## 3 Computational Analysis
### Computational Results
Tables 11 and 12 provide the results achieved by the developed GVNS algorithms with a 2 min time limit within the First and Best improvement search strategy respectively. A notable observation is that in general there are not any significant differences between different methods. However, we notice that on First Improvement for both 1 and 2 min GVNS_3 outperforms GVNS_1 and GVNS_2 implementations. Contrariwise, on Best Improvement all three methods perform better in general than on First Improvement. However, there is no significant difference between them. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Instance** & **zOpt** & **GVNS\_1** & **GVNS\_2** & **GVNS\_3** & **GAP\_1** & **GAP\_2** & **GAP\_3** \\ \hline rl1323.tsp & 270199 & 291236 & 298519 & 285864 & 7.79 & 10.48 & 5.80 \\ rl1889.tsp & 316536 & 343698 & 353960 & 341771 & 8.58 & 11.82 & 7.97 \\ rl5915.tsp & 565530 & 677844 & 654919 & 633460 & 19.86 & 15.81 & 12.01 \\ rl5934.tsp & 556045 & 661867 & 644987 & 604596 & 19.03 & 16.00 & 8.73 \\ si535.tsp & 48450 & 48588 & 48769 & 48812 & 0.28 & 0.66 & 0.75 \\ si1032.tsp & 92650 & 92889 & 93382 & 92896 & 0.26 & 0.79 & 0.27 \\ u574.tsp & 36905 & 41429 & 39874 & 39865 & 12.26 & 8.04 & 8.02 \\ u724.tsp & 41910 & 44377 & 45604 & 44785 & 5.89 & 8.81 & 6.86 \\ u1060.tsp & 224094 & 241290 & 245211 & 243817 & 7.67 & 9.42 & 8.80 \\ u1432.tsp & 152970 & 164667 & 170476 & 165505 & 7.65 & 11.44 & 8.19 \\ u1817.tsp & 57201 & 62417 & 65840 & 61861 & 9.12 & 15.10 & 8.15 \\ u2152.tsp & 64253 & 69701 & 74338 & 70656 & 8.48 & 15.70 & 9.97 \\ u2319.tsp & 234256 & 243207 & 249416 & 245493 & 3.82 & 6.47 & 4.80 \\ vm1084.tsp & 239297 & 254315 & 262020 & 256838 & 6.28 & 9.50 & 7.33 \\ vm1748.tsp & 336556 & 359808 & 373774 & 356880 & 6.91 & 11.06 & 6.04 \\ \hline
**Average** & **253944.1262** & **272756.94** & **277586.89** & **273027.78** & **3.55** & **4.49** & **4.24** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Instance** & **zOpt** & **GVNS\_1** & **GVNS\_2** & **GVNS\_3** & **GAP\_1** (\%) & **GAP\_2** (\%) & **GAP\_3** (\%) \\ \hline ar9152.tsp & 837479 & 1648442 & 1648596 & 1648596 & 96.83 & 96.85 & 96.85 \\ gr9882.tsp & 300899 & 388910 & 388944 & 388944 & 29.25 & 29.26 & 29.26 \\ eg7146.tsp & 172387 & 220232 & 220315 & 220315 & 27.75 & 27.80 & 27.80 \\ fi10639.tsp & 520527 & 49604 & 649604 & 649604 & 24.80 & 24.80 & 24.80 \\ h14473.tsp & 177105 & 484571 & 484812 & 484812 & 173.61 & 173.74 & 173.74 \\ ei8246.tsp & 206171 & 258581 & 258889 & 258889 & 25.55 & 25.57 & 25.57 \\ ja9847.tsp & 491924 & 612157 & 612304 & 612304 & 24.44 & 24.47 & 24.47 \\ kz9976.tsp & 1061882 & 1358247 & 1358247 & 1358247 & 27.91 & 27.91 & 27.91 \\ lu980.tsp & 11340 & 18708 & 23688 & 12236 & 64.97 & 108.89 & 7.90 \\ mo14185.tsp & 427377 & 529729 & 529729 & 529729 & 23.95 & 23.95 & 23.95 \\ nu3496.tsp & 96132 & 220359 & 221920 & 221920 & 129.23 & 130.85 & 130.85 \\ mu1979.tsp & 86891 & 119104 & 120908 & 120908 & 37.07 & 39.15 & 39.15 \\ qu294.tsp & 9352 & 9501 & 9727 & 9706 & 1.59 & 4.01 & 3.79 \\ rw1621.tsp & 26051 & 53343 & 58148 & 58052 & 104.76 & 123.21 & 122.84 \\ tz6117.tsp & 394718 & 500936 & 501184 & 501184 & 26.91 & 26.97 & 26.97 \\ uy734.tsp & 79114 & 84131 & 86022 & 83282 & 6.34 & 8.73 & 5.27 \\ wi29.tsp & 27603 & 27603 & 27603 & 27681 & 0.00 & 0.00 & 0.28 \\ sym7663.tsp & 238314 & 308477 & 308747 & 308747 & 29.44 & 29.55 & 29.55 \\ zi929.tsp & 95345 & 101541 & 112775 & 100572 & 6.50 & 18.28 & 5.48 \\ ca4663.tsp & 1290319 & 1646429 & 1646889 & 1646889 & 27.60 & 27.63 & 27.63 \\ \hline
**Average** & **327546.50** & **462043.75** & **463452.55** & **462130.85** & **44.43** & **48.58** & **42.70** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results using the First Improvement search strategy and an execution time limit of 1 min.