Table 2.
Results and runtimes of the nine techniques applied to the TSP. For each instance, the results, average runtime, and their standard deviations are shown.
| TSP | GA1 | GA2 | EA1 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Instance | Results | Time (s) | Results | Time (s) | Results | Time (s) | |||||||
| Instance | Optimum | Avg. | St.d. | Avg. | St.d. | Avg. | St.d. | Avg. | St.d. | Avg. | St.d. | Avg. | St.d. |
| St70 | 675 | 711.1 | 25.5 | 8.9 | 2.3 | 714.4 | 18.3 | 4.6 | 1.3 | 705.0 | 13.9 | 1.5 | 0.5 |
| Eilon75 | 535 | 574.7 | 11.8 | 12.2 | 3.1 | 580.9 | 14.0 | 7.5 | 2.2 | 570.1 | 10.9 | 2.2 | 0.6 |
| Eil76 | 538 | 575.6 | 11.4 | 13.0 | 3.0 | 586.1 | 13.1 | 6.7 | 1.9 | 574.0 | 11.2 | 2.0 | 0.7 |
| KroA100 | 21282 | 22129.5 | 557.5 | 22.5 | 6.0 | 22376.5 | 546.5 | 14.3 | 4.3 | 22117.0 | 454.2 | 3.9 | 0.8 |
| KroB100 | 22140 | 23133.2 | 561.3 | 24.5 | 5.6 | 23332.5 | 420.9 | 13.1 | 4.0 | 23098.1 | 401.6 | 4.0 | 0.8 |
| KroC100 | 20749 | 21822.5 | 706.7 | 21.1 | 3.4 | 21924.4 | 479.2 | 15.4 | 4.4 | 21642.5 | 544.7 | 4.1 | 1.2 |
| KroD100 | 21294 | 22347.9 | 573.2 | 24.4 | 7.5 | 22550.2 | 463.5 | 15.9 | 5.2 | 22239.8 | 383.4 | 4.2 | 1.0 |
| Eil101 | 629 | 680.1 | 11.3 | 42.6 | 9.9 | 685.8 | 13.2 | 22.8 | 6.5 | 680.0 | 9.2 | 4.4 | 0.9 |
| Pr107 | 44303 | 46282.2 | 1528.9 | 36.4 | 13.7 | 46470.5 | 1401.2 | 23.1 | 7.9 | 45587.8 | 936.4 | 5.8 | 1.8 |
| Pr124 | 59030 | 60407.6 | 722.2 | 47.0 | 11.0 | 60678.3 | 1170.1 | 26.4 | 6.5 | 60384.6 | 927.8 | 7.5 | 1.2 |
|
| |||||||||||||
| Instance | GA3 | GA4 | EA2 | ||||||||||
|
| |||||||||||||
| St70 | 675 | 744.6 | 21.9 | 3.6 | 1.1 | 725.2 | 20.5 | 3.4 | 0.8 | 713.0 | 10.9 | 0.5 | 0.1 |
| Eilon75 | 535 | 604.2 | 26.6 | 4.6 | 1.1 | 603.9 | 16.5 | 4.9 | 1.2 | 579.6 | 14.1 | 0.7 | 0.1 |
| Eil76 | 538 | 619.5 | 19.9 | 4.8 | 0.9 | 597.5 | 26.1 | 5.4 | 1.1 | 583.7 | 8.5 | 0.7 | 0.1 |
| KroA100 | 21282 | 22416.4 | 518.4 | 13.3 | 3.0 | 22375.6 | 533.5 | 10.0 | 2.6 | 22202.0 | 539.4 | 1.7 | 0.3 |
| KroB100 | 22140 | 23425.4 | 421.7 | 11.8 | 2.6 | 23542.6 | 612.1 | 10.1 | 1.9 | 23024.2 | 458.9 | 1.7 | 0.3 |
| KroC100 | 20749 | 22304.0 | 634.9 | 11.8 | 2.5 | 22302.1 | 733.7 | 10.2 | 3.3 | 21539.1 | 468.3 | 1.8 | 0.3 |
| KroD100 | 21294 | 22592.3 | 434.4 | 13.0 | 2.6 | 22797.8 | 629.6 | 8.9 | 2.1 | 22370.8 | 525.3 | 1.6 | 0.2 |
| Eil101 | 629 | 718.9 | 17.6 | 16.4 | 3.7 | 712.7 | 15.3 | 17.7 | 3.9 | 687.4 | 11.1 | 1.6 | 0.3 |
| Pr107 | 44303 | 46810.9 | 1100.7 | 17.1 | 3.1 | 46661.2 | 1242.7 | 13.2 | 3.4 | 45319.4 | 694.5 | 2.4 | 0.5 |
| Pr124 | 59030 | 61421.5 | 1500.9 | 27.1 | 6.1 | 61148.1 | 1286.2 | 18.0 | 3.0 | 60380.6 | 669.8 | 3.6 | 0.5 |
|
| |||||||||||||
| Instance | GA5 | GA6 | EA3 | ||||||||||
|
| |||||||||||||
| St70 | 675 | 716.1 | 19.8 | 2.8 | 0.6 | 712.4 | 11.6 | 4.9 | 1.0 | 705.3 | 10.3 | 1.3 | 0.2 |
| Eilon75 | 535 | 582.8 | 11.9 | 4.0 | 1.1 | 576.2 | 9.9 | 7.7 | 1.5 | 569.0 | 7.4 | 1.9 | 0.6 |
| Eil76 | 538 | 582.0 | 12.9 | 4.0 | 1.2 | 576.5 | 13.4 | 8.5 | 2.7 | 572.7 | 10.3 | 1.8 | 0.3 |
| KroA100 | 21282 | 22366.4 | 522.9 | 5.5 | 1.5 | 22279.4 | 614.0 | 13.9 | 5.7 | 21838.6 | 294.3 | 3.6 | 0.6 |
| KroB100 | 22140 | 23123.7 | 371.7 | 7.0 | 2.8 | 23134.9 | 375.8 | 12.7 | 3.9 | 22964.2 | 529.3 | 3.6 | 0.5 |
| KroC100 | 20749 | 22005.9 | 584.2 | 6.0 | 1.8 | 21718.2 | 456.8 | 10.7 | 2.4 | 21468.0 | 400.8 | 3.8 | 0.8 |
| KroD100 | 21294 | 22404.3 | 317.7 | 7.7 | 2.6 | 22163.7 | 356.9 | 13.3 | 4.2 | 22039.1 | 441.6 | 3.5 | 0.5 |
| Eil101 | 629 | 696.9 | 16.3 | 11.4 | 2.1 | 689.5 | 12.1 | 24.6 | 5.1 | 675.3 | 9.8 | 4.3 | 0.6 |
| Pr107 | 44303 | 46276.0 | 1153.6 | 10.5 | 4.2 | 45542.7 | 1053.5 | 25.5 | 9.4 | 45145.4 | 590.4 | 4.9 | 1.2 |
| Pr124 | 59030 | 60450.1 | 675.1 | 13.7 | 3.2 | 60020.6 | 564.1 | 26.7 | 8.3 | 59962.0 | 740.7 | 6.9 | 0.9 |