------------------------------------------------------------
                           α=3.0 —— eil51 —— 51 nodes       
------------------------------------------------------------

——————— Sat, 06 Jan 2024 12:09:27 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 52 hubs —— 1—22—8—26—31—28—3—36—35—20—2—29—21—16—50—34—30—9—49—10—39—33—45—15—44—42—19—40—41—13—25—14—24—43—7—23—48—6—27—51—46—12—47—18—4—17—37—5—38—11—32—52
total time           43.04                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1299.39<=1299.39     subtour              106.0                
connectivity cuts    10.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—22—8—26—31—28—3—36—35—20—2—29—21—16—50—34—30—9—49—10—39—33—45—15—44—42—19—40—41—13—25—14—24—43—7—23—48—6—27—51—46—12—47—18—4—17—37—5—38—11—32—52

RING
1  --- 22 | cost [21.0]
1  --- 52 | cost [0.0]
2  --- 20 | cost [36.0]
2  --- 29 | cost [27.0]
3  --- 28 | cost [27.0]
3  --- 36 | cost [36.0]
4  --- 17 | cost [24.0]
4  --- 18 | cost [24.0]
5  --- 37 | cost [33.0]
5  --- 38 | cost [21.0]
6  --- 27 | cost [27.0]
6  --- 48 | cost [27.0]
7  --- 23 | cost [18.0]
7  --- 43 | cost [36.0]
8  --- 22 | cost [36.0]
8  --- 26 | cost [21.0]
9  --- 30 | cost [24.0]
9  --- 49 | cost [18.0]
10 --- 39 | cost [30.0]
10 --- 49 | cost [24.0]
11 --- 32 | cost [18.0]
11 --- 38 | cost [21.0]
12 --- 46 | cost [21.0]
12 --- 47 | cost [18.0]
13 --- 25 | cost [39.0]
13 --- 41 | cost [27.0]
14 --- 24 | cost [33.0]
14 --- 25 | cost [18.0]
15 --- 44 | cost [18.0]
15 --- 45 | cost [21.0]
16 --- 21 | cost [30.0]
16 --- 50 | cost [18.0]
17 --- 37 | cost [15.0]
18 --- 47 | cost [24.0]
19 --- 40 | cost [33.0]
19 --- 42 | cost [27.0]
20 --- 35 | cost [21.0]
21 --- 29 | cost [21.0]
23 --- 48 | cost [27.0]
24 --- 43 | cost [36.0]
26 --- 31 | cost [30.0]
27 --- 51 | cost [24.0]
28 --- 31 | cost [18.0]
30 --- 34 | cost [21.0]
32 --- 52 | cost [18.0]
33 --- 39 | cost [42.0]
33 --- 45 | cost [21.0]
34 --- 50 | cost [18.0]
35 --- 36 | cost [18.0]
40 --- 41 | cost [36.0]
42 --- 44 | cost [30.0]
46 --- 51 | cost [6.0]

STAR

BACKUP RING
1  ---  8 | cost [0.36]
2  --- 21 | cost [0.45]
2  --- 35 | cost [0.5700000000000001]
3  --- 31 | cost [0.48]
3  --- 35 | cost [0.3]
4  --- 37 | cost [0.39]
4  --- 47 | cost [0.24]
5  --- 11 | cost [0.33]
5  --- 17 | cost [0.45]
6  --- 23 | cost [0.33]
6  --- 51 | cost [0.33]
7  --- 24 | cost [0.42]
7  --- 48 | cost [0.33]
8  --- 31 | cost [0.27]
9  --- 10 | cost [0.36]
9  --- 34 | cost [0.27]
10 --- 33 | cost [0.36]
11 --- 52 | cost [0.36]
12 --- 18 | cost [0.42]
12 --- 51 | cost [0.24]
13 --- 14 | cost [0.54]
13 --- 40 | cost [0.5700000000000001]
14 --- 43 | cost [0.6900000000000001]
15 --- 33 | cost [0.36]
15 --- 42 | cost [0.48]
16 --- 29 | cost [0.27]
16 --- 34 | cost [0.36]
17 --- 18 | cost [0.42]
19 --- 41 | cost [0.15]
19 --- 44 | cost [0.51]
20 --- 29 | cost [0.3]
20 --- 36 | cost [0.39]
21 --- 50 | cost [0.24]
22 --- 26 | cost [0.5700000000000001]
23 --- 43 | cost [0.39]
24 --- 25 | cost [0.42]
25 --- 41 | cost [0.63]
26 --- 28 | cost [0.48]
27 --- 46 | cost [0.27]
27 --- 48 | cost [0.27]
28 --- 36 | cost [0.6]
30 --- 49 | cost [0.3]
30 --- 50 | cost [0.3]
32 --- 38 | cost [0.39]
37 --- 38 | cost [0.54]
39 --- 45 | cost [0.63]
39 --- 49 | cost [0.51]
40 --- 42 | cost [0.48]
44 --- 45 | cost [0.3]
46 --- 47 | cost [0.3]

BACKUP STAR

B = 0.6900000000000001
i★ = 14
j★ = 24
k★ = 43

       
——————— Sat, 06 Jan 2024 12:10:03 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 52 hubs —— 1-22-8-26-31-28-3-36-35-20-2-29-21-16-50-34-30-9-49-10-39-33-45-15-44-42-19-40-41-13-25-14-24-43-7-23-48-6-27-51-46-12-47-18-4-17-37-5-38-11-32-52-1
total time           7.56                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1299.39<=1299.39     Master/SP costs      1278/21.39           
Master time          7.31                 SP time              0.25                 
subtour              151.0                connectivity cuts    31.0                 
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            13.0                 SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       120                  
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—22—8—26—31—28—3—36—35—20—2—29—21—16—50—34—30—9—49—10—39—33—45—15—44—42—19—40—41—13—25—14—24—43—7—23—48—6—27—51—46—12—47—18—4—17—37—5—38—11—32—52

RING
1  --- 22 | cost [21.0]
1  --- 52 | cost [0.0]
2  --- 20 | cost [36.0]
2  --- 29 | cost [27.0]
3  --- 28 | cost [27.0]
3  --- 36 | cost [36.0]
4  --- 17 | cost [24.0]
4  --- 18 | cost [24.0]
5  --- 37 | cost [33.0]
5  --- 38 | cost [21.0]
6  --- 27 | cost [27.0]
6  --- 48 | cost [27.0]
7  --- 23 | cost [18.0]
7  --- 43 | cost [36.0]
8  --- 22 | cost [36.0]
8  --- 26 | cost [21.0]
9  --- 30 | cost [24.0]
9  --- 49 | cost [18.0]
10 --- 39 | cost [30.0]
10 --- 49 | cost [24.0]
11 --- 32 | cost [18.0]
11 --- 38 | cost [21.0]
12 --- 46 | cost [21.0]
12 --- 47 | cost [18.0]
13 --- 25 | cost [39.0]
13 --- 41 | cost [27.0]
14 --- 24 | cost [33.0]
14 --- 25 | cost [18.0]
15 --- 44 | cost [18.0]
15 --- 45 | cost [21.0]
16 --- 21 | cost [30.0]
16 --- 50 | cost [18.0]
17 --- 37 | cost [15.0]
18 --- 47 | cost [24.0]
19 --- 40 | cost [33.0]
19 --- 42 | cost [27.0]
20 --- 35 | cost [21.0]
21 --- 29 | cost [21.0]
23 --- 48 | cost [27.0]
24 --- 43 | cost [36.0]
26 --- 31 | cost [30.0]
27 --- 51 | cost [24.0]
28 --- 31 | cost [18.0]
30 --- 34 | cost [21.0]
32 --- 52 | cost [18.0]
33 --- 39 | cost [42.0]
33 --- 45 | cost [21.0]
34 --- 50 | cost [18.0]
35 --- 36 | cost [18.0]
40 --- 41 | cost [36.0]
42 --- 44 | cost [30.0]
46 --- 51 | cost [6.0]

STAR

BACKUP RING
1  ---  8 | cost [0.36]
2  --- 21 | cost [0.45]
2  --- 35 | cost [0.5700000000000001]
3  --- 31 | cost [0.48]
3  --- 35 | cost [0.3]
4  --- 37 | cost [0.39]
4  --- 47 | cost [0.24]
5  --- 11 | cost [0.33]
5  --- 17 | cost [0.45]
6  --- 23 | cost [0.33]
6  --- 51 | cost [0.33]
7  --- 24 | cost [0.42]
7  --- 48 | cost [0.33]
8  --- 31 | cost [0.27]
9  --- 10 | cost [0.36]
9  --- 34 | cost [0.27]
10 --- 33 | cost [0.36]
11 --- 52 | cost [0.36]
12 --- 18 | cost [0.42]
12 --- 51 | cost [0.24]
13 --- 14 | cost [0.54]
13 --- 40 | cost [0.5700000000000001]
14 --- 43 | cost [0.6900000000000001]
15 --- 33 | cost [0.36]
15 --- 42 | cost [0.48]
16 --- 29 | cost [0.27]
16 --- 34 | cost [0.36]
17 --- 18 | cost [0.42]
19 --- 41 | cost [0.15]
19 --- 44 | cost [0.51]
20 --- 29 | cost [0.3]
20 --- 36 | cost [0.39]
21 --- 50 | cost [0.24]
22 --- 26 | cost [0.5700000000000001]
23 --- 43 | cost [0.39]
24 --- 25 | cost [0.42]
25 --- 41 | cost [0.63]
26 --- 28 | cost [0.48]
27 --- 46 | cost [0.27]
27 --- 48 | cost [0.27]
28 --- 36 | cost [0.6]
30 --- 49 | cost [0.3]
30 --- 50 | cost [0.3]
32 --- 38 | cost [0.39]
37 --- 38 | cost [0.54]
39 --- 45 | cost [0.63]
39 --- 49 | cost [0.51]
40 --- 42 | cost [0.48]
44 --- 45 | cost [0.3]
46 --- 47 | cost [0.3]

BACKUP STAR

B = 0.6900000000000001
i★ = 14
j★ = 24
k★ = 43

       
——————— Sun, 07 Jan 2024 09:17:33 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 52 hubs —— 1—22—8—26—31—28—3—36—35—20—2—29—21—16—50—34—30—9—49—10—39—33—45—15—44—42—19—40—41—13—25—14—24—43—7—23—48—6—27—51—46—12—47—18—4—17—37—5—38—11—32—52
total time           43.32                gap                  0.0                  
blossom time         0.07                 nb blossom           4.0                  
LB <= UB             1299.39<=1299.39     subtour              146.0                
connectivity cuts    8.0                  uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—22—8—26—31—28—3—36—35—20—2—29—21—16—50—34—30—9—49—10—39—33—45—15—44—42—19—40—41—13—25—14—24—43—7—23—48—6—27—51—46—12—47—18—4—17—37—5—38—11—32—52

RING
1  --- 22 | cost [21.0]
1  --- 52 | cost [0.0]
2  --- 20 | cost [36.0]
2  --- 29 | cost [27.0]
3  --- 28 | cost [27.0]
3  --- 36 | cost [36.0]
4  --- 17 | cost [24.0]
4  --- 18 | cost [24.0]
5  --- 37 | cost [33.0]
5  --- 38 | cost [21.0]
6  --- 27 | cost [27.0]
6  --- 48 | cost [27.0]
7  --- 23 | cost [18.0]
7  --- 43 | cost [36.0]
8  --- 22 | cost [36.0]
8  --- 26 | cost [21.0]
9  --- 30 | cost [24.0]
9  --- 49 | cost [18.0]
10 --- 39 | cost [30.0]
10 --- 49 | cost [24.0]
11 --- 32 | cost [18.0]
11 --- 38 | cost [21.0]
12 --- 46 | cost [21.0]
12 --- 47 | cost [18.0]
13 --- 25 | cost [39.0]
13 --- 41 | cost [27.0]
14 --- 24 | cost [33.0]
14 --- 25 | cost [18.0]
15 --- 44 | cost [18.0]
15 --- 45 | cost [21.0]
16 --- 21 | cost [30.0]
16 --- 50 | cost [18.0]
17 --- 37 | cost [15.0]
18 --- 47 | cost [24.0]
19 --- 40 | cost [33.0]
19 --- 42 | cost [27.0]
20 --- 35 | cost [21.0]
21 --- 29 | cost [21.0]
23 --- 48 | cost [27.0]
24 --- 43 | cost [36.0]
26 --- 31 | cost [30.0]
27 --- 51 | cost [24.0]
28 --- 31 | cost [18.0]
30 --- 34 | cost [21.0]
32 --- 52 | cost [18.0]
33 --- 39 | cost [42.0]
33 --- 45 | cost [21.0]
34 --- 50 | cost [18.0]
35 --- 36 | cost [18.0]
40 --- 41 | cost [36.0]
42 --- 44 | cost [30.0]
46 --- 51 | cost [6.0]

STAR

BACKUP RING
1  ---  8 | cost [0.36]
2  --- 21 | cost [0.45]
2  --- 35 | cost [0.5700000000000001]
3  --- 31 | cost [0.48]
3  --- 35 | cost [0.3]
4  --- 37 | cost [0.39]
4  --- 47 | cost [0.24]
5  --- 11 | cost [0.33]
5  --- 17 | cost [0.45]
6  --- 23 | cost [0.33]
6  --- 51 | cost [0.33]
7  --- 24 | cost [0.42]
7  --- 48 | cost [0.33]
8  --- 31 | cost [0.27]
9  --- 10 | cost [0.36]
9  --- 34 | cost [0.27]
10 --- 33 | cost [0.36]
11 --- 52 | cost [0.36]
12 --- 18 | cost [0.42]
12 --- 51 | cost [0.24]
13 --- 14 | cost [0.54]
13 --- 40 | cost [0.5700000000000001]
14 --- 43 | cost [0.6900000000000001]
15 --- 33 | cost [0.36]
15 --- 42 | cost [0.48]
16 --- 29 | cost [0.27]
16 --- 34 | cost [0.36]
17 --- 18 | cost [0.42]
19 --- 41 | cost [0.15]
19 --- 44 | cost [0.51]
20 --- 29 | cost [0.3]
20 --- 36 | cost [0.39]
21 --- 50 | cost [0.24]
22 --- 26 | cost [0.5700000000000001]
23 --- 43 | cost [0.39]
24 --- 25 | cost [0.42]
25 --- 41 | cost [0.63]
26 --- 28 | cost [0.48]
27 --- 46 | cost [0.27]
27 --- 48 | cost [0.27]
28 --- 36 | cost [0.6]
30 --- 49 | cost [0.3]
30 --- 50 | cost [0.3]
32 --- 38 | cost [0.39]
37 --- 38 | cost [0.54]
39 --- 45 | cost [0.63]
39 --- 49 | cost [0.51]
40 --- 42 | cost [0.48]
44 --- 45 | cost [0.3]
46 --- 47 | cost [0.3]

BACKUP STAR

B = 0.6900000000000001
i★ = 14
j★ = 24
k★ = 43

       
——————— Sun, 07 Jan 2024 09:18:15 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 52 hubs —— 1-22-8-26-31-28-3-36-35-20-2-29-21-16-50-34-30-9-49-10-39-33-45-15-44-42-19-40-41-13-25-14-24-43-7-23-48-6-27-51-46-12-47-18-4-17-37-5-38-11-32-52-1
total time           9.46                 gap                  0.0                  
blossom time         0.99                 nb blossom           49.0                 
LB <= UB             1299.39<=1299.39     Master/SP costs      1278/21.39           
Master time          9.15                 SP time              0.31                 
subtour              111.0                connectivity cuts    30.0                 
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            14.0                 SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       102                  
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—22—8—26—31—28—3—36—35—20—2—29—21—16—50—34—30—9—49—10—39—33—45—15—44—42—19—40—41—13—25—14—24—43—7—23—48—6—27—51—46—12—47—18—4—17—37—5—38—11—32—52

RING
1  --- 22 | cost [21.0]
1  --- 52 | cost [0.0]
2  --- 20 | cost [36.0]
2  --- 29 | cost [27.0]
3  --- 28 | cost [27.0]
3  --- 36 | cost [36.0]
4  --- 17 | cost [24.0]
4  --- 18 | cost [24.0]
5  --- 37 | cost [33.0]
5  --- 38 | cost [21.0]
6  --- 27 | cost [27.0]
6  --- 48 | cost [27.0]
7  --- 23 | cost [18.0]
7  --- 43 | cost [36.0]
8  --- 22 | cost [36.0]
8  --- 26 | cost [21.0]
9  --- 30 | cost [24.0]
9  --- 49 | cost [18.0]
10 --- 39 | cost [30.0]
10 --- 49 | cost [24.0]
11 --- 32 | cost [18.0]
11 --- 38 | cost [21.0]
12 --- 46 | cost [21.0]
12 --- 47 | cost [18.0]
13 --- 25 | cost [39.0]
13 --- 41 | cost [27.0]
14 --- 24 | cost [33.0]
14 --- 25 | cost [18.0]
15 --- 44 | cost [18.0]
15 --- 45 | cost [21.0]
16 --- 21 | cost [30.0]
16 --- 50 | cost [18.0]
17 --- 37 | cost [15.0]
18 --- 47 | cost [24.0]
19 --- 40 | cost [33.0]
19 --- 42 | cost [27.0]
20 --- 35 | cost [21.0]
21 --- 29 | cost [21.0]
23 --- 48 | cost [27.0]
24 --- 43 | cost [36.0]
26 --- 31 | cost [30.0]
27 --- 51 | cost [24.0]
28 --- 31 | cost [18.0]
30 --- 34 | cost [21.0]
32 --- 52 | cost [18.0]
33 --- 39 | cost [42.0]
33 --- 45 | cost [21.0]
34 --- 50 | cost [18.0]
35 --- 36 | cost [18.0]
40 --- 41 | cost [36.0]
42 --- 44 | cost [30.0]
46 --- 51 | cost [6.0]

STAR

BACKUP RING
1  ---  8 | cost [0.36]
2  --- 21 | cost [0.45]
2  --- 35 | cost [0.5700000000000001]
3  --- 31 | cost [0.48]
3  --- 35 | cost [0.3]
4  --- 37 | cost [0.39]
4  --- 47 | cost [0.24]
5  --- 11 | cost [0.33]
5  --- 17 | cost [0.45]
6  --- 23 | cost [0.33]
6  --- 51 | cost [0.33]
7  --- 24 | cost [0.42]
7  --- 48 | cost [0.33]
8  --- 31 | cost [0.27]
9  --- 10 | cost [0.36]
9  --- 34 | cost [0.27]
10 --- 33 | cost [0.36]
11 --- 52 | cost [0.36]
12 --- 18 | cost [0.42]
12 --- 51 | cost [0.24]
13 --- 14 | cost [0.54]
13 --- 40 | cost [0.5700000000000001]
14 --- 43 | cost [0.6900000000000001]
15 --- 33 | cost [0.36]
15 --- 42 | cost [0.48]
16 --- 29 | cost [0.27]
16 --- 34 | cost [0.36]
17 --- 18 | cost [0.42]
19 --- 41 | cost [0.15]
19 --- 44 | cost [0.51]
20 --- 29 | cost [0.3]
20 --- 36 | cost [0.39]
21 --- 50 | cost [0.24]
22 --- 26 | cost [0.5700000000000001]
23 --- 43 | cost [0.39]
24 --- 25 | cost [0.42]
25 --- 41 | cost [0.63]
26 --- 28 | cost [0.48]
27 --- 46 | cost [0.27]
27 --- 48 | cost [0.27]
28 --- 36 | cost [0.6]
30 --- 49 | cost [0.3]
30 --- 50 | cost [0.3]
32 --- 38 | cost [0.39]
37 --- 38 | cost [0.54]
39 --- 45 | cost [0.63]
39 --- 49 | cost [0.51]
40 --- 42 | cost [0.48]
44 --- 45 | cost [0.3]
46 --- 47 | cost [0.3]

BACKUP STAR

B = 0.6900000000000001
i★ = 14
j★ = 24
k★ = 43