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                           α=5.0 —— rat99 —— 99 nodes       
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——————— Tue, 09 Jan 2024 08:33:45 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 90 hubs —— 1-2-3-4-14-5-6-7-8-9-18-17-16-15-23-24-25-26-35-36-44-45-54-53-52-51-60-61-62-63-72-81-80-71-70-69-78-77-76-85-86-87-88-89-90-99-98-97-96-94-93-92-91-83-82-73-74-65-66-67-59-58-57-56-55-46-47-48-39-40-41-42-43-34-33-32-31-30-29-37-28-19-20-21-22-13-12-11-10-100-1
total time           3603.43 (TL 3600)    gap                  0.036                
blossom time         0                    nb blossom           0.0                  
LB <= UB             6011.15<=6238.55     Master/SP costs      5900/338.55          
Master time          3498.47              SP time              104.96               
subtour              10734.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            684.0                SP method            poly                 
tildeV               2:99                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       118623               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—3—4—14—5—6—7—8—9—18—17—16—15—23—24—25—26—35—36—44—45—54—53—52—51—60—61—62—63—72—81—80—71—70—69—78—77—76—85—86—87—88—89—90—99—98—97—96—94—93—92—91—83—82—73—74—65—66—67—59—58—57—56—55—46—47—48—39—40—41—42—43—34—33—32—31—30—29—37—28—19—20—21—22—13—12—11—10—100

RING
1  ---  2 | cost [70.0]
1  --- 100 | cost [0.0]
2  ---  3 | cost [45.0]
3  ---  4 | cost [55.0]
4  --- 14 | cost [75.0]
5  ---  6 | cost [45.0]
5  --- 14 | cost [60.0]
6  ---  7 | cost [55.0]
7  ---  8 | cost [50.0]
8  ---  9 | cost [50.0]
9  --- 18 | cost [100.0]
10 --- 11 | cost [60.0]
10 --- 100 | cost [85.0]
11 --- 12 | cost [30.0]
12 --- 13 | cost [65.0]
13 --- 22 | cost [70.0]
15 --- 16 | cost [50.0]
15 --- 23 | cost [70.0]
16 --- 17 | cost [65.0]
17 --- 18 | cost [50.0]
19 --- 20 | cost [65.0]
19 --- 28 | cost [95.0]
20 --- 21 | cost [90.0]
21 --- 22 | cost [30.0]
23 --- 24 | cost [50.0]
24 --- 25 | cost [45.0]
25 --- 26 | cost [50.0]
26 --- 35 | cost [60.0]
28 --- 37 | cost [45.0]
29 --- 30 | cost [55.0]
29 --- 37 | cost [45.0]
30 --- 31 | cost [60.0]
31 --- 32 | cost [55.0]
32 --- 33 | cost [60.0]
33 --- 34 | cost [60.0]
34 --- 43 | cost [30.0]
35 --- 36 | cost [55.0]
36 --- 44 | cost [65.0]
39 --- 40 | cost [30.0]
39 --- 48 | cost [20.0]
40 --- 41 | cost [70.0]
41 --- 42 | cost [70.0]
42 --- 43 | cost [40.0]
44 --- 45 | cost [80.0]
45 --- 54 | cost [65.0]
46 --- 47 | cost [40.0]
46 --- 55 | cost [75.0]
47 --- 48 | cost [75.0]
51 --- 52 | cost [45.0]
51 --- 60 | cost [70.0]
52 --- 53 | cost [40.0]
53 --- 54 | cost [70.0]
55 --- 56 | cost [90.0]
56 --- 57 | cost [40.0]
57 --- 58 | cost [65.0]
58 --- 59 | cost [40.0]
59 --- 67 | cost [90.0]
60 --- 61 | cost [80.0]
61 --- 62 | cost [45.0]
62 --- 63 | cost [80.0]
63 --- 72 | cost [100.0]
65 --- 66 | cost [55.0]
65 --- 74 | cost [75.0]
66 --- 67 | cost [65.0]
69 --- 70 | cost [45.0]
69 --- 78 | cost [60.0]
70 --- 71 | cost [35.0]
71 --- 80 | cost [50.0]
72 --- 81 | cost [65.0]
73 --- 74 | cost [85.0]
73 --- 82 | cost [90.0]
76 --- 77 | cost [60.0]
76 --- 85 | cost [50.0]
77 --- 78 | cost [50.0]
80 --- 81 | cost [65.0]
82 --- 83 | cost [60.0]
83 --- 91 | cost [80.0]
85 --- 86 | cost [55.0]
86 --- 87 | cost [55.0]
87 --- 88 | cost [40.0]
88 --- 89 | cost [75.0]
89 --- 90 | cost [40.0]
90 --- 99 | cost [50.0]
91 --- 92 | cost [35.0]
92 --- 93 | cost [60.0]
93 --- 94 | cost [65.0]
94 --- 96 | cost [120.0]
96 --- 97 | cost [55.0]
97 --- 98 | cost [65.0]
98 --- 99 | cost [45.0]

STAR
27 --> 26 | cost [80.0]
38 --> 39 | cost [45.0]
49 --> 58 | cost [60.0]
50 --> 51 | cost [60.0]
64 --> 65 | cost [70.0]
68 --> 67 | cost [25.0]
75 --> 76 | cost [65.0]
79 --> 88 | cost [70.0]
84 --> 85 | cost [50.0]
95 --> 86 | cost [40.0]

BACKUP RING
1  ---  3 | cost [1.1500000000000001]
2  ---  4 | cost [0.9]
3  --- 14 | cost [1.0]
4  ---  5 | cost [0.75]
5  ---  7 | cost [0.9500000000000001]
6  ---  8 | cost [1.0]
6  --- 14 | cost [0.85]
7  ---  9 | cost [1.0]
8  --- 18 | cost [1.35]
9  --- 17 | cost [1.25]
10 --- 12 | cost [0.85]
11 --- 13 | cost [0.85]
11 --- 100 | cost [1.25]
12 --- 22 | cost [1.3]
13 --- 21 | cost [0.9]
15 --- 17 | cost [1.1500000000000001]
15 --- 24 | cost [0.85]
16 --- 18 | cost [1.1]
16 --- 23 | cost [1.05]
19 --- 21 | cost [1.25]
19 --- 37 | cost [1.4000000000000001]
20 --- 22 | cost [1.1]
20 --- 28 | cost [1.45]
23 --- 25 | cost [0.85]
24 --- 26 | cost [0.85]
25 --- 35 | cost [1.1]
26 --- 36 | cost [1.1500000000000001]
28 --- 29 | cost [0.65]
29 --- 31 | cost [1.0]
30 --- 32 | cost [1.1]
30 --- 37 | cost [0.9500000000000001]
31 --- 33 | cost [1.05]
32 --- 34 | cost [1.2]
33 --- 43 | cost [0.65]
34 --- 42 | cost [0.65]
35 --- 44 | cost [0.8]
36 --- 45 | cost [1.25]
39 --- 41 | cost [1.0]
39 --- 47 | cost [0.9]
40 --- 42 | cost [1.3]
40 --- 48 | cost [0.45]
41 --- 43 | cost [1.05]
44 --- 54 | cost [1.45]
45 --- 53 | cost [0.85]
46 --- 48 | cost [1.05]
46 --- 56 | cost [1.4000000000000001]
47 --- 55 | cost [0.85]
51 --- 53 | cost [0.8]
51 --- 61 | cost [1.25]
52 --- 54 | cost [1.05]
52 --- 60 | cost [0.9500000000000001]
55 --- 57 | cost [1.1]
56 --- 58 | cost [0.9500000000000001]
57 --- 59 | cost [1.05]
58 --- 67 | cost [1.2]
59 --- 66 | cost [1.1500000000000001]
60 --- 62 | cost [1.1]
61 --- 63 | cost [1.25]
62 --- 72 | cost [1.05]
63 --- 81 | cost [1.6500000000000001]
65 --- 67 | cost [1.1500000000000001]
65 --- 73 | cost [1.6]
66 --- 74 | cost [0.75]
69 --- 71 | cost [0.8]
69 --- 77 | cost [1.05]
70 --- 78 | cost [0.9500000000000001]
70 --- 80 | cost [0.6]
71 --- 81 | cost [0.85]
72 --- 80 | cost [0.9]
73 --- 83 | cost [1.05]
74 --- 82 | cost [1.75]
76 --- 78 | cost [1.1]
76 --- 86 | cost [1.05]
77 --- 85 | cost [0.85]
82 --- 91 | cost [0.85]
83 --- 92 | cost [1.05]
85 --- 87 | cost [1.0]
86 --- 88 | cost [0.9]
87 --- 89 | cost [1.0]
88 --- 90 | cost [1.1500000000000001]
89 --- 99 | cost [0.7000000000000001]
90 --- 98 | cost [0.85]
91 --- 93 | cost [0.7000000000000001]
92 --- 94 | cost [1.1]
93 --- 96 | cost [1.8]
94 --- 97 | cost [1.7]
96 --- 98 | cost [1.0]
97 --- 99 | cost [0.9500000000000001]

BACKUP STAR
27 --> 35 | cost [0.65]
38 --> 48 | cost [0.55]
49 --> 60 | cost [0.8]
50 --> 40 | cost [0.85]
64 --> 56 | cost [0.9500000000000001]
68 --> 78 | cost [0.7000000000000001]
75 --> 74 | cost [0.7000000000000001]
79 --> 78 | cost [0.7000000000000001]
84 --> 76 | cost [0.7000000000000001]
95 --> 87 | cost [0.65]

B = 1.85
i★ = 57
j★ = 58
k★ = 59