------------------------------------------------------------
                            α=7.0 —— gr96 —— 96 nodes       
------------------------------------------------------------

——————— Thu, 18 Jan 2024 08:20:38 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 4 hubs —— 1—32—35—97
total time           3636.39 (TL 3600)    gap                  0.484                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2395.24<=4643.35     subtour              914.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:96                 
2-opt strategy       0                                                              
explored_nodes       559                  n lazycuts edges     1.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—32—35—97

RING
1  --- 32 | cost [63.0]
5  ---  6 | cost [7.0]
5  ---  9 | cost [49.0]
6  --- 11 | cost [112.0]
9  --- 13 | cost [77.0]
11 --- 15 | cost [91.0]
13 --- 14 | cost [14.0]
14 --- 16 | cost [70.0]
15 --- 16 | cost [49.0]
23 --- 25 | cost [49.0]
23 --- 62 | cost [119.0]
25 --- 47 | cost [84.0]
32 --- 35 | cost [42.0]
35 --- 97 | cost [105.0]
43 --- 50 | cost [35.0]
43 --- 53 | cost [63.0]
46 --- 47 | cost [35.0]
46 --- 50 | cost [42.0]
53 --- 79 | cost [175.0]
61 --- 63 | cost [35.0]
61 --- 76 | cost [98.0]
62 --- 63 | cost [21.0]
71 --- 72 | cost [7.0]
71 --- 76 | cost [63.0]
72 --- 74 | cost [56.0]
74 --- 83 | cost [105.0]
79 --- 83 | cost [161.0]

STAR
2  -->  1 | cost [48.0]
3  -->  6 | cost [30.0]
4  -->  6 | cost [9.0]
7  --> 35 | cost [72.0]
8  --> 16 | cost [78.0]
10 -->  9 | cost [12.0]
12 -->  9 | cost [21.0]
17 --> 16 | cost [30.0]
18 --> 16 | cost [36.0]
19 --> 16 | cost [39.0]
20 --> 23 | cost [45.0]
21 --> 23 | cost [27.0]
22 --> 23 | cost [18.0]
24 --> 23 | cost [9.0]
26 --> 23 | cost [18.0]
27 --> 23 | cost [27.0]
28 --> 23 | cost [33.0]
29 -->  1 | cost [24.0]
30 -->  1 | cost [18.0]
31 -->  1 | cost [21.0]
33 --> 35 | cost [27.0]
34 --> 35 | cost [6.0]
36 --> 35 | cost [12.0]
37 --> 35 | cost [12.0]
38 --> 35 | cost [12.0]
39 --> 35 | cost [21.0]
40 --> 35 | cost [27.0]
41 --> 35 | cost [30.0]
42 --> 46 | cost [27.0]
44 --> 35 | cost [24.0]
45 --> 46 | cost [18.0]
48 --> 46 | cost [21.0]
49 --> 46 | cost [24.0]
51 --> 46 | cost [36.0]
52 --> 46 | cost [27.0]
54 --> 46 | cost [39.0]
55 --> 46 | cost [36.0]
56 --> 72 | cost [45.0]
57 --> 72 | cost [45.0]
58 --> 50 | cost [39.0]
59 --> 72 | cost [27.0]
60 --> 72 | cost [39.0]
64 --> 72 | cost [42.0]
65 --> 23 | cost [57.0]
66 --> 62 | cost [30.0]
67 --> 72 | cost [39.0]
68 --> 72 | cost [39.0]
69 --> 72 | cost [48.0]
70 --> 46 | cost [75.0]
73 --> 72 | cost [9.0]
75 --> 72 | cost [18.0]
77 --> 72 | cost [27.0]
78 --> 72 | cost [42.0]
80 --> 72 | cost [141.0]
81 --> 74 | cost [42.0]
82 --> 62 | cost [72.0]
84 --> 72 | cost [36.0]
85 --> 72 | cost [39.0]
86 --> 72 | cost [42.0]
87 --> 72 | cost [51.0]
88 --> 72 | cost [51.0]
89 --> 72 | cost [63.0]
90 --> 72 | cost [63.0]
91 --> 63 | cost [111.0]
92 --> 62 | cost [75.0]
93 --> 72 | cost [60.0]
94 --> 72 | cost [63.0]
95 --> 72 | cost [90.0]
96 --> 72 | cost [84.0]

BACKUP RING
1  --- 35 | cost [1.05]
5  --- 11 | cost [1.19]
5  --- 13 | cost [1.26]
6  ---  9 | cost [0.42]
6  --- 15 | cost [1.4000000000000001]
9  --- 14 | cost [0.77]
11 --- 16 | cost [1.26]
13 --- 16 | cost [0.77]
14 --- 15 | cost [0.21]
23 --- 47 | cost [1.4000000000000001]
23 --- 63 | cost [1.05]
25 --- 46 | cost [1.19]
25 --- 62 | cost [1.12]
32 --- 97 | cost [0.63]
43 --- 46 | cost [0.56]
43 --- 79 | cost [1.61]
47 --- 50 | cost [0.56]
50 --- 53 | cost [0.35000000000000003]
53 --- 83 | cost [2.1]
61 --- 62 | cost [0.14]
61 --- 71 | cost [0.56]
63 --- 76 | cost [1.12]
71 --- 74 | cost [0.63]
72 --- 76 | cost [0.49]
72 --- 83 | cost [1.33]
74 --- 79 | cost [2.38]

BACKUP STAR
3  -->  5 | cost [0.27]
4  -->  5 | cost [0.06]
7  -->  6 | cost [0.06]
8  -->  6 | cost [0.06]
10 --> 13 | cost [0.21]
12 --> 13 | cost [0.12]
17 --> 15 | cost [0.48]
18 --> 23 | cost [0.48]
19 --> 23 | cost [0.42]
20 --> 16 | cost [0.33]
21 --> 25 | cost [0.39]
22 --> 25 | cost [0.39]
24 --> 25 | cost [0.15]
26 --> 25 | cost [0.39]
27 --> 63 | cost [0.33]
28 --> 63 | cost [0.48]
33 --> 11 | cost [0.3]
34 --> 32 | cost [0.21]
36 --> 32 | cost [0.09]
37 --> 32 | cost [0.12]
38 --> 32 | cost [0.21]
39 --> 43 | cost [0.18]
40 --> 43 | cost [0.12]
41 --> 43 | cost [0.09]
42 --> 43 | cost [0.03]
44 --> 43 | cost [0.21]
45 --> 43 | cost [0.21]
48 --> 47 | cost [0.06]
49 --> 43 | cost [0.03]
51 --> 50 | cost [0.18]
52 --> 50 | cost [0.09]
54 --> 53 | cost [0.21]
55 --> 53 | cost [0.12]
56 --> 53 | cost [0.27]
57 --> 53 | cost [0.27]
58 --> 53 | cost [0.24]
59 --> 61 | cost [0.21]
60 --> 61 | cost [0.15]
64 --> 63 | cost [0.12]
65 --> 63 | cost [0.39]
66 --> 63 | cost [0.24]
67 --> 63 | cost [0.27]
68 --> 61 | cost [0.3]
69 --> 53 | cost [0.36]
70 --> 71 | cost [0.36]
73 --> 71 | cost [0.12]
75 --> 74 | cost [0.12]
77 --> 76 | cost [0.12]
78 --> 74 | cost [0.21]
80 --> 79 | cost [0.6900000000000001]
81 --> 83 | cost [0.12]
82 --> 83 | cost [0.12]
84 --> 74 | cost [0.15]
85 --> 74 | cost [0.15]
86 --> 74 | cost [0.18]
87 --> 74 | cost [0.27]
88 --> 74 | cost [0.3]
89 --> 74 | cost [0.39]
90 --> 83 | cost [0.39]
91 --> 83 | cost [0.24]
92 --> 76 | cost [0.33]
93 --> 76 | cost [0.39]
94 --> 76 | cost [0.45]
95 --> 76 | cost [0.6900000000000001]
96 --> 63 | cost [0.6900000000000001]

B = 7.89
i★ = 71
j★ = 72
k★ = 74

       
——————— Thu, 18 Jan 2024 09:21:44 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 47 hubs —— 1-30-31-32-36-35-44-40-41-42-43-49-50-52-55-57-56-69-70-82-87-85-74-75-76-93-94-67-66-64-27-26-23-21-20-16-15-14-12-10-9-7-6-5-4-2-97-1
total time           3603.98 (TL 3600)    gap                  0.052                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2452.1<=2586.98      Master/SP costs      2565/21.98           
Master time          3583.86              SP time              20.12                
subtour              17905.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            56.0                 SP method            poly                 
tildeV               2:96                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       64159                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—30—31—32—36—35—44—40—41—42—43—49—50—52—55—57—56—69—70—82—87—85—74—75—76—93—94—67—66—64—27—26—23—21—20—16—15—14—12—10—9—7—6—5—4—2—97

RING
1  --- 30 | cost [42.0]
2  ---  4 | cost [56.0]
2  --- 97 | cost [112.0]
4  ---  5 | cost [14.0]
5  ---  6 | cost [7.0]
6  ---  7 | cost [14.0]
7  ---  9 | cost [28.0]
9  --- 10 | cost [28.0]
10 --- 12 | cost [21.0]
12 --- 14 | cost [28.0]
14 --- 15 | cost [21.0]
15 --- 16 | cost [49.0]
16 --- 20 | cost [77.0]
20 --- 21 | cost [42.0]
21 --- 23 | cost [63.0]
23 --- 26 | cost [42.0]
26 --- 27 | cost [42.0]
27 --- 64 | cost [70.0]
30 --- 31 | cost [7.0]
31 --- 32 | cost [14.0]
32 --- 36 | cost [21.0]
35 --- 36 | cost [28.0]
35 --- 44 | cost [56.0]
40 --- 41 | cost [14.0]
40 --- 44 | cost [42.0]
41 --- 42 | cost [7.0]
42 --- 43 | cost [7.0]
43 --- 49 | cost [7.0]
49 --- 50 | cost [28.0]
50 --- 52 | cost [21.0]
52 --- 55 | cost [21.0]
55 --- 57 | cost [49.0]
56 --- 57 | cost [0.0]
56 --- 69 | cost [35.0]
64 --- 66 | cost [28.0]
66 --- 67 | cost [14.0]
67 --- 94 | cost [84.0]
69 --- 70 | cost [35.0]
70 --- 82 | cost [70.0]
74 --- 75 | cost [28.0]
74 --- 85 | cost [35.0]
75 --- 76 | cost [28.0]
76 --- 93 | cost [91.0]
82 --- 87 | cost [77.0]
85 --- 87 | cost [28.0]
93 --- 94 | cost [49.0]

STAR
3  -->  2 | cost [15.0]
8  -->  7 | cost [6.0]
11 --> 44 | cost [36.0]
13 --> 14 | cost [6.0]
17 --> 20 | cost [6.0]
18 --> 20 | cost [6.0]
19 --> 20 | cost [3.0]
22 --> 26 | cost [12.0]
24 --> 23 | cost [9.0]
25 --> 23 | cost [21.0]
28 --> 27 | cost [15.0]
29 --> 30 | cost [12.0]
33 --> 44 | cost [15.0]
34 --> 35 | cost [6.0]
37 --> 36 | cost [3.0]
38 --> 36 | cost [12.0]
39 --> 40 | cost [9.0]
45 --> 44 | cost [12.0]
46 --> 50 | cost [18.0]
47 --> 50 | cost [24.0]
48 --> 50 | cost [30.0]
51 --> 55 | cost [9.0]
53 --> 52 | cost [9.0]
54 --> 57 | cost [27.0]
58 --> 57 | cost [15.0]
59 --> 57 | cost [21.0]
60 --> 64 | cost [33.0]
61 --> 64 | cost [24.0]
62 --> 64 | cost [18.0]
63 --> 64 | cost [12.0]
65 --> 66 | cost [24.0]
68 --> 67 | cost [0.0]
71 --> 75 | cost [21.0]
72 --> 75 | cost [18.0]
73 --> 75 | cost [12.0]
77 --> 75 | cost [12.0]
78 --> 85 | cost [12.0]
79 --> 70 | cost [63.0]
80 --> 82 | cost [99.0]
81 --> 82 | cost [9.0]
83 --> 82 | cost [12.0]
84 --> 85 | cost [9.0]
86 --> 85 | cost [3.0]
88 --> 85 | cost [15.0]
89 --> 87 | cost [12.0]
90 --> 87 | cost [15.0]
91 --> 87 | cost [27.0]
92 --> 93 | cost [18.0]
95 --> 93 | cost [30.0]
96 --> 94 | cost [30.0]

BACKUP RING
1  --- 31 | cost [0.49]
2  ---  5 | cost [0.7000000000000001]
4  ---  6 | cost [0.21]
4  --- 97 | cost [1.61]
5  ---  7 | cost [0.21]
6  ---  9 | cost [0.42]
7  --- 10 | cost [0.56]
9  --- 12 | cost [0.49]
10 --- 14 | cost [0.56]
12 --- 15 | cost [0.56]
14 --- 16 | cost [0.7000000000000001]
15 --- 20 | cost [1.26]
16 --- 21 | cost [1.05]
20 --- 23 | cost [1.05]
21 --- 26 | cost [0.77]
23 --- 27 | cost [0.63]
26 --- 64 | cost [1.12]
27 --- 66 | cost [0.91]
30 --- 32 | cost [0.21]
31 --- 36 | cost [0.35000000000000003]
32 --- 35 | cost [0.42]
35 --- 40 | cost [0.63]
36 --- 44 | cost [0.84]
40 --- 42 | cost [0.21]
41 --- 43 | cost [0.21]
41 --- 44 | cost [0.49]
42 --- 49 | cost [0.14]
43 --- 50 | cost [0.35000000000000003]
49 --- 52 | cost [0.42]
50 --- 55 | cost [0.42]
52 --- 57 | cost [0.7000000000000001]
55 --- 56 | cost [0.49]
56 --- 70 | cost [0.56]
57 --- 69 | cost [0.35000000000000003]
64 --- 67 | cost [0.42]
66 --- 94 | cost [0.91]
67 --- 93 | cost [1.05]
69 --- 82 | cost [0.98]
70 --- 87 | cost [1.4000000000000001]
74 --- 76 | cost [0.56]
74 --- 87 | cost [0.63]
75 --- 85 | cost [0.56]
75 --- 93 | cost [1.12]
76 --- 94 | cost [1.05]
82 --- 85 | cost [0.77]

BACKUP STAR
3  -->  4 | cost [0.27]
8  -->  6 | cost [0.06]
11 --> 14 | cost [0.39]
13 --> 12 | cost [0.12]
17 --> 21 | cost [0.24]
18 --> 21 | cost [0.21]
19 --> 21 | cost [0.18]
22 --> 23 | cost [0.18]
24 --> 26 | cost [0.27]
25 --> 21 | cost [0.39]
28 --> 26 | cost [0.18]
29 --> 31 | cost [0.15]
33 --> 35 | cost [0.27]
34 --> 36 | cost [0.18]
37 --> 32 | cost [0.12]
38 --> 35 | cost [0.12]
39 --> 41 | cost [0.12]
45 --> 42 | cost [0.21]
46 --> 43 | cost [0.24]
47 --> 52 | cost [0.27]
48 --> 52 | cost [0.33]
51 --> 52 | cost [0.12]
53 --> 55 | cost [0.12]
54 --> 56 | cost [0.27]
58 --> 56 | cost [0.15]
59 --> 56 | cost [0.21]
60 --> 56 | cost [0.33]
61 --> 66 | cost [0.3]
62 --> 66 | cost [0.3]
63 --> 66 | cost [0.24]
65 --> 64 | cost [0.27]
68 --> 66 | cost [0.06]
71 --> 74 | cost [0.27]
72 --> 76 | cost [0.21]
73 --> 74 | cost [0.15]
77 --> 76 | cost [0.12]
78 --> 74 | cost [0.21]
79 --> 69 | cost [0.6]
80 --> 70 | cost [1.11]
81 --> 70 | cost [0.3]
83 --> 87 | cost [0.33]
84 --> 74 | cost [0.15]
86 --> 87 | cost [0.12]
88 --> 87 | cost [0.15]
89 --> 85 | cost [0.24]
90 --> 85 | cost [0.27]
91 --> 82 | cost [0.33]
92 --> 76 | cost [0.33]
95 --> 94 | cost [0.33]
96 --> 66 | cost [0.48]

B = 3.14
i★ = 70
j★ = 82
k★ = 87