------------------------------------------------------------
                            α=5.0 —— gr96 —— 96 nodes       
------------------------------------------------------------

——————— Tue, 09 Jan 2024 06:19:49 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 78 hubs —— 1-30-31-32-36-37-38-35-34-33-44-40-41-42-43-49-50-52-55-57-56-69-70-81-83-82-91-90-87-88-78-86-85-84-74-73-72-75-76-92-93-94-68-67-66-64-63-62-61-60-54-47-48-25-24-23-27-28-26-22-21-19-20-17-16-15-14-12-10-9-7-8-6-5-4-2-29-97-1
total time           3603.76 (TL 3600)    gap                  0.115                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2414.17<=2726.95     Master/SP costs      2425/301.95          
Master time          3521.37              SP time              82.39                
subtour              19787.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            585.0                SP method            poly                 
tildeV               2:96                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       60738                
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—30—31—32—36—37—38—35—34—33—44—40—41—42—43—49—50—52—55—57—56—69—70—81—83—82—91—90—87—88—78—86—85—84—74—73—72—75—76—92—93—94—68—67—66—64—63—62—61—60—54—47—48—25—24—23—27—28—26—22—21—19—20—17—16—15—14—12—10—9—7—8—6—5—4—2—29—97

RING
1  --- 30 | cost [30.0]
1  --- 97 | cost [0.0]
2  ---  4 | cost [40.0]
2  --- 29 | cost [50.0]
4  ---  5 | cost [10.0]
5  ---  6 | cost [5.0]
6  ---  8 | cost [10.0]
7  ---  8 | cost [10.0]
7  ---  9 | cost [20.0]
9  --- 10 | cost [20.0]
10 --- 12 | cost [15.0]
12 --- 14 | cost [20.0]
14 --- 15 | cost [15.0]
15 --- 16 | cost [35.0]
16 --- 17 | cost [50.0]
17 --- 20 | cost [10.0]
19 --- 20 | cost [5.0]
19 --- 21 | cost [30.0]
21 --- 22 | cost [35.0]
22 --- 26 | cost [20.0]
23 --- 24 | cost [15.0]
23 --- 27 | cost [45.0]
24 --- 25 | cost [25.0]
25 --- 48 | cost [50.0]
26 --- 28 | cost [30.0]
27 --- 28 | cost [25.0]
29 --- 97 | cost [40.0]
30 --- 31 | cost [5.0]
31 --- 32 | cost [10.0]
32 --- 36 | cost [15.0]
33 --- 34 | cost [30.0]
33 --- 44 | cost [25.0]
34 --- 35 | cost [10.0]
35 --- 38 | cost [20.0]
36 --- 37 | cost [5.0]
37 --- 38 | cost [15.0]
40 --- 41 | cost [10.0]
40 --- 44 | cost [30.0]
41 --- 42 | cost [5.0]
42 --- 43 | cost [5.0]
43 --- 49 | cost [5.0]
47 --- 48 | cost [10.0]
47 --- 54 | cost [45.0]
49 --- 50 | cost [20.0]
50 --- 52 | cost [15.0]
52 --- 55 | cost [15.0]
54 --- 60 | cost [40.0]
55 --- 57 | cost [35.0]
56 --- 57 | cost [0.0]
56 --- 69 | cost [25.0]
60 --- 61 | cost [25.0]
61 --- 62 | cost [10.0]
62 --- 63 | cost [15.0]
63 --- 64 | cost [20.0]
64 --- 66 | cost [20.0]
66 --- 67 | cost [10.0]
67 --- 68 | cost [0.0]
68 --- 94 | cost [60.0]
69 --- 70 | cost [25.0]
70 --- 81 | cost [50.0]
72 --- 73 | cost [15.0]
72 --- 75 | cost [30.0]
73 --- 74 | cost [25.0]
74 --- 84 | cost [25.0]
75 --- 76 | cost [20.0]
76 --- 92 | cost [55.0]
78 --- 86 | cost [20.0]
78 --- 88 | cost [20.0]
81 --- 83 | cost [20.0]
82 --- 83 | cost [20.0]
82 --- 91 | cost [55.0]
84 --- 85 | cost [15.0]
85 --- 86 | cost [5.0]
87 --- 88 | cost [25.0]
87 --- 90 | cost [25.0]
90 --- 91 | cost [35.0]
92 --- 93 | cost [30.0]
93 --- 94 | cost [35.0]

STAR
3  -->  2 | cost [25.0]
11 --> 33 | cost [50.0]
13 --> 14 | cost [10.0]
18 --> 19 | cost [10.0]
39 --> 40 | cost [15.0]
45 --> 44 | cost [20.0]
46 --> 47 | cost [25.0]
51 --> 55 | cost [15.0]
53 --> 52 | cost [15.0]
58 --> 54 | cost [20.0]
59 --> 57 | cost [35.0]
65 --> 66 | cost [40.0]
71 --> 72 | cost [5.0]
77 --> 75 | cost [20.0]
79 --> 69 | cost [100.0]
80 --> 83 | cost [145.0]
89 --> 90 | cost [10.0]
95 --> 93 | cost [50.0]
96 --> 94 | cost [50.0]

BACKUP RING
1  --- 31 | cost [0.35000000000000003]
2  ---  5 | cost [0.5]
2  --- 97 | cost [0.8]
4  ---  6 | cost [0.15]
4  --- 29 | cost [0.75]
5  ---  8 | cost [0.15]
6  ---  7 | cost [0.1]
7  --- 10 | cost [0.4]
8  ---  9 | cost [0.25]
9  --- 12 | cost [0.35000000000000003]
10 --- 14 | cost [0.4]
12 --- 15 | cost [0.4]
14 --- 16 | cost [0.5]
15 --- 17 | cost [0.8]
16 --- 20 | cost [0.55]
17 --- 19 | cost [0.15]
19 --- 22 | cost [0.55]
20 --- 21 | cost [0.3]
21 --- 26 | cost [0.55]
22 --- 28 | cost [0.5]
23 --- 25 | cost [0.35000000000000003]
23 --- 28 | cost [0.55]
24 --- 27 | cost [0.45]
24 --- 48 | cost [0.75]
25 --- 47 | cost [0.6]
26 --- 27 | cost [0.3]
30 --- 32 | cost [0.15]
31 --- 36 | cost [0.25]
32 --- 37 | cost [0.2]
33 --- 35 | cost [0.45]
33 --- 40 | cost [0.5]
34 --- 38 | cost [0.35000000000000003]
34 --- 44 | cost [0.35000000000000003]
35 --- 37 | cost [0.2]
36 --- 38 | cost [0.2]
40 --- 42 | cost [0.15]
41 --- 43 | cost [0.15]
41 --- 44 | cost [0.35000000000000003]
42 --- 49 | cost [0.1]
43 --- 50 | cost [0.25]
47 --- 60 | cost [0.8]
48 --- 54 | cost [0.45]
49 --- 52 | cost [0.3]
50 --- 55 | cost [0.3]
52 --- 57 | cost [0.5]
54 --- 61 | cost [0.65]
55 --- 56 | cost [0.35000000000000003]
56 --- 70 | cost [0.4]
57 --- 69 | cost [0.25]
60 --- 62 | cost [0.25]
61 --- 63 | cost [0.25]
62 --- 64 | cost [0.3]
63 --- 66 | cost [0.4]
64 --- 67 | cost [0.3]
66 --- 68 | cost [0.1]
67 --- 94 | cost [0.6]
68 --- 93 | cost [0.75]
69 --- 81 | cost [0.7000000000000001]
70 --- 83 | cost [0.7000000000000001]
72 --- 74 | cost [0.4]
72 --- 76 | cost [0.35000000000000003]
73 --- 75 | cost [0.2]
73 --- 84 | cost [0.5]
74 --- 85 | cost [0.25]
75 --- 92 | cost [0.7000000000000001]
76 --- 93 | cost [0.65]
78 --- 85 | cost [0.2]
78 --- 87 | cost [0.35000000000000003]
81 --- 82 | cost [0.15]
82 --- 90 | cost [0.7000000000000001]
83 --- 91 | cost [0.4]
84 --- 86 | cost [0.15]
86 --- 88 | cost [0.2]
87 --- 91 | cost [0.45]
88 --- 90 | cost [0.35000000000000003]
92 --- 94 | cost [0.6]

BACKUP STAR
3  -->  4 | cost [0.45]
11 --> 44 | cost [0.6]
13 --> 12 | cost [0.2]
18 --> 20 | cost [0.1]
39 --> 41 | cost [0.2]
45 --> 33 | cost [0.3]
46 --> 50 | cost [0.3]
51 --> 52 | cost [0.2]
53 --> 55 | cost [0.2]
58 --> 56 | cost [0.25]
59 --> 56 | cost [0.35000000000000003]
65 --> 64 | cost [0.45]
71 --> 73 | cost [0.2]
77 --> 76 | cost [0.2]
79 --> 70 | cost [1.05]
80 --> 81 | cost [1.5]
89 --> 87 | cost [0.2]
95 --> 94 | cost [0.55]
96 --> 66 | cost [0.8]

B = 1.65
i★ = 81
j★ = 83
k★ = 82

       
——————— Fri, 12 Jan 2024 19:09:25 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 77 hubs —— 1—29—2—4—5—6—8—7—9—10—12—13—14—15—16—17—20—19—21—22—26—23—24—25—48—47—54—58—60—61—62—63—64—66—68—67—94—93—92—77—76—72—73—75—74—84—86—85—87—89—90—91—83—82—70—69—57—56—55—51—52—50—49—43—42—41—40—44—33—34—35—37—36—32—31—30—97
total time           3631.8 (TL 3600)     gap                  0.098                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2476.82<=2746.1      subtour              1529.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:96                 
2-opt strategy       0                                                              
explored_nodes       1026                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—29—2—4—5—6—8—7—9—10—12—13—14—15—16—17—20—19—21—22—26—23—24—25—48—47—54—58—60—61—62—63—64—66—68—67—94—93—92—77—76—72—73—75—74—84—86—85—87—89—90—91—83—82—70—69—57—56—55—51—52—50—49—43—42—41—40—44—33—34—35—37—36—32—31—30—97

RING
1  --- 29 | cost [40.0]
2  ---  4 | cost [40.0]
2  --- 29 | cost [50.0]
4  ---  5 | cost [10.0]
5  ---  6 | cost [5.0]
6  ---  8 | cost [10.0]
7  ---  8 | cost [10.0]
7  ---  9 | cost [20.0]
9  --- 10 | cost [20.0]
10 --- 12 | cost [15.0]
12 --- 13 | cost [20.0]
13 --- 14 | cost [10.0]
14 --- 15 | cost [15.0]
15 --- 16 | cost [35.0]
16 --- 17 | cost [50.0]
17 --- 20 | cost [10.0]
19 --- 20 | cost [5.0]
19 --- 21 | cost [30.0]
21 --- 22 | cost [35.0]
22 --- 26 | cost [20.0]
23 --- 24 | cost [15.0]
23 --- 26 | cost [30.0]
24 --- 25 | cost [25.0]
25 --- 48 | cost [50.0]
30 --- 31 | cost [5.0]
30 --- 97 | cost [30.0]
31 --- 32 | cost [10.0]
32 --- 36 | cost [15.0]
33 --- 34 | cost [30.0]
33 --- 44 | cost [25.0]
34 --- 35 | cost [10.0]
35 --- 37 | cost [20.0]
36 --- 37 | cost [5.0]
40 --- 41 | cost [10.0]
40 --- 44 | cost [30.0]
41 --- 42 | cost [5.0]
42 --- 43 | cost [5.0]
43 --- 49 | cost [5.0]
47 --- 48 | cost [10.0]
47 --- 54 | cost [45.0]
49 --- 50 | cost [20.0]
50 --- 52 | cost [15.0]
51 --- 52 | cost [20.0]
51 --- 55 | cost [15.0]
54 --- 58 | cost [20.0]
55 --- 56 | cost [35.0]
56 --- 57 | cost [0.0]
57 --- 69 | cost [25.0]
58 --- 60 | cost [35.0]
60 --- 61 | cost [25.0]
61 --- 62 | cost [10.0]
62 --- 63 | cost [15.0]
63 --- 64 | cost [20.0]
64 --- 66 | cost [20.0]
66 --- 68 | cost [10.0]
67 --- 68 | cost [0.0]
67 --- 94 | cost [60.0]
69 --- 70 | cost [25.0]
70 --- 82 | cost [50.0]
72 --- 73 | cost [15.0]
72 --- 76 | cost [35.0]
73 --- 75 | cost [20.0]
74 --- 75 | cost [20.0]
74 --- 84 | cost [25.0]
76 --- 77 | cost [20.0]
77 --- 92 | cost [50.0]
82 --- 83 | cost [20.0]
83 --- 91 | cost [40.0]
84 --- 86 | cost [15.0]
85 --- 86 | cost [5.0]
85 --- 87 | cost [20.0]
87 --- 89 | cost [20.0]
89 --- 90 | cost [10.0]
90 --- 91 | cost [35.0]
92 --- 93 | cost [30.0]
93 --- 94 | cost [35.0]

STAR
3  -->  2 | cost [25.0]
11 --> 33 | cost [50.0]
18 --> 19 | cost [10.0]
27 --> 26 | cost [30.0]
28 --> 26 | cost [30.0]
38 --> 37 | cost [15.0]
39 --> 40 | cost [15.0]
45 --> 44 | cost [20.0]
46 --> 47 | cost [25.0]
53 --> 52 | cost [15.0]
59 --> 61 | cost [35.0]
65 --> 66 | cost [40.0]
71 --> 72 | cost [5.0]
78 --> 86 | cost [20.0]
79 --> 51 | cost [100.0]
80 --> 89 | cost [200.0]
81 --> 82 | cost [15.0]
88 --> 86 | cost [20.0]
95 --> 93 | cost [50.0]
96 --> 94 | cost [50.0]

BACKUP RING
1  ---  2 | cost [0.8]
2  ---  5 | cost [0.5]
4  ---  6 | cost [0.15]
4  --- 29 | cost [0.75]
5  ---  8 | cost [0.15]
6  ---  7 | cost [0.1]
7  --- 10 | cost [0.4]
8  ---  9 | cost [0.25]
9  --- 12 | cost [0.35000000000000003]
10 --- 13 | cost [0.35000000000000003]
12 --- 14 | cost [0.2]
13 --- 15 | cost [0.25]
14 --- 16 | cost [0.5]
15 --- 17 | cost [0.8]
16 --- 20 | cost [0.55]
17 --- 19 | cost [0.15]
19 --- 22 | cost [0.55]
20 --- 21 | cost [0.3]
21 --- 26 | cost [0.55]
22 --- 23 | cost [0.3]
23 --- 25 | cost [0.35000000000000003]
24 --- 26 | cost [0.45]
24 --- 48 | cost [0.75]
25 --- 47 | cost [0.6]
30 --- 32 | cost [0.15]
31 --- 36 | cost [0.25]
31 --- 97 | cost [0.35000000000000003]
32 --- 37 | cost [0.2]
33 --- 35 | cost [0.45]
33 --- 40 | cost [0.5]
34 --- 37 | cost [0.35000000000000003]
34 --- 44 | cost [0.35000000000000003]
35 --- 36 | cost [0.2]
40 --- 42 | cost [0.15]
41 --- 43 | cost [0.15]
41 --- 44 | cost [0.35000000000000003]
42 --- 49 | cost [0.1]
43 --- 50 | cost [0.25]
47 --- 58 | cost [0.65]
48 --- 54 | cost [0.45]
49 --- 52 | cost [0.3]
50 --- 51 | cost [0.3]
51 --- 56 | cost [0.5]
52 --- 55 | cost [0.15]
54 --- 60 | cost [0.4]
55 --- 57 | cost [0.35000000000000003]
56 --- 69 | cost [0.25]
57 --- 70 | cost [0.4]
58 --- 61 | cost [0.6]
60 --- 62 | cost [0.25]
61 --- 63 | cost [0.25]
62 --- 64 | cost [0.3]
63 --- 66 | cost [0.4]
64 --- 68 | cost [0.3]
66 --- 67 | cost [0.1]
67 --- 93 | cost [0.75]
68 --- 94 | cost [0.6]
69 --- 82 | cost [0.7000000000000001]
70 --- 83 | cost [0.7000000000000001]
72 --- 75 | cost [0.3]
72 --- 77 | cost [0.45]
73 --- 74 | cost [0.25]
73 --- 76 | cost [0.35000000000000003]
74 --- 86 | cost [0.3]
75 --- 84 | cost [0.45]
76 --- 92 | cost [0.55]
77 --- 93 | cost [0.65]
82 --- 91 | cost [0.55]
83 --- 90 | cost [0.65]
84 --- 85 | cost [0.15]
85 --- 89 | cost [0.4]
86 --- 87 | cost [0.2]
87 --- 90 | cost [0.25]
89 --- 91 | cost [0.45]
92 --- 94 | cost [0.6]

BACKUP STAR
3  -->  4 | cost [0.45]
11 --> 44 | cost [0.6]
18 --> 20 | cost [0.1]
27 --> 23 | cost [0.45]
28 --> 22 | cost [0.5]
38 --> 35 | cost [0.2]
39 --> 41 | cost [0.2]
45 --> 33 | cost [0.3]
46 --> 50 | cost [0.3]
53 --> 55 | cost [0.2]
59 --> 56 | cost [0.35000000000000003]
65 --> 64 | cost [0.45]
71 --> 73 | cost [0.2]
78 --> 85 | cost [0.2]
79 --> 69 | cost [1.0]
80 --> 83 | cost [1.45]
81 --> 83 | cost [0.2]
88 --> 85 | cost [0.25]
95 --> 94 | cost [0.55]
96 --> 66 | cost [0.8]

B = 1.7
i★ = 87
j★ = 89
k★ = 90