8 & 3.556 & 8.2 & 8.9 & 0.1 & **0.1** \\
5 & ta041-ta050 & \(50\times 10\) & 79.8 & 101.346 & 32.3 & 35.2 & 19.9 & **19.9** \\
6 & ta051-ta060 & \(50\times 20\) & 168.1 & 213.487 & 55 & 60.0 & 34.3 & **34.3** \\
7 & ta051-ta070 & \(100\times 5\) & 52.6 & 66.802 & 30.8 & 33.6 & 1.5 & **1.5** \\
8 & ta071-ta080 & \(100\times 10\) & 211 & 267.97 & 58.7 & 64.0 & 39.3 & **39.3** \\
9 & ta081-ta090 & \(100\times 20\) & 310.8 & 394.716 & 122.7 & 133.7 & 75.0 & **75.0** \\
10 & ta091-ta100 & \(200\times 10\) & 191.3 & 242.951 & 134.5 & 146.6 & 49.8 & **49.8** \\
11 & ta101-ta110 & \(200\times 20\) & 438.7 & 557.149 & 271.7 & 296.2 & 170.0 & **170.0** \\
12 & ta111-ta120 & \(500\times 20\) & – & – & 523.4 & 570.5 & 482.3 & **482.3** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of average time needed to reach the best solution for PSOVNS, NEGAVNS, RAMP, and RDIS. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Clock Speed (GHz)** & **Scaling Factor** \\ \hline RDIS & 2.2 & 1.00 \\ RAMP & 2.2 & 1.00 \\ NEGAVNS & 2.4 & 1.09 \\ HGA_RMA & 2.6 & 1.18 \\ ILS & 2.6 & 1.18 \\ SAOP & 2.6 & 1.18 \\ M-MMAS & 2.6 & 1.18 \\ PACO & 2.6 & 1.18 \\ PSOVNS & 2.8 & 1.27 \\ \hline \hline \end{tabular}
\end{table}