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

——————— Mon, 08 Jan 2024 08:19:59 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 77 hubs —— 1—30—31—32—36—37—38—35—34—33—44—40—41—42—43—49—50—52—55—57—56—69—70—82—81—83—91—90—89—87—86—85—84—74—75—73—72—76—77—92—93—94—68—67—66—64—63—62—61—60—58—54—47—48—25—24—23—26—22—21—20—17—16—15—14—13—12—10—9—7—8—6—5—4—2—29—97
total time           25.48                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2375<=2375           subtour              806.0                
connectivity cuts    604.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       882                  n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
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—82—81—83—91—90—89—87—86—85—84—74—75—73—72—76—77—92—93—94—68—67—66—64—63—62—61—60—58—54—47—48—25—24—23—26—22—21—20—17—16—15—14—13—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 --- 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]
20 --- 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]
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 --- 58 | cost [20.0]
55 --- 57 | cost [35.0]
56 --- 57 | cost [0.0]
56 --- 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 --- 67 | cost [10.0]
67 --- 68 | cost [0.0]
68 --- 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]
81 --- 82 | cost [15.0]
81 --- 83 | cost [20.0]
83 --- 91 | cost [40.0]
84 --- 85 | cost [15.0]
85 --- 86 | cost [5.0]
86 --- 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 --> 20 | cost [10.0]
19 --> 20 | cost [5.0]
27 --> 26 | cost [30.0]
28 --> 26 | cost [30.0]
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]
59 --> 58 | cost [35.0]
65 --> 66 | cost [40.0]
71 --> 72 | cost [5.0]
78 --> 85 | cost [20.0]
79 --> 69 | cost [100.0]
80 --> 83 | cost [145.0]
88 --> 86 | cost [20.0]
95 --> 93 | cost [50.0]
96 --> 94 | cost [50.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:21:29 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 77 hubs —— 1-29-2-4-5-6-8-7-9-10-12-13-14-15-16-17-20-19-21-22-26-23-24-25-48-47-54-58-60-61-62-63-64-66-68-67-94-93-92-77-76-75-72-73-74-84-86-85-87-89-90-91-83-81-82-70-69-56-57-55-52-50-49-43-42-41-40-44-33-34-35-37-36-32-31-30-97-1
total time           61.76                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2375<=2375           Master/SP costs      2375/0               
Master time          61.76                SP time              0.0                  
subtour              1517.0               connectivity cuts    1669.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1721                 
F                    0.0                  
                                          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—75—72—73—74—84—86—85—87—89—90—91—83—81—82—70—69—56—57—55—52—50—49—43—42—41—40—44—33—34—35—37—36—32—31—30—97

RING
1  --- 29 | cost [40.0]
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 --- 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]
52 --- 55 | cost [15.0]
54 --- 58 | cost [20.0]
55 --- 57 | cost [35.0]
56 --- 57 | cost [0.0]
56 --- 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 --- 75 | cost [30.0]
73 --- 74 | cost [25.0]
74 --- 84 | cost [25.0]
75 --- 76 | cost [20.0]
76 --- 77 | cost [20.0]
77 --- 92 | cost [50.0]
81 --- 82 | cost [15.0]
81 --- 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]
51 --> 55 | cost [15.0]
53 --> 52 | cost [15.0]
59 --> 56 | cost [35.0]
65 --> 66 | cost [40.0]
71 --> 72 | cost [5.0]
78 --> 85 | cost [20.0]
79 --> 69 | cost [100.0]
80 --> 83 | cost [145.0]
88 --> 86 | cost [20.0]
95 --> 93 | cost [50.0]
96 --> 94 | cost [50.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 17:18:52 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 74 hubs —— 1—29—2—4—5—6—7—9—10—12—14—15—16—17—20—21—22—26—23—24—25—48—47—54—58—59—61—62—63—64—66—67—68—94—93—92—77—76—72—73—75—74—85—86—87—89—90—91—83—82—81—70—69—56—57—55—52—50—49—43—42—41—40—44—33—34—35—38—37—36—32—31—30—97
total time           32.98                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2375<=2375           subtour              3120.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1299                 n lazycuts edges     3.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—29—2—4—5—6—7—9—10—12—14—15—16—17—20—21—22—26—23—24—25—48—47—54—58—59—61—62—63—64—66—67—68—94—93—92—77—76—72—73—75—74—85—86—87—89—90—91—83—82—81—70—69—56—57—55—52—50—49—43—42—41—40—44—33—34—35—38—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  ---  7 | 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]
20 --- 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 --- 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 --- 58 | cost [20.0]
55 --- 57 | cost [35.0]
56 --- 57 | cost [0.0]
56 --- 69 | cost [25.0]
58 --- 59 | cost [35.0]
59 --- 61 | cost [35.0]
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 --- 76 | cost [35.0]
73 --- 75 | cost [20.0]
74 --- 75 | cost [20.0]
74 --- 85 | cost [25.0]
76 --- 77 | cost [20.0]
77 --- 92 | cost [50.0]
81 --- 82 | cost [15.0]
82 --- 83 | cost [20.0]
83 --- 91 | cost [40.0]
85 --- 86 | cost [5.0]
86 --- 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]
8  -->  7 | cost [10.0]
11 --> 33 | cost [50.0]
13 --> 14 | cost [10.0]
18 --> 20 | cost [10.0]
19 --> 20 | cost [5.0]
27 --> 26 | cost [30.0]
28 --> 26 | cost [30.0]
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]
60 --> 61 | cost [25.0]
65 --> 66 | cost [40.0]
71 --> 72 | cost [5.0]
78 --> 85 | cost [20.0]
79 --> 69 | cost [100.0]
80 --> 83 | cost [145.0]
84 --> 86 | cost [15.0]
88 --> 86 | cost [20.0]
95 --> 93 | cost [50.0]
96 --> 94 | cost [50.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 17:22:32 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 74 hubs —— 1-30-31-32-36-37-35-34-33-44-40-41-42-43-49-50-52-55-56-57-69-70-81-82-83-91-90-89-87-85-86-84-74-73-72-75-77-92-93-94-67-66-64-63-62-61-60-58-54-47-48-25-24-23-26-22-21-19-20-17-16-15-14-13-12-10-9-7-6-5-4-2-29-97-1
total time           191.41               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2375<=2375           Master/SP costs      2375/0               
Master time          191.41               SP time              0.0                  
subtour              9129.0               connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       4744                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—30—31—32—36—37—35—34—33—44—40—41—42—43—49—50—52—55—56—57—69—70—81—82—83—91—90—89—87—85—86—84—74—73—72—75—77—92—93—94—67—66—64—63—62—61—60—58—54—47—48—25—24—23—26—22—21—19—20—17—16—15—14—13—12—10—9—7—6—5—4—2—29—97

RING
1  --- 30 | cost [30.0]
2  ---  4 | cost [40.0]
2  --- 29 | cost [50.0]
4  ---  5 | cost [10.0]
5  ---  6 | cost [5.0]
6  ---  7 | 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]
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 --- 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]
52 --- 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 --- 67 | cost [10.0]
67 --- 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 --- 77 | cost [20.0]
77 --- 92 | cost [50.0]
81 --- 82 | cost [15.0]
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]
8  -->  6 | cost [10.0]
11 --> 33 | cost [50.0]
18 --> 20 | 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]
51 --> 55 | cost [15.0]
53 --> 52 | cost [15.0]
59 --> 58 | cost [35.0]
65 --> 66 | cost [40.0]
68 --> 67 | cost [0.0]
71 --> 72 | cost [5.0]
76 --> 75 | cost [20.0]
78 --> 86 | cost [20.0]
79 --> 69 | cost [100.0]
80 --> 83 | cost [145.0]
88 --> 86 | cost [20.0]
95 --> 93 | cost [50.0]
96 --> 94 | cost [50.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1