Table 3 Overall comparison on OPTW test instances
From: Iterated local search algorithm for solving the orienteering problem with soft time windows
Set | I3CH | ABC | VNS | ILS | ACS | GVNS | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Gap (%) | CPU (s) | Gap (%) | CPU (s) | Gap (%) | CPU (s) | Gap (%) | CPU (s) | Gap (%) | CPU (s) | Gap (%) | CPU (s) | |
C100-100 | 0.0 | 16.9 | 0.1 | 0.8 | 0.1 | <21.6 | 0.0 | 1.0 | 0.0 | 1.4 | 1.3 | 36.6 |
R100-100 | 0.6 | 19.2 | 1.0 | 1.1 | 0.1 | <19.6 | 0.0 | 1.8 | 0.2 | 84.3 | 2.8 | 6.5 |
RC100-100 | 1.9 | 17.2 | 0.1 | 2.4 | 0.0 | <14.4 | 0.0 | 1.0 | 0.0 | 31.5 | 3.7 | 2.2 |
PR01-10 | 1.1 | 73.0 | 1.5 | 24.3 | 1.1 | <163.7 | 0.7 | 50.4 | 1.2 | 357.9 | 1.6 | 2.7 |
C200-100 | 0.4 | 56.5 | 0.5 | 3.4 | 0.2 | <123.2 | 0.1 | 90.0 | 0.6 | 75.4 | 1.1 | 42.3 |
R200-100 | 1.4 | 118.1 | 2.1 | 8.2 | 1.4 | <234.5 | 1.3 | 162.1 | 3.5 | 342.5 | 3.8 | 7.4 |
RC200-100 | 2.8 | 79.9 | 1.8 | 7.5 | 1.5 | <191.3 | 1.1 | 120.5 | 2.2 | 191.3 | 4.1 | 3.5 |
PR11-20 | 4.3 | 87.2 | 3.6 | 32.4 | 3.4 | <230.1 | 2.1 | 97.9 | 11.9 | 195.3 | 4.3 | 5.3 |
Set | GRASP-ELS | SSA | IterLS | FSA | DABC | HILS | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Gap (%) | CPU (s) | Gap (%) | CPU (s) | Gap (%) | CPU (s) | Gap (%) | CPU (s) | Gap (%) | CPU (s) | Gap (%) | CPU (s) | |
C100-100 | 0.0 | 5.0 | 0.0 | 11.2 | 1.2 | 0.2 | 0.9 | 0.3 | 1.7 | ≤11.6 | 0.3 | 0.2 |
R100-100 | 0.2 | 0.8 | 0.1 | 12.3 | 2.0 | 0.2 | 3.2 | 0.1 | 2.6 | ≤17.0 | 0.6 | 0.3 |
RC100-100 | 0.4 | 0.4 | 0.0 | 11.8 | 3.1 | 0.2 | 7.4 | 0.1 | 5.5 | ≤19.2 | 3.5 | 0.1 |
PR01-10 | 1.5 | 1.1 | 1.0 | 59.5 | 4.7 | 1.0 | 5.3 | 1.0 | – | – | 6.8 | 1.2 |
C200-100 | 0.6 | 7.1 | 0.1 | 19.9 | 2.3 | 0.9 | 1.1 | 0.9 | 0.6 | ≤72.2 | 0.8 | 2.6 |
R200-100 | 2.0 | 2.5 | 1.7 | 24.3 | 3.3 | 0.9 | 3.9 | 0.9 | 1.0 | ≤90.9 | 5.1 | 8.3 |
RC200-100 | 2.3 | 1.8 | 1.1 | 26.7 | 3.6 | 0.8 | 5.5 | 0.8 | 1.8 | ≤72.0 | 4.9 | 3.9 |
PR11-20 | 3.4 | 1.7 | 3.7 | 86.1 | 9.6 | 1.1 | 10.2 | 1.1 | – | – | 9.4 | 2.7 |
Set | GA | ACS* | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Gap (%) | CPU (s) | Gap (%) | CPU (s) | |||||||||
C100-100 | 1.1 | ≤0.2 | 0.0 | 1.4 | ||||||||
R100-100 | 1.8 | ≤0.2 | 0.2 | 84.8 | ||||||||
RC100-100 | 2.4 | ≤0.2 | 0.0 | 31.7 | ||||||||
PR01-10 | – | – | 1.2 | 359.8 | ||||||||
C200-100 | 2.5 | ≤0.7 | 0.6 | 75.8 | ||||||||
R200-100 | 7.1 | ≤1.4 | 3.2 | 344.4 | ||||||||
RC200-100 | 7.6 | ≤1.1 | 2.0 | 341.7 | ||||||||
PR11-20 | – | – | 11.9 | 196.4 | ||||||||