Table 12: Branch-and-cut-and-price results for a special class of instances containing many labels and isolated optima with a relatively low number of labels.

| 𝑉 | , | 𝐸 | , 𝑎 , | 𝐿 | Method cnt opt objt bbn cuts priced

100, 247, 2, 61 E C t n 10 10 5.0 0 1 32 −1
D C u t t n 10 10 5.0 0 1 7 −1
E C t n p 10 10 5.0 0 1 64 14
D C u t t n p 10 10 5.0 0 1 13 17

100, 247, 2, 185 E C t n 10 10 10.0 0 1 1 −1
D C u t t n 10 10 10.0 0 1 2 −1
E C t n p 10 10 10.0 0 1 2 11
D C u t t n p 10 10 10.0 0 1 3 7

100, 900, 2, 247 E C t n 10 10 5.0 0 1 30 −1
D C u t t n 10 10 5.0 1 1 15 −1
E C t n p 10 10 5.0 0 1 72 29
D C u t t n p 10 10 5.0 0 2 19 28

100, 900, 2, 742 E C t n 10 10 10.0 0 14 42 −1
D C u t t n 10 10 10.0 8 13 25 −1
E C t n p 10 10 10.0 2 497 328 30
D C u t t n p 10 10 10.0 12 32 41 25

100, 2475, 2, 618 E C t n 10 10 5.0 1 2 46 −1
DCuttn 10 10 5.0 19 4 15 −1
ECtnp 10 10 5.0 1 6 51 27
DCuttnp 10 10 5.0 11 4 19 26

100, 2475, 2, 1856 ECtn 10 10 10.0 2 15 48 −1
D C u t t n 10 10 10.0 40 11 23 −1
E C t n p 10 10 10.0 10 237 174 24
D C u t t n p 10 10 10.0 36 23 26 16

300, 22425, 2, 1856 ECtn 10 10 10.0 228 1 273 −1
DCuttn10 10 10.0 617 1 6 −1
ECtnp 10 10 10.0 105 1 257 2
DCuttnp 10 10 10.0 459 1 13 2

300, 35880, 2, 8970 ECtn 9 6 6.7 3846 1 600 −1
DCuttn 9 8 8.9 4113 1 17 −1
ECtnp 9 9 10.0 880 1 674 14
DCuttnp 9 9 10.0 1131 1 20 12

300, 35880, 2, 26910 ECtn10 10 10.0 627 1 254 −1
D C u t t n 10 10 10.0 2735 1 10 −1
E C t n p 10 10 10.0 259 1 262 2
D C u t t n p 10 10 10.0 1212 1 18 3