| Instance name | Optimal result | HCA | FOGS-ACO | GSAACS-PSO | IBA | S-CLPSO | C3D-PSO | ASA-GS | FA | ACOMAC-DNN | DPSO | ABNET-TSP | IDCS |
| berlin52 | 7542 | 7542 | 7546.6 | 7542 | 7542 | 7542 |
| 7544.7 | 7544.36 | - | 7542 | 7542 | 7542 |
| ch130 | 6110 | 6110 | - | 6141 | - | - |
| 6110.7 | - | - | - | 6145 | 6110 |
| ch150 | 6528 | 6528 | - | 6528 | - | - |
| 6530.9 | - | - | - | 6602 | 6528 |
| eil51 | 426 | 426 | 426 | 427 | 426 | 426 | 426 | 428.87 | 428.87 | 430.01 | 427 | 427 | 426 |
| eil76 | 538 | 538 | 546.83 | 538 | 539 | 538 | 538 | 544.37 |
| 552.61 | 546 | 541 | 538 |
| eil101 | 629 | 629 | 633.40 | 630 | 634 | 629 |
| 640.21 |
|
| - | 638 | 629 |
| d198 | 15,780 | 15,780 |
| - | - | 15,809 |
| 15830.6 |
| 15,955.6 | - |
| 15,781 |
| kroA100 | 21,282 | 21,282 | 22,414 | 21,282 | 21,282 | 21,282 | 21,282 | 21285.4 | 21285.4 | 21,408.2 | - | 21,333 | 21,282 |
| kroA150 | 26,524 | 26,614 | - | 26,524 | - | 26,537 |
| 26524.9 |
| - | - | 26,678 | 26,524 |
| kroA200 | 29,368 | 29,368 | 29,717 | 29383 | - | 29,399 |
| 29411.5 |
| - | - | 29,600 | 29,382 |
| kroB100 | 22,141 | 22,141 | - | 22141 | 22,140* | - |
| 22139.1 | 22139.1 | - | - | 22,343 | 22,141 |
| kroB150 | 26,130 | 26,132 | - | 26130 | - | - |
| 26140.7 | - | - | - | 26,264 | 26,130 |
| kroB200 | 29,437 | 29,455 | - | 29541 | - | - |
| 29504.2 | - | - | - | 29,637 | 29,448 |
| kroC100 | 20,749 | 20,749 | - | 20,749 | 20,749 | 20824.6 |
| 20750.8 | - | - | - | 20,915 | 20,749 |
| kroD100 | 21,294 | 21,294 | - | 21,309 | 21,294 | 21405.6 |
| 21294.3 | - | - | - | 21,374 | 21,294 |
| kroE100 | 22,068 | 22,068 | - | 22,068 | 22,068 | - |
| 22106.3 | - | - | - | 22,395 | 22,068 |
| lin105 | 14,379 | 14,379 | - | 14,379 | - | 14379 |
| 14383 | 14383 | - | - | 14,379 | 14,379 |
| pr76 | 108,159 | 108,159 | 108,864 | - | - | 108159 |
| 108159 |
| - | 108280 | - | 108,159 |
| pr107 | 44,303 | 44,303 | - | - | 44,303 |
|
| 44301.7* | 44346 | - | - | - | 44,303 |
| pr124 | 59,030 | 59,030 | - | - | 59,030 |
|
| 59030.7 | 59030 | - | - | - | 59,030 |
| pr136 | 96,772 | 96,861 | - | - | 97,547 |
|
| 96966.3 | 97182.7 | - | - | - | 96,790 |
| rat195 | 2323 | 2323 | - | - | - |
|
| 2345.2 |
| - | - | - | 2324 |
| st70 | 675 | 675 | 678.93 | - | 675 | 675 | 675 | 677.11 | 677.11 | - | 675 | - | 675 |
| ts225 | 126,643 | 126,643 | - | - | - | - |
| 126646 | - | - | - | - | 126,643 |
| Average | 29534.6 | 29542.9 | 21353.3 | 16062.2 | 24479.2 | 20585.0 | 5730 | 29,554 | 29,669 | 9587 | 23,494 | 16,051 | 29536.5 |
| P-values versus HCA | 0.1120 | 0.6755 | 0.3327 | 0.3088 | - | 0.1129 | 0.2684 | 0.1536 | 0.3360 | 0.0014 | 0.1890 | ||