------------------------------------------------------------
                         α=7.0 —— lin105 —— 105 nodes       
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——————— Wed, 31 Jan 2024 06:40:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 62 hubs —— 1—10—6—8—40—50—34—35—5—103—64—44—45—97—92—67—82—76—39—78—96—101—47—62—61—60—74—89—90—23—28—22—24—7—51—57—55—65—66—94—95—75—81—30—33—84—83—71—68—72—9—88—87—104—41—46—11—16—18—36—2—106
total time           3637.71 (TL 3600)    gap                  0.778                
blossom time         0                    nb blossom           0.0                  
LB <= UB             77810.75<=350494.25  subtour              443.0                
connectivity cuts    119.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:105                
2-opt strategy       0                                                              
explored_nodes       23                   n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—10—6—8—40—50—34—35—5—103—64—44—45—97—92—67—82—76—39—78—96—101—47—62—61—60—74—89—90—23—28—22—24—7—51—57—55—65—66—94—95—75—81—30—33—84—83—71—68—72—9—88—87—104—41—46—11—16—18—36—2—106

RING
1  --- 10 | cost [2093.0]
2  --- 36 | cost [7406.0]
2  --- 106 | cost [217.0]
5  --- 35 | cost [5012.0]
5  --- 103 | cost [7497.0]
6  ---  8 | cost [3955.0]
6  --- 10 | cost [1043.0]
7  --- 24 | cost [4256.0]
7  --- 51 | cost [9205.0]
8  --- 40 | cost [7609.0]
9  --- 72 | cost [14252.0]
9  --- 88 | cost [16282.0]
11 --- 16 | cost [4144.0]
11 --- 46 | cost [8295.0]
16 --- 18 | cost [420.0]
18 --- 36 | cost [2485.0]
22 --- 24 | cost [2478.0]
22 --- 28 | cost [1246.0]
23 --- 28 | cost [224.0]
23 --- 90 | cost [14035.0]
30 --- 33 | cost [1239.0]
30 --- 81 | cost [11480.0]
33 --- 84 | cost [10857.0]
34 --- 35 | cost [490.0]
34 --- 50 | cost [8064.0]
39 --- 76 | cost [9114.0]
39 --- 78 | cost [10759.0]
40 --- 50 | cost [1603.0]
41 --- 46 | cost [896.0]
41 --- 104 | cost [2044.0]
44 --- 45 | cost [1435.0]
44 --- 64 | cost [5152.0]
45 --- 97 | cost [11137.0]
47 --- 62 | cost [3542.0]
47 --- 101 | cost [11795.0]
51 --- 57 | cost [882.0]
55 --- 57 | cost [1498.0]
55 --- 65 | cost [7959.0]
60 --- 61 | cost [497.0]
60 --- 74 | cost [5439.0]
61 --- 62 | cost [4109.0]
64 --- 103 | cost [10423.0]
65 --- 66 | cost [497.0]
66 --- 94 | cost [4816.0]
67 --- 82 | cost [1288.0]
67 --- 92 | cost [4291.0]
68 --- 71 | cost [371.0]
68 --- 72 | cost [966.0]
71 --- 83 | cost [1113.0]
74 --- 89 | cost [2485.0]
75 --- 81 | cost [217.0]
75 --- 95 | cost [5495.0]
76 --- 82 | cost [2499.0]
78 --- 96 | cost [4060.0]
83 --- 84 | cost [441.0]
87 --- 88 | cost [490.0]
87 --- 104 | cost [11459.0]
89 --- 90 | cost [714.0]
92 --- 97 | cost [1050.0]
94 --- 95 | cost [490.0]
96 --- 101 | cost [1043.0]

STAR
3  -->  2 | cost [909.0]
4  -->  5 | cost [213.0]
12 --> 103 | cost [651.0]
13 -->  1 | cost [3825.0]
14 -->  1 | cost [3681.0]
15 --> 22 | cost [426.0]
17 --> 18 | cost [273.0]
19 --> 24 | cost [117.0]
20 --> 28 | cost [213.0]
21 -->  1 | cost [1737.0]
25 --> 18 | cost [117.0]
26 --> 39 | cost [2289.0]
27 --> 24 | cost [96.0]
29 --> 22 | cost [96.0]
31 --> 30 | cost [168.0]
32 --> 30 | cost [276.0]
37 -->  1 | cost [3441.0]
38 --> 34 | cost [921.0]
42 --> 41 | cost [306.0]
43 --> 46 | cost [189.0]
48 --> 50 | cost [189.0]
49 --> 50 | cost [414.0]
52 --> 33 | cost [2073.0]
53 --> 46 | cost [378.0]
54 --> 51 | cost [189.0]
56 --> 50 | cost [378.0]
58 -->  1 | cost [4971.0]
59 --> 55 | cost [624.0]
63 --> 66 | cost [1599.0]
69 --> 74 | cost [183.0]
70 --> 74 | cost [276.0]
73 --> 76 | cost [117.0]
77 --> 72 | cost [117.0]
79 --> 72 | cost [210.0]
80 --> 76 | cost [93.0]
85 --> 84 | cost [330.0]
86 --> 84 | cost [531.0]
91 --> 96 | cost [450.0]
93 --> 92 | cost [903.0]
98 --> 89 | cost [921.0]
99 --> 90 | cost [921.0]
100 --> 95 | cost [489.0]
102 --> 97 | cost [450.0]
105 -->  1 | cost [5229.0]

BACKUP RING
1  ---  6 | cost [10.5]
2  --- 18 | cost [55.79]
5  --- 34 | cost [48.160000000000004]
5  --- 64 | cost [144.34]
6  --- 40 | cost [75.04]
7  --- 22 | cost [30.17]
7  --- 57 | cost [100.45]
8  --- 10 | cost [39.76]
8  --- 50 | cost [88.13]
9  --- 68 | cost [140.84]
9  --- 87 | cost [161.70000000000002]
11 --- 18 | cost [44.38]
11 --- 41 | cost [74.55]
16 --- 36 | cost [28.63]
16 --- 46 | cost [58.94]
22 --- 23 | cost [12.11]
23 --- 89 | cost [138.46]
24 --- 28 | cost [12.88]
24 --- 51 | cost [56.77]
28 --- 90 | cost [138.18]
30 --- 75 | cost [112.77]
30 --- 84 | cost [114.66]
33 --- 81 | cost [106.05]
33 --- 83 | cost [109.13]
34 --- 40 | cost [79.66]
35 --- 50 | cost [75.74]
35 --- 103 | cost [72.94]
36 --- 106 | cost [75.88]
39 --- 82 | cost [109.2]
39 --- 96 | cost [142.17000000000002]
41 --- 87 | cost [97.16]
44 --- 97 | cost [114.24000000000001]
44 --- 103 | cost [56.35]
45 --- 64 | cost [51.03]
45 --- 92 | cost [100.94]
46 --- 104 | cost [26.95]
47 --- 61 | cost [58.1]
47 --- 96 | cost [107.87]
51 --- 55 | cost [14.98]
55 --- 66 | cost [76.93]
57 --- 65 | cost [65.03]
60 --- 62 | cost [45.78]
60 --- 89 | cost [73.01]
61 --- 74 | cost [49.49]
62 --- 101 | cost [89.04]
65 --- 94 | cost [50.19]
66 --- 95 | cost [50.120000000000005]
67 --- 76 | cost [22.19]
67 --- 97 | cost [53.2]
68 --- 83 | cost [12.950000000000001]
71 --- 72 | cost [12.32]
71 --- 84 | cost [12.32]
72 --- 88 | cost [65.94]
74 --- 90 | cost [25.900000000000002]
75 --- 94 | cost [56.77]
76 --- 78 | cost [24.78]
78 --- 101 | cost [50.96]
81 --- 95 | cost [53.410000000000004]
82 --- 92 | cost [30.17]
88 --- 104 | cost [114.03]

BACKUP STAR
3  -->  8 | cost [8.76]
4  -->  9 | cost [16.65]
12 --> 23 | cost [7.05]
15 --> 103 | cost [3.0]
17 --> 16 | cost [3.06]
19 --> 16 | cost [4.3500000000000005]
20 --> 23 | cost [1.17]
25 --> 16 | cost [2.91]
26 --> 18 | cost [2.13]
27 --> 18 | cost [5.19]
29 --> 30 | cost [3.0]
31 --> 22 | cost [4.5]
32 --> 22 | cost [5.3100000000000005]
38 --> 39 | cost [2.1]
42 --> 46 | cost [4.23]
43 --> 41 | cost [2.0100000000000002]
48 --> 45 | cost [1.8900000000000001]
49 --> 45 | cost [3.9]
52 --> 46 | cost [1.8900000000000001]
53 --> 51 | cost [5.1000000000000005]
54 --> 57 | cost [1.8900000000000001]
56 --> 55 | cost [1.8900000000000001]
59 --> 50 | cost [7.92]
63 --> 62 | cost [3.06]
69 --> 75 | cost [2.94]
70 --> 75 | cost [3.5100000000000002]
73 --> 74 | cost [4.74]
77 --> 84 | cost [3.87]
79 --> 84 | cost [3.3000000000000003]
80 --> 81 | cost [4.74]
85 --> 83 | cost [2.37]
86 --> 76 | cost [6.63]
91 --> 92 | cost [0.93]
93 --> 89 | cost [9.36]
98 --> 90 | cost [9.48]
99 --> 89 | cost [9.93]
100 --> 94 | cost [5.43]
102 --> 101 | cost [0.96]

B = 161.70000000000002
i★ = 9
j★ = 88
k★ = 87