Table 1.
Comparison for the small size instances
| Instance | α | λ | Node-based formulation | Flow-based formulation | VNS | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Obj | Gap | TT | Obj | Gap | TT | Best | Avg | Dev | TT | |||
| eil51 | 0.25 | 0.25 | 230 | 0.00 | 1.11 | 230 | 0.00 | 1.44 | 230 | 230 | 0.00 | 0.03 |
| eil51 | 0.25 | 0.50 | 360 | 0.00 | 1.08 | 360 | 0.00 | 1.55 | 360 | 360 | 0.00 | 0.03 |
| eil51 | 0.25 | 0.75 | 467 | 0.00 | 0.45 | 467 | 0.00 | 2.23 | 467 | 467 | 0.00 | 0.03 |
| eil51 | 0.50 | 0.25 | 174 | 0.00 | 3.18 | 174 | 0.00 | 10.86 | 174 | 174 | 0.00 | 0.06 |
| eil51 | 0.50 | 0.50 | 266 | 0.00 | 15.49 | 266 | 0.00 | 18.40 | 266 | 266 | 0.00 | 0.09 |
| eil51 | 0.50 | 0.75 | 333 | 0.00 | 9.87 | 333 | 0.00 | 17.50 | 333 | 333 | 0.00 | 0.09 |
| eil51 | 0.75 | 0.25 | 105 | 0.00 | 2.34 | 105 | 0.00 | 7.25 | 105 | 105 | 0.00 | 0.06 |
| eil51 | 0.75 | 0.50 | 169 | 0.00 | 21.45 | 169 | 0.00 | 36.40 | 169 | 169 | 0.00 | 0.09 |
| eil51 | 0.75 | 0.75 | 216 | 0.00 | 112.01 | 216 | 0.00 | 44.20 | 216 | 216 | 0.00 | 0.09 |
| eil76 | 0.25 | 0.25 | 304 | 0.00 | 3.90 | 304 | 0.00 | 3.40 | 304 | 304 | 0.00 | 0.06 |
| eil76 | 0.25 | 0.50 | 483 | 0.00 | 3.72 | 483 | 0.00 | 4.15 | 483 | 483 | 0.00 | 0.08 |
| eil76 | 0.25 | 0.75 | 618 | 0.00 | 1.06 | 618 | 0.00 | 2.77 | 618 | 618 | 0.00 | 0.05 |
| eil76 | 0.50 | 0.25 | 234 | 0.00 | 1841.36 | 234 | 0.00 | 790.72 | 234 | 234 | 0.00 | 0.11 |
| eil76 | 0.50 | 0.50 | 343 | 0.00 | 1518.44 | 343 | 0.00 | 238.40 | 343 | 343 | 0.00 | 0.10 |
| eil76 | 0.50 | 0.75 | 417 | 0.00 | 73.14 | 417 | 0.00 | 100.20 | 417 | 417 | 0.00 | 0.10 |
| eil76 | 0.75 | 0.25 | 149 | 5.31 | 3600.00 | 149 | 0.00 | 1390.10 | 149 | 149 | 0.00 | 0.08 |
| eil76 | 0.75 | 0.50 | 225 | 16.02 | 3600.00 | 224 | 5.70 | 3600.00 | 224 | 224 | 0.00 | 0.09 |
| eil76 | 0.75 | 0.75 | 271 | 13.17 | 3600.00 | 271 | 11.30 | 3600.00 | 271 | 271 | 0.00 | 0.09 |
| rd100 | 0.25 | 0.25 | 5261 | 0.00 | 23.76 | 5261 | 0.00 | 15.33 | 5261 | 5261 | 0.00 | 0.09 |
| rd100 | 0.25 | 0.50 | 7950 | 0.00 | 8.45 | 7950 | 0.00 | 6.48 | 7950 | 7950 | 0.00 | 0.08 |
| rd100 | 0.25 | 0.75 | 10,502 | 0.00 | 8.08 | 10,502 | 0.00 | 4.69 | 10,502 | 10,502 | 0.00 | 0.07 |
| rd100 | 0.50 | 0.25 | 3975 | 18.60 | 3600.00 | 3975 | 4.40 | 3600.00 | 3975 | 3975 | 0.00 | 0.30 |
| rd100 | 0.50 | 0.50 | 5550 | 8.52 | 3600.00 | 5550 | 0.00 | 2436.41 | 5550 | 5550 | 0.00 | 0.20 |
| rd100 | 0.50 | 0.75 | 6769 | 0.00 | 2182.02 | 6769 | 0.00 | 104.96 | 6769 | 6769 | 0.00 | 0.23 |
| rd100 | 0.75 | 0.25 | 2730 | 32.91 | 3600.00 | 2704 | 26.31 | 3600.00 | 2694 | 2694 | 0.00 | 0.30 |
| rd100 | 0.75 | 0.50 | 3400 | 18.40 | 3600.00 | 3400 | 10.36 | 3600.00 | 3400 | 3400 | 0.00 | 0.33 |
| rd100 | 0.75 | 0.75 | 3953 | 11.21 | 3600.00 | 3953 | 2.13 | 3600.00 | 3953 | 3953 | 0.00 | 0.20 |
| eil101 | 0.25 | 0.25 | 344 | 0.00 | 15.52 | 344 | 0.00 | 13.65 | 344 | 344 | 0.00 | 0.13 |
| eil101 | 0.25 | 0.50 | 521 | 0.00 | 3.69 | 521 | 0.00 | 8.87 | 521 | 521 | 0.00 | 0.13 |
| eil101 | 0.25 | 0.75 | 670 | 0.00 | 2.87 | 670 | 0.00 | 6.65 | 670 | 670 | 0.00 | 0.10 |
| eil101 | 0.50 | 0.25 | 235 | 0.00 | 981.76 | 235 | 0.00 | 315.82 | 235 | 235 | 0.00 | 0.20 |
| eil101 | 0.50 | 0.50 | 354 | 2.41 | 3600.00 | 354 | 0.00 | 186.73 | 354 | 354 | 0.00 | 0.26 |
| eil101 | 0.50 | 0.75 | 436 | 0.00 | 428.33 | 436 | 0.00 | 69.51 | 436 | 436 | 0.00 | 0.22 |
| eil101 | 0.75 | 0.25 | 129 | 0.00 | 2100.00 | 129 | 0.00 | 1809.20 | 129 | 129 | 0.00 | 0.16 |
| eil101 | 0.75 | 0.50 | 180 | 12.83 | 3600.00 | 180 | 0.00 | 958.45 | 180 | 180 | 0.00 | 0.21 |
| eil101 | 0.75 | 0.75 | 212 | 0.00 | 931.00 | 212 | 0.00 | 383.24 | 212 | 212 | 0.00 | 0.24 |
| Avg | 1626.0 | 1285.95 | 1625.2 | 849.71 | 1624.9 | 1624.9 | 0.00 | 0.13 | ||||