------------------------------------------------------------
                         α=7.0 —— lin105 —— 105 nodes       
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——————— Fri, 19 Jan 2024 13:55:44 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 20 hubs —— 1—7—12—17—18—27—33—43—52—105—55—63—66—49—104—31—32—103—15—106
total time           3644.82 (TL 3600)    gap                  0.573                
blossom time         0                    nb blossom           0.0                  
LB <= UB             72520.93<=169987.08  subtour              713.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:105                
2-opt strategy       0                                                              
explored_nodes       463                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—7—12—17—18—27—33—43—52—105—55—63—66—49—104—31—32—103—15—106

RING
1  ---  7 | cost [1267.0]
7  --- 12 | cost [2548.0]
12 --- 17 | cost [2723.0]
15 --- 103 | cost [700.0]
15 --- 106 | cost [3311.0]
17 --- 18 | cost [637.0]
18 --- 27 | cost [1211.0]
27 --- 33 | cost [1365.0]
31 --- 32 | cost [252.0]
31 --- 104 | cost [2786.0]
32 --- 103 | cost [1694.0]
33 --- 43 | cost [4053.0]
43 --- 52 | cost [882.0]
49 --- 66 | cost [8904.0]
49 --- 104 | cost [2240.0]
52 --- 105 | cost [2849.0]
55 --- 63 | cost [4032.0]
55 --- 105 | cost [1694.0]
63 --- 66 | cost [3731.0]

STAR
2  -->  1 | cost [93.0]
3  --> 12 | cost [921.0]
4  --> 17 | cost [2058.0]
5  --> 17 | cost [1851.0]
6  -->  1 | cost [450.0]
8  --> 12 | cost [936.0]
9  --> 17 | cost [924.0]
10 --> 15 | cost [564.0]
11 --> 15 | cost [480.0]
13 --> 17 | cost [1665.0]
14 --> 17 | cost [1461.0]
16 --> 18 | cost [180.0]
19 --> 18 | cost [474.0]
20 --> 15 | cost [576.0]
21 --> 15 | cost [333.0]
22 --> 15 | cost [426.0]
23 --> 33 | cost [567.0]
24 --> 18 | cost [489.0]
25 --> 18 | cost [117.0]
26 --> 18 | cost [213.0]
28 --> 33 | cost [477.0]
29 --> 15 | cost [522.0]
30 --> 33 | cost [531.0]
34 --> 17 | cost [1863.0]
35 --> 17 | cost [1749.0]
36 --> 33 | cost [876.0]
37 --> 18 | cost [1110.0]
38 --> 52 | cost [2061.0]
39 --> 52 | cost [1851.0]
40 --> 33 | cost [1347.0]
41 --> 52 | cost [573.0]
42 --> 52 | cost [591.0]
44 --> 52 | cost [606.0]
45 --> 52 | cost [1152.0]
46 --> 52 | cost [189.0]
47 --> 52 | cost [510.0]
48 --> 105 | cost [1092.0]
50 --> 105 | cost [906.0]
51 --> 52 | cost [474.0]
53 --> 52 | cost [189.0]
54 --> 52 | cost [510.0]
56 --> 105 | cost [552.0]
57 --> 52 | cost [606.0]
58 --> 52 | cost [378.0]
59 --> 105 | cost [561.0]
60 --> 66 | cost [1035.0]
61 --> 66 | cost [921.0]
62 --> 105 | cost [876.0]
64 --> 105 | cost [921.0]
65 --> 66 | cost [213.0]
67 --> 105 | cost [1323.0]
68 --> 105 | cost [1428.0]
69 --> 105 | cost [1533.0]
70 --> 66 | cost [1461.0]
71 --> 105 | cost [1551.0]
72 --> 105 | cost [1497.0]
73 --> 105 | cost [1536.0]
74 --> 105 | cost [1716.0]
75 --> 66 | cost [1749.0]
76 --> 105 | cost [1650.0]
77 --> 105 | cost [1614.0]
78 --> 105 | cost [1788.0]
79 --> 105 | cost [1707.0]
80 --> 105 | cost [1740.0]
81 --> 66 | cost [1776.0]
82 --> 105 | cost [1875.0]
83 --> 105 | cost [1971.0]
84 --> 105 | cost [1920.0]
85 --> 105 | cost [2208.0]
86 --> 105 | cost [2148.0]
87 --> 66 | cost [1149.0]
88 --> 66 | cost [1227.0]
89 --> 66 | cost [2265.0]
90 --> 66 | cost [2055.0]
91 --> 105 | cost [3063.0]
92 --> 105 | cost [3153.0]
93 --> 105 | cost [3069.0]
94 --> 66 | cost [2064.0]
95 --> 66 | cost [2148.0]
96 --> 105 | cost [3498.0]
97 --> 105 | cost [3588.0]
98 --> 66 | cost [2937.0]
99 --> 66 | cost [2787.0]
100 --> 66 | cost [2604.0]
101 --> 105 | cost [3930.0]
102 --> 105 | cost [4023.0]

BACKUP RING
1  --- 12 | cost [34.160000000000004]
7  --- 17 | cost [52.36]
12 --- 18 | cost [23.87]
15 --- 32 | cost [22.05]
17 --- 27 | cost [18.48]
18 --- 33 | cost [25.13]
27 --- 43 | cost [47.04]
31 --- 49 | cost [42.42]
31 --- 103 | cost [14.49]
32 --- 104 | cost [26.39]
33 --- 52 | cost [48.370000000000005]
43 --- 105 | cost [35.35]
49 --- 63 | cost [52.71]
52 --- 55 | cost [25.76]
55 --- 66 | cost [76.93]
63 --- 105 | cost [27.16]
66 --- 104 | cost [90.72]
103 --- 106 | cost [39.410000000000004]

BACKUP STAR
3  -->  1 | cost [9.27]
4  --> 18 | cost [23.31]
5  --> 18 | cost [21.21]
8  --> 17 | cost [9.93]
9  --> 18 | cost [10.89]
10 -->  7 | cost [3.54]
11 -->  7 | cost [4.5]
13 --> 18 | cost [19.26]
14 --> 18 | cost [17.19]
16 --> 17 | cost [3.06]
19 --> 27 | cost [2.13]
20 --> 103 | cost [2.97]
21 --> 103 | cost [2.52]
22 --> 103 | cost [3.0]
23 --> 103 | cost [3.5700000000000003]
24 --> 27 | cost [0.96]
25 --> 17 | cost [3.48]
26 --> 17 | cost [4.23]
28 --> 103 | cost [4.2]
29 --> 31 | cost [3.6]
30 --> 31 | cost [1.68]
34 --> 18 | cost [20.13]
35 --> 18 | cost [18.81]
36 --> 104 | cost [9.36]
37 --> 43 | cost [11.1]
38 --> 43 | cost [19.32]
39 --> 43 | cost [17.25]
40 --> 49 | cost [4.3500000000000005]
41 --> 43 | cost [2.0100000000000002]
42 --> 43 | cost [2.85]
44 --> 43 | cost [4.74]
45 --> 49 | cost [3.9]
46 --> 43 | cost [1.8900000000000001]
47 --> 43 | cost [5.1000000000000005]
48 --> 49 | cost [3.54]
50 --> 55 | cost [1.8900000000000001]
51 --> 43 | cost [6.0600000000000005]
53 --> 43 | cost [5.67]
54 --> 55 | cost [6.15]
56 --> 55 | cost [1.8900000000000001]
57 --> 105 | cost [6.24]
58 --> 43 | cost [7.5600000000000005]
59 --> 55 | cost [6.24]
60 --> 63 | cost [16.65]
61 --> 63 | cost [14.61]
62 --> 63 | cost [3.06]
64 --> 63 | cost [11.94]
65 --> 63 | cost [17.37]
67 --> 63 | cost [17.73]
68 --> 63 | cost [18.6]
69 --> 63 | cost [9.48]
70 --> 63 | cost [9.21]
71 --> 63 | cost [20.19]
72 --> 63 | cost [16.44]
73 --> 63 | cost [12.780000000000001]
74 --> 63 | cost [10.89]
75 --> 63 | cost [12.06]
76 --> 63 | cost [13.77]
77 --> 63 | cost [17.22]
78 --> 63 | cost [21.54]
79 --> 63 | cost [17.85]
80 --> 63 | cost [14.58]
81 --> 63 | cost [12.96]
82 --> 63 | cost [22.11]
83 --> 63 | cost [22.5]
84 --> 63 | cost [21.06]
85 --> 63 | cost [24.39]
86 --> 63 | cost [20.37]
87 --> 63 | cost [24.45]
88 --> 63 | cost [23.97]
89 --> 63 | cost [21.48]
90 --> 63 | cost [21.51]
91 --> 63 | cost [31.98]
92 --> 63 | cost [32.730000000000004]
93 --> 63 | cost [28.59]
94 --> 63 | cost [31.92]
95 --> 63 | cost [31.8]
96 --> 63 | cost [35.61]
97 --> 63 | cost [36.39]
98 --> 63 | cost [30.63]
99 --> 63 | cost [30.72]
100 --> 63 | cost [36.69]
101 --> 63 | cost [39.42]
102 --> 63 | cost [40.230000000000004]

B = 600.77
i★ = 52
j★ = 105
k★ = 55