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

——————— Sat, 06 Jan 2024 14:21:11 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 52 hubs —— 1—22—2—16—50—9—30—34—21—29—20—35—36—3—28—31—8—26—7—43—24—23—48—6—27—51—46—12—47—4—18—14—25—13—41—40—19—42—44—17—37—15—45—33—39—10—49—5—38—11—32—52
total time           81.62                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1401.78<=1401.78     subtour              88.0                 
connectivity cuts    140.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       565                  n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—22—2—16—50—9—30—34—21—29—20—35—36—3—28—31—8—26—7—43—24—23—48—6—27—51—46—12—47—4—18—14—25—13—41—40—19—42—44—17—37—15—45—33—39—10—49—5—38—11—32—52

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

STAR

BACKUP RING
1  ---  2 | cost [0.36]
2  --- 50 | cost [0.42]
3  --- 31 | cost [0.48]
3  --- 35 | cost [0.3]
4  --- 12 | cost [0.39]
4  --- 14 | cost [0.54]
5  --- 10 | cost [0.42]
5  --- 11 | cost [0.33]
6  --- 23 | cost [0.33]
6  --- 51 | cost [0.33]
7  ---  8 | cost [0.42]
7  --- 24 | cost [0.42]
8  --- 28 | cost [0.39]
9  --- 16 | cost [0.24]
9  --- 34 | cost [0.27]
10 --- 33 | cost [0.36]
11 --- 52 | cost [0.36]
12 --- 51 | cost [0.24]
13 --- 14 | cost [0.54]
13 --- 40 | cost [0.5700000000000001]
15 --- 17 | cost [0.33]
15 --- 33 | cost [0.36]
16 --- 22 | cost [0.5700000000000001]
17 --- 42 | cost [0.42]
18 --- 25 | cost [0.33]
18 --- 47 | cost [0.24]
19 --- 41 | cost [0.15]
19 --- 44 | cost [0.51]
20 --- 21 | cost [0.51]
20 --- 36 | cost [0.39]
21 --- 30 | cost [0.48]
23 --- 43 | cost [0.39]
24 --- 48 | cost [0.51]
25 --- 41 | cost [0.63]
26 --- 31 | cost [0.3]
26 --- 43 | cost [0.66]
27 --- 46 | cost [0.27]
27 --- 48 | cost [0.27]
28 --- 36 | cost [0.6]
29 --- 34 | cost [0.45]
29 --- 35 | cost [0.48]
30 --- 50 | cost [0.3]
32 --- 38 | cost [0.39]
37 --- 44 | cost [0.21]
37 --- 45 | cost [0.42]
38 --- 49 | cost [0.24]
39 --- 45 | cost [0.63]
39 --- 49 | cost [0.51]
40 --- 42 | cost [0.48]
46 --- 47 | cost [0.3]

BACKUP STAR

B = 0.66
i★ = 26
j★ = 7
k★ = 43

       
——————— Sat, 06 Jan 2024 14:23:27 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 52 hubs —— 1-22-2-16-21-29-20-35-36-3-28-31-8-26-7-43-24-23-48-6-27-51-46-12-47-4-18-14-25-13-41-40-19-42-44-17-37-15-45-33-39-10-30-34-50-9-49-5-38-11-32-52-1
total time           108.28               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1401.78<=1401.78     Master/SP costs      1281/120.78          
Master time          105.89               SP time              2.38                 
subtour              3218.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            260.0                SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       17125                
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—22—2—16—21—29—20—35—36—3—28—31—8—26—7—43—24—23—48—6—27—51—46—12—47—4—18—14—25—13—41—40—19—42—44—17—37—15—45—33—39—10—30—34—50—9—49—5—38—11—32—52

RING
1  --- 22 | cost [21.0]
1  --- 52 | cost [0.0]
2  --- 16 | cost [27.0]
2  --- 22 | cost [33.0]
3  --- 28 | cost [27.0]
3  --- 36 | cost [36.0]
4  --- 18 | cost [24.0]
4  --- 47 | cost [24.0]
5  --- 38 | cost [21.0]
5  --- 49 | cost [24.0]
6  --- 27 | cost [27.0]
6  --- 48 | cost [27.0]
7  --- 26 | cost [33.0]
7  --- 43 | cost [36.0]
8  --- 26 | cost [21.0]
8  --- 31 | cost [27.0]
9  --- 49 | cost [18.0]
9  --- 50 | cost [18.0]
10 --- 30 | cost [27.0]
10 --- 39 | cost [30.0]
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 --- 18 | cost [30.0]
14 --- 25 | cost [18.0]
15 --- 37 | cost [21.0]
15 --- 45 | cost [21.0]
16 --- 21 | cost [30.0]
17 --- 37 | cost [15.0]
17 --- 44 | cost [27.0]
19 --- 40 | cost [33.0]
19 --- 42 | cost [27.0]
20 --- 29 | cost [30.0]
20 --- 35 | cost [21.0]
21 --- 29 | cost [21.0]
23 --- 24 | cost [27.0]
23 --- 48 | cost [27.0]
24 --- 43 | cost [36.0]
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  ---  2 | cost [0.36]
2  --- 21 | cost [0.45]
3  --- 31 | cost [0.48]
3  --- 35 | cost [0.3]
4  --- 12 | cost [0.39]
4  --- 14 | cost [0.54]
5  ---  9 | cost [0.36]
5  --- 11 | cost [0.33]
6  --- 23 | cost [0.33]
6  --- 51 | cost [0.33]
7  ---  8 | cost [0.42]
7  --- 24 | cost [0.42]
8  --- 28 | cost [0.39]
9  --- 34 | cost [0.27]
10 --- 33 | cost [0.36]
10 --- 34 | cost [0.48]
11 --- 52 | cost [0.36]
12 --- 51 | cost [0.24]
13 --- 14 | cost [0.54]
13 --- 40 | cost [0.5700000000000001]
15 --- 17 | cost [0.33]
15 --- 33 | cost [0.36]
16 --- 22 | cost [0.5700000000000001]
16 --- 29 | cost [0.27]
17 --- 42 | cost [0.42]
18 --- 25 | cost [0.33]
18 --- 47 | cost [0.24]
19 --- 41 | cost [0.15]
19 --- 44 | cost [0.51]
20 --- 21 | cost [0.51]
20 --- 36 | cost [0.39]
23 --- 43 | cost [0.39]
24 --- 48 | cost [0.51]
25 --- 41 | cost [0.63]
26 --- 31 | cost [0.3]
26 --- 43 | cost [0.66]
27 --- 46 | cost [0.27]
27 --- 48 | cost [0.27]
28 --- 36 | cost [0.6]
29 --- 35 | cost [0.48]
30 --- 39 | cost [0.36]
30 --- 50 | cost [0.3]
32 --- 38 | cost [0.39]
37 --- 44 | cost [0.21]
37 --- 45 | cost [0.42]
38 --- 49 | cost [0.24]
39 --- 45 | cost [0.63]
40 --- 42 | cost [0.48]
46 --- 47 | cost [0.3]
49 --- 50 | cost [0.36]

BACKUP STAR

B = 0.66
i★ = 26
j★ = 7
k★ = 43

       
——————— Sun, 07 Jan 2024 11:51:27 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 52 hubs —— 1—32—11—38—5—49—9—30—10—39—33—45—15—37—17—44—42—19—40—41—13—18—4—47—12—46—51—27—6—14—25—24—43—7—23—48—8—26—31—28—3—36—35—20—29—21—34—50—16—2—22—52
total time           71.1                 gap                  0.0                  
blossom time         0.14                 nb blossom           15.0                 
LB <= UB             1429.74<=1429.74     subtour              153.0                
connectivity cuts    12.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—32—11—38—5—49—9—30—10—39—33—45—15—37—17—44—42—19—40—41—13—18—4—47—12—46—51—27—6—14—25—24—43—7—23—48—8—26—31—28—3—36—35—20—29—21—34—50—16—2—22—52

RING
1  --- 32 | cost [18.0]
1  --- 52 | cost [0.0]
2  --- 16 | cost [27.0]
2  --- 22 | cost [33.0]
3  --- 28 | cost [27.0]
3  --- 36 | cost [36.0]
4  --- 18 | cost [24.0]
4  --- 47 | cost [24.0]
5  --- 38 | cost [21.0]
5  --- 49 | cost [24.0]
6  --- 14 | cost [30.0]
6  --- 27 | cost [27.0]
7  --- 23 | cost [18.0]
7  --- 43 | cost [36.0]
8  --- 26 | cost [21.0]
8  --- 48 | cost [27.0]
9  --- 30 | cost [24.0]
9  --- 49 | cost [18.0]
10 --- 30 | cost [27.0]
10 --- 39 | cost [30.0]
11 --- 32 | cost [18.0]
11 --- 38 | cost [21.0]
12 --- 46 | cost [21.0]
12 --- 47 | cost [18.0]
13 --- 18 | cost [42.0]
13 --- 41 | cost [27.0]
14 --- 25 | cost [18.0]
15 --- 37 | cost [21.0]
15 --- 45 | cost [21.0]
16 --- 50 | cost [18.0]
17 --- 37 | cost [15.0]
17 --- 44 | cost [27.0]
19 --- 40 | cost [33.0]
19 --- 42 | cost [27.0]
20 --- 29 | cost [30.0]
20 --- 35 | cost [21.0]
21 --- 29 | cost [21.0]
21 --- 34 | cost [27.0]
22 --- 52 | cost [21.0]
23 --- 48 | cost [27.0]
24 --- 25 | cost [42.0]
24 --- 43 | cost [36.0]
26 --- 31 | cost [30.0]
27 --- 51 | cost [24.0]
28 --- 31 | 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  --- 11 | cost [0.36]
2  --- 50 | cost [0.42]
2  --- 52 | cost [0.36]
3  --- 31 | cost [0.48]
3  --- 35 | cost [0.3]
4  --- 12 | cost [0.39]
4  --- 13 | cost [0.45]
5  ---  9 | cost [0.36]
5  --- 11 | cost [0.33]
6  --- 25 | cost [0.51]
6  --- 51 | cost [0.33]
7  --- 24 | cost [0.42]
7  --- 48 | cost [0.33]
8  --- 23 | cost [0.48]
8  --- 31 | cost [0.27]
9  --- 10 | cost [0.36]
10 --- 33 | cost [0.36]
12 --- 51 | cost [0.24]
13 --- 40 | cost [0.5700000000000001]
14 --- 24 | cost [0.33]
14 --- 27 | cost [0.5700000000000001]
15 --- 17 | cost [0.33]
15 --- 33 | cost [0.36]
16 --- 22 | cost [0.5700000000000001]
16 --- 34 | cost [0.36]
17 --- 42 | cost [0.42]
18 --- 41 | cost [0.51]
18 --- 47 | cost [0.24]
19 --- 41 | cost [0.15]
19 --- 44 | cost [0.51]
20 --- 21 | cost [0.51]
20 --- 36 | cost [0.39]
21 --- 50 | cost [0.24]
23 --- 43 | cost [0.39]
25 --- 43 | cost [0.78]
26 --- 28 | cost [0.48]
26 --- 48 | cost [0.39]
27 --- 46 | cost [0.27]
28 --- 36 | cost [0.6]
29 --- 34 | cost [0.45]
29 --- 35 | cost [0.48]
30 --- 39 | cost [0.36]
30 --- 49 | cost [0.3]
32 --- 38 | cost [0.39]
37 --- 44 | cost [0.21]
37 --- 45 | cost [0.42]
38 --- 49 | cost [0.24]
39 --- 45 | cost [0.63]
40 --- 42 | cost [0.48]
46 --- 47 | cost [0.3]

BACKUP STAR

B = 0.78
i★ = 25
j★ = 24
k★ = 43

       
——————— Sun, 07 Jan 2024 11:52:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 52 hubs —— 1-22-2-16-21-29-20-35-36-3-28-31-8-26-7-43-24-23-48-6-27-51-46-12-47-4-18-14-25-13-41-40-19-42-44-17-37-15-45-33-39-10-30-34-50-9-49-5-38-11-32-52-1
total time           41.22                gap                  0.0                  
blossom time         4.92                 nb blossom           1036.0               
LB <= UB             1401.78<=1401.78     Master/SP costs      1281/120.78          
Master time          39.48                SP time              1.74                 
subtour              1910.0               connectivity cuts    897.0                
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            129.0                SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       2694                 
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—22—2—16—21—29—20—35—36—3—28—31—8—26—7—43—24—23—48—6—27—51—46—12—47—4—18—14—25—13—41—40—19—42—44—17—37—15—45—33—39—10—30—34—50—9—49—5—38—11—32—52

RING
1  --- 22 | cost [21.0]
1  --- 52 | cost [0.0]
2  --- 16 | cost [27.0]
2  --- 22 | cost [33.0]
3  --- 28 | cost [27.0]
3  --- 36 | cost [36.0]
4  --- 18 | cost [24.0]
4  --- 47 | cost [24.0]
5  --- 38 | cost [21.0]
5  --- 49 | cost [24.0]
6  --- 27 | cost [27.0]
6  --- 48 | cost [27.0]
7  --- 26 | cost [33.0]
7  --- 43 | cost [36.0]
8  --- 26 | cost [21.0]
8  --- 31 | cost [27.0]
9  --- 49 | cost [18.0]
9  --- 50 | cost [18.0]
10 --- 30 | cost [27.0]
10 --- 39 | cost [30.0]
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 --- 18 | cost [30.0]
14 --- 25 | cost [18.0]
15 --- 37 | cost [21.0]
15 --- 45 | cost [21.0]
16 --- 21 | cost [30.0]
17 --- 37 | cost [15.0]
17 --- 44 | cost [27.0]
19 --- 40 | cost [33.0]
19 --- 42 | cost [27.0]
20 --- 29 | cost [30.0]
20 --- 35 | cost [21.0]
21 --- 29 | cost [21.0]
23 --- 24 | cost [27.0]
23 --- 48 | cost [27.0]
24 --- 43 | cost [36.0]
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  ---  2 | cost [0.36]
2  --- 21 | cost [0.45]
3  --- 31 | cost [0.48]
3  --- 35 | cost [0.3]
4  --- 12 | cost [0.39]
4  --- 14 | cost [0.54]
5  ---  9 | cost [0.36]
5  --- 11 | cost [0.33]
6  --- 23 | cost [0.33]
6  --- 51 | cost [0.33]
7  ---  8 | cost [0.42]
7  --- 24 | cost [0.42]
8  --- 28 | cost [0.39]
9  --- 34 | cost [0.27]
10 --- 33 | cost [0.36]
10 --- 34 | cost [0.48]
11 --- 52 | cost [0.36]
12 --- 51 | cost [0.24]
13 --- 14 | cost [0.54]
13 --- 40 | cost [0.5700000000000001]
15 --- 17 | cost [0.33]
15 --- 33 | cost [0.36]
16 --- 22 | cost [0.5700000000000001]
16 --- 29 | cost [0.27]
17 --- 42 | cost [0.42]
18 --- 25 | cost [0.33]
18 --- 47 | cost [0.24]
19 --- 41 | cost [0.15]
19 --- 44 | cost [0.51]
20 --- 21 | cost [0.51]
20 --- 36 | cost [0.39]
23 --- 43 | cost [0.39]
24 --- 48 | cost [0.51]
25 --- 41 | cost [0.63]
26 --- 31 | cost [0.3]
26 --- 43 | cost [0.66]
27 --- 46 | cost [0.27]
27 --- 48 | cost [0.27]
28 --- 36 | cost [0.6]
29 --- 35 | cost [0.48]
30 --- 39 | cost [0.36]
30 --- 50 | cost [0.3]
32 --- 38 | cost [0.39]
37 --- 44 | cost [0.21]
37 --- 45 | cost [0.42]
38 --- 49 | cost [0.24]
39 --- 45 | cost [0.63]
40 --- 42 | cost [0.48]
46 --- 47 | cost [0.3]
49 --- 50 | cost [0.36]

BACKUP STAR

B = 0.66
i★ = 26
j★ = 7
k★ = 43