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                           α=7.0 —— rat99 —— 99 nodes       
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——————— Tue, 09 Jan 2024 09:37:22 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 49 hubs —— 1-2-3-12-13-22-21-30-29-38-39-48-47-57-56-65-66-75-76-84-83-93-94-95-97-89-88-79-80-71-70-61-62-53-52-51-42-43-34-35-26-25-17-16-7-6-5-4-100-1
total time           3603.31 (TL 3600)    gap                  0.078                
blossom time         0                    nb blossom           0.0                  
LB <= UB             6569.88<=7128.47     Master/SP costs      6563/565.47          
Master time          3311.04              SP time              292.27               
subtour              1819.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            1970.0               SP method            poly                 
tildeV               2:99                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       123196               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—3—12—13—22—21—30—29—38—39—48—47—57—56—65—66—75—76—84—83—93—94—95—97—89—88—79—80—71—70—61—62—53—52—51—42—43—34—35—26—25—17—16—7—6—5—4—100

RING
1  ---  2 | cost [98.0]
1  --- 100 | cost [0.0]
2  ---  3 | cost [63.0]
3  --- 12 | cost [49.0]
4  ---  5 | cost [105.0]
4  --- 100 | cost [196.0]
5  ---  6 | cost [63.0]
6  ---  7 | cost [77.0]
7  --- 16 | cost [182.0]
12 --- 13 | cost [91.0]
13 --- 22 | cost [98.0]
16 --- 17 | cost [91.0]
17 --- 25 | cost [126.0]
21 --- 22 | cost [42.0]
21 --- 30 | cost [126.0]
25 --- 26 | cost [70.0]
26 --- 35 | cost [84.0]
29 --- 30 | cost [77.0]
29 --- 38 | cost [119.0]
34 --- 35 | cost [119.0]
34 --- 43 | cost [42.0]
38 --- 39 | cost [63.0]
39 --- 48 | cost [28.0]
42 --- 43 | cost [56.0]
42 --- 51 | cost [147.0]
47 --- 48 | cost [105.0]
47 --- 57 | cost [147.0]
51 --- 52 | cost [63.0]
52 --- 53 | cost [56.0]
53 --- 62 | cost [147.0]
56 --- 57 | cost [56.0]
56 --- 65 | cost [91.0]
61 --- 62 | cost [63.0]
61 --- 70 | cost [112.0]
65 --- 66 | cost [77.0]
66 --- 75 | cost [112.0]
70 --- 71 | cost [49.0]
71 --- 80 | cost [70.0]
75 --- 76 | cost [91.0]
76 --- 84 | cost [98.0]
79 --- 80 | cost [105.0]
79 --- 88 | cost [98.0]
83 --- 84 | cost [112.0]
83 --- 93 | cost [112.0]
88 --- 89 | cost [105.0]
89 --- 97 | cost [119.0]
93 --- 94 | cost [91.0]
94 --- 95 | cost [126.0]
95 --- 97 | cost [133.0]

STAR
8  -->  7 | cost [30.0]
9  -->  7 | cost [60.0]
10 -->  2 | cost [33.0]
11 --> 12 | cost [18.0]
14 -->  5 | cost [36.0]
15 --> 16 | cost [30.0]
18 --> 17 | cost [30.0]
19 --> 21 | cost [75.0]
20 --> 21 | cost [54.0]
23 --> 22 | cost [42.0]
24 --> 25 | cost [27.0]
27 --> 35 | cost [39.0]
28 --> 29 | cost [39.0]
31 --> 30 | cost [36.0]
32 --> 42 | cost [54.0]
33 --> 34 | cost [36.0]
36 --> 35 | cost [33.0]
37 --> 29 | cost [27.0]
40 --> 39 | cost [18.0]
41 --> 42 | cost [42.0]
44 --> 34 | cost [39.0]
45 --> 53 | cost [51.0]
46 --> 47 | cost [24.0]
49 --> 57 | cost [54.0]
50 --> 51 | cost [36.0]
54 --> 53 | cost [42.0]
55 --> 47 | cost [51.0]
58 --> 57 | cost [39.0]
59 --> 61 | cost [63.0]
60 --> 51 | cost [42.0]
63 --> 62 | cost [48.0]
64 --> 65 | cost [42.0]
67 --> 66 | cost [39.0]
68 --> 66 | cost [54.0]
69 --> 70 | cost [27.0]
72 --> 71 | cost [39.0]
73 --> 83 | cost [63.0]
74 --> 75 | cost [42.0]
77 --> 76 | cost [36.0]
78 --> 79 | cost [42.0]
81 --> 80 | cost [39.0]
82 --> 83 | cost [36.0]
85 --> 84 | cost [30.0]
86 --> 95 | cost [24.0]
87 --> 88 | cost [24.0]
90 --> 89 | cost [24.0]
91 --> 93 | cost [42.0]
92 --> 93 | cost [36.0]
96 --> 97 | cost [33.0]
98 --> 89 | cost [51.0]
99 --> 89 | cost [42.0]

BACKUP RING
1  ---  3 | cost [1.61]
2  --- 12 | cost [0.91]
3  --- 13 | cost [1.33]
4  ---  6 | cost [1.68]
5  ---  7 | cost [1.33]
5  --- 100 | cost [3.0100000000000002]
6  --- 16 | cost [1.61]
7  --- 17 | cost [2.17]
12 --- 22 | cost [1.82]
13 --- 21 | cost [1.26]
16 --- 25 | cost [0.98]
17 --- 26 | cost [1.33]
21 --- 29 | cost [1.96]
22 --- 30 | cost [1.68]
25 --- 35 | cost [1.54]
26 --- 34 | cost [1.61]
29 --- 39 | cost [1.61]
30 --- 38 | cost [1.75]
34 --- 42 | cost [0.91]
35 --- 43 | cost [1.61]
38 --- 48 | cost [0.77]
39 --- 47 | cost [1.26]
42 --- 52 | cost [1.61]
43 --- 51 | cost [1.82]
47 --- 56 | cost [1.61]
48 --- 57 | cost [1.8900000000000001]
51 --- 53 | cost [1.12]
52 --- 62 | cost [1.75]
53 --- 61 | cost [1.75]
56 --- 66 | cost [1.47]
57 --- 65 | cost [1.33]
61 --- 71 | cost [1.33]
62 --- 70 | cost [1.26]
65 --- 75 | cost [1.68]
66 --- 76 | cost [1.82]
70 --- 80 | cost [0.84]
71 --- 79 | cost [1.68]
75 --- 84 | cost [1.4000000000000001]
76 --- 83 | cost [1.96]
79 --- 89 | cost [1.54]
80 --- 88 | cost [2.0300000000000002]
83 --- 94 | cost [1.96]
84 --- 93 | cost [1.54]
88 --- 97 | cost [1.26]
89 --- 95 | cost [2.24]
93 --- 95 | cost [1.82]
94 --- 97 | cost [2.38]

BACKUP STAR
8  -->  6 | cost [0.6]
9  --> 17 | cost [0.75]
10 -->  1 | cost [0.51]
11 -->  2 | cost [0.33]
14 -->  4 | cost [0.45]
15 --> 25 | cost [0.51]
18 --> 16 | cost [0.66]
19 --> 30 | cost [0.75]
20 --> 12 | cost [0.66]
23 --> 25 | cost [0.51]
24 --> 26 | cost [0.51]
27 --> 26 | cost [0.48]
28 --> 30 | cost [0.54]
31 --> 21 | cost [0.5700000000000001]
32 --> 30 | cost [0.66]
33 --> 42 | cost [0.36]
36 --> 34 | cost [0.66]
37 --> 38 | cost [0.51]
40 --> 48 | cost [0.27]
41 --> 39 | cost [0.6]
44 --> 43 | cost [0.42]
45 --> 52 | cost [0.6]
46 --> 38 | cost [0.54]
49 --> 48 | cost [0.63]
50 --> 42 | cost [0.63]
54 --> 52 | cost [0.63]
55 --> 56 | cost [0.54]
58 --> 56 | cost [0.5700000000000001]
59 --> 57 | cost [0.63]
60 --> 61 | cost [0.48]
63 --> 53 | cost [0.63]
64 --> 56 | cost [0.5700000000000001]
67 --> 75 | cost [0.5700000000000001]
68 --> 75 | cost [0.6]
69 --> 71 | cost [0.48]
72 --> 80 | cost [0.54]
73 --> 75 | cost [0.66]
74 --> 65 | cost [0.45]
77 --> 79 | cost [0.5700000000000001]
78 --> 70 | cost [0.5700000000000001]
81 --> 71 | cost [0.51]
82 --> 93 | cost [0.75]
85 --> 76 | cost [0.3]
86 --> 88 | cost [0.54]
87 --> 95 | cost [0.39]
90 --> 97 | cost [0.66]
91 --> 83 | cost [0.48]
92 --> 83 | cost [0.63]
96 --> 95 | cost [0.45]
98 --> 97 | cost [0.39]
99 --> 97 | cost [0.5700000000000001]

B = 3.09
i★ = 22
j★ = 21
k★ = 30