------------------------------------------------------------
                            α=7.0 —— gr96 —— 96 nodes       
------------------------------------------------------------

——————— Mon, 08 Jan 2024 08:22:28 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 47 hubs —— 1—30—31—32—36—35—44—40—41—42—43—49—50—52—55—56—57—69—70—82—87—85—74—75—76—67—68—66—64—63—27—26—23—21—20—16—15—14—12—10—9—7—6—5—4—2—97
total time           32.53                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2548<=2548           subtour              286.0                
connectivity cuts    152.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—30—31—32—36—35—44—40—41—42—43—49—50—52—55—56—57—69—70—82—87—85—74—75—76—67—68—66—64—63—27—26—23—21—20—16—15—14—12—10—9—7—6—5—4—2—97

RING
1  --- 30 | cost [42.0]
1  --- 97 | cost [0.0]
2  ---  4 | cost [56.0]
2  --- 97 | cost [112.0]
4  ---  5 | cost [14.0]
5  ---  6 | cost [7.0]
6  ---  7 | cost [14.0]
7  ---  9 | cost [28.0]
9  --- 10 | cost [28.0]
10 --- 12 | cost [21.0]
12 --- 14 | cost [28.0]
14 --- 15 | cost [21.0]
15 --- 16 | cost [49.0]
16 --- 20 | cost [77.0]
20 --- 21 | cost [42.0]
21 --- 23 | cost [63.0]
23 --- 26 | cost [42.0]
26 --- 27 | cost [42.0]
27 --- 63 | cost [77.0]
30 --- 31 | cost [7.0]
31 --- 32 | cost [14.0]
32 --- 36 | cost [21.0]
35 --- 36 | cost [28.0]
35 --- 44 | cost [56.0]
40 --- 41 | cost [14.0]
40 --- 44 | cost [42.0]
41 --- 42 | cost [7.0]
42 --- 43 | cost [7.0]
43 --- 49 | cost [7.0]
49 --- 50 | cost [28.0]
50 --- 52 | cost [21.0]
52 --- 55 | cost [21.0]
55 --- 56 | cost [49.0]
56 --- 57 | cost [0.0]
57 --- 69 | cost [35.0]
63 --- 64 | cost [28.0]
64 --- 66 | cost [28.0]
66 --- 68 | cost [14.0]
67 --- 68 | cost [0.0]
67 --- 76 | cost [70.0]
69 --- 70 | cost [35.0]
70 --- 82 | cost [70.0]
74 --- 75 | cost [28.0]
74 --- 85 | cost [35.0]
75 --- 76 | cost [28.0]
82 --- 87 | cost [77.0]
85 --- 87 | cost [28.0]

STAR
3  -->  2 | cost [15.0]
8  -->  7 | cost [6.0]
11 --> 44 | cost [36.0]
13 --> 14 | cost [6.0]
17 --> 20 | cost [6.0]
18 --> 20 | cost [6.0]
19 --> 20 | cost [3.0]
22 --> 26 | cost [12.0]
24 --> 23 | cost [9.0]
25 --> 23 | cost [21.0]
28 --> 27 | cost [15.0]
29 --> 30 | cost [12.0]
33 --> 44 | cost [15.0]
34 --> 35 | cost [6.0]
37 --> 36 | cost [3.0]
38 --> 36 | cost [12.0]
39 --> 40 | cost [9.0]
45 --> 44 | cost [12.0]
46 --> 50 | cost [18.0]
47 --> 50 | cost [24.0]
48 --> 50 | cost [30.0]
51 --> 55 | cost [9.0]
53 --> 52 | cost [9.0]
54 --> 57 | cost [27.0]
58 --> 56 | cost [15.0]
59 --> 56 | cost [21.0]
60 --> 63 | cost [21.0]
61 --> 63 | cost [15.0]
62 --> 63 | cost [9.0]
65 --> 66 | cost [24.0]
71 --> 75 | cost [21.0]
72 --> 75 | cost [18.0]
73 --> 75 | cost [12.0]
77 --> 76 | cost [12.0]
78 --> 85 | cost [12.0]
79 --> 69 | cost [60.0]
80 --> 82 | cost [99.0]
81 --> 82 | cost [9.0]
83 --> 82 | cost [12.0]
84 --> 85 | cost [9.0]
86 --> 85 | cost [3.0]
88 --> 85 | cost [15.0]
89 --> 87 | cost [12.0]
90 --> 87 | cost [15.0]
91 --> 87 | cost [27.0]
92 --> 76 | cost [33.0]
93 --> 76 | cost [39.0]
94 --> 68 | cost [36.0]
95 --> 76 | cost [69.0]
96 --> 67 | cost [48.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:23:20 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 47 hubs —— 1-2-4-5-6-7-9-10-12-14-15-16-20-21-23-26-27-63-64-66-68-67-76-75-74-85-87-82-70-69-56-57-55-52-50-49-43-42-41-40-44-35-36-32-31-30-97-1
total time           24.32                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2548<=2548           Master/SP costs      2548/0               
Master time          24.32                SP time              0.0                  
subtour              257.0                connectivity cuts    184.0                
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       1                    
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—4—5—6—7—9—10—12—14—15—16—20—21—23—26—27—63—64—66—68—67—76—75—74—85—87—82—70—69—56—57—55—52—50—49—43—42—41—40—44—35—36—32—31—30—97

RING
1  ---  2 | cost [112.0]
1  --- 97 | cost [0.0]
2  ---  4 | cost [56.0]
4  ---  5 | cost [14.0]
5  ---  6 | cost [7.0]
6  ---  7 | cost [14.0]
7  ---  9 | cost [28.0]
9  --- 10 | cost [28.0]
10 --- 12 | cost [21.0]
12 --- 14 | cost [28.0]
14 --- 15 | cost [21.0]
15 --- 16 | cost [49.0]
16 --- 20 | cost [77.0]
20 --- 21 | cost [42.0]
21 --- 23 | cost [63.0]
23 --- 26 | cost [42.0]
26 --- 27 | cost [42.0]
27 --- 63 | cost [77.0]
30 --- 31 | cost [7.0]
30 --- 97 | cost [42.0]
31 --- 32 | cost [14.0]
32 --- 36 | cost [21.0]
35 --- 36 | cost [28.0]
35 --- 44 | cost [56.0]
40 --- 41 | cost [14.0]
40 --- 44 | cost [42.0]
41 --- 42 | cost [7.0]
42 --- 43 | cost [7.0]
43 --- 49 | cost [7.0]
49 --- 50 | cost [28.0]
50 --- 52 | cost [21.0]
52 --- 55 | cost [21.0]
55 --- 57 | cost [49.0]
56 --- 57 | cost [0.0]
56 --- 69 | cost [35.0]
63 --- 64 | cost [28.0]
64 --- 66 | cost [28.0]
66 --- 68 | cost [14.0]
67 --- 68 | cost [0.0]
67 --- 76 | cost [70.0]
69 --- 70 | cost [35.0]
70 --- 82 | cost [70.0]
74 --- 75 | cost [28.0]
74 --- 85 | cost [35.0]
75 --- 76 | cost [28.0]
82 --- 87 | cost [77.0]
85 --- 87 | cost [28.0]

STAR
3  -->  2 | cost [15.0]
8  -->  6 | cost [6.0]
11 --> 44 | cost [36.0]
13 --> 14 | cost [6.0]
17 --> 20 | cost [6.0]
18 --> 20 | cost [6.0]
19 --> 20 | cost [3.0]
22 --> 26 | cost [12.0]
24 --> 23 | cost [9.0]
25 --> 23 | cost [21.0]
28 --> 27 | cost [15.0]
29 --> 30 | cost [12.0]
33 --> 44 | cost [15.0]
34 --> 35 | cost [6.0]
37 --> 36 | cost [3.0]
38 --> 36 | cost [12.0]
39 --> 40 | cost [9.0]
45 --> 44 | cost [12.0]
46 --> 50 | cost [18.0]
47 --> 50 | cost [24.0]
48 --> 50 | cost [30.0]
51 --> 55 | cost [9.0]
53 --> 52 | cost [9.0]
54 --> 57 | cost [27.0]
58 --> 56 | cost [15.0]
59 --> 56 | cost [21.0]
60 --> 63 | cost [21.0]
61 --> 63 | cost [15.0]
62 --> 63 | cost [9.0]
65 --> 66 | cost [24.0]
71 --> 75 | cost [21.0]
72 --> 75 | cost [18.0]
73 --> 75 | cost [12.0]
77 --> 75 | cost [12.0]
78 --> 85 | cost [12.0]
79 --> 69 | cost [60.0]
80 --> 82 | cost [99.0]
81 --> 82 | cost [9.0]
83 --> 82 | cost [12.0]
84 --> 85 | cost [9.0]
86 --> 85 | cost [3.0]
88 --> 85 | cost [15.0]
89 --> 87 | cost [12.0]
90 --> 87 | cost [15.0]
91 --> 87 | cost [27.0]
92 --> 76 | cost [33.0]
93 --> 76 | cost [39.0]
94 --> 68 | cost [36.0]
95 --> 67 | cost [69.0]
96 --> 67 | cost [48.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 17:32:33 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 6 hubs —— 1—30—31—32—36—97
total time           572.1                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2438<=2438           subtour              3573.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       48588                n lazycuts edges     7.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—30—31—32—36—97

RING
1  --- 30 | cost [42.0]
6  ---  7 | cost [14.0]
6  ---  8 | cost [14.0]
7  --- 10 | cost [56.0]
8  ---  9 | cost [35.0]
9  --- 14 | cost [77.0]
10 --- 12 | cost [21.0]
12 --- 14 | cost [28.0]
17 --- 20 | cost [14.0]
17 --- 21 | cost [56.0]
19 --- 20 | cost [7.0]
19 --- 21 | cost [42.0]
22 --- 23 | cost [42.0]
22 --- 26 | cost [28.0]
23 --- 26 | cost [42.0]
30 --- 31 | cost [7.0]
31 --- 32 | cost [14.0]
32 --- 36 | cost [21.0]
36 --- 97 | cost [77.0]
40 --- 41 | cost [14.0]
40 --- 42 | cost [21.0]
41 --- 42 | cost [7.0]
47 --- 53 | cost [56.0]
47 --- 54 | cost [63.0]
52 --- 53 | cost [21.0]
52 --- 55 | cost [21.0]
54 --- 58 | cost [28.0]
55 --- 69 | cost [70.0]
56 --- 58 | cost [35.0]
56 --- 69 | cost [35.0]
64 --- 66 | cost [28.0]
64 --- 67 | cost [42.0]
66 --- 67 | cost [14.0]
72 --- 73 | cost [21.0]
72 --- 75 | cost [42.0]
73 --- 75 | cost [28.0]
84 --- 86 | cost [21.0]
84 --- 87 | cost [35.0]
86 --- 87 | cost [28.0]
92 --- 93 | cost [42.0]
92 --- 94 | cost [84.0]
93 --- 94 | cost [49.0]

STAR
2  -->  6 | cost [33.0]
3  -->  6 | cost [30.0]
4  -->  6 | cost [9.0]
5  -->  6 | cost [3.0]
11 --> 14 | cost [39.0]
13 --> 14 | cost [6.0]
15 --> 14 | cost [9.0]
16 --> 14 | cost [30.0]
18 --> 19 | cost [6.0]
24 --> 23 | cost [9.0]
25 --> 23 | cost [21.0]
27 --> 26 | cost [18.0]
28 --> 26 | cost [18.0]
29 --> 30 | cost [12.0]
33 --> 40 | cost [30.0]
34 --> 36 | cost [18.0]
35 --> 36 | cost [12.0]
37 --> 36 | cost [3.0]
38 --> 36 | cost [12.0]
39 --> 40 | cost [9.0]
43 --> 42 | cost [3.0]
44 --> 40 | cost [18.0]
45 --> 42 | cost [21.0]
46 --> 47 | cost [15.0]
48 --> 47 | cost [6.0]
49 --> 42 | cost [6.0]
50 --> 52 | cost [9.0]
51 --> 55 | cost [9.0]
57 --> 56 | cost [0.0]
59 --> 58 | cost [21.0]
60 --> 58 | cost [21.0]
61 --> 64 | cost [24.0]
62 --> 64 | cost [18.0]
63 --> 64 | cost [12.0]
65 --> 66 | cost [24.0]
68 --> 67 | cost [0.0]
70 --> 69 | cost [15.0]
71 --> 72 | cost [3.0]
74 --> 75 | cost [12.0]
76 --> 75 | cost [12.0]
77 --> 75 | cost [12.0]
78 --> 86 | cost [12.0]
79 --> 69 | cost [60.0]
80 --> 69 | cost [114.0]
81 --> 84 | cost [33.0]
82 --> 84 | cost [27.0]
83 --> 84 | cost [33.0]
85 --> 86 | cost [3.0]
88 --> 86 | cost [12.0]
89 --> 87 | cost [12.0]
90 --> 87 | cost [15.0]
91 --> 87 | cost [27.0]
95 --> 93 | cost [30.0]
96 --> 94 | cost [30.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 18:33:08 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 44 hubs —— 1-2-4-5-6-7-9-10-12-14-15-16-20-21-23-27-63-64-66-67-76-75-74-85-87-82-70-69-57-55-52-50-49-43-42-41-40-44-35-36-32-31-30-97-1
total time           3604.76 (TL 3600)    gap                  0.013                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2517<=2551           Master/SP costs      2551/0               
Master time          3604.76              SP time              0.0                  
subtour              17152.0              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       42885                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—4—5—6—7—9—10—12—14—15—16—20—21—23—27—63—64—66—67—76—75—74—85—87—82—70—69—57—55—52—50—49—43—42—41—40—44—35—36—32—31—30—97

RING
1  ---  2 | cost [112.0]
2  ---  4 | cost [56.0]
4  ---  5 | cost [14.0]
5  ---  6 | cost [7.0]
6  ---  7 | cost [14.0]
7  ---  9 | cost [28.0]
9  --- 10 | cost [28.0]
10 --- 12 | cost [21.0]
12 --- 14 | cost [28.0]
14 --- 15 | cost [21.0]
15 --- 16 | cost [49.0]
16 --- 20 | cost [77.0]
20 --- 21 | cost [42.0]
21 --- 23 | cost [63.0]
23 --- 27 | cost [63.0]
27 --- 63 | cost [77.0]
30 --- 31 | cost [7.0]
30 --- 97 | cost [42.0]
31 --- 32 | cost [14.0]
32 --- 36 | cost [21.0]
35 --- 36 | cost [28.0]
35 --- 44 | cost [56.0]
40 --- 41 | cost [14.0]
40 --- 44 | cost [42.0]
41 --- 42 | cost [7.0]
42 --- 43 | cost [7.0]
43 --- 49 | cost [7.0]
49 --- 50 | cost [28.0]
50 --- 52 | cost [21.0]
52 --- 55 | cost [21.0]
55 --- 57 | cost [49.0]
57 --- 69 | cost [35.0]
63 --- 64 | cost [28.0]
64 --- 66 | cost [28.0]
66 --- 67 | cost [14.0]
67 --- 76 | cost [70.0]
69 --- 70 | cost [35.0]
70 --- 82 | cost [70.0]
74 --- 75 | cost [28.0]
74 --- 85 | cost [35.0]
75 --- 76 | cost [28.0]
82 --- 87 | cost [77.0]
85 --- 87 | cost [28.0]

STAR
3  -->  2 | cost [15.0]
8  -->  7 | cost [6.0]
11 --> 44 | cost [36.0]
13 --> 14 | cost [6.0]
17 --> 20 | cost [6.0]
18 --> 20 | cost [6.0]
19 --> 20 | cost [3.0]
22 --> 23 | cost [18.0]
24 --> 23 | cost [9.0]
25 --> 23 | cost [21.0]
26 --> 23 | cost [18.0]
28 --> 27 | cost [15.0]
29 --> 30 | cost [12.0]
33 --> 44 | cost [15.0]
34 --> 35 | cost [6.0]
37 --> 36 | cost [3.0]
38 --> 36 | cost [12.0]
39 --> 40 | cost [9.0]
45 --> 44 | cost [12.0]
46 --> 50 | cost [18.0]
47 --> 50 | cost [24.0]
48 --> 50 | cost [30.0]
51 --> 55 | cost [9.0]
53 --> 52 | cost [9.0]
54 --> 57 | cost [27.0]
56 --> 57 | cost [0.0]
58 --> 57 | cost [15.0]
59 --> 57 | cost [21.0]
60 --> 63 | cost [21.0]
61 --> 63 | cost [15.0]
62 --> 63 | cost [9.0]
65 --> 66 | cost [24.0]
68 --> 67 | cost [0.0]
71 --> 75 | cost [21.0]
72 --> 75 | cost [18.0]
73 --> 75 | cost [12.0]
77 --> 76 | cost [12.0]
78 --> 85 | cost [12.0]
79 --> 69 | cost [60.0]
80 --> 82 | cost [99.0]
81 --> 82 | cost [9.0]
83 --> 82 | cost [12.0]
84 --> 85 | cost [9.0]
86 --> 85 | cost [3.0]
88 --> 85 | cost [15.0]
89 --> 87 | cost [12.0]
90 --> 87 | cost [15.0]
91 --> 87 | cost [27.0]
92 --> 76 | cost [33.0]
93 --> 76 | cost [39.0]
94 --> 67 | cost [36.0]
95 --> 76 | cost [69.0]
96 --> 66 | cost [48.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1