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

——————— Sat, 27 Jan 2024 13:22:31 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 43 hubs —— 1—2—3—6—9—12—13—15—16—17—18—37—36—38—39—40—41—60—59—61—62—64—63—57—56—51—52—53—54—42—43—28—29—27—44—48—47—45—46—24—22—23—77
total time           3615.16 (TL 3600)    gap                  0.017                
blossom time         0                    nb blossom           0.0                  
LB <= UB             563247.48<=572864.98 subtour              270.0                
connectivity cuts    1361.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               2:76                 
2-opt strategy       0                                                              
explored_nodes       3725                 n lazycuts edges     2.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—3—6—9—12—13—15—16—17—18—37—36—38—39—40—41—60—59—61—62—64—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]
12 --- 13 | cost [8148.0]
13 --- 15 | cost [9730.0]
15 --- 16 | cost [4900.0]
16 --- 17 | cost [10584.0]
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 --- 64 | cost [14175.0]
63 --- 64 | cost [4669.0]

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]
11 --> 12 | cost [3354.0]
14 --> 13 | cost [1566.0]
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]
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 --> 48 | cost [22866.0]
71 --> 64 | cost [9441.0]
72 --> 64 | cost [9441.0]
73 --> 64 | cost [9750.0]
74 --> 13 | cost [11031.0]
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  --- 13 | cost [181.65]
12 --- 15 | cost [112.77]
13 --- 16 | cost [139.37]
15 --- 17 | cost [148.89000000000001]
16 --- 18 | cost [141.75]
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 --- 64 | cost [133.91]
59 --- 62 | cost [139.37]
60 --- 61 | cost [122.22]
61 --- 64 | cost [188.51]
62 --- 63 | cost [105.84]

BACKUP STAR
4  -->  6 | cost [48.84]
5  -->  9 | cost [48.72]
7  -->  3 | cost [48.84]
8  -->  9 | cost [60.0]
10 -->  6 | cost [48.75]
11 --> 17 | cost [38.4]
14 --> 12 | cost [49.71]
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]
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 --> 47 | cost [205.98000000000002]
71 --> 63 | cost [112.11]
72 --> 63 | cost [114.36]
73 --> 63 | cost [117.27]
74 --> 15 | cost [135.99]

B = 449.58
i★ = 62
j★ = 64
k★ = 63

       
——————— Sat, 27 Jan 2024 14:23:15 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 42 hubs —— 1-23-22-24-46-45-44-27-29-28-43-42-54-53-49-50-51-56-57-63-64-62-61-59-60-41-40-39-38-36-37-18-17-16-15-13-12-9-6-3-2-77-1
total time           3603.51 (TL 3600)    gap                  0.006                
blossom time         0                    nb blossom           0.0                  
LB <= UB             569422.04<=572989.55 Master/SP costs      558674.99/14314.56   
Master time          3585.52              SP time              17.99                
subtour              3349.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            356.0                SP method            poly                 
tildeV               2:76                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       387298               
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—23—22—24—46—45—44—27—29—28—43—42—54—53—49—50—51—56—57—63—64—62—61—59—60—41—40—39—38—36—37—18—17—16—15—13—12—9—6—3—2—77

RING
1  --- 23 | cost [13517.0]
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]
12 --- 13 | cost [8148.0]
13 --- 15 | cost [9730.0]
15 --- 16 | cost [4900.0]
16 --- 17 | cost [10584.0]
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 --- 45 | cost [8351.0]
45 --- 46 | cost [10031.0]
49 --- 50 | cost [4900.0]
49 --- 53 | cost [11396.0]
50 --- 51 | cost [9583.0]
51 --- 56 | cost [9541.0]
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 --- 64 | cost [14175.0]
63 --- 64 | cost [4669.0]

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]
11 --> 12 | cost [3354.0]
14 --> 13 | cost [1566.0]
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]
47 --> 44 | cost [4350.0]
48 --> 44 | cost [1650.0]
52 --> 53 | cost [2718.0]
55 --> 56 | cost [2100.0]
58 --> 57 | cost [3354.0]
65 --> 51 | cost [5094.0]
66 --> 51 | cost [3159.0]
67 --> 50 | cost [9300.0]
68 --> 49 | cost [11889.0]
69 --> 44 | cost [9957.0]
70 --> 50 | cost [20895.0]
71 --> 64 | cost [9441.0]
72 --> 64 | cost [9441.0]
73 --> 64 | cost [9750.0]
74 --> 13 | cost [11031.0]
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  --- 13 | cost [181.65]
12 --- 15 | cost [112.77]
13 --- 16 | cost [139.37]
15 --- 17 | cost [148.89000000000001]
16 --- 18 | cost [141.75]
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 --- 45 | cost [256.83]
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 --- 46 | cost [178.5]
49 --- 51 | cost [114.03]
49 --- 54 | cost [153.51]
50 --- 53 | cost [151.41]
50 --- 56 | cost [189.0]
51 --- 57 | cost [206.5]
56 --- 63 | cost [186.34]
57 --- 64 | cost [133.91]
59 --- 62 | cost [139.37]
60 --- 61 | cost [122.22]
61 --- 64 | cost [188.51]
62 --- 63 | cost [105.84]

BACKUP STAR
4  -->  6 | cost [48.84]
5  -->  9 | cost [48.72]
7  -->  3 | cost [48.84]
8  -->  9 | cost [60.0]
10 -->  6 | cost [48.75]
11 --> 17 | cost [38.4]
14 --> 12 | cost [49.71]
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]
47 --> 45 | cost [51.0]
48 --> 45 | cost [46.86]
52 --> 51 | cost [33.45]
55 --> 51 | cost [48.72]
58 --> 59 | cost [34.92]
65 --> 56 | cost [67.41]
66 --> 50 | cost [51.99]
67 --> 49 | cost [107.16]
68 --> 50 | cost [110.07000000000001]
69 --> 45 | cost [107.07000000000001]
70 --> 49 | cost [224.22]
71 --> 63 | cost [112.11]
72 --> 63 | cost [114.36]
73 --> 63 | cost [117.27]
74 --> 15 | cost [135.99]

B = 461.76
i★ = 27
j★ = 44
k★ = 45