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

——————— Mon, 29 Jan 2024 18:44:09 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 47 hubs —— 1—2—3—6—5—10—12—13—15—16—17—18—37—36—38—39—40—41—60—59—61—62—64—63—57—56—51—50—67—68—69—47—44—48—53—54—42—43—28—29—30—26—25—21—22—23—77
total time           3615.36 (TL 3600)    gap                  0.109                
blossom time         0                    nb blossom           0.0                  
LB <= UB             562993.99<=631826.94 subtour              335.0                
connectivity cuts    654.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:76                 
2-opt strategy       0                                                              
explored_nodes       1058                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—3—6—5—10—12—13—15—16—17—18—37—36—38—39—40—41—60—59—61—62—64—63—57—56—51—50—67—68—69—47—44—48—53—54—42—43—28—29—30—26—25—21—22—23—77

RING
1  ---  2 | cost [7826.0]
2  ---  3 | cost [20482.0]
3  ---  6 | cost [9576.0]
5  ---  6 | cost [7805.0]
5  --- 10 | cost [9541.0]
10 --- 12 | cost [12887.0]
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]
21 --- 22 | cost [8351.0]
21 --- 25 | cost [3850.0]
22 --- 23 | cost [10031.0]
23 --- 77 | cost [13517.0]
25 --- 26 | cost [20482.0]
26 --- 30 | cost [11396.0]
28 --- 29 | cost [7805.0]
28 --- 43 | cost [7371.0]
29 --- 30 | cost [6342.0]
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 --- 47 | cost [10150.0]
44 --- 48 | cost [3850.0]
47 --- 69 | cost [13517.0]
48 --- 53 | cost [25788.0]
50 --- 51 | cost [9583.0]
50 --- 67 | cost [21700.0]
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]
67 --- 68 | cost [8351.0]
68 --- 69 | cost [10031.0]

STAR
4  -->  3 | cost [2100.0]
7  -->  6 | cost [2718.0]
8  -->  6 | cost [4203.0]
9  --> 10 | cost [2100.0]
11 --> 12 | cost [3354.0]
14 --> 13 | cost [1566.0]
19 --> 30 | cost [3276.0]
20 -->  5 | cost [3159.0]
24 --> 25 | cost [3354.0]
27 --> 26 | cost [2100.0]
31 --> 30 | cost [1749.0]
32 --> 29 | cost [4092.0]
33 --> 28 | cost [4089.0]
34 --> 40 | cost [3840.0]
35 --> 36 | cost [3492.0]
45 --> 44 | cost [3579.0]
46 --> 44 | cost [7650.0]
49 --> 50 | cost [2100.0]
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]
70 --> 68 | cost [11838.0]
71 --> 63 | cost [11211.0]
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  ---  5 | cost [114.03]
5  --- 12 | cost [220.71]
6  --- 10 | cost [113.75]
10 --- 13 | cost [207.20000000000002]
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]
21 --- 23 | cost [178.5]
21 --- 26 | cost [228.20000000000002]
22 --- 25 | cost [109.34]
22 --- 77 | cost [213.5]
25 --- 30 | cost [257.88]
26 --- 29 | cost [95.76]
28 --- 30 | cost [140.98]
28 --- 42 | cost [118.86]
29 --- 43 | cost [151.34]
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 --- 53 | cost [265.86]
44 --- 69 | cost [232.33]
47 --- 48 | cost [78.26]
47 --- 68 | cost [213.5]
48 --- 54 | cost [276.5]
50 --- 56 | cost [189.0]
50 --- 68 | cost [256.83]
51 --- 57 | cost [206.5]
51 --- 67 | cost [291.34000000000003]
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]
67 --- 69 | cost [178.5]

BACKUP STAR
4  -->  5 | cost [41.07]
7  -->  3 | cost [48.84]
8  -->  3 | cost [65.79]
9  -->  6 | cost [40.92]
11 --> 17 | cost [38.4]
14 --> 12 | cost [49.71]
19 -->  5 | cost [50.94]
20 --> 30 | cost [51.0]
24 --> 21 | cost [43.5]
27 --> 28 | cost [41.07]
31 --> 29 | cost [42.03]
32 --> 28 | cost [48.72]
33 --> 29 | cost [48.75]
34 --> 39 | cost [48.33]
35 --> 38 | cost [48.33]
45 --> 48 | cost [46.86]
46 --> 25 | cost [85.8]
49 --> 53 | cost [48.84]
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]
70 --> 67 | cost [117.15]
71 --> 64 | cost [94.41]
72 --> 63 | cost [114.36]
73 --> 63 | cost [117.27]
74 --> 15 | cost [135.99]

B = 340.18000000000006
i★ = 51
j★ = 50
k★ = 67

       
——————— Mon, 29 Jan 2024 19:44:56 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 41 hubs —— 1-2-3-6-9-12-13-15-16-17-18-19-31-30-29-28-33-34-40-41-60-59-61-62-64-63-57-55-52-51-50-67-68-69-47-45-46-24-22-23-77-1
total time           3604.44 (TL 3600)    gap                  0.118                
blossom time         0                    nb blossom           0.0                  
LB <= UB             557995.85<=632418.43 Master/SP costs      563755/68663.43      
Master time          3518.9               SP time              85.53                
subtour              10029.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            1712.0               SP method            poly                 
tildeV               2:76                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       73046                
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—3—6—9—12—13—15—16—17—18—19—31—30—29—28—33—34—40—41—60—59—61—62—64—63—57—55—52—51—50—67—68—69—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 --- 19 | cost [25900.0]
19 --- 31 | cost [3850.0]
22 --- 23 | cost [10031.0]
22 --- 24 | cost [11900.0]
23 --- 77 | cost [13517.0]
24 --- 46 | cost [13517.0]
28 --- 29 | cost [7805.0]
28 --- 33 | cost [9541.0]
29 --- 30 | cost [6342.0]
30 --- 31 | cost [4081.0]
33 --- 34 | cost [11319.0]
34 --- 40 | cost [8960.0]
40 --- 41 | cost [4669.0]
41 --- 60 | cost [3850.0]
45 --- 46 | cost [10031.0]
45 --- 47 | cost [11900.0]
47 --- 69 | cost [13517.0]
50 --- 51 | cost [9583.0]
50 --- 67 | cost [21700.0]
51 --- 52 | cost [7805.0]
52 --- 55 | cost [9548.0]
55 --- 57 | cost [12901.0]
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]
67 --- 68 | cost [8351.0]
68 --- 69 | cost [10031.0]

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]
20 --> 19 | cost [2148.0]
21 --> 22 | cost [3579.0]
25 --> 24 | cost [3354.0]
26 --> 29 | cost [4104.0]
27 --> 28 | cost [4107.0]
32 --> 33 | cost [2100.0]
35 --> 34 | cost [3354.0]
36 --> 18 | cost [3183.0]
37 --> 18 | cost [1650.0]
38 --> 34 | cost [5514.0]
39 --> 40 | cost [4536.0]
42 --> 28 | cost [5094.0]
43 --> 28 | cost [3159.0]
44 --> 45 | cost [3579.0]
48 --> 47 | cost [3354.0]
49 --> 50 | cost [2100.0]
53 --> 52 | cost [2718.0]
54 --> 52 | cost [4203.0]
56 --> 55 | cost [2100.0]
58 --> 57 | cost [3354.0]
65 --> 51 | cost [5094.0]
66 --> 51 | cost [3159.0]
70 --> 67 | cost [11715.0]
71 --> 64 | cost [9441.0]
72 --> 64 | cost [9441.0]
73 --> 63 | cost [11727.0]
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 --- 19 | cost [252.63]
18 --- 31 | cost [261.87]
19 --- 30 | cost [76.44]
22 --- 46 | cost [249.83]
22 --- 77 | cost [213.5]
23 --- 24 | cost [212.24]
24 --- 45 | cost [213.5]
28 --- 30 | cost [140.98]
28 --- 34 | cost [206.5]
29 --- 31 | cost [98.07000000000001]
29 --- 33 | cost [113.75]
33 --- 40 | cost [186.34]
34 --- 41 | cost [133.91]
40 --- 60 | cost [84.63]
41 --- 59 | cost [74.27]
45 --- 69 | cost [249.83]
46 --- 47 | cost [212.24]
47 --- 68 | cost [213.5]
50 --- 52 | cost [113.96000000000001]
50 --- 68 | cost [256.83]
51 --- 55 | cost [113.68]
51 --- 67 | cost [291.34000000000003]
52 --- 57 | cost [220.85]
55 --- 63 | cost [213.78]
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]
67 --- 69 | cost [178.5]

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]
20 --> 31 | cost [37.11]
21 --> 24 | cost [43.5]
25 --> 22 | cost [46.86]
26 --> 30 | cost [48.84]
27 --> 29 | cost [48.84]
32 --> 29 | cost [40.92]
35 --> 33 | cost [55.230000000000004]
36 --> 17 | cost [51.0]
37 --> 17 | cost [36.27]
38 --> 40 | cost [63.81]
39 --> 34 | cost [48.33]
42 --> 52 | cost [58.47]
43 --> 33 | cost [58.59]
44 --> 47 | cost [43.5]
48 --> 45 | cost [46.86]
49 --> 52 | cost [41.04]
53 --> 55 | cost [55.800000000000004]
54 --> 55 | cost [60.0]
56 --> 51 | cost [40.89]
58 --> 59 | cost [34.92]
65 --> 50 | cost [72.63]
66 --> 50 | cost [51.99]
70 --> 68 | cost [118.38]
71 --> 63 | cost [112.11]
72 --> 63 | cost [114.36]
73 --> 64 | cost [97.5]
74 --> 15 | cost [135.99]

B = 375.21
i★ = 50
j★ = 67
k★ = 68