------------------------------------------------------------
                            α=7.0 —— pr76 —— 76 nodes       
------------------------------------------------------------

——————— Mon, 08 Jan 2024 08:16:00 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 40 hubs —— 1—2—3—6—9—12—11—17—18—37—36—38—39—40—41—60—59—61—62—63—57—56—51—52—53—54—42—43—28—29—27—44—48—47—45—46—24—22—23—77
total time           71.87                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             555845<=555845       subtour              578.0                
connectivity cuts    813.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1586                 n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—3—6—9—12—11—17—18—37—36—38—39—40—41—60—59—61—62—63—57—56—51—52—53—54—42—43—28—29—27—44—48—47—45—46—24—22—23—77

RING
1  ---  2 | cost [7826.0]
1  --- 77 | cost [0.0]
2  ---  3 | cost [20482.0]
3  ---  6 | cost [9576.0]
6  ---  9 | cost [9548.0]
9  --- 12 | cost [11305.0]
11 --- 12 | cost [7826.0]
11 --- 17 | cost [8960.0]
17 --- 18 | cost [4669.0]
18 --- 37 | cost [3850.0]
22 --- 23 | cost [10031.0]
22 --- 24 | cost [11900.0]
23 --- 77 | cost [13517.0]
24 --- 46 | cost [13517.0]
27 --- 29 | cost [11396.0]
27 --- 44 | cost [21700.0]
28 --- 29 | cost [7805.0]
28 --- 43 | cost [7371.0]
36 --- 37 | cost [3654.0]
36 --- 38 | cost [9730.0]
38 --- 39 | cost [4900.0]
39 --- 40 | cost [10584.0]
40 --- 41 | cost [4669.0]
41 --- 60 | cost [3850.0]
42 --- 43 | cost [5012.0]
42 --- 54 | cost [3850.0]
44 --- 48 | cost [3850.0]
45 --- 46 | cost [10031.0]
45 --- 47 | cost [11900.0]
47 --- 48 | cost [7826.0]
51 --- 52 | cost [7805.0]
51 --- 56 | cost [9541.0]
52 --- 53 | cost [6342.0]
53 --- 54 | cost [4081.0]
56 --- 57 | cost [11319.0]
57 --- 63 | cost [8960.0]
59 --- 60 | cost [3654.0]
59 --- 61 | cost [9730.0]
61 --- 62 | cost [4900.0]
62 --- 63 | cost [10584.0]

STAR
4  -->  3 | cost [2100.0]
5  -->  6 | cost [3345.0]
7  -->  6 | cost [2718.0]
8  -->  6 | cost [4203.0]
10 -->  9 | cost [2100.0]
13 --> 12 | cost [3492.0]
14 --> 12 | cost [4971.0]
15 --> 12 | cost [4833.0]
16 --> 17 | cost [4536.0]
19 --> 29 | cost [5847.0]
20 -->  6 | cost [6486.0]
21 --> 22 | cost [3579.0]
25 --> 24 | cost [3354.0]
26 --> 27 | cost [2100.0]
30 --> 29 | cost [2718.0]
31 --> 29 | cost [4203.0]
32 --> 29 | cost [4092.0]
33 --> 28 | cost [4089.0]
34 --> 40 | cost [3840.0]
35 --> 36 | cost [3492.0]
49 --> 52 | cost [4104.0]
50 --> 51 | cost [4107.0]
55 --> 56 | cost [2100.0]
58 --> 57 | cost [3354.0]
64 --> 63 | cost [2001.0]
65 --> 51 | cost [5094.0]
66 --> 51 | cost [3159.0]
67 --> 47 | cost [11499.0]
68 --> 47 | cost [9150.0]
69 --> 47 | cost [5793.0]
70 --> 47 | cost [20598.0]
71 --> 63 | cost [11211.0]
72 --> 63 | cost [11436.0]
73 --> 63 | cost [11727.0]
74 --> 12 | cost [14397.0]
75 -->  1 | cost [10818.0]
76 -->  1 | cost [11148.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:17:47 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 40 hubs —— 1-23-22-24-46-45-47-48-44-27-29-28-43-42-54-53-52-51-56-57-63-62-61-59-60-41-40-39-38-36-37-18-17-11-12-9-6-3-2-77-1
total time           80.66                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             555845<=555845       Master/SP costs      555845/0             
Master time          80.66                SP time              0.0                  
subtour              649.0                connectivity cuts    1631.0               
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       2745                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—23—22—24—46—45—47—48—44—27—29—28—43—42—54—53—52—51—56—57—63—62—61—59—60—41—40—39—38—36—37—18—17—11—12—9—6—3—2—77

RING
1  --- 23 | cost [13517.0]
1  --- 77 | cost [0.0]
2  ---  3 | cost [20482.0]
2  --- 77 | cost [7826.0]
3  ---  6 | cost [9576.0]
6  ---  9 | cost [9548.0]
9  --- 12 | cost [11305.0]
11 --- 12 | cost [7826.0]
11 --- 17 | cost [8960.0]
17 --- 18 | cost [4669.0]
18 --- 37 | cost [3850.0]
22 --- 23 | cost [10031.0]
22 --- 24 | cost [11900.0]
24 --- 46 | cost [13517.0]
27 --- 29 | cost [11396.0]
27 --- 44 | cost [21700.0]
28 --- 29 | cost [7805.0]
28 --- 43 | cost [7371.0]
36 --- 37 | cost [3654.0]
36 --- 38 | cost [9730.0]
38 --- 39 | cost [4900.0]
39 --- 40 | cost [10584.0]
40 --- 41 | cost [4669.0]
41 --- 60 | cost [3850.0]
42 --- 43 | cost [5012.0]
42 --- 54 | cost [3850.0]
44 --- 48 | cost [3850.0]
45 --- 46 | cost [10031.0]
45 --- 47 | cost [11900.0]
47 --- 48 | cost [7826.0]
51 --- 52 | cost [7805.0]
51 --- 56 | cost [9541.0]
52 --- 53 | cost [6342.0]
53 --- 54 | cost [4081.0]
56 --- 57 | cost [11319.0]
57 --- 63 | cost [8960.0]
59 --- 60 | cost [3654.0]
59 --- 61 | cost [9730.0]
61 --- 62 | cost [4900.0]
62 --- 63 | cost [10584.0]

STAR
4  -->  3 | cost [2100.0]
5  -->  6 | cost [3345.0]
7  -->  6 | cost [2718.0]
8  -->  6 | cost [4203.0]
10 -->  9 | cost [2100.0]
13 --> 12 | cost [3492.0]
14 --> 12 | cost [4971.0]
15 --> 12 | cost [4833.0]
16 --> 17 | cost [4536.0]
19 --> 29 | cost [5847.0]
20 -->  6 | cost [6486.0]
21 --> 22 | cost [3579.0]
25 --> 24 | cost [3354.0]
26 --> 27 | cost [2100.0]
30 --> 29 | cost [2718.0]
31 --> 29 | cost [4203.0]
32 --> 29 | cost [4092.0]
33 --> 28 | cost [4089.0]
34 --> 40 | cost [3840.0]
35 --> 36 | cost [3492.0]
49 --> 52 | cost [4104.0]
50 --> 51 | cost [4107.0]
55 --> 56 | cost [2100.0]
58 --> 57 | cost [3354.0]
64 --> 63 | cost [2001.0]
65 --> 51 | cost [5094.0]
66 --> 51 | cost [3159.0]
67 --> 47 | cost [11499.0]
68 --> 47 | cost [9150.0]
69 --> 47 | cost [5793.0]
70 --> 47 | cost [20598.0]
71 --> 63 | cost [11211.0]
72 --> 63 | cost [11436.0]
73 --> 63 | cost [11727.0]
74 --> 12 | cost [14397.0]
75 -->  1 | cost [10818.0]
76 -->  1 | cost [11148.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 16:15:48 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—2—77
total time           10.5                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             479677<=479677       subtour              169.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       863                  n lazycuts edges     3.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—77

RING
1  ---  2 | cost [7826.0]
2  --- 77 | cost [7826.0]
5  ---  6 | cost [7805.0]
5  --- 20 | cost [7371.0]
6  --- 20 | cost [15134.0]
12 --- 13 | cost [8148.0]
12 --- 14 | cost [11599.0]
13 --- 14 | cost [3654.0]
18 --- 36 | cost [7427.0]
18 --- 37 | cost [3850.0]
21 --- 22 | cost [8351.0]
21 --- 25 | cost [3850.0]
22 --- 25 | cost [10934.0]
29 --- 32 | cost [9548.0]
29 --- 33 | cost [11375.0]
32 --- 33 | cost [4900.0]
36 --- 37 | cost [3654.0]
42 --- 53 | cost [7644.0]
42 --- 54 | cost [3850.0]
44 --- 45 | cost [8351.0]
44 --- 48 | cost [3850.0]
45 --- 48 | cost [10934.0]
51 --- 56 | cost [9541.0]
51 --- 66 | cost [7371.0]
53 --- 54 | cost [4081.0]
56 --- 66 | cost [13671.0]
59 --- 60 | cost [3654.0]
59 --- 61 | cost [9730.0]
60 --- 61 | cost [12222.0]
67 --- 68 | cost [8351.0]
67 --- 69 | cost [17850.0]
68 --- 69 | cost [10031.0]
71 --- 72 | cost [13300.0]
71 --- 73 | cost [15400.0]
72 --- 73 | cost [2100.0]

STAR
3  -->  6 | cost [4104.0]
4  -->  5 | cost [4107.0]
7  -->  6 | cost [2718.0]
8  -->  6 | cost [4203.0]
9  -->  6 | cost [4092.0]
10 -->  5 | cost [4089.0]
11 --> 12 | cost [3354.0]
15 --> 13 | cost [4170.0]
16 --> 12 | cost [5514.0]
17 --> 18 | cost [2001.0]
19 --> 20 | cost [2148.0]
23 --> 22 | cost [4299.0]
24 --> 25 | cost [3354.0]
26 --> 29 | cost [4104.0]
27 --> 29 | cost [4884.0]
28 --> 29 | cost [3345.0]
30 --> 29 | cost [2718.0]
31 --> 20 | cost [3711.0]
34 --> 33 | cost [4851.0]
35 --> 36 | cost [3492.0]
38 --> 36 | cost [4170.0]
39 --> 36 | cost [5973.0]
40 --> 60 | cost [3627.0]
41 --> 60 | cost [1650.0]
43 --> 42 | cost [2148.0]
46 --> 45 | cost [4299.0]
47 --> 48 | cost [3354.0]
49 --> 53 | cost [4884.0]
50 --> 51 | cost [4107.0]
52 --> 53 | cost [2718.0]
55 --> 56 | cost [2100.0]
57 --> 56 | cost [4851.0]
58 --> 59 | cost [3492.0]
62 --> 61 | cost [2100.0]
63 --> 61 | cost [6381.0]
64 --> 61 | cost [8079.0]
65 --> 66 | cost [2148.0]
70 --> 67 | cost [11715.0]
74 --> 14 | cost [9474.0]
75 -->  1 | cost [10818.0]
76 -->  1 | cost [11148.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 17:16:23 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 45 hubs —— 1-23-22-25-24-46-45-47-69-48-31-30-29-28-43-42-53-52-51-56-57-63-64-62-59-60-41-40-39-16-18-37-36-35-32-12-13-14-6-5-9-7-3-2-77-1
total time           3606.22 (TL 3600)    gap                  0.23                 
blossom time         0                    nb blossom           0.0                  
LB <= UB             511992.64<=665356    Master/SP costs      665356/0             
Master time          3606.22              SP time              0.0                  
subtour              47293.0              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       15971                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—23—22—25—24—46—45—47—69—48—31—30—29—28—43—42—53—52—51—56—57—63—64—62—59—60—41—40—39—16—18—37—36—35—32—12—13—14—6—5—9—7—3—2—77

RING
1  --- 23 | cost [13517.0]
2  ---  3 | cost [20482.0]
2  --- 77 | cost [7826.0]
3  ---  7 | cost [11396.0]
5  ---  6 | cost [7805.0]
5  ---  9 | cost [11368.0]
6  --- 14 | cost [28644.0]
7  ---  9 | cost [13020.0]
12 --- 13 | cost [8148.0]
12 --- 32 | cost [36470.0]
13 --- 14 | cost [3654.0]
16 --- 18 | cost [14175.0]
16 --- 39 | cost [33250.0]
18 --- 37 | cost [3850.0]
22 --- 23 | cost [10031.0]
22 --- 25 | cost [10934.0]
24 --- 25 | cost [7826.0]
24 --- 46 | cost [13517.0]
28 --- 29 | cost [7805.0]
28 --- 43 | cost [7371.0]
29 --- 30 | cost [6342.0]
30 --- 31 | cost [4081.0]
31 --- 48 | cost [43246.0]
32 --- 35 | cost [11305.0]
35 --- 36 | cost [8148.0]
36 --- 37 | cost [3654.0]
39 --- 40 | cost [10584.0]
40 --- 41 | cost [4669.0]
41 --- 60 | cost [3850.0]
42 --- 43 | cost [5012.0]
42 --- 53 | cost [7644.0]
45 --- 46 | cost [10031.0]
45 --- 47 | cost [11900.0]
47 --- 69 | cost [13517.0]
48 --- 69 | cost [20020.0]
51 --- 52 | cost [7805.0]
51 --- 56 | cost [9541.0]
52 --- 53 | cost [6342.0]
56 --- 57 | cost [11319.0]
57 --- 63 | cost [8960.0]
59 --- 60 | cost [3654.0]
59 --- 62 | cost [13937.0]
62 --- 64 | cost [14175.0]
63 --- 64 | cost [4669.0]

STAR
4  -->  3 | cost [2100.0]
8  -->  7 | cost [1749.0]
10 -->  9 | cost [2100.0]
11 --> 12 | cost [3354.0]
15 --> 16 | cost [2100.0]
17 --> 18 | cost [2001.0]
19 --> 31 | cost [1650.0]
20 -->  5 | cost [3159.0]
21 --> 25 | cost [1650.0]
26 --> 29 | cost [4104.0]
27 --> 28 | cost [4107.0]
33 --> 32 | cost [2100.0]
34 --> 35 | cost [3354.0]
38 --> 39 | cost [2100.0]
44 --> 48 | cost [1650.0]
49 --> 52 | cost [4104.0]
50 --> 51 | cost [4107.0]
54 --> 42 | cost [1650.0]
55 --> 56 | cost [2100.0]
58 --> 57 | cost [3354.0]
61 --> 62 | cost [2100.0]
65 --> 51 | cost [5094.0]
66 --> 51 | cost [3159.0]
67 --> 69 | cost [7650.0]
68 --> 69 | cost [4299.0]
70 --> 69 | cost [14895.0]
71 --> 64 | cost [9441.0]
72 --> 64 | cost [9441.0]
73 --> 64 | cost [9750.0]
74 --> 14 | cost [9474.0]
75 -->  1 | cost [10818.0]
76 -->  1 | cost [11148.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1