Advances in Operations Research

Research Article

Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

Table 10

Comparison of best formulations used without and with primal heuristics, that is, MVCA and ACO.
| 𝐿 | = 1 / 4 ⋅ | 𝐸 | | 𝐿 | = 3 / 4 ⋅ | 𝐸 |
𝑑 alg cnt opt obj 𝑡 bbn cuts cnt opt obj 𝑡 bbn cuts
E C t n 10 10 19.6 14 4944 4486 10 2 51.2 5760 163875 182801
0.05 E C s n 10 10 19.6 1 1313 966 10 0 55.5 7200 133833 151889
D C u t t n 10 10 19.6 12 1148 759 10 6 49.8 3195 87152 60318
D C u t s n 10 10 19.6 10 1336 895 10 6 49.8 3195 87152 60318
E C t n + M V C A 10 10 19.6 12 5474 4866 10 2 51.3 5771 145352 166307
E C s n + M V C A 10 10 19.6 2 1635 1255 10 0 52.3 7200 137776 154933
D C u t t n + M V C A 10 10 19.6 11 1056 714 10 6 49.8 2902 57282 41009
D C u t s n + M V C A 10 10 19.6 12 1530 993 10 0 50.4 7200 371927 343330
E C t n + A C O 10 10 19.6 12 4425 3916 8 4 49.6 3600 107155 110775
E C s n + A C O 10 10 19.6 2 1339 978 10 0 49.9 7200 134930 151941
D C u t t n + A C O 10 10 19.6 10 937 627 9 4 49.8 4019 74506 52846
D C u t s n + A C O 10 10 19.6 11 1303 828 10 0 50.4 7200 371927 343330
E C t n 10 10 14.8 344 36386 16745 10 2 37.1 6450 120465 121687
0.2 E C s n 10 4 14.8 4894 231148 95062 10 0 39.2 7200 65167 63256
D C u t t n 10 10 14.8 835 13677 8698 10 7 35.8 2432 36099 27852
D C u t s n 10 10 14.8 835 13677 8698 10 0 38.0 7200 88645 73235
E C t n + M V C A 10 10 14.8 767 52496 28531 10 2 36.9 6004 120042 120862
E C s n + M V C A 10 4 14.8 4904 212222 89873 10 0 38.7 7200 63308 60554
D C u t t n + M V C A 10 10 14.8 799 12503 8284 10 8 35.7 2169 34219 25835
D C u t s n + M V C A 10 1 15.5 7067 72658 54894 10 0 38.1 7200 82575 67712
E C t n + A C O 10 10 14.8 345 31157 14313 9 5 36.0 4135 67362 66292
E C s n + A C O 10 3 14.9 5323 228273 94410 10 0 36.1 7200 64340 60405
D C u t t n + A C O 10 10 14.8 640 11034 7149 9 6 35.8 2524 35560 26632
D C u t s n + A C O 10 2 15.0 6977 80725 54925 10 0 36.2 7200 83553 69016
E C t n 9 8 13.2 1400 34106 18769 10 4 31.0 5038 59605 57375
0.5 E C s n 10 0 13.7 7200 296782 88962 10 0 33.8 7200 63430 64801
D C u t t n 10 5 13.5 4557 9195 8543 10 7 30.2 3552 12337 9780
D C u t s n 10 0 14.4 7200 12834 8154 10 7 30.2 3552 12337 9780
E C t n + M V C A 10 8 13.3 1991 40440 23995 10 5 30.5 4274 53202 50948
E C s n + M V C A 10 0 13.7 7200 279895 79633 10 0 32.4 7200 67026 66888
D C u t t n + M V C A 10 7 13.3 3321 6462 5852 10 9 30.0 2728 8479 7236
D C u t s n + M V C A 10 0 14.3 7200 11154 7224 10 0 32.2 7200 14878 10082
E C t n + A C O 9 7 13.3 2261 44962 25718 6 2 31.3 5419 61481 59297
E C s n + A C O 10 0 13.7 7200 345358 80054 10 0 31.1 7200 64469 63099
D C u t t n + A C O 10 7 13.4 3534 7659 6933 8 5 30.5 3374 10577 8304
D C u t s n + A C O 10 0 13.8 7200 12035 7319 10 0 31.2 7200 13919 9175