------------------------------------------------------------
                           α=7.0 —— eil76 —— 76 nodes       
------------------------------------------------------------

——————— Mon, 08 Jan 2024 09:20:59 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 33 hubs —— 1—43—23—49—3—44—32—9—39—72—10—38—11—53—35—8—46—34—67—76—75—4—45—29—5—37—36—47—21—28—62—73—77
total time           1175.99              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2518.77<=2518.77     subtour              47.0                 
connectivity cuts    158.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:76                 
2-opt strategy       0                                                              
explored_nodes       161                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—43—23—49—3—44—32—9—39—72—10—38—11—53—35—8—46—34—67—76—75—4—45—29—5—37—36—47—21—28—62—73—77

RING
1  --- 43 | cost [49.0]
1  --- 77 | cost [0.0]
3  --- 44 | cost [21.0]
3  --- 49 | cost [77.0]
4  --- 45 | cost [49.0]
4  --- 75 | cost [35.0]
5  --- 29 | cost [49.0]
5  --- 37 | cost [49.0]
8  --- 35 | cost [35.0]
8  --- 46 | cost [35.0]
9  --- 32 | cost [49.0]
9  --- 39 | cost [28.0]
10 --- 38 | cost [49.0]
10 --- 72 | cost [56.0]
11 --- 38 | cost [56.0]
11 --- 53 | cost [56.0]
21 --- 28 | cost [63.0]
21 --- 47 | cost [42.0]
23 --- 43 | cost [70.0]
23 --- 49 | cost [70.0]
28 --- 62 | cost [42.0]
29 --- 45 | cost [28.0]
32 --- 44 | cost [35.0]
34 --- 46 | cost [14.0]
34 --- 67 | cost [35.0]
35 --- 53 | cost [49.0]
36 --- 37 | cost [56.0]
36 --- 47 | cost [42.0]
39 --- 72 | cost [35.0]
62 --- 73 | cost [35.0]
67 --- 76 | cost [35.0]
73 --- 77 | cost [35.0]
75 --- 76 | cost [21.0]

STAR
2  --> 62 | cost [24.0]
6  --> 75 | cost [24.0]
7  --> 35 | cost [15.0]
12 --> 72 | cost [27.0]
13 -->  8 | cost [36.0]
14 --> 53 | cost [21.0]
15 -->  5 | cost [24.0]
16 -->  3 | cost [27.0]
17 --> 76 | cost [24.0]
18 --> 32 | cost [39.0]
19 --> 35 | cost [21.0]
20 --> 37 | cost [18.0]
22 --> 62 | cost [24.0]
24 --> 49 | cost [21.0]
25 -->  9 | cost [30.0]
26 --> 67 | cost [18.0]
27 --> 45 | cost [18.0]
30 --> 45 | cost [24.0]
31 --> 10 | cost [39.0]
33 --> 73 | cost [15.0]
40 --> 32 | cost [27.0]
41 --> 43 | cost [12.0]
42 --> 43 | cost [15.0]
48 --> 29 | cost [18.0]
50 --> 32 | cost [24.0]
51 -->  3 | cost [30.0]
52 --> 34 | cost [12.0]
54 -->  8 | cost [39.0]
55 -->  9 | cost [57.0]
56 --> 23 | cost [18.0]
57 -->  5 | cost [36.0]
58 --> 72 | cost [15.0]
59 --> 11 | cost [45.0]
60 --> 37 | cost [36.0]
61 --> 28 | cost [30.0]
63 -->  1 | cost [24.0]
64 --> 43 | cost [42.0]
65 --> 38 | cost [15.0]
66 --> 11 | cost [21.0]
68 --> 75 | cost [12.0]
69 --> 36 | cost [21.0]
70 --> 37 | cost [27.0]
71 --> 36 | cost [21.0]
74 --> 28 | cost [18.0]

BACKUP RING
1  --- 23 | cost [0.91]
3  --- 23 | cost [1.4000000000000001]
3  --- 32 | cost [0.56]
4  --- 29 | cost [0.77]
4  --- 76 | cost [0.49]
5  --- 36 | cost [0.7000000000000001]
5  --- 45 | cost [0.77]
8  --- 34 | cost [0.49]
8  --- 53 | cost [0.84]
9  --- 44 | cost [0.84]
9  --- 72 | cost [0.63]
10 --- 11 | cost [1.05]
10 --- 39 | cost [0.84]
11 --- 35 | cost [1.05]
21 --- 36 | cost [0.7000000000000001]
21 --- 62 | cost [1.12]
28 --- 47 | cost [1.05]
28 --- 73 | cost [0.77]
29 --- 37 | cost [0.98]
32 --- 39 | cost [0.77]
34 --- 76 | cost [0.7000000000000001]
35 --- 46 | cost [0.63]
37 --- 47 | cost [0.7000000000000001]
38 --- 53 | cost [0.84]
38 --- 72 | cost [0.91]
43 --- 49 | cost [1.33]
44 --- 49 | cost [0.91]
45 --- 75 | cost [0.84]
46 --- 67 | cost [0.42]
62 --- 77 | cost [0.56]
67 --- 75 | cost [0.49]

BACKUP STAR
2  --> 73 | cost [0.27]
6  --> 76 | cost [0.27]
7  -->  8 | cost [0.21]
12 --> 39 | cost [0.3]
13 --> 29 | cost [0.39]
14 --> 35 | cost [0.3]
15 --> 37 | cost [0.27]
16 --> 49 | cost [0.27]
17 --> 75 | cost [0.3]
18 --> 44 | cost [0.42]
19 -->  8 | cost [0.24]
20 -->  5 | cost [0.39]
22 --> 28 | cost [0.27]
24 -->  3 | cost [0.42]
25 --> 32 | cost [0.36]
26 --> 76 | cost [0.18]
27 --> 34 | cost [0.24]
30 -->  4 | cost [0.27]
31 --> 39 | cost [0.48]
33 -->  1 | cost [0.24]
40 --> 44 | cost [0.27]
41 -->  1 | cost [0.33]
42 -->  1 | cost [0.33]
48 --> 47 | cost [0.18]
50 --> 44 | cost [0.3]
51 --> 75 | cost [0.33]
52 --> 46 | cost [0.15]
54 --> 35 | cost [0.45]
55 --> 32 | cost [0.63]
56 --> 43 | cost [0.36]
57 --> 29 | cost [0.39]
58 --> 10 | cost [0.18]
59 --> 53 | cost [0.51]
60 --> 36 | cost [0.36]
61 --> 21 | cost [0.33]
64 -->  1 | cost [0.54]
65 --> 11 | cost [0.21]
66 --> 38 | cost [0.36]
68 -->  4 | cost [0.21]
69 --> 21 | cost [0.33]
70 --> 36 | cost [0.36]
71 --> 37 | cost [0.3]
74 --> 21 | cost [0.24]

B = 2.1100000000000003
i★ = 1
j★ = 43
k★ = 23

       
——————— Mon, 08 Jan 2024 09:21:58 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 33 hubs —— 1-43-23-49-3-44-32-9-39-72-10-38-11-53-35-8-46-34-67-76-75-4-45-29-5-37-36-47-21-28-62-73-77-1
total time           22.33                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2518.77<=2518.77     Master/SP costs      2504/14.77           
Master time          20.69                SP time              1.64                 
subtour              388.0                connectivity cuts    257.0                
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            24.0                 SP method            poly                 
tildeV               2:76                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       369                  
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—43—23—49—3—44—32—9—39—72—10—38—11—53—35—8—46—34—67—76—75—4—45—29—5—37—36—47—21—28—62—73—77

RING
1  --- 43 | cost [49.0]
1  --- 77 | cost [0.0]
3  --- 44 | cost [21.0]
3  --- 49 | cost [77.0]
4  --- 45 | cost [49.0]
4  --- 75 | cost [35.0]
5  --- 29 | cost [49.0]
5  --- 37 | cost [49.0]
8  --- 35 | cost [35.0]
8  --- 46 | cost [35.0]
9  --- 32 | cost [49.0]
9  --- 39 | cost [28.0]
10 --- 38 | cost [49.0]
10 --- 72 | cost [56.0]
11 --- 38 | cost [56.0]
11 --- 53 | cost [56.0]
21 --- 28 | cost [63.0]
21 --- 47 | cost [42.0]
23 --- 43 | cost [70.0]
23 --- 49 | cost [70.0]
28 --- 62 | cost [42.0]
29 --- 45 | cost [28.0]
32 --- 44 | cost [35.0]
34 --- 46 | cost [14.0]
34 --- 67 | cost [35.0]
35 --- 53 | cost [49.0]
36 --- 37 | cost [56.0]
36 --- 47 | cost [42.0]
39 --- 72 | cost [35.0]
62 --- 73 | cost [35.0]
67 --- 76 | cost [35.0]
73 --- 77 | cost [35.0]
75 --- 76 | cost [21.0]

STAR
2  --> 62 | cost [24.0]
6  --> 75 | cost [24.0]
7  --> 35 | cost [15.0]
12 --> 72 | cost [27.0]
13 -->  8 | cost [36.0]
14 --> 53 | cost [21.0]
15 -->  5 | cost [24.0]
16 --> 49 | cost [27.0]
17 --> 76 | cost [24.0]
18 --> 32 | cost [39.0]
19 --> 35 | cost [21.0]
20 --> 37 | cost [18.0]
22 --> 62 | cost [24.0]
24 --> 49 | cost [21.0]
25 -->  9 | cost [30.0]
26 --> 76 | cost [18.0]
27 --> 45 | cost [18.0]
30 --> 45 | cost [24.0]
31 --> 10 | cost [39.0]
33 --> 73 | cost [15.0]
40 --> 32 | cost [27.0]
41 --> 43 | cost [12.0]
42 --> 43 | cost [15.0]
48 --> 47 | cost [18.0]
50 --> 32 | cost [24.0]
51 -->  3 | cost [30.0]
52 --> 34 | cost [12.0]
54 -->  8 | cost [39.0]
55 -->  9 | cost [57.0]
56 --> 23 | cost [18.0]
57 -->  5 | cost [36.0]
58 --> 72 | cost [15.0]
59 --> 11 | cost [45.0]
60 --> 37 | cost [36.0]
61 --> 28 | cost [30.0]
63 -->  1 | cost [24.0]
64 --> 43 | cost [42.0]
65 --> 38 | cost [15.0]
66 --> 11 | cost [21.0]
68 --> 75 | cost [12.0]
69 --> 36 | cost [21.0]
70 --> 37 | cost [27.0]
71 --> 36 | cost [21.0]
74 --> 28 | cost [18.0]

BACKUP RING
1  --- 23 | cost [0.91]
3  --- 23 | cost [1.4000000000000001]
3  --- 32 | cost [0.56]
4  --- 29 | cost [0.77]
4  --- 76 | cost [0.49]
5  --- 36 | cost [0.7000000000000001]
5  --- 45 | cost [0.77]
8  --- 34 | cost [0.49]
8  --- 53 | cost [0.84]
9  --- 44 | cost [0.84]
9  --- 72 | cost [0.63]
10 --- 11 | cost [1.05]
10 --- 39 | cost [0.84]
11 --- 35 | cost [1.05]
21 --- 36 | cost [0.7000000000000001]
21 --- 62 | cost [1.12]
28 --- 47 | cost [1.05]
28 --- 73 | cost [0.77]
29 --- 37 | cost [0.98]
32 --- 39 | cost [0.77]
34 --- 76 | cost [0.7000000000000001]
35 --- 46 | cost [0.63]
37 --- 47 | cost [0.7000000000000001]
38 --- 53 | cost [0.84]
38 --- 72 | cost [0.91]
43 --- 49 | cost [1.33]
44 --- 49 | cost [0.91]
45 --- 75 | cost [0.84]
46 --- 67 | cost [0.42]
62 --- 77 | cost [0.56]
67 --- 75 | cost [0.49]

BACKUP STAR
2  --> 73 | cost [0.27]
6  --> 76 | cost [0.27]
7  -->  8 | cost [0.21]
12 --> 39 | cost [0.3]
13 --> 29 | cost [0.39]
14 --> 35 | cost [0.3]
15 --> 37 | cost [0.27]
16 -->  3 | cost [0.27]
17 --> 75 | cost [0.3]
18 --> 44 | cost [0.42]
19 -->  8 | cost [0.24]
20 -->  5 | cost [0.39]
22 --> 28 | cost [0.27]
24 -->  3 | cost [0.42]
25 --> 32 | cost [0.36]
26 --> 67 | cost [0.18]
27 --> 34 | cost [0.24]
30 -->  4 | cost [0.27]
31 --> 39 | cost [0.48]
33 -->  1 | cost [0.24]
40 --> 44 | cost [0.27]
41 -->  1 | cost [0.33]
42 -->  1 | cost [0.33]
48 --> 29 | cost [0.18]
50 --> 44 | cost [0.3]
51 --> 75 | cost [0.33]
52 --> 46 | cost [0.15]
54 --> 35 | cost [0.45]
55 --> 32 | cost [0.63]
56 --> 43 | cost [0.36]
57 --> 29 | cost [0.39]
58 --> 10 | cost [0.18]
59 --> 53 | cost [0.51]
60 --> 36 | cost [0.36]
61 --> 21 | cost [0.33]
64 -->  1 | cost [0.54]
65 --> 11 | cost [0.21]
66 --> 38 | cost [0.36]
68 -->  4 | cost [0.21]
69 --> 21 | cost [0.33]
70 --> 36 | cost [0.36]
71 --> 37 | cost [0.3]
74 --> 21 | cost [0.24]

B = 2.1100000000000003
i★ = 1
j★ = 43
k★ = 23

       
——————— Wed, 10 Jan 2024 04:16:33 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 34 hubs —— 1—43—63—16—44—32—9—39—72—58—38—11—53—35—46—76—67—34—27—13—57—37—70—60—71—36—47—48—29—30—2—62—73—77
total time           3617.9 (TL 3600)     gap                  0.108                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2459.4<=2757.74      subtour              4071.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:76                 
2-opt strategy       0                                                              
explored_nodes       2078                 n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—43—63—16—44—32—9—39—72—58—38—11—53—35—46—76—67—34—27—13—57—37—70—60—71—36—47—48—29—30—2—62—73—77

RING
1  --- 43 | cost [49.0]
2  --- 30 | cost [49.0]
2  --- 62 | cost [56.0]
9  --- 32 | cost [49.0]
9  --- 39 | cost [28.0]
11 --- 38 | cost [56.0]
11 --- 53 | cost [56.0]
13 --- 27 | cost [49.0]
13 --- 57 | cost [63.0]
16 --- 44 | cost [84.0]
16 --- 63 | cost [42.0]
27 --- 34 | cost [56.0]
29 --- 30 | cost [63.0]
29 --- 48 | cost [42.0]
32 --- 44 | cost [35.0]
34 --- 67 | cost [35.0]
35 --- 46 | cost [63.0]
35 --- 53 | cost [49.0]
36 --- 47 | cost [42.0]
36 --- 71 | cost [49.0]
37 --- 57 | cost [91.0]
37 --- 70 | cost [63.0]
38 --- 58 | cost [63.0]
39 --- 72 | cost [35.0]
43 --- 63 | cost [84.0]
46 --- 76 | cost [77.0]
47 --- 48 | cost [42.0]
58 --- 72 | cost [35.0]
60 --- 70 | cost [28.0]
60 --- 71 | cost [35.0]
62 --- 73 | cost [35.0]
67 --- 76 | cost [35.0]
73 --- 77 | cost [35.0]

STAR
3  --> 44 | cost [9.0]
4  --> 30 | cost [27.0]
5  --> 37 | cost [21.0]
6  --> 76 | cost [27.0]
7  --> 35 | cost [15.0]
8  --> 35 | cost [15.0]
10 --> 58 | cost [18.0]
12 --> 76 | cost [36.0]
14 --> 53 | cost [21.0]
15 --> 57 | cost [12.0]
17 --> 76 | cost [24.0]
18 --> 32 | cost [39.0]
19 --> 35 | cost [21.0]
20 --> 70 | cost [18.0]
21 --> 47 | cost [18.0]
22 --> 62 | cost [24.0]
23 --> 63 | cost [27.0]
24 --> 44 | cost [45.0]
25 -->  9 | cost [30.0]
26 --> 67 | cost [18.0]
28 --> 62 | cost [18.0]
31 --> 39 | cost [48.0]
33 --> 73 | cost [15.0]
40 --> 32 | cost [27.0]
41 --> 43 | cost [12.0]
42 --> 43 | cost [15.0]
45 --> 29 | cost [12.0]
49 --> 16 | cost [27.0]
50 --> 32 | cost [24.0]
51 --> 76 | cost [33.0]
52 --> 34 | cost [12.0]
54 --> 13 | cost [24.0]
55 -->  9 | cost [57.0]
56 --> 43 | cost [36.0]
59 --> 11 | cost [45.0]
61 --> 62 | cost [45.0]
64 --> 43 | cost [42.0]
65 --> 38 | cost [15.0]
66 --> 11 | cost [21.0]
68 --> 76 | cost [21.0]
69 --> 36 | cost [21.0]
74 -->  2 | cost [21.0]
75 --> 76 | cost [9.0]

BACKUP RING
1  --- 63 | cost [0.56]
2  --- 29 | cost [1.12]
2  --- 73 | cost [0.63]
9  --- 44 | cost [0.84]
9  --- 72 | cost [0.63]
11 --- 35 | cost [1.05]
11 --- 58 | cost [1.12]
13 --- 34 | cost [0.91]
13 --- 37 | cost [1.4000000000000001]
16 --- 32 | cost [1.19]
16 --- 43 | cost [1.26]
27 --- 57 | cost [0.84]
27 --- 67 | cost [0.91]
29 --- 47 | cost [0.77]
30 --- 48 | cost [0.49]
30 --- 62 | cost [0.98]
32 --- 39 | cost [0.77]
34 --- 76 | cost [0.7000000000000001]
35 --- 76 | cost [1.26]
36 --- 48 | cost [0.91]
36 --- 60 | cost [0.84]
37 --- 60 | cost [0.84]
38 --- 53 | cost [0.84]
38 --- 72 | cost [0.91]
39 --- 58 | cost [0.7000000000000001]
44 --- 63 | cost [1.26]
46 --- 53 | cost [1.12]
46 --- 67 | cost [0.42]
47 --- 71 | cost [0.91]
57 --- 70 | cost [1.33]
62 --- 77 | cost [0.56]
70 --- 71 | cost [0.56]

BACKUP STAR
3  --> 32 | cost [0.24]
4  --> 34 | cost [0.21]
5  --> 29 | cost [0.21]
6  -->  2 | cost [0.27]
7  --> 46 | cost [0.24]
8  --> 46 | cost [0.15]
10 --> 38 | cost [0.21]
12 --> 72 | cost [0.27]
14 --> 35 | cost [0.3]
15 --> 37 | cost [0.27]
17 --> 67 | cost [0.36]
18 --> 44 | cost [0.42]
19 --> 53 | cost [0.33]
20 --> 37 | cost [0.18]
21 --> 48 | cost [0.27]
22 -->  1 | cost [0.3]
23 --> 43 | cost [0.3]
24 --> 16 | cost [0.48]
25 --> 32 | cost [0.36]
26 --> 76 | cost [0.18]
28 -->  2 | cost [0.3]
31 --> 72 | cost [0.48]
33 --> 63 | cost [0.18]
40 --> 44 | cost [0.27]
41 -->  1 | cost [0.33]
42 -->  1 | cost [0.33]
45 --> 27 | cost [0.18]
49 --> 63 | cost [0.33]
50 --> 44 | cost [0.3]
51 --> 16 | cost [0.27]
52 --> 27 | cost [0.12]
54 --> 27 | cost [0.42]
55 --> 32 | cost [0.63]
56 --> 63 | cost [0.45]
59 --> 53 | cost [0.51]
61 --> 47 | cost [0.51]
64 -->  1 | cost [0.54]
65 --> 11 | cost [0.21]
66 --> 38 | cost [0.36]
68 -->  2 | cost [0.21]
69 --> 71 | cost [0.27]
74 --> 30 | cost [0.21]
75 --> 67 | cost [0.21]

B = 2.21
i★ = 1
j★ = 43
k★ = 63

       
——————— Wed, 10 Jan 2024 05:17:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 33 hubs —— 1-43-23-49-3-44-32-9-39-72-10-38-11-53-35-8-46-34-67-76-75-4-45-29-5-37-36-47-21-28-62-73-77-1
total time           3603.86 (TL 3600)    gap                  0.012                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2489.11<=2518.77     Master/SP costs      2504/14.77           
Master time          3598.66              SP time              5.2                  
subtour              60773.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            66.0                 SP method            poly                 
tildeV               2:76                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       39509                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—43—23—49—3—44—32—9—39—72—10—38—11—53—35—8—46—34—67—76—75—4—45—29—5—37—36—47—21—28—62—73—77

RING
1  --- 43 | cost [49.0]
3  --- 44 | cost [21.0]
3  --- 49 | cost [77.0]
4  --- 45 | cost [49.0]
4  --- 75 | cost [35.0]
5  --- 29 | cost [49.0]
5  --- 37 | cost [49.0]
8  --- 35 | cost [35.0]
8  --- 46 | cost [35.0]
9  --- 32 | cost [49.0]
9  --- 39 | cost [28.0]
10 --- 38 | cost [49.0]
10 --- 72 | cost [56.0]
11 --- 38 | cost [56.0]
11 --- 53 | cost [56.0]
21 --- 28 | cost [63.0]
21 --- 47 | cost [42.0]
23 --- 43 | cost [70.0]
23 --- 49 | cost [70.0]
28 --- 62 | cost [42.0]
29 --- 45 | cost [28.0]
32 --- 44 | cost [35.0]
34 --- 46 | cost [14.0]
34 --- 67 | cost [35.0]
35 --- 53 | cost [49.0]
36 --- 37 | cost [56.0]
36 --- 47 | cost [42.0]
39 --- 72 | cost [35.0]
62 --- 73 | cost [35.0]
67 --- 76 | cost [35.0]
73 --- 77 | cost [35.0]
75 --- 76 | cost [21.0]

STAR
2  --> 62 | cost [24.0]
6  --> 75 | cost [24.0]
7  --> 35 | cost [15.0]
12 --> 72 | cost [27.0]
13 -->  8 | cost [36.0]
14 --> 53 | cost [21.0]
15 -->  5 | cost [24.0]
16 -->  3 | cost [27.0]
17 --> 76 | cost [24.0]
18 --> 32 | cost [39.0]
19 --> 35 | cost [21.0]
20 --> 37 | cost [18.0]
22 --> 62 | cost [24.0]
24 --> 49 | cost [21.0]
25 -->  9 | cost [30.0]
26 --> 67 | cost [18.0]
27 --> 45 | cost [18.0]
30 --> 45 | cost [24.0]
31 --> 10 | cost [39.0]
33 --> 73 | cost [15.0]
40 --> 32 | cost [27.0]
41 --> 43 | cost [12.0]
42 --> 43 | cost [15.0]
48 --> 29 | cost [18.0]
50 --> 32 | cost [24.0]
51 -->  3 | cost [30.0]
52 --> 34 | cost [12.0]
54 -->  8 | cost [39.0]
55 -->  9 | cost [57.0]
56 --> 23 | cost [18.0]
57 -->  5 | cost [36.0]
58 --> 72 | cost [15.0]
59 --> 11 | cost [45.0]
60 --> 37 | cost [36.0]
61 --> 28 | cost [30.0]
63 -->  1 | cost [24.0]
64 --> 43 | cost [42.0]
65 --> 38 | cost [15.0]
66 --> 11 | cost [21.0]
68 --> 75 | cost [12.0]
69 --> 36 | cost [21.0]
70 --> 37 | cost [27.0]
71 --> 36 | cost [21.0]
74 --> 28 | cost [18.0]

BACKUP RING
1  --- 23 | cost [0.91]
3  --- 23 | cost [1.4000000000000001]
3  --- 32 | cost [0.56]
4  --- 29 | cost [0.77]
4  --- 76 | cost [0.49]
5  --- 36 | cost [0.7000000000000001]
5  --- 45 | cost [0.77]
8  --- 34 | cost [0.49]
8  --- 53 | cost [0.84]
9  --- 44 | cost [0.84]
9  --- 72 | cost [0.63]
10 --- 11 | cost [1.05]
10 --- 39 | cost [0.84]
11 --- 35 | cost [1.05]
21 --- 36 | cost [0.7000000000000001]
21 --- 62 | cost [1.12]
28 --- 47 | cost [1.05]
28 --- 73 | cost [0.77]
29 --- 37 | cost [0.98]
32 --- 39 | cost [0.77]
34 --- 76 | cost [0.7000000000000001]
35 --- 46 | cost [0.63]
37 --- 47 | cost [0.7000000000000001]
38 --- 53 | cost [0.84]
38 --- 72 | cost [0.91]
43 --- 49 | cost [1.33]
44 --- 49 | cost [0.91]
45 --- 75 | cost [0.84]
46 --- 67 | cost [0.42]
62 --- 77 | cost [0.56]
67 --- 75 | cost [0.49]

BACKUP STAR
2  --> 73 | cost [0.27]
6  --> 76 | cost [0.27]
7  -->  8 | cost [0.21]
12 --> 39 | cost [0.3]
13 --> 29 | cost [0.39]
14 --> 35 | cost [0.3]
15 --> 37 | cost [0.27]
16 --> 49 | cost [0.27]
17 --> 75 | cost [0.3]
18 --> 44 | cost [0.42]
19 -->  8 | cost [0.24]
20 -->  5 | cost [0.39]
22 --> 28 | cost [0.27]
24 -->  3 | cost [0.42]
25 --> 32 | cost [0.36]
26 --> 76 | cost [0.18]
27 --> 34 | cost [0.24]
30 -->  4 | cost [0.27]
31 --> 39 | cost [0.48]
33 -->  1 | cost [0.24]
40 --> 44 | cost [0.27]
41 -->  1 | cost [0.33]
42 -->  1 | cost [0.33]
48 --> 47 | cost [0.18]
50 --> 44 | cost [0.3]
51 --> 75 | cost [0.33]
52 --> 46 | cost [0.15]
54 --> 35 | cost [0.45]
55 --> 32 | cost [0.63]
56 --> 43 | cost [0.36]
57 --> 29 | cost [0.39]
58 --> 10 | cost [0.18]
59 --> 53 | cost [0.51]
60 --> 36 | cost [0.36]
61 --> 21 | cost [0.33]
64 -->  1 | cost [0.54]
65 --> 11 | cost [0.21]
66 --> 38 | cost [0.36]
68 -->  4 | cost [0.21]
69 --> 21 | cost [0.33]
70 --> 36 | cost [0.36]
71 --> 37 | cost [0.3]
74 --> 21 | cost [0.24]

B = 2.1100000000000003
i★ = 1
j★ = 43
k★ = 23