## 3 Computational Analysis
### Computational Results
\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 a280.tsp & 2579 & 2632 & 2738 & 2734 & 2.06 & 6.17 & 6.01 \\ att48.tsp & 10628 & 10628 & 10628 & 10631 & 0.00 & 0.00 & 0.03 \\ bayg29.tsp & 1610 & 1610 & 1610 & 1610 & 0.00 & 0.00 & 0.00 \\ bayg29.tsp & 2020 & 2020 & 2020 & 2020 & 0.00 & 0.00 & 0.00 \\ bier127.tsp & 118282 & 118411 & 119593 & 119962 & 0.11 & 1.11 & 1.42 \\ kroA100.tsp & 21282 & 21282 & 21332 & 21413 & 0.00 & 0.23 & 0.62 \\ burma14.tsp & 3323 & 3323 & 3323 & 3323 & 0.00 & 0.00 & 0.00 \\ ch130.tsp & 6110 & 6147 & 6219 & 6237 & 0.61 & 1.78 & 2.08 \\ ch150.tsp & 6528 & 6571 & 6704 & 6725 & 0.66 & 2.70 & 3.02 \\ d493.tsp & 35002 & 36559 & 37182 & 37119 & 4.45 & 6.23 & 6.05 \\ kroB100.tsp & 22141 & 22162 & 22282 & 22362 & 0.09 & 0.64 & 1.00 \\ kroC100.tsp & 20749 & 20749 & 20837 & 20880 & 0.00 & 0.42 & 0.63 \\ kroD100.tsp & 21294 & 21346 & 21507 & 21581 & 0.24 & 1.00 & 1.35 \\ kroE100.tsp & 22068 & 22129 & 22241 & 22264 & 0.28 & 0.78 & 0.89 \\ kroA150.tsp & 26524 & 26696 & 27169 & 27220 & 0.65 & 2.43 & 2.62 \\ kroB150.tsp & 26130 & 26233 & 26631 & 26696 & 0.39 & 1.92 & 2.17 \\ kroA200.tsp & 29368 & 29549 & 30416 & 30381 & 0.62 & 3.57 & 3.45 \\ kroB200.tsp & 29437 & 29888 & 30618 & 30688 & 1.53 & 4.01 & 4.25 \\ d198.tsp & 15780 & 15845 & 16077 & 16090 & 0.41 & 1.88 & 1.96 \\ brig180.tsp & 1950 & 1963 & 2024 & 2035 & 0.67 & 3.79 & 4.36 \\ berlin52.tsp & 7542 & 7542 & 7542 & 7563 & 0.00 & 0.00 & 0.28 \\ dantzig42.tsp & 699 & 699 & 699 & 699 & 0.00 & 0.00 & 0.00 \\ eil51.tsp & 426 & 426 & 426 & 428 & 0.00 & 0.00 & 0.47 \\ eil76.tsp & 538 & 538 & 544 & 547 & 0.00 & 1.12 & 1.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results using the Best Improvement search strategy and an execution time limit of \(1\) min. \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 gr66.tsp & 294358 & 317446 & 324339 & 309556 & 7.84 & 10.19 & 5.16 \\ nrw1379.tsp & 56638 & 67679 & 68964 & 61769 & 19.49 & 21.76 & 9.06 \\ p654.tsp & 34643 & 36502 & 36558 & 35569 & 5.37 & 5.53 & 2.67 \\ pa561.tsp & 2763 & 2928 & 3053 & 3003 & 5.97 & 10.49 & 8.69 \\ pcb1173.tsp & 56892 & 70520 & 71978 & 61273 & 23.95 & 26.52 & 7.70 \\ pcb3038.tsp & 137694 & 175926 & 176310 & 176310 & 27.77 & 28.04 & 28.04 \\ pr1002.tsp & 259045 & 323543 & 331103 & 277196 & 24.90 & 27.82 & 7.01 \\ pr2392.tsp & 378032 & 460547 & 461170 & 461170 & 21.83 & 21.99 & 21.99 \\ rat575.tsp & 6773 & 7179 & 7190 & 7153 & 5.99 & 6.15 & 5.61 \\ rat783.tsp & 8806 & 9634 & 9610 & 9341 & 9.40 & 9.13 & 6.08 \\ rl1304.tsp & 252948 & 330540 & 33579 & 277603 & 30.68 & 32.75 & 9.75 \\ rl1323.tsp & 270199 & 331586 & 332103 & 293133 & 27.22 & 22.91 & 8.49 \\ rl1889.tsp & 316536 & 388695 & 389270 & 389270 & 22.80 & 22.98 & 22.98 \\ rl5915.tsp & 565530 & 695602 & 695602 & 695602 & 23.00 & 23.00 & 23.00 \\ rl5934.tsp & 556045 & 672412 & 672412 & 672412 & 20.93 & 20.93 & 20.93 \\ si535.tsp & 48450 & 48697 & 48848 & 48807 & 0.51 & 0.82 & 0.74 \\ si1032.tsp & 92650 & 92883 & 94571 & 92909 & 0.25 & 2.07 & 0.28 \\ u574.tsp & 36905 & 40206 & 40020 & 39488 & 8.94 & 8.44 & 7.00 \\ u724.tsp & 41910 & 45583 & 45988 & 44646 & 8.76 & 9.73 & 6.53 \\ u1060.tsp & 224094 & 297757 & 308980 & 242181 & 32.87 & 37.88 & 8.07 \\ u1432.tsp & 152970 & 185839 & 188807 & 166714 & 21.49 & 23.43 & 8.98 \\ u1817.tsp & 57201 & 71999 & 72030 & 72030 & 25.87 & 25.92 & 25.92 \\ u2152.tsp & 64253 & 78870 & 79260 & 79260 & 22.75 & 23.36 & 23.36 \\ u2319.tsp & 234256 & 275453 & 278765 & 278765 & 17.59 & 19.00 & 19.00 \\ vm1084.tsp & 239297 & 295088 & 301477 & 258248 & 23.31 & 25.98 & 7.92 \\ vm1748.tsp & 336556 & 406536 & 408102 & 408102 & 20.79 & 21.26 & 21.26 \\ \hline
**Average** & **266956.86** & **317607.30** & **323886.60** & **276033.63** & **7.31** & **8.06** & **6.03** \\ \hline \hline \end{tabular}
\end{table}