------------------------------------------------------------
                           α=7.0 —— eil51 —— 51 nodes       
------------------------------------------------------------

——————— Sat, 06 Jan 2024 16:45:10 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 24 hubs —— 1—27—48—23—24—14—18—4—41—19—42—44—15—37—5—49—9—16—29—20—3—28—22—52
total time           3606.54 (TL 3600)    gap                  0.103                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2222.22<=2477.06     subtour              314.0                
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       5210                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—27—48—23—24—14—18—4—41—19—42—44—15—37—5—49—9—16—29—20—3—28—22—52

RING
1  --- 27 | cost [56.0]
1  --- 52 | cost [0.0]
3  --- 20 | cost [56.0]
3  --- 28 | cost [63.0]
4  --- 18 | cost [56.0]
4  --- 41 | cost [91.0]
5  --- 37 | cost [77.0]
5  --- 49 | cost [56.0]
9  --- 16 | cost [56.0]
9  --- 49 | cost [42.0]
14 --- 18 | cost [70.0]
14 --- 24 | cost [77.0]
15 --- 37 | cost [49.0]
15 --- 44 | cost [42.0]
16 --- 29 | cost [63.0]
19 --- 41 | cost [35.0]
19 --- 42 | cost [63.0]
20 --- 29 | cost [70.0]
22 --- 28 | cost [70.0]
22 --- 52 | cost [49.0]
23 --- 24 | cost [63.0]
23 --- 48 | cost [63.0]
27 --- 48 | cost [63.0]
42 --- 44 | cost [70.0]

STAR
2  --> 16 | cost [27.0]
6  --> 48 | cost [27.0]
7  --> 23 | cost [18.0]
8  --> 48 | cost [27.0]
10 --> 49 | cost [24.0]
11 --> 16 | cost [30.0]
12 -->  5 | cost [27.0]
13 --> 41 | cost [27.0]
17 --> 37 | cost [15.0]
21 --> 29 | cost [21.0]
25 --> 14 | cost [18.0]
26 --> 28 | cost [48.0]
30 -->  9 | cost [24.0]
31 --> 28 | cost [18.0]
32 -->  1 | cost [18.0]
33 --> 15 | cost [36.0]
34 -->  9 | cost [27.0]
35 --> 20 | cost [21.0]
36 -->  3 | cost [36.0]
38 -->  5 | cost [21.0]
39 --> 49 | cost [51.0]
40 --> 19 | cost [33.0]
43 --> 24 | cost [36.0]
45 --> 15 | cost [21.0]
46 --> 27 | cost [27.0]
47 -->  4 | cost [24.0]
50 -->  9 | cost [18.0]
51 --> 27 | cost [24.0]

BACKUP RING
1  --- 48 | cost [0.84]
3  --- 22 | cost [0.84]
3  --- 29 | cost [1.19]
4  --- 14 | cost [1.26]
4  --- 19 | cost [1.05]
5  ---  9 | cost [0.84]
5  --- 15 | cost [1.05]
9  --- 29 | cost [1.12]
14 --- 23 | cost [1.12]
15 --- 42 | cost [1.12]
16 --- 20 | cost [1.26]
16 --- 49 | cost [0.98]
18 --- 24 | cost [1.47]
18 --- 41 | cost [1.19]
19 --- 44 | cost [1.19]
20 --- 28 | cost [1.19]
23 --- 27 | cost [1.19]
24 --- 48 | cost [1.19]
28 --- 52 | cost [1.12]
37 --- 44 | cost [0.49]
37 --- 49 | cost [1.19]
41 --- 42 | cost [0.91]

BACKUP STAR
2  --> 29 | cost [0.27]
6  --> 27 | cost [0.27]
7  --> 48 | cost [0.33]
8  -->  1 | cost [0.36]
10 -->  9 | cost [0.36]
11 -->  5 | cost [0.33]
12 --> 37 | cost [0.3]
13 --> 18 | cost [0.42]
17 -->  4 | cost [0.24]
21 --> 16 | cost [0.3]
25 --> 18 | cost [0.33]
26 --> 48 | cost [0.39]
30 --> 49 | cost [0.3]
31 --> 22 | cost [0.39]
33 --> 44 | cost [0.51]
34 --> 16 | cost [0.36]
35 -->  3 | cost [0.3]
36 --> 20 | cost [0.39]
38 -->  9 | cost [0.21]
39 -->  9 | cost [0.5700000000000001]
40 --> 41 | cost [0.36]
43 --> 23 | cost [0.39]
45 --> 44 | cost [0.3]
46 -->  5 | cost [0.36]
47 --> 18 | cost [0.24]
50 --> 16 | cost [0.18]
51 -->  1 | cost [0.42]

B = 1.82
i★ = 16
j★ = 9
k★ = 49

       
——————— Sat, 06 Jan 2024 17:45:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 23 hubs —— 1-22-3-20-29-50-9-49-5-37-15-44-42-19-41-4-18-14-24-23-48-27-52-1
total time           3603.04 (TL 3600)    gap                  0.131                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2159.13<=2485.87     Master/SP costs      2140/345.87          
Master time          3556.06              SP time              46.99                
subtour              4153.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            5595.0               SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       305769               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—22—3—20—29—50—9—49—5—37—15—44—42—19—41—4—18—14—24—23—48—27—52

RING
1  --- 22 | cost [49.0]
1  --- 52 | cost [0.0]
3  --- 20 | cost [56.0]
3  --- 22 | cost [84.0]
4  --- 18 | cost [56.0]
4  --- 41 | cost [91.0]
5  --- 37 | cost [77.0]
5  --- 49 | cost [56.0]
9  --- 49 | cost [42.0]
9  --- 50 | cost [42.0]
14 --- 18 | cost [70.0]
14 --- 24 | cost [77.0]
15 --- 37 | cost [49.0]
15 --- 44 | cost [42.0]
19 --- 41 | cost [35.0]
19 --- 42 | cost [63.0]
20 --- 29 | cost [70.0]
23 --- 24 | cost [63.0]
23 --- 48 | cost [63.0]
27 --- 48 | cost [63.0]
27 --- 52 | cost [56.0]
29 --- 50 | cost [77.0]
42 --- 44 | cost [70.0]

STAR
2  --> 29 | cost [27.0]
6  --> 27 | cost [27.0]
7  --> 23 | cost [18.0]
8  -->  1 | cost [36.0]
10 --> 49 | cost [24.0]
11 -->  5 | cost [33.0]
12 -->  5 | cost [27.0]
13 --> 41 | cost [27.0]
16 --> 50 | cost [18.0]
17 --> 37 | cost [15.0]
21 --> 50 | cost [24.0]
25 --> 14 | cost [18.0]
26 --> 48 | cost [39.0]
28 -->  3 | cost [27.0]
30 -->  9 | cost [24.0]
31 --> 22 | cost [39.0]
32 -->  1 | cost [18.0]
33 --> 15 | cost [36.0]
34 --> 50 | cost [18.0]
35 --> 20 | cost [21.0]
36 -->  3 | cost [36.0]
38 -->  9 | cost [21.0]
39 --> 49 | cost [51.0]
40 --> 19 | cost [33.0]
43 --> 24 | cost [36.0]
45 --> 15 | cost [21.0]
46 --> 27 | cost [27.0]
47 -->  4 | cost [24.0]
51 --> 27 | cost [24.0]

BACKUP RING
1  ---  3 | cost [1.33]
3  --- 29 | cost [1.19]
4  --- 14 | cost [1.26]
4  --- 19 | cost [1.05]
5  ---  9 | cost [0.84]
5  --- 15 | cost [1.05]
9  --- 29 | cost [1.12]
14 --- 23 | cost [1.12]
15 --- 42 | cost [1.12]
18 --- 24 | cost [1.47]
18 --- 41 | cost [1.19]
19 --- 44 | cost [1.19]
20 --- 22 | cost [1.05]
20 --- 50 | cost [1.47]
23 --- 27 | cost [1.19]
24 --- 48 | cost [1.19]
37 --- 44 | cost [0.49]
37 --- 49 | cost [1.19]
41 --- 42 | cost [0.91]
48 --- 52 | cost [0.84]
49 --- 50 | cost [0.84]

BACKUP STAR
2  --> 22 | cost [0.33]
6  --> 48 | cost [0.27]
7  --> 48 | cost [0.33]
10 -->  9 | cost [0.36]
11 -->  1 | cost [0.36]
12 --> 37 | cost [0.3]
13 --> 18 | cost [0.42]
16 -->  9 | cost [0.24]
17 -->  4 | cost [0.24]
21 --> 29 | cost [0.21]
25 --> 18 | cost [0.33]
26 --> 23 | cost [0.48]
28 --> 22 | cost [0.3]
30 --> 49 | cost [0.3]
31 -->  3 | cost [0.48]
33 --> 44 | cost [0.51]
34 -->  9 | cost [0.27]
35 -->  3 | cost [0.3]
36 --> 20 | cost [0.39]
38 -->  5 | cost [0.21]
39 -->  9 | cost [0.5700000000000001]
40 --> 41 | cost [0.36]
43 --> 23 | cost [0.39]
45 --> 44 | cost [0.3]
46 -->  5 | cost [0.36]
47 --> 18 | cost [0.24]
51 -->  1 | cost [0.42]

B = 1.8899999999999997
i★ = 48
j★ = 27
k★ = 52

       
——————— Sun, 07 Jan 2024 14:34:07 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 22 hubs —— 1—22—28—3—20—29—50—9—49—5—46—51—47—37—17—4—18—14—24—23—48—52
total time           5556.81 (TL 3600)    gap                  0.209                
blossom time         0.76                 nb blossom           118.0                
LB <= UB             2087.92<=2639.3      subtour              250.0                
connectivity cuts    386.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       477                  n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—22—28—3—20—29—50—9—49—5—46—51—47—37—17—4—18—14—24—23—48—52

RING
1  --- 22 | cost [49.0]
1  --- 52 | cost [0.0]
3  --- 20 | cost [56.0]
3  --- 28 | cost [63.0]
4  --- 17 | cost [56.0]
4  --- 18 | cost [56.0]
5  --- 46 | cost [84.0]
5  --- 49 | cost [56.0]
9  --- 49 | cost [42.0]
9  --- 50 | cost [42.0]
14 --- 18 | cost [70.0]
14 --- 24 | cost [77.0]
17 --- 37 | cost [35.0]
20 --- 29 | cost [70.0]
22 --- 28 | cost [70.0]
23 --- 24 | cost [63.0]
23 --- 48 | cost [63.0]
29 --- 50 | cost [77.0]
37 --- 47 | cost [84.0]
46 --- 51 | cost [14.0]
47 --- 51 | cost [63.0]
48 --- 52 | cost [84.0]

STAR
2  --> 29 | cost [27.0]
6  --> 48 | cost [27.0]
7  --> 23 | cost [18.0]
8  -->  1 | cost [36.0]
10 -->  9 | cost [36.0]
11 --> 46 | cost [30.0]
12 -->  5 | cost [27.0]
13 --> 18 | cost [42.0]
15 --> 37 | cost [21.0]
16 --> 50 | cost [18.0]
19 -->  4 | cost [45.0]
21 --> 50 | cost [24.0]
25 --> 14 | cost [18.0]
26 --> 28 | cost [48.0]
27 -->  1 | cost [24.0]
30 -->  9 | cost [24.0]
31 --> 28 | cost [18.0]
32 -->  1 | cost [18.0]
33 --> 49 | cost [54.0]
34 --> 50 | cost [18.0]
35 --> 20 | cost [21.0]
36 -->  3 | cost [36.0]
38 -->  9 | cost [21.0]
39 --> 49 | cost [51.0]
40 --> 47 | cost [99.0]
41 -->  4 | cost [39.0]
42 --> 17 | cost [42.0]
43 --> 24 | cost [36.0]
44 --> 37 | cost [21.0]
45 --> 37 | cost [42.0]

BACKUP RING
1  --- 28 | cost [1.12]
3  --- 22 | cost [0.84]
3  --- 29 | cost [1.19]
4  --- 14 | cost [1.26]
4  --- 37 | cost [0.91]
5  ---  9 | cost [0.84]
5  --- 51 | cost [0.98]
9  --- 29 | cost [1.12]
14 --- 23 | cost [1.12]
17 --- 18 | cost [0.98]
17 --- 47 | cost [0.63]
18 --- 24 | cost [1.47]
20 --- 28 | cost [1.19]
20 --- 50 | cost [1.47]
23 --- 52 | cost [1.54]
24 --- 48 | cost [1.19]
37 --- 51 | cost [1.26]
46 --- 47 | cost [0.7000000000000001]
46 --- 49 | cost [1.33]
49 --- 50 | cost [0.84]

BACKUP STAR
2  --> 22 | cost [0.33]
6  --> 14 | cost [0.3]
7  --> 48 | cost [0.33]
10 --> 49 | cost [0.24]
11 -->  5 | cost [0.33]
12 --> 47 | cost [0.18]
13 -->  4 | cost [0.45]
15 --> 17 | cost [0.33]
16 -->  9 | cost [0.24]
19 --> 17 | cost [0.51]
21 --> 29 | cost [0.21]
25 --> 18 | cost [0.33]
26 --> 48 | cost [0.39]
30 --> 49 | cost [0.3]
31 --> 22 | cost [0.39]
33 --> 37 | cost [0.54]
34 -->  9 | cost [0.27]
35 -->  3 | cost [0.3]
36 --> 20 | cost [0.39]
38 -->  5 | cost [0.21]
39 -->  9 | cost [0.5700000000000001]
40 -->  4 | cost [0.75]
41 --> 18 | cost [0.51]
42 -->  4 | cost [0.48]
43 --> 23 | cost [0.39]
44 --> 17 | cost [0.27]
45 --> 17 | cost [0.54]

B = 2.01
i★ = 37
j★ = 47
k★ = 51

       
——————— Sun, 07 Jan 2024 15:34:39 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 25 hubs —— 1-27-48-23-24-14-18-4-41-19-42-44-15-37-5-49-9-50-16-29-20-3-28-22-52-1
total time           3603.56 (TL 3600)    gap                  0.127                
blossom time         745.46               nb blossom           225491.0             
LB <= UB             2167.88<=2483.4      Master/SP costs      2154/329.4           
Master time          3563.18              SP time              40.38                
subtour              4376.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            4806.0               SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       258825               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—27—48—23—24—14—18—4—41—19—42—44—15—37—5—49—9—50—16—29—20—3—28—22—52

RING
1  --- 27 | cost [56.0]
1  --- 52 | cost [0.0]
3  --- 20 | cost [56.0]
3  --- 28 | cost [63.0]
4  --- 18 | cost [56.0]
4  --- 41 | cost [91.0]
5  --- 37 | cost [77.0]
5  --- 49 | cost [56.0]
9  --- 49 | cost [42.0]
9  --- 50 | cost [42.0]
14 --- 18 | cost [70.0]
14 --- 24 | cost [77.0]
15 --- 37 | cost [49.0]
15 --- 44 | cost [42.0]
16 --- 29 | cost [63.0]
16 --- 50 | cost [42.0]
19 --- 41 | cost [35.0]
19 --- 42 | cost [63.0]
20 --- 29 | cost [70.0]
22 --- 28 | cost [70.0]
22 --- 52 | cost [49.0]
23 --- 24 | cost [63.0]
23 --- 48 | cost [63.0]
27 --- 48 | cost [63.0]
42 --- 44 | cost [70.0]

STAR
2  --> 16 | cost [27.0]
6  --> 48 | cost [27.0]
7  --> 23 | cost [18.0]
8  --> 22 | cost [36.0]
10 --> 49 | cost [24.0]
11 --> 16 | cost [30.0]
12 -->  5 | cost [27.0]
13 --> 41 | cost [27.0]
17 --> 37 | cost [15.0]
21 --> 29 | cost [21.0]
25 --> 14 | cost [18.0]
26 --> 28 | cost [48.0]
30 -->  9 | cost [24.0]
31 --> 28 | cost [18.0]
32 -->  1 | cost [18.0]
33 --> 15 | cost [36.0]
34 --> 50 | cost [18.0]
35 --> 20 | cost [21.0]
36 -->  3 | cost [36.0]
38 -->  5 | cost [21.0]
39 --> 49 | cost [51.0]
40 --> 19 | cost [33.0]
43 --> 24 | cost [36.0]
45 --> 15 | cost [21.0]
46 --> 27 | cost [27.0]
47 --> 18 | cost [24.0]
51 --> 27 | cost [24.0]

BACKUP RING
1  --- 48 | cost [0.84]
3  --- 22 | cost [0.84]
3  --- 29 | cost [1.19]
4  --- 14 | cost [1.26]
4  --- 19 | cost [1.05]
5  ---  9 | cost [0.84]
5  --- 15 | cost [1.05]
9  --- 16 | cost [0.56]
14 --- 23 | cost [1.12]
15 --- 42 | cost [1.12]
16 --- 20 | cost [1.26]
18 --- 24 | cost [1.47]
18 --- 41 | cost [1.19]
19 --- 44 | cost [1.19]
20 --- 28 | cost [1.19]
23 --- 27 | cost [1.19]
24 --- 48 | cost [1.19]
28 --- 52 | cost [1.12]
29 --- 50 | cost [0.77]
37 --- 44 | cost [0.49]
37 --- 49 | cost [1.19]
41 --- 42 | cost [0.91]
49 --- 50 | cost [0.84]

BACKUP STAR
2  --> 29 | cost [0.27]
6  --> 27 | cost [0.27]
7  --> 48 | cost [0.33]
8  --> 48 | cost [0.27]
10 -->  9 | cost [0.36]
11 -->  5 | cost [0.33]
12 --> 37 | cost [0.3]
13 --> 18 | cost [0.42]
17 -->  4 | cost [0.24]
21 --> 50 | cost [0.24]
25 --> 18 | cost [0.33]
26 --> 48 | cost [0.39]
30 --> 49 | cost [0.3]
31 --> 22 | cost [0.39]
33 --> 44 | cost [0.51]
34 -->  9 | cost [0.27]
35 -->  3 | cost [0.3]
36 --> 20 | cost [0.39]
38 -->  9 | cost [0.21]
39 -->  9 | cost [0.5700000000000001]
40 --> 41 | cost [0.36]
43 --> 23 | cost [0.39]
45 --> 44 | cost [0.3]
46 -->  5 | cost [0.36]
47 -->  4 | cost [0.24]
51 -->  1 | cost [0.42]

B = 1.8
i★ = 18
j★ = 14
k★ = 24