Table 9: Comparison of various formulations based on cycle elimination, that is, the Miller-Tucker-Zemlin formulation MTZ and the CEF on the instances from SET-III with | 𝑉 | = 1 0 0 , 𝑎 = 1 . Furthermore results for connectivity-based formulations (EC and DCut), enhanced by cycle elimination inequalities are reported.

| 𝐿 | = 1 / 4 | 𝐸 | | 𝐿 | = 3 / 4 | 𝐸 |
𝑑 alg cnt opt obj 𝑡 bbn cuts cec cnt opt obj 𝑡 bbn cuts cec

0.05 M T Z 𝑡 𝑛 10 5 19.7 3931 502063 −1−1 10 7 49.9 3112 721279 −1 −1
C E F 𝑡 𝑛 10 6 19.6 3000 135407 −1 16638 10 10 49.8 901 94205 −1 6389
C E F 𝑡 ̃ 𝑛 10 5 19.6 3998 155632 −1 17642 10 7 49.9 2208 208113 −1 14321
E C n c 10 10 19.6 14 1353 121 59 10 0 50.3 7200 532836 170798 1783
E C t n c 10 10 19.6 12 915 153 96 10 7 49.8 2566 62656 44607 5502
D C u t n c 10 10 19.6 13 1433 931 55 10 0 50.4 7200 376649 351288 1630
D C u t t n c 10 10 19.6 13 1029 700 94 10 7 49.8 2291 36745 27748 2859

0.2 M T Z 𝑡 𝑛 10 7 15.0 4276 45276 −1 −1 10 5 35.8 4272 87003 −1 −1
C E F 𝑡 𝑛 10 7 14.9 3217 36913 −1 3298 10 7 35.7 2313 91215 −1 5422
C E F 𝑡 ̃ 𝑛 10 3 15.2 5307 61399 −1 5690 10 7 35.7 2668 40566 −1 2478
E C n c 10 0 15.6 7200 31835 143 118 10 0 37.8 7200 59337 1533 30
E C t n c 10 10 14.8 701 10687 196 670 10 8 35.7 1871 51079 15544 3426
D C u t n c 10 0 15.9 7200 39225 29755 171 10 0 39.4 7200 47294 39206 3
D C u t t n c 10 10 14.8 737 11214 7212 581 10 8 35.7 1537 21721 13795 1400

0.5 M T Z 𝑡 𝑛 10 5 13.5 5555 7818 −1 −1 10 3 30.9 5658 13851 −1 −1
C E F 𝑡 𝑛 10 5 13.6 5038 8686 −1 763 10 7 30.1 4444 19156 −1 1653
C E F 𝑡 ̃ 𝑛 10 3 13.6 5791 8399 −1 1063 10 5 30.5 5570 6646 −1 711
E C n c 10 0 14.1 7200 3463 26 35 10 0 32.7 7200 6497 118 25
E C t n c 10 7 13.5 3865 8772 116 913 10 9 30.1 2112 9120 1344 665
D C u t n c 10 0 15.6 7200 5353 3395 24 10 0 38.2 7200 6964 5357 6
D C u t t n c 10 8 13.5 3394 7452 6433 675 10 9 30.0 2427 7475 5918 576