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

——————— Thu, 25 Jan 2024 23:59:14 ————————— 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           3490.94              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             560460.1<=560460.1   subtour              364.0                
connectivity cuts    1300.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               2:76                 
2-opt strategy       0                                                              
explored_nodes       5220                 n lazycuts edges     2.0                  
F                    7.0                  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
1  ---  3 | cost [253.47]
2  ---  6 | cost [283.43]
3  ---  9 | cost [189.0]
6  --- 12 | cost [206.5]
9  --- 11 | cost [129.01]
11 --- 18 | cost [133.91]
12 --- 17 | cost [159.88]
17 --- 37 | cost [84.63]
18 --- 36 | cost [74.27]
22 --- 46 | cost [249.83]
22 --- 77 | cost [213.5]
23 --- 24 | cost [212.24]
24 --- 45 | cost [213.5]
27 --- 28 | cost [95.83]
27 --- 48 | cost [242.55]
28 --- 42 | cost [118.86]
29 --- 43 | cost [151.34]
29 --- 44 | cost [330.82]
36 --- 39 | cost [139.37]
37 --- 38 | cost [122.22]
38 --- 40 | cost [148.89000000000001]
39 --- 41 | cost [141.75]
40 --- 60 | cost [84.63]
41 --- 59 | cost [74.27]
42 --- 53 | cost [76.44]
43 --- 54 | cost [86.59]
44 --- 47 | cost [101.5]
45 --- 48 | cost [109.34]
46 --- 47 | cost [212.24]
51 --- 53 | cost [140.98]
51 --- 57 | cost [206.5]
52 --- 54 | cost [98.07000000000001]
52 --- 56 | cost [113.75]
56 --- 63 | cost [186.34]
57 --- 62 | cost [112.77]
59 --- 62 | cost [139.37]
60 --- 61 | cost [122.22]
61 --- 63 | cost [148.89000000000001]

BACKUP STAR
4  -->  6 | cost [48.84]
5  -->  9 | cost [48.72]
7  -->  3 | cost [48.84]
8  -->  9 | cost [60.0]
10 --> 11 | cost [48.51]
13 --> 11 | cost [64.32000000000001]
14 --> 11 | cost [79.95]
15 --> 11 | cost [55.14]
16 --> 11 | cost [48.33]
19 -->  6 | cost [84.33]
20 -->  3 | cost [68.7]
21 --> 24 | cost [43.5]
25 --> 22 | cost [46.86]
26 --> 29 | cost [41.04]
30 --> 28 | cost [60.42]
31 --> 28 | cost [75.36]
32 --> 28 | cost [48.72]
33 --> 29 | cost [48.75]
34 --> 39 | cost [48.33]
35 --> 38 | cost [48.33]
49 --> 53 | cost [48.84]
50 --> 52 | cost [48.84]
55 --> 52 | cost [40.92]
58 --> 59 | cost [34.92]
64 --> 57 | cost [57.39]
65 --> 56 | cost [67.41]
66 --> 56 | cost [58.59]
67 --> 51 | cost [124.86]
68 --> 48 | cost [110.64]
69 --> 48 | cost [85.8]
70 --> 48 | cost [228.66]
71 --> 57 | cost [140.70000000000002]
72 --> 62 | cost [147.18]
73 --> 62 | cost [147.93]
74 --> 11 | cost [174.6]

B = 659.3
i★ = 45
j★ = 47
k★ = 48

       
——————— Fri, 26 Jan 2024 00:01:42 ————————— 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           106.37               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             560460.09<=560460.09 Master/SP costs      555844.99/4615.1     
Master time          104.68               SP time              1.69                 
subtour              892.0                connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            26.0                 SP method            poly                 
tildeV               2:76                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       4268                 
F                    7.0                  
                                          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
1  --- 22 | cost [213.5]
2  ---  6 | cost [283.43]
3  ---  9 | cost [189.0]
3  --- 77 | cost [253.47]
6  --- 12 | cost [206.5]
9  --- 11 | cost [129.01]
11 --- 18 | cost [133.91]
12 --- 17 | cost [159.88]
17 --- 37 | cost [84.63]
18 --- 36 | cost [74.27]
22 --- 46 | cost [249.83]
23 --- 24 | cost [212.24]
24 --- 45 | cost [213.5]
27 --- 28 | cost [95.83]
27 --- 48 | cost [242.55]
28 --- 42 | cost [118.86]
29 --- 43 | cost [151.34]
29 --- 44 | cost [330.82]
36 --- 39 | cost [139.37]
37 --- 38 | cost [122.22]
38 --- 40 | cost [148.89000000000001]
39 --- 41 | cost [141.75]
40 --- 60 | cost [84.63]
41 --- 59 | cost [74.27]
42 --- 53 | cost [76.44]
43 --- 54 | cost [86.59]
44 --- 47 | cost [101.5]
45 --- 48 | cost [109.34]
46 --- 47 | cost [212.24]
51 --- 53 | cost [140.98]
51 --- 57 | cost [206.5]
52 --- 54 | cost [98.07000000000001]
52 --- 56 | cost [113.75]
56 --- 63 | cost [186.34]
57 --- 62 | cost [112.77]
59 --- 62 | cost [139.37]
60 --- 61 | cost [122.22]
61 --- 63 | cost [148.89000000000001]

BACKUP STAR
4  -->  6 | cost [48.84]
5  -->  9 | cost [48.72]
7  -->  3 | cost [48.84]
8  -->  9 | cost [60.0]
10 --> 11 | cost [48.51]
13 --> 11 | cost [64.32000000000001]
14 --> 11 | cost [79.95]
15 --> 11 | cost [55.14]
16 --> 11 | cost [48.33]
19 -->  6 | cost [84.33]
20 -->  3 | cost [68.7]
21 --> 24 | cost [43.5]
25 --> 22 | cost [46.86]
26 --> 29 | cost [41.04]
30 --> 28 | cost [60.42]
31 --> 28 | cost [75.36]
32 --> 28 | cost [48.72]
33 --> 29 | cost [48.75]
34 --> 39 | cost [48.33]
35 --> 38 | cost [48.33]
49 --> 53 | cost [48.84]
50 --> 52 | cost [48.84]
55 --> 52 | cost [40.92]
58 --> 59 | cost [34.92]
64 --> 57 | cost [57.39]
65 --> 56 | cost [67.41]
66 --> 56 | cost [58.59]
67 --> 51 | cost [124.86]
68 --> 48 | cost [110.64]
69 --> 48 | cost [85.8]
70 --> 48 | cost [228.66]
71 --> 57 | cost [140.70000000000002]
72 --> 62 | cost [147.18]
73 --> 62 | cost [147.93]
74 --> 11 | cost [174.6]

B = 659.3
i★ = 45
j★ = 47
k★ = 48