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

——————— Sat, 27 Jan 2024 14:41:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 97 hubs —— 1—30—31—32—36—37—38—35—34—33—11—45—44—49—43—42—41—40—39—79—80—81—82—83—91—90—89—87—88—78—85—86—84—74—73—71—72—75—76—77—92—93—95—94—96—65—66—68—67—64—63—62—61—60—59—70—69—56—57—58—54—53—55—51—52—50—46—47—48—25—24—23—27—28—26—22—21—18—19—20—17—16—15—14—13—12—10—9—7—8—6—5—4—3—2—29—97
total time           1077.06              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1572.99<=1572.99     subtour              263.0                
connectivity cuts    55.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:96                 
2-opt strategy       0                                                              
explored_nodes       10                   n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—30—31—32—36—37—38—35—34—33—11—45—44—49—43—42—41—40—39—79—80—81—82—83—91—90—89—87—88—78—85—86—84—74—73—71—72—75—76—77—92—93—95—94—96—65—66—68—67—64—63—62—61—60—59—70—69—56—57—58—54—53—55—51—52—50—46—47—48—25—24—23—27—28—26—22—21—18—19—20—17—16—15—14—13—12—10—9—7—8—6—5—4—3—2—29—97

RING
1  --- 30 | cost [18.0]
1  --- 97 | cost [0.0]
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 --- 33 | cost [30.0]
11 --- 45 | cost [30.0]
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 --- 20 | cost [6.0]
18 --- 19 | cost [6.0]
18 --- 21 | cost [21.0]
19 --- 20 | cost [3.0]
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 --- 48 | cost [30.0]
26 --- 28 | cost [18.0]
27 --- 28 | cost [15.0]
29 --- 97 | cost [24.0]
30 --- 31 | cost [3.0]
31 --- 32 | cost [6.0]
32 --- 36 | cost [9.0]
33 --- 34 | cost [18.0]
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]
44 --- 49 | cost [21.0]
46 --- 47 | cost [15.0]
46 --- 50 | cost [18.0]
47 --- 48 | cost [6.0]
50 --- 52 | cost [9.0]
51 --- 52 | cost [12.0]
51 --- 55 | cost [9.0]
53 --- 54 | cost [21.0]
53 --- 55 | cost [12.0]
54 --- 58 | cost [12.0]
56 --- 57 | cost [0.0]
56 --- 69 | cost [15.0]
57 --- 58 | 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 --- 68 | cost [6.0]
67 --- 68 | cost [0.0]
69 --- 70 | cost [15.0]
71 --- 72 | cost [3.0]
71 --- 73 | cost [12.0]
72 --- 75 | cost [18.0]
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

BACKUP RING
1  --- 31 | cost [0.21]
2  ---  4 | cost [0.24]
2  --- 97 | cost [0.48]
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 --- 34 | cost [0.51]
11 --- 44 | cost [0.36]
12 --- 14 | cost [0.12]
13 --- 15 | cost [0.15]
14 --- 16 | cost [0.3]
15 --- 17 | cost [0.48]
16 --- 20 | cost [0.33]
17 --- 19 | cost [0.09]
18 --- 20 | cost [0.06]
18 --- 22 | cost [0.39]
19 --- 21 | cost [0.18]
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 --- 48 | cost [0.45]
25 --- 47 | cost [0.36]
26 --- 27 | cost [0.18]
30 --- 32 | cost [0.09]
31 --- 36 | cost [0.15]
32 --- 37 | cost [0.12]
33 --- 35 | cost [0.27]
33 --- 45 | cost [0.18]
34 --- 38 | 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 --- 44 | cost [0.21]
45 --- 49 | cost [0.21]
46 --- 48 | cost [0.21]
46 --- 52 | cost [0.27]
47 --- 50 | cost [0.24]
50 --- 51 | cost [0.18]
51 --- 53 | cost [0.18]
52 --- 55 | cost [0.09]
53 --- 58 | cost [0.24]
54 --- 55 | cost [0.3]
54 --- 57 | cost [0.27]
56 --- 58 | cost [0.15]
56 --- 70 | cost [0.24]
57 --- 69 | cost [0.15]
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 --- 68 | cost [0.18]
65 --- 68 | cost [0.3]
65 --- 94 | cost [0.45]
66 --- 67 | cost [0.06]
66 --- 96 | cost [0.48]
71 --- 74 | cost [0.27]
71 --- 75 | cost [0.21]
72 --- 73 | cost [0.09]
72 --- 76 | cost [0.21]
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

B = 1.29
i★ = 39
j★ = 79
k★ = 80

       
——————— Sat, 27 Jan 2024 14:43:29 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 96 hubs —— 1-30-31-32-36-37-38-35-34-33-44-45-11-46-47-48-53-55-51-52-50-49-43-42-41-40-39-79-80-81-82-83-91-90-89-87-88-78-85-86-84-74-75-73-71-72-76-77-92-93-95-94-96-65-66-68-64-63-62-61-60-59-70-69-56-57-58-54-25-24-23-27-28-26-22-21-20-19-18-17-16-15-14-13-12-10-9-7-8-6-5-4-3-2-29-97-1
total time           50.53                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1572.99<=1572.99     Master/SP costs      1533/39.99           
Master time          43.62                SP time              6.92                 
subtour              839.0                connectivity cuts    565.0                
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            43.0                 SP method            poly                 
tildeV               2:96                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1500                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—30—31—32—36—37—38—35—34—33—44—45—11—46—47—48—53—55—51—52—50—49—43—42—41—40—39—79—80—81—82—83—91—90—89—87—88—78—85—86—84—74—75—73—71—72—76—77—92—93—95—94—96—65—66—68—64—63—62—61—60—59—70—69—56—57—58—54—25—24—23—27—28—26—22—21—20—19—18—17—16—15—14—13—12—10—9—7—8—6—5—4—3—2—29—97

RING
1  --- 30 | cost [18.0]
1  --- 97 | cost [0.0]
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]
29 --- 97 | cost [24.0]
30 --- 31 | cost [3.0]
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 --- 69 | cost [15.0]
57 --- 58 | 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 --- 68 | cost [18.0]
65 --- 66 | cost [24.0]
65 --- 96 | cost [36.0]
66 --- 68 | cost [6.0]
69 --- 70 | cost [15.0]
71 --- 72 | cost [3.0]
71 --- 73 | cost [12.0]
72 --- 76 | cost [21.0]
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
67 --> 68 | cost [0.0]

BACKUP RING
1  --- 31 | cost [0.21]
2  ---  4 | cost [0.24]
2  --- 97 | cost [0.48]
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]
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 --- 57 | cost [0.27]
56 --- 58 | cost [0.15]
56 --- 70 | cost [0.24]
57 --- 69 | cost [0.15]
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 --- 68 | cost [0.3]
64 --- 66 | cost [0.12]
65 --- 68 | cost [0.3]
65 --- 94 | cost [0.45]
66 --- 96 | cost [0.48]
71 --- 75 | cost [0.21]
71 --- 76 | cost [0.27]
72 --- 73 | cost [0.09]
72 --- 77 | cost [0.27]
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
67 --> 66 | cost [0.14]

B = 1.29
i★ = 39
j★ = 79
k★ = 80