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

——————— Sat, 27 Jan 2024 16:25:51 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 48 hubs —— 1—30—31—32—36—35—44—40—41—42—43—49—50—52—55—56—57—69—70—82—83—87—85—74—75—76—68—67—66—64—63—27—26—23—21—20—16—15—14—12—10—9—7—6—5—4—2—97
total time           3629.54 (TL 3600)    gap                  0.021                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2554.56<=2610.28     subtour              97.0                 
connectivity cuts    276.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:96                 
2-opt strategy       0                                                              
explored_nodes       396                  n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—30—31—32—36—35—44—40—41—42—43—49—50—52—55—56—57—69—70—82—83—87—85—74—75—76—68—67—66—64—63—27—26—23—21—20—16—15—14—12—10—9—7—6—5—4—2—97

RING
1  --- 30 | cost [42.0]
1  --- 97 | cost [0.0]
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 --- 63 | cost [77.0]
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 --- 56 | cost [49.0]
56 --- 57 | cost [0.0]
57 --- 69 | cost [35.0]
63 --- 64 | cost [28.0]
64 --- 66 | cost [28.0]
66 --- 67 | cost [14.0]
67 --- 68 | cost [0.0]
68 --- 76 | cost [70.0]
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]
82 --- 83 | cost [28.0]
83 --- 87 | cost [77.0]
85 --- 87 | cost [28.0]

STAR
3  -->  2 | cost [15.0]
8  -->  6 | 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 --> 63 | cost [21.0]
61 --> 63 | cost [15.0]
62 --> 63 | cost [9.0]
65 --> 66 | cost [24.0]
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 --> 69 | cost [60.0]
80 --> 83 | cost [87.0]
81 --> 82 | cost [9.0]
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 --> 76 | cost [33.0]
93 --> 76 | cost [39.0]
94 --> 68 | cost [36.0]
95 --> 68 | cost [69.0]
96 --> 66 | cost [48.0]

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 --- 63 | cost [1.12]
27 --- 64 | cost [0.7000000000000001]
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 --- 56 | cost [0.7000000000000001]
55 --- 57 | cost [0.49]
56 --- 69 | cost [0.35000000000000003]
57 --- 70 | cost [0.56]
63 --- 66 | cost [0.56]
64 --- 67 | cost [0.42]
66 --- 68 | cost [0.14]
67 --- 76 | cost [0.7000000000000001]
68 --- 75 | cost [0.98]
69 --- 82 | cost [0.98]
70 --- 83 | cost [0.98]
74 --- 76 | cost [0.56]
74 --- 87 | cost [0.63]
75 --- 85 | cost [0.56]
82 --- 87 | cost [0.77]
83 --- 85 | cost [0.91]

BACKUP STAR
3  -->  4 | cost [0.27]
8  -->  7 | 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 --> 64 | cost [0.24]
62 --> 64 | cost [0.18]
65 --> 64 | cost [0.27]
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 --> 70 | cost [0.63]
80 --> 82 | cost [0.99]
81 --> 83 | cost [0.12]
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 --> 83 | cost [0.24]
92 --> 75 | cost [0.42]
93 --> 67 | cost [0.45]
94 --> 67 | cost [0.36]
95 --> 67 | cost [0.6900000000000001]
96 --> 67 | cost [0.48]

B = 1.8800000000000001
i★ = 4
j★ = 2
k★ = 97

       
——————— Sat, 27 Jan 2024 16:37:14 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 48 hubs —— 1-2-4-5-6-7-9-10-12-14-15-16-20-21-23-26-27-63-64-66-67-68-76-75-74-85-87-82-81-70-69-56-57-55-52-50-49-43-42-41-40-44-35-36-32-31-30-97-1
total time           625                  gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2609.04<=2609.28     Master/SP costs      2551/58.28           
Master time          582.27               SP time              42.73                
subtour              450.0                connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            274.0                SP method            poly                 
tildeV               2:96                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       100954               
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—4—5—6—7—9—10—12—14—15—16—20—21—23—26—27—63—64—66—67—68—76—75—74—85—87—82—81—70—69—56—57—55—52—50—49—43—42—41—40—44—35—36—32—31—30—97

RING
1  ---  2 | cost [112.0]
1  --- 97 | cost [0.0]
2  ---  4 | cost [56.0]
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 --- 63 | cost [77.0]
30 --- 31 | cost [7.0]
30 --- 97 | cost [42.0]
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]
63 --- 64 | cost [28.0]
64 --- 66 | cost [28.0]
66 --- 67 | cost [14.0]
67 --- 68 | cost [0.0]
68 --- 76 | cost [70.0]
69 --- 70 | cost [35.0]
70 --- 81 | cost [70.0]
74 --- 75 | cost [28.0]
74 --- 85 | cost [35.0]
75 --- 76 | cost [28.0]
81 --- 82 | cost [21.0]
82 --- 87 | cost [77.0]
85 --- 87 | cost [28.0]

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 --> 56 | cost [15.0]
59 --> 57 | cost [21.0]
60 --> 63 | cost [21.0]
61 --> 63 | cost [15.0]
62 --> 63 | cost [9.0]
65 --> 66 | cost [24.0]
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 --> 69 | cost [60.0]
80 --> 81 | cost [90.0]
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 --> 76 | cost [33.0]
93 --> 76 | cost [39.0]
94 --> 67 | cost [36.0]
95 --> 67 | cost [69.0]
96 --> 68 | cost [48.0]

BACKUP RING
1  ---  4 | cost [1.61]
2  ---  5 | cost [0.7000000000000001]
4  ---  6 | cost [0.21]
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 --- 63 | cost [1.12]
27 --- 64 | cost [0.7000000000000001]
30 --- 32 | cost [0.21]
31 --- 36 | cost [0.35000000000000003]
31 --- 97 | cost [0.49]
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]
63 --- 66 | cost [0.56]
64 --- 67 | cost [0.42]
66 --- 68 | cost [0.14]
67 --- 76 | cost [0.7000000000000001]
68 --- 75 | cost [0.98]
69 --- 81 | cost [0.98]
70 --- 82 | cost [0.7000000000000001]
74 --- 76 | cost [0.56]
74 --- 87 | cost [0.63]
75 --- 85 | cost [0.56]
81 --- 87 | cost [0.91]
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 --> 57 | cost [0.15]
59 --> 56 | cost [0.21]
60 --> 56 | cost [0.33]
61 --> 64 | cost [0.24]
62 --> 64 | cost [0.18]
65 --> 64 | cost [0.27]
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 --> 70 | cost [0.63]
80 --> 82 | cost [0.99]
83 --> 81 | cost [0.12]
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 --> 75 | cost [0.42]
93 --> 67 | cost [0.45]
94 --> 68 | cost [0.36]
95 --> 68 | cost [0.6900000000000001]
96 --> 66 | cost [0.48]

B = 1.8800000000000001
i★ = 1
j★ = 2
k★ = 4