------------------------------------------------------------
                            α=3.0 —— gr96 —— 96 nodes       
------------------------------------------------------------

——————— Sun, 21 Jan 2024 05:26:01 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 85 hubs —— 1—29—2—3—4—5—6—8—7—9—10—12—13—14—15—16—17—18—20—19—21—25—24—23—22—26—28—27—65—96—94—95—93—92—77—76—68—67—66—64—63—62—61—60—59—71—72—73—75—74—84—86—85—78—88—87—89—90—91—83—82—81—80—79—70—69—57—58—54—48—47—46—11—45—44—33—34—35—38—37—36—32—31—30—97
total time           1969.92              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1567.41<=1567.41     subtour              988.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:96                 
2-opt strategy       0                                                              
explored_nodes       107                  n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—29—2—3—4—5—6—8—7—9—10—12—13—14—15—16—17—18—20—19—21—25—24—23—22—26—28—27—65—96—94—95—93—92—77—76—68—67—66—64—63—62—61—60—59—71—72—73—75—74—84—86—85—78—88—87—89—90—91—83—82—81—80—79—70—69—57—58—54—48—47—46—11—45—44—33—34—35—38—37—36—32—31—30—97

RING
1  --- 29 | cost [24.0]
2  ---  3 | cost [15.0]
2  --- 29 | cost [30.0]
3  ---  4 | cost [27.0]
4  ---  5 | cost [6.0]
5  ---  6 | cost [3.0]
6  ---  8 | cost [6.0]
7  ---  8 | cost [6.0]
7  ---  9 | cost [12.0]
9  --- 10 | cost [12.0]
10 --- 12 | cost [9.0]
11 --- 45 | cost [30.0]
11 --- 46 | cost [33.0]
12 --- 13 | cost [12.0]
13 --- 14 | cost [6.0]
14 --- 15 | cost [9.0]
15 --- 16 | cost [21.0]
16 --- 17 | cost [30.0]
17 --- 18 | cost [9.0]
18 --- 20 | cost [6.0]
19 --- 20 | cost [3.0]
19 --- 21 | cost [18.0]
21 --- 25 | cost [39.0]
22 --- 23 | cost [18.0]
22 --- 26 | cost [12.0]
23 --- 24 | cost [9.0]
24 --- 25 | cost [15.0]
26 --- 28 | cost [18.0]
27 --- 28 | cost [15.0]
27 --- 65 | cost [30.0]
30 --- 31 | cost [3.0]
30 --- 97 | cost [18.0]
31 --- 32 | cost [6.0]
32 --- 36 | cost [9.0]
33 --- 34 | cost [18.0]
33 --- 44 | cost [15.0]
34 --- 35 | cost [6.0]
35 --- 38 | cost [12.0]
36 --- 37 | cost [3.0]
37 --- 38 | cost [9.0]
39 --- 40 | cost [9.0]
39 --- 49 | cost [21.0]
40 --- 41 | cost [6.0]
41 --- 42 | cost [3.0]
42 --- 43 | cost [3.0]
43 --- 49 | cost [3.0]
44 --- 45 | cost [12.0]
46 --- 47 | cost [15.0]
47 --- 48 | cost [6.0]
48 --- 54 | cost [27.0]
50 --- 52 | cost [9.0]
50 --- 53 | cost [15.0]
51 --- 52 | cost [12.0]
51 --- 55 | cost [9.0]
53 --- 55 | cost [12.0]
54 --- 58 | cost [12.0]
57 --- 58 | cost [15.0]
57 --- 69 | cost [15.0]
59 --- 60 | cost [21.0]
59 --- 71 | cost [24.0]
60 --- 61 | cost [15.0]
61 --- 62 | cost [6.0]
62 --- 63 | cost [9.0]
63 --- 64 | cost [12.0]
64 --- 66 | cost [12.0]
65 --- 96 | cost [36.0]
66 --- 67 | cost [6.0]
67 --- 68 | cost [0.0]
68 --- 76 | cost [30.0]
69 --- 70 | cost [15.0]
70 --- 79 | cost [63.0]
71 --- 72 | cost [3.0]
72 --- 73 | cost [9.0]
73 --- 75 | cost [12.0]
74 --- 75 | cost [12.0]
74 --- 84 | cost [15.0]
76 --- 77 | cost [12.0]
77 --- 92 | cost [30.0]
78 --- 85 | cost [12.0]
78 --- 88 | cost [12.0]
79 --- 80 | cost [69.0]
80 --- 81 | cost [90.0]
81 --- 82 | cost [9.0]
82 --- 83 | cost [12.0]
83 --- 91 | cost [24.0]
84 --- 86 | cost [9.0]
85 --- 86 | cost [3.0]
87 --- 88 | cost [15.0]
87 --- 89 | cost [12.0]
89 --- 90 | cost [6.0]
90 --- 91 | cost [21.0]
92 --- 93 | cost [18.0]
93 --- 95 | cost [30.0]
94 --- 95 | cost [33.0]
94 --- 96 | cost [30.0]

STAR
56 --> 57 | cost [0.0]

BACKUP RING
1  ---  2 | cost [0.48]
2  ---  4 | cost [0.24]
3  ---  5 | cost [0.27]
3  --- 29 | cost [0.42]
4  ---  6 | cost [0.09]
5  ---  8 | cost [0.09]
6  ---  7 | cost [0.06]
7  --- 10 | cost [0.24]
8  ---  9 | cost [0.15]
9  --- 12 | cost [0.21]
10 --- 13 | cost [0.21]
11 --- 44 | cost [0.36]
11 --- 47 | cost [0.42]
12 --- 14 | cost [0.12]
13 --- 15 | cost [0.15]
14 --- 16 | cost [0.3]
15 --- 17 | cost [0.48]
16 --- 18 | cost [0.36]
17 --- 20 | cost [0.06]
18 --- 19 | cost [0.06]
19 --- 25 | cost [0.54]
20 --- 21 | cost [0.18]
21 --- 24 | cost [0.33]
22 --- 24 | cost [0.27]
22 --- 28 | cost [0.3]
23 --- 25 | cost [0.21]
23 --- 26 | cost [0.18]
26 --- 27 | cost [0.18]
27 --- 96 | cost [0.63]
28 --- 65 | cost [0.3]
30 --- 32 | cost [0.09]
31 --- 36 | cost [0.15]
31 --- 97 | cost [0.21]
32 --- 37 | cost [0.12]
33 --- 35 | cost [0.27]
33 --- 45 | cost [0.18]
34 --- 38 | cost [0.21]
34 --- 44 | cost [0.21]
35 --- 37 | cost [0.12]
36 --- 38 | cost [0.12]
39 --- 41 | cost [0.12]
39 --- 43 | cost [0.18]
40 --- 42 | cost [0.09]
40 --- 49 | cost [0.15]
41 --- 43 | cost [0.09]
42 --- 49 | cost [0.06]
45 --- 46 | cost [0.18]
46 --- 48 | cost [0.21]
47 --- 54 | cost [0.27]
48 --- 58 | cost [0.36]
50 --- 51 | cost [0.18]
50 --- 55 | cost [0.18]
51 --- 53 | cost [0.18]
52 --- 53 | cost [0.09]
52 --- 55 | cost [0.09]
54 --- 57 | cost [0.27]
57 --- 70 | cost [0.24]
58 --- 69 | cost [0.3]
59 --- 61 | cost [0.21]
59 --- 72 | cost [0.27]
60 --- 62 | cost [0.15]
60 --- 71 | cost [0.36]
61 --- 63 | cost [0.15]
62 --- 64 | cost [0.18]
63 --- 66 | cost [0.24]
64 --- 67 | cost [0.18]
65 --- 94 | cost [0.45]
66 --- 68 | cost [0.06]
67 --- 76 | cost [0.3]
68 --- 77 | cost [0.42]
69 --- 79 | cost [0.6]
70 --- 80 | cost [1.11]
71 --- 73 | cost [0.12]
72 --- 75 | cost [0.18]
73 --- 74 | cost [0.15]
74 --- 86 | cost [0.18]
75 --- 84 | cost [0.27]
76 --- 92 | cost [0.33]
77 --- 93 | cost [0.39]
78 --- 86 | cost [0.12]
78 --- 87 | cost [0.21]
79 --- 81 | cost [0.63]
80 --- 82 | cost [0.99]
81 --- 83 | cost [0.12]
82 --- 91 | cost [0.33]
83 --- 90 | cost [0.39]
84 --- 85 | cost [0.09]
85 --- 88 | cost [0.15]
87 --- 90 | cost [0.15]
88 --- 89 | cost [0.15]
89 --- 91 | cost [0.27]
92 --- 95 | cost [0.42]
93 --- 94 | cost [0.21]
95 --- 96 | cost [0.48]

BACKUP STAR
56 --> 58 | cost [0.35000000000000003]

B = 1.11
i★ = 70
j★ = 79
k★ = 80

       
——————— Sun, 21 Jan 2024 05:28:00 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 96 hubs —— 1-29-2-3-4-5-6-8-7-9-10-12-13-14-15-16-17-18-19-20-21-22-26-28-27-23-24-25-54-58-56-57-69-70-59-60-61-62-63-64-67-66-65-96-94-95-93-92-77-76-75-71-72-73-74-84-86-85-78-88-87-89-90-91-83-82-81-80-79-39-40-41-42-43-49-50-52-51-55-53-48-47-46-11-45-44-33-34-35-38-37-36-32-31-30-97-1
total time           54.25                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1572.99<=1572.99     Master/SP costs      1533/39.99           
Master time          41.5                 SP time              12.75                
subtour              2363.0               connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            45.0                 SP method            poly                 
tildeV               2:96                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       4789                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—29—2—3—4—5—6—8—7—9—10—12—13—14—15—16—17—18—19—20—21—22—26—28—27—23—24—25—54—58—56—57—69—70—59—60—61—62—63—64—67—66—65—96—94—95—93—92—77—76—75—71—72—73—74—84—86—85—78—88—87—89—90—91—83—82—81—80—79—39—40—41—42—43—49—50—52—51—55—53—48—47—46—11—45—44—33—34—35—38—37—36—32—31—30—97

RING
1  --- 29 | cost [24.0]
2  ---  3 | cost [15.0]
2  --- 29 | cost [30.0]
3  ---  4 | cost [27.0]
4  ---  5 | cost [6.0]
5  ---  6 | cost [3.0]
6  ---  8 | cost [6.0]
7  ---  8 | cost [6.0]
7  ---  9 | cost [12.0]
9  --- 10 | cost [12.0]
10 --- 12 | cost [9.0]
11 --- 45 | cost [30.0]
11 --- 46 | cost [33.0]
12 --- 13 | cost [12.0]
13 --- 14 | cost [6.0]
14 --- 15 | cost [9.0]
15 --- 16 | cost [21.0]
16 --- 17 | cost [30.0]
17 --- 18 | cost [9.0]
18 --- 19 | cost [6.0]
19 --- 20 | cost [3.0]
20 --- 21 | cost [18.0]
21 --- 22 | cost [21.0]
22 --- 26 | cost [12.0]
23 --- 24 | cost [9.0]
23 --- 27 | cost [27.0]
24 --- 25 | cost [15.0]
25 --- 54 | cost [33.0]
26 --- 28 | cost [18.0]
27 --- 28 | cost [15.0]
30 --- 31 | cost [3.0]
30 --- 97 | cost [18.0]
31 --- 32 | cost [6.0]
32 --- 36 | cost [9.0]
33 --- 34 | cost [18.0]
33 --- 44 | cost [15.0]
34 --- 35 | cost [6.0]
35 --- 38 | cost [12.0]
36 --- 37 | cost [3.0]
37 --- 38 | cost [9.0]
39 --- 40 | cost [9.0]
39 --- 79 | cost [63.0]
40 --- 41 | cost [6.0]
41 --- 42 | cost [3.0]
42 --- 43 | cost [3.0]
43 --- 49 | cost [3.0]
44 --- 45 | cost [12.0]
46 --- 47 | cost [15.0]
47 --- 48 | cost [6.0]
48 --- 53 | cost [27.0]
49 --- 50 | cost [12.0]
50 --- 52 | cost [9.0]
51 --- 52 | cost [12.0]
51 --- 55 | cost [9.0]
53 --- 55 | cost [12.0]
54 --- 58 | cost [12.0]
56 --- 57 | cost [0.0]
56 --- 58 | cost [15.0]
57 --- 69 | cost [15.0]
59 --- 60 | cost [21.0]
59 --- 70 | cost [30.0]
60 --- 61 | cost [15.0]
61 --- 62 | cost [6.0]
62 --- 63 | cost [9.0]
63 --- 64 | cost [12.0]
64 --- 67 | cost [18.0]
65 --- 66 | cost [24.0]
65 --- 96 | cost [36.0]
66 --- 67 | cost [6.0]
69 --- 70 | cost [15.0]
71 --- 72 | cost [3.0]
71 --- 75 | cost [21.0]
72 --- 73 | cost [9.0]
73 --- 74 | cost [15.0]
74 --- 84 | cost [15.0]
75 --- 76 | cost [12.0]
76 --- 77 | cost [12.0]
77 --- 92 | cost [30.0]
78 --- 85 | cost [12.0]
78 --- 88 | cost [12.0]
79 --- 80 | cost [69.0]
80 --- 81 | cost [90.0]
81 --- 82 | cost [9.0]
82 --- 83 | cost [12.0]
83 --- 91 | cost [24.0]
84 --- 86 | cost [9.0]
85 --- 86 | cost [3.0]
87 --- 88 | cost [15.0]
87 --- 89 | cost [12.0]
89 --- 90 | cost [6.0]
90 --- 91 | cost [21.0]
92 --- 93 | cost [18.0]
93 --- 95 | cost [30.0]
94 --- 95 | cost [33.0]
94 --- 96 | cost [30.0]

STAR
68 --> 67 | cost [0.0]

BACKUP RING
1  ---  2 | cost [0.48]
2  ---  4 | cost [0.24]
3  ---  5 | cost [0.27]
3  --- 29 | cost [0.42]
4  ---  6 | cost [0.09]
5  ---  8 | cost [0.09]
6  ---  7 | cost [0.06]
7  --- 10 | cost [0.24]
8  ---  9 | cost [0.15]
9  --- 12 | cost [0.21]
10 --- 13 | cost [0.21]
11 --- 44 | cost [0.36]
11 --- 47 | cost [0.42]
12 --- 14 | cost [0.12]
13 --- 15 | cost [0.15]
14 --- 16 | cost [0.3]
15 --- 17 | cost [0.48]
16 --- 18 | cost [0.36]
17 --- 19 | cost [0.09]
18 --- 20 | cost [0.06]
19 --- 21 | cost [0.18]
20 --- 22 | cost [0.36]
21 --- 26 | cost [0.33]
22 --- 28 | cost [0.3]
23 --- 25 | cost [0.21]
23 --- 28 | cost [0.33]
24 --- 27 | cost [0.27]
24 --- 54 | cost [0.45]
25 --- 58 | cost [0.45]
26 --- 27 | cost [0.18]
30 --- 32 | cost [0.09]
31 --- 36 | cost [0.15]
31 --- 97 | cost [0.21]
32 --- 37 | cost [0.12]
33 --- 35 | cost [0.27]
33 --- 45 | cost [0.18]
34 --- 38 | cost [0.21]
34 --- 44 | cost [0.21]
35 --- 37 | cost [0.12]
36 --- 38 | cost [0.12]
39 --- 41 | cost [0.12]
39 --- 80 | cost [1.29]
40 --- 42 | cost [0.09]
40 --- 79 | cost [0.66]
41 --- 43 | cost [0.09]
42 --- 49 | cost [0.06]
43 --- 50 | cost [0.15]
45 --- 46 | cost [0.18]
46 --- 48 | cost [0.21]
47 --- 53 | cost [0.24]
48 --- 55 | cost [0.39]
49 --- 52 | cost [0.18]
50 --- 51 | cost [0.18]
51 --- 53 | cost [0.18]
52 --- 55 | cost [0.09]
54 --- 56 | cost [0.27]
56 --- 69 | cost [0.15]
57 --- 58 | cost [0.15]
57 --- 70 | cost [0.24]
59 --- 61 | cost [0.21]
59 --- 69 | cost [0.3]
60 --- 62 | cost [0.15]
60 --- 70 | cost [0.48]
61 --- 63 | cost [0.15]
62 --- 64 | cost [0.18]
63 --- 67 | cost [0.27]
64 --- 66 | cost [0.12]
65 --- 67 | cost [0.3]
65 --- 94 | cost [0.45]
66 --- 96 | cost [0.48]
71 --- 73 | cost [0.12]
71 --- 76 | cost [0.27]
72 --- 74 | cost [0.24]
72 --- 75 | cost [0.18]
73 --- 84 | cost [0.3]
74 --- 86 | cost [0.18]
75 --- 77 | cost [0.12]
76 --- 92 | cost [0.33]
77 --- 93 | cost [0.39]
78 --- 86 | cost [0.12]
78 --- 87 | cost [0.21]
79 --- 81 | cost [0.63]
80 --- 82 | cost [0.99]
81 --- 83 | cost [0.12]
82 --- 91 | cost [0.33]
83 --- 90 | cost [0.39]
84 --- 85 | cost [0.09]
85 --- 88 | cost [0.15]
87 --- 90 | cost [0.15]
88 --- 89 | cost [0.15]
89 --- 91 | cost [0.27]
92 --- 95 | cost [0.42]
93 --- 94 | cost [0.21]
95 --- 96 | cost [0.48]

BACKUP STAR
68 --> 66 | cost [0.14]

B = 1.29
i★ = 39
j★ = 79
k★ = 80