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

——————— Sat, 06 Jan 2024 11:18:25 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 18 hubs —— 1—22—20—29—50—9—49—5—37—17—4—18—14—24—23—48—27—52
total time           522.66               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2132.88<=2132.88     subtour              39.0                 
connectivity cuts    381.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       768                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—22—20—29—50—9—49—5—37—17—4—18—14—24—23—48—27—52

RING
1  --- 22 | cost [49.0]
1  --- 52 | cost [0.0]
4  --- 17 | cost [56.0]
4  --- 18 | cost [56.0]
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]
17 --- 37 | cost [35.0]
20 --- 22 | cost [105.0]
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]

STAR
2  --> 29 | cost [27.0]
3  --> 20 | cost [24.0]
6  --> 27 | cost [27.0]
7  --> 23 | cost [18.0]
8  --> 48 | cost [27.0]
10 --> 49 | cost [24.0]
11 -->  5 | cost [33.0]
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 --> 29 | cost [21.0]
25 --> 14 | cost [18.0]
26 --> 48 | cost [39.0]
28 --> 22 | cost [30.0]
30 -->  9 | cost [24.0]
31 --> 22 | cost [39.0]
32 -->  1 | cost [18.0]
33 --> 49 | cost [54.0]
34 --> 50 | cost [18.0]
35 --> 20 | cost [21.0]
36 --> 20 | cost [39.0]
38 -->  9 | cost [21.0]
39 --> 49 | cost [51.0]
40 -->  4 | cost [75.0]
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]
46 --> 27 | cost [27.0]
47 --> 18 | cost [24.0]
51 --> 27 | cost [24.0]

BACKUP RING
1  --- 20 | cost [1.47]
4  --- 14 | cost [1.26]
4  --- 37 | cost [0.91]
5  ---  9 | cost [0.84]
5  --- 17 | cost [1.05]
9  --- 29 | cost [1.12]
14 --- 23 | cost [1.12]
17 --- 18 | cost [0.98]
18 --- 24 | cost [1.47]
20 --- 50 | cost [1.47]
22 --- 29 | cost [1.26]
23 --- 27 | cost [1.19]
24 --- 48 | cost [1.19]
37 --- 49 | cost [1.19]
48 --- 52 | cost [0.84]
49 --- 50 | cost [0.84]

BACKUP STAR
2  --> 22 | cost [0.33]
3  --> 22 | cost [0.36]
6  --> 48 | cost [0.27]
7  --> 48 | cost [0.33]
8  -->  1 | cost [0.36]
10 -->  9 | cost [0.36]
11 -->  1 | cost [0.36]
12 --> 17 | cost [0.3]
13 -->  4 | cost [0.45]
15 --> 17 | cost [0.33]
16 -->  9 | cost [0.24]
19 --> 17 | cost [0.51]
21 --> 50 | cost [0.24]
25 --> 18 | cost [0.33]
26 --> 23 | cost [0.48]
28 -->  1 | cost [0.48]
30 --> 49 | cost [0.3]
31 -->  1 | cost [0.51]
33 --> 37 | cost [0.54]
34 -->  9 | cost [0.27]
35 --> 29 | cost [0.48]
36 --> 29 | cost [0.66]
38 -->  5 | cost [0.21]
39 -->  9 | cost [0.5700000000000001]
40 --> 17 | cost [0.84]
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]
46 -->  5 | cost [0.36]
47 -->  4 | cost [0.24]
51 -->  1 | cost [0.42]

B = 2.84
i★ = 17
j★ = 4
k★ = 18

       
——————— Sat, 06 Jan 2024 11:19:13 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 18 hubs —— 1-27-48-23-24-14-18-4-17-37-5-49-9-50-29-20-22-52-1
total time           18.31                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2132.88<=2132.88     Master/SP costs      2113/19.88           
Master time          17.44                SP time              0.86                 
subtour              124.0                connectivity cuts    578.0                
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            78.0                 SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1588                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—27—48—23—24—14—18—4—17—37—5—49—9—50—29—20—22—52

RING
1  --- 27 | cost [56.0]
1  --- 52 | cost [0.0]
4  --- 17 | cost [56.0]
4  --- 18 | cost [56.0]
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]
17 --- 37 | cost [35.0]
20 --- 22 | cost [105.0]
20 --- 29 | cost [70.0]
22 --- 52 | cost [49.0]
23 --- 24 | cost [63.0]
23 --- 48 | cost [63.0]
27 --- 48 | cost [63.0]
29 --- 50 | cost [77.0]

STAR
2  --> 29 | cost [27.0]
3  --> 20 | cost [24.0]
6  --> 48 | cost [27.0]
7  --> 23 | cost [18.0]
8  --> 48 | cost [27.0]
10 --> 49 | cost [24.0]
11 -->  5 | cost [33.0]
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 --> 29 | cost [21.0]
25 --> 14 | cost [18.0]
26 --> 48 | cost [39.0]
28 --> 22 | cost [30.0]
30 -->  9 | cost [24.0]
31 --> 22 | cost [39.0]
32 -->  1 | cost [18.0]
33 --> 49 | cost [54.0]
34 --> 50 | cost [18.0]
35 --> 20 | cost [21.0]
36 --> 20 | cost [39.0]
38 -->  9 | cost [21.0]
39 --> 49 | cost [51.0]
40 -->  4 | cost [75.0]
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]
46 --> 27 | cost [27.0]
47 --> 18 | cost [24.0]
51 --> 27 | cost [24.0]

BACKUP RING
1  --- 48 | cost [0.84]
4  --- 14 | cost [1.26]
4  --- 37 | cost [0.91]
5  ---  9 | cost [0.84]
5  --- 17 | cost [1.05]
9  --- 29 | cost [1.12]
14 --- 23 | cost [1.12]
17 --- 18 | cost [0.98]
18 --- 24 | cost [1.47]
20 --- 50 | cost [1.47]
20 --- 52 | cost [1.47]
22 --- 29 | cost [1.26]
23 --- 27 | cost [1.19]
24 --- 48 | cost [1.19]
37 --- 49 | cost [1.19]
49 --- 50 | cost [0.84]

BACKUP STAR
2  --> 22 | cost [0.33]
3  --> 22 | cost [0.36]
6  --> 27 | cost [0.27]
7  --> 48 | cost [0.33]
8  -->  1 | cost [0.36]
10 -->  9 | cost [0.36]
11 -->  1 | cost [0.36]
12 --> 17 | cost [0.3]
13 -->  4 | cost [0.45]
15 --> 17 | cost [0.33]
16 -->  9 | cost [0.24]
19 --> 17 | cost [0.51]
21 --> 50 | cost [0.24]
25 --> 18 | cost [0.33]
26 --> 23 | cost [0.48]
28 -->  1 | cost [0.48]
30 --> 49 | cost [0.3]
31 -->  1 | cost [0.51]
33 --> 37 | cost [0.54]
34 -->  9 | cost [0.27]
35 --> 29 | cost [0.48]
36 --> 29 | cost [0.66]
38 -->  5 | cost [0.21]
39 -->  9 | cost [0.5700000000000001]
40 --> 17 | cost [0.84]
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]
46 -->  5 | cost [0.36]
47 -->  4 | cost [0.24]
51 -->  1 | cost [0.42]

B = 2.84
i★ = 17
j★ = 4
k★ = 18

       
——————— Sun, 07 Jan 2024 08:19:27 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 18 hubs —— 1—22—20—29—50—9—49—5—37—17—4—18—14—24—23—48—27—52
total time           564.94               gap                  0.0                  
blossom time         0.62                 nb blossom           126.0                
LB <= UB             2132.88<=2132.88     subtour              69.0                 
connectivity cuts    372.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       798                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—22—20—29—50—9—49—5—37—17—4—18—14—24—23—48—27—52

RING
1  --- 22 | cost [49.0]
1  --- 52 | cost [0.0]
4  --- 17 | cost [56.0]
4  --- 18 | cost [56.0]
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]
17 --- 37 | cost [35.0]
20 --- 22 | cost [105.0]
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]

STAR
2  --> 29 | cost [27.0]
3  --> 20 | cost [24.0]
6  --> 48 | cost [27.0]
7  --> 23 | cost [18.0]
8  --> 48 | cost [27.0]
10 --> 49 | cost [24.0]
11 -->  5 | cost [33.0]
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 --> 29 | cost [21.0]
25 --> 14 | cost [18.0]
26 --> 48 | cost [39.0]
28 --> 22 | cost [30.0]
30 -->  9 | cost [24.0]
31 --> 22 | cost [39.0]
32 -->  1 | cost [18.0]
33 --> 49 | cost [54.0]
34 --> 50 | cost [18.0]
35 --> 20 | cost [21.0]
36 --> 20 | cost [39.0]
38 -->  9 | cost [21.0]
39 --> 49 | cost [51.0]
40 -->  4 | cost [75.0]
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]
46 --> 27 | cost [27.0]
47 --> 18 | cost [24.0]
51 --> 27 | cost [24.0]

BACKUP RING
1  --- 20 | cost [1.47]
4  --- 14 | cost [1.26]
4  --- 37 | cost [0.91]
5  ---  9 | cost [0.84]
5  --- 17 | cost [1.05]
9  --- 29 | cost [1.12]
14 --- 23 | cost [1.12]
17 --- 18 | cost [0.98]
18 --- 24 | cost [1.47]
20 --- 50 | cost [1.47]
22 --- 29 | cost [1.26]
23 --- 27 | cost [1.19]
24 --- 48 | cost [1.19]
37 --- 49 | cost [1.19]
48 --- 52 | cost [0.84]
49 --- 50 | cost [0.84]

BACKUP STAR
2  --> 22 | cost [0.33]
3  --> 22 | cost [0.36]
6  --> 27 | cost [0.27]
7  --> 48 | cost [0.33]
8  -->  1 | cost [0.36]
10 -->  9 | cost [0.36]
11 -->  1 | cost [0.36]
12 --> 17 | cost [0.3]
13 -->  4 | cost [0.45]
15 --> 17 | cost [0.33]
16 -->  9 | cost [0.24]
19 --> 17 | cost [0.51]
21 --> 50 | cost [0.24]
25 --> 18 | cost [0.33]
26 --> 23 | cost [0.48]
28 -->  1 | cost [0.48]
30 --> 49 | cost [0.3]
31 -->  1 | cost [0.51]
33 --> 37 | cost [0.54]
34 -->  9 | cost [0.27]
35 --> 29 | cost [0.48]
36 --> 29 | cost [0.66]
38 -->  5 | cost [0.21]
39 -->  9 | cost [0.5700000000000001]
40 --> 17 | cost [0.84]
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]
46 -->  5 | cost [0.36]
47 -->  4 | cost [0.24]
51 -->  1 | cost [0.42]

B = 2.84
i★ = 17
j★ = 4
k★ = 18

       
——————— Sun, 07 Jan 2024 08:20:21 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 18 hubs —— 1-27-48-23-24-14-18-4-17-37-5-49-9-50-29-20-22-52-1
total time           21.8                 gap                  0.0                  
blossom time         2.12                 nb blossom           375.0                
LB <= UB             2132.88<=2132.88     Master/SP costs      2113/19.88           
Master time          20.95                SP time              0.85                 
subtour              124.0                connectivity cuts    382.0                
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            65.0                 SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1257                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—27—48—23—24—14—18—4—17—37—5—49—9—50—29—20—22—52

RING
1  --- 27 | cost [56.0]
1  --- 52 | cost [0.0]
4  --- 17 | cost [56.0]
4  --- 18 | cost [56.0]
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]
17 --- 37 | cost [35.0]
20 --- 22 | cost [105.0]
20 --- 29 | cost [70.0]
22 --- 52 | cost [49.0]
23 --- 24 | cost [63.0]
23 --- 48 | cost [63.0]
27 --- 48 | cost [63.0]
29 --- 50 | cost [77.0]

STAR
2  --> 29 | cost [27.0]
3  --> 20 | cost [24.0]
6  --> 48 | cost [27.0]
7  --> 23 | cost [18.0]
8  --> 48 | cost [27.0]
10 --> 49 | cost [24.0]
11 -->  5 | cost [33.0]
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 --> 29 | cost [21.0]
25 --> 14 | cost [18.0]
26 --> 48 | cost [39.0]
28 --> 22 | cost [30.0]
30 -->  9 | cost [24.0]
31 --> 22 | cost [39.0]
32 -->  1 | cost [18.0]
33 --> 49 | cost [54.0]
34 --> 50 | cost [18.0]
35 --> 20 | cost [21.0]
36 --> 20 | cost [39.0]
38 -->  5 | cost [21.0]
39 --> 49 | cost [51.0]
40 -->  4 | cost [75.0]
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]
46 --> 27 | cost [27.0]
47 --> 18 | cost [24.0]
51 --> 27 | cost [24.0]

BACKUP RING
1  --- 48 | cost [0.84]
4  --- 14 | cost [1.26]
4  --- 37 | cost [0.91]
5  ---  9 | cost [0.84]
5  --- 17 | cost [1.05]
9  --- 29 | cost [1.12]
14 --- 23 | cost [1.12]
17 --- 18 | cost [0.98]
18 --- 24 | cost [1.47]
20 --- 50 | cost [1.47]
20 --- 52 | cost [1.47]
22 --- 29 | cost [1.26]
23 --- 27 | cost [1.19]
24 --- 48 | cost [1.19]
37 --- 49 | cost [1.19]
49 --- 50 | cost [0.84]

BACKUP STAR
2  --> 22 | cost [0.33]
3  --> 22 | cost [0.36]
6  --> 27 | cost [0.27]
7  --> 48 | cost [0.33]
8  -->  1 | cost [0.36]
10 -->  9 | cost [0.36]
11 -->  1 | cost [0.36]
12 --> 17 | cost [0.3]
13 -->  4 | cost [0.45]
15 --> 17 | cost [0.33]
16 -->  9 | cost [0.24]
19 --> 17 | cost [0.51]
21 --> 50 | cost [0.24]
25 --> 18 | cost [0.33]
26 --> 23 | cost [0.48]
28 -->  1 | cost [0.48]
30 --> 49 | cost [0.3]
31 -->  1 | cost [0.51]
33 --> 37 | cost [0.54]
34 -->  9 | cost [0.27]
35 --> 29 | cost [0.48]
36 --> 29 | cost [0.66]
38 -->  9 | cost [0.21]
39 -->  9 | cost [0.5700000000000001]
40 --> 17 | cost [0.84]
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]
46 -->  5 | cost [0.36]
47 -->  4 | cost [0.24]
51 -->  1 | cost [0.42]

B = 2.84
i★ = 17
j★ = 4
k★ = 18