------------------------------------------------------------
                           α=5.0 —— eil51 —— 51 nodes       
------------------------------------------------------------

——————— Sat, 06 Jan 2024 14:44:07 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 42 hubs —— 1—27—51—46—12—47—4—17—37—15—45—44—42—19—41—13—25—14—24—23—7—48—8—26—31—28—3—35—20—29—2—16—50—34—30—10—49—9—38—11—32—52
total time           1215.47              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2243.75<=2243.75     subtour              157.0                
connectivity cuts    1379.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       4193                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—27—51—46—12—47—4—17—37—15—45—44—42—19—41—13—25—14—24—23—7—48—8—26—31—28—3—35—20—29—2—16—50—34—30—10—49—9—38—11—32—52

RING
1  --- 27 | cost [40.0]
1  --- 52 | cost [0.0]
2  --- 16 | cost [45.0]
2  --- 29 | cost [45.0]
3  --- 28 | cost [45.0]
3  --- 35 | cost [50.0]
4  --- 17 | cost [40.0]
4  --- 47 | cost [40.0]
7  --- 23 | cost [30.0]
7  --- 48 | cost [55.0]
8  --- 26 | cost [35.0]
8  --- 48 | cost [45.0]
9  --- 38 | cost [35.0]
9  --- 49 | cost [30.0]
10 --- 30 | cost [45.0]
10 --- 49 | cost [40.0]
11 --- 32 | cost [30.0]
11 --- 38 | cost [35.0]
12 --- 46 | cost [35.0]
12 --- 47 | cost [30.0]
13 --- 25 | cost [65.0]
13 --- 41 | cost [45.0]
14 --- 24 | cost [55.0]
14 --- 25 | cost [30.0]
15 --- 37 | cost [35.0]
15 --- 45 | cost [35.0]
16 --- 50 | cost [30.0]
17 --- 37 | cost [25.0]
19 --- 41 | cost [25.0]
19 --- 42 | cost [45.0]
20 --- 29 | cost [50.0]
20 --- 35 | cost [35.0]
23 --- 24 | cost [45.0]
26 --- 31 | cost [50.0]
27 --- 51 | cost [40.0]
28 --- 31 | cost [30.0]
30 --- 34 | cost [35.0]
32 --- 52 | cost [30.0]
34 --- 50 | cost [30.0]
42 --- 44 | cost [50.0]
44 --- 45 | cost [50.0]
46 --- 51 | cost [10.0]

STAR
5  --> 38 | cost [35.0]
6  --> 48 | cost [45.0]
18 -->  4 | cost [40.0]
21 --> 29 | cost [35.0]
22 -->  1 | cost [35.0]
33 --> 45 | cost [35.0]
36 --> 35 | cost [30.0]
39 --> 10 | cost [50.0]
40 --> 19 | cost [55.0]
43 -->  7 | cost [60.0]

BACKUP RING
1  --- 51 | cost [0.7000000000000001]
2  --- 20 | cost [0.6]
2  --- 50 | cost [0.7000000000000001]
3  --- 20 | cost [0.4]
3  --- 31 | cost [0.8]
4  --- 12 | cost [0.65]
4  --- 37 | cost [0.65]
7  ---  8 | cost [0.7000000000000001]
7  --- 24 | cost [0.7000000000000001]
8  --- 31 | cost [0.45]
9  --- 10 | cost [0.6]
9  --- 11 | cost [0.65]
10 --- 34 | cost [0.8]
11 --- 52 | cost [0.6]
12 --- 51 | cost [0.4]
13 --- 14 | cost [0.9]
13 --- 19 | cost [0.7000000000000001]
14 --- 23 | cost [0.8]
15 --- 17 | cost [0.55]
15 --- 44 | cost [0.3]
16 --- 29 | cost [0.45]
16 --- 34 | cost [0.6]
17 --- 47 | cost [0.45]
19 --- 44 | cost [0.85]
23 --- 48 | cost [0.45]
24 --- 25 | cost [0.7000000000000001]
25 --- 41 | cost [1.05]
26 --- 28 | cost [0.8]
26 --- 48 | cost [0.65]
27 --- 46 | cost [0.45]
28 --- 35 | cost [0.9500000000000001]
29 --- 35 | cost [0.8]
30 --- 49 | cost [0.5]
30 --- 50 | cost [0.5]
32 --- 38 | cost [0.65]
37 --- 45 | cost [0.7000000000000001]
38 --- 49 | cost [0.4]
41 --- 42 | cost [0.65]
42 --- 45 | cost [0.9]
46 --- 47 | cost [0.5]

BACKUP STAR
5  --> 49 | cost [0.4]
6  --> 27 | cost [0.45]
18 --> 47 | cost [0.4]
21 --> 50 | cost [0.4]
33 --> 10 | cost [0.6]
36 -->  3 | cost [0.6]
39 --> 30 | cost [0.6]
40 --> 41 | cost [0.6]
43 --> 24 | cost [0.6]

B = 1.25
i★ = 41
j★ = 19
k★ = 42

       
——————— Sat, 06 Jan 2024 15:44:38 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 43 hubs —— 1-27-51-46-12-47-18-4-17-37-15-45-44-42-19-41-13-25-14-24-23-7-48-8-26-31-28-3-35-20-29-2-16-50-34-30-10-49-9-38-11-32-52-1
total time           3603.0 (TL 3600)     gap                  0.043                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2147.92<=2243.75     Master/SP costs      2015/228.75          
Master time          3595.07              SP time              7.93                 
subtour              11209.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            906.0                SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       188786               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—27—51—46—12—47—18—4—17—37—15—45—44—42—19—41—13—25—14—24—23—7—48—8—26—31—28—3—35—20—29—2—16—50—34—30—10—49—9—38—11—32—52

RING
1  --- 27 | cost [40.0]
1  --- 52 | cost [0.0]
2  --- 16 | cost [45.0]
2  --- 29 | cost [45.0]
3  --- 28 | cost [45.0]
3  --- 35 | cost [50.0]
4  --- 17 | cost [40.0]
4  --- 18 | cost [40.0]
7  --- 23 | cost [30.0]
7  --- 48 | cost [55.0]
8  --- 26 | cost [35.0]
8  --- 48 | cost [45.0]
9  --- 38 | cost [35.0]
9  --- 49 | cost [30.0]
10 --- 30 | cost [45.0]
10 --- 49 | cost [40.0]
11 --- 32 | cost [30.0]
11 --- 38 | cost [35.0]
12 --- 46 | cost [35.0]
12 --- 47 | cost [30.0]
13 --- 25 | cost [65.0]
13 --- 41 | cost [45.0]
14 --- 24 | cost [55.0]
14 --- 25 | cost [30.0]
15 --- 37 | cost [35.0]
15 --- 45 | cost [35.0]
16 --- 50 | cost [30.0]
17 --- 37 | cost [25.0]
18 --- 47 | cost [40.0]
19 --- 41 | cost [25.0]
19 --- 42 | cost [45.0]
20 --- 29 | cost [50.0]
20 --- 35 | cost [35.0]
23 --- 24 | cost [45.0]
26 --- 31 | cost [50.0]
27 --- 51 | cost [40.0]
28 --- 31 | cost [30.0]
30 --- 34 | cost [35.0]
32 --- 52 | cost [30.0]
34 --- 50 | cost [30.0]
42 --- 44 | cost [50.0]
44 --- 45 | cost [50.0]
46 --- 51 | cost [10.0]

STAR
5  --> 38 | cost [35.0]
6  --> 27 | cost [45.0]
21 --> 29 | cost [35.0]
22 -->  1 | cost [35.0]
33 --> 45 | cost [35.0]
36 --> 35 | cost [30.0]
39 --> 10 | cost [50.0]
40 --> 19 | cost [55.0]
43 -->  7 | cost [60.0]

BACKUP RING
1  --- 51 | cost [0.7000000000000001]
2  --- 20 | cost [0.6]
2  --- 50 | cost [0.7000000000000001]
3  --- 20 | cost [0.4]
3  --- 31 | cost [0.8]
4  --- 37 | cost [0.65]
4  --- 47 | cost [0.4]
7  ---  8 | cost [0.7000000000000001]
7  --- 24 | cost [0.7000000000000001]
8  --- 31 | cost [0.45]
9  --- 10 | cost [0.6]
9  --- 11 | cost [0.65]
10 --- 34 | cost [0.8]
11 --- 52 | cost [0.6]
12 --- 18 | cost [0.7000000000000001]
12 --- 51 | cost [0.4]
13 --- 14 | cost [0.9]
13 --- 19 | cost [0.7000000000000001]
14 --- 23 | cost [0.8]
15 --- 17 | cost [0.55]
15 --- 44 | cost [0.3]
16 --- 29 | cost [0.45]
16 --- 34 | cost [0.6]
17 --- 18 | cost [0.7000000000000001]
19 --- 44 | cost [0.85]
23 --- 48 | cost [0.45]
24 --- 25 | cost [0.7000000000000001]
25 --- 41 | cost [1.05]
26 --- 28 | cost [0.8]
26 --- 48 | cost [0.65]
27 --- 46 | cost [0.45]
28 --- 35 | cost [0.9500000000000001]
29 --- 35 | cost [0.8]
30 --- 49 | cost [0.5]
30 --- 50 | cost [0.5]
32 --- 38 | cost [0.65]
37 --- 45 | cost [0.7000000000000001]
38 --- 49 | cost [0.4]
41 --- 42 | cost [0.65]
42 --- 45 | cost [0.9]
46 --- 47 | cost [0.5]

BACKUP STAR
5  --> 49 | cost [0.4]
6  --> 48 | cost [0.45]
21 --> 50 | cost [0.4]
33 --> 10 | cost [0.6]
36 -->  3 | cost [0.6]
39 --> 30 | cost [0.6]
40 --> 41 | cost [0.6]
43 --> 24 | cost [0.6]

B = 1.25
i★ = 41
j★ = 19
k★ = 42

       
——————— Sun, 07 Jan 2024 12:00:25 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 43 hubs —— 1—32—11—38—9—49—10—30—34—50—21—29—2—20—35—3—28—31—26—8—48—7—23—24—14—25—13—41—19—42—44—45—15—37—17—4—18—47—12—46—51—27—52
total time           436.54               gap                  0.0                  
blossom time         1.58                 nb blossom           330.0                
LB <= UB             2248.75<=2248.75     subtour              102.0                
connectivity cuts    445.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       966                  n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—32—11—38—9—49—10—30—34—50—21—29—2—20—35—3—28—31—26—8—48—7—23—24—14—25—13—41—19—42—44—45—15—37—17—4—18—47—12—46—51—27—52

RING
1  --- 32 | cost [30.0]
1  --- 52 | cost [0.0]
2  --- 20 | cost [60.0]
2  --- 29 | cost [45.0]
3  --- 28 | cost [45.0]
3  --- 35 | cost [50.0]
4  --- 17 | cost [40.0]
4  --- 18 | cost [40.0]
7  --- 23 | cost [30.0]
7  --- 48 | cost [55.0]
8  --- 26 | cost [35.0]
8  --- 48 | cost [45.0]
9  --- 38 | cost [35.0]
9  --- 49 | cost [30.0]
10 --- 30 | cost [45.0]
10 --- 49 | cost [40.0]
11 --- 32 | cost [30.0]
11 --- 38 | cost [35.0]
12 --- 46 | cost [35.0]
12 --- 47 | cost [30.0]
13 --- 25 | cost [65.0]
13 --- 41 | cost [45.0]
14 --- 24 | cost [55.0]
14 --- 25 | cost [30.0]
15 --- 37 | cost [35.0]
15 --- 45 | cost [35.0]
17 --- 37 | cost [25.0]
18 --- 47 | cost [40.0]
19 --- 41 | cost [25.0]
19 --- 42 | cost [45.0]
20 --- 35 | cost [35.0]
21 --- 29 | cost [35.0]
21 --- 50 | cost [40.0]
23 --- 24 | cost [45.0]
26 --- 31 | cost [50.0]
27 --- 51 | cost [40.0]
27 --- 52 | cost [40.0]
28 --- 31 | cost [30.0]
30 --- 34 | cost [35.0]
34 --- 50 | cost [30.0]
42 --- 44 | cost [50.0]
44 --- 45 | cost [50.0]
46 --- 51 | cost [10.0]

STAR
5  --> 38 | cost [35.0]
6  --> 27 | cost [45.0]
16 --> 50 | cost [30.0]
22 -->  1 | cost [35.0]
33 --> 45 | cost [35.0]
36 --> 35 | cost [30.0]
39 --> 10 | cost [50.0]
40 --> 19 | cost [55.0]
43 -->  7 | cost [60.0]

BACKUP RING
1  --- 11 | cost [0.6]
2  --- 21 | cost [0.75]
2  --- 35 | cost [0.9500000000000001]
3  --- 20 | cost [0.4]
3  --- 31 | cost [0.8]
4  --- 37 | cost [0.65]
4  --- 47 | cost [0.4]
7  ---  8 | cost [0.7000000000000001]
7  --- 24 | cost [0.7000000000000001]
8  --- 31 | cost [0.45]
9  --- 10 | cost [0.6]
9  --- 11 | cost [0.65]
10 --- 34 | cost [0.8]
12 --- 18 | cost [0.7000000000000001]
12 --- 51 | cost [0.4]
13 --- 14 | cost [0.9]
13 --- 19 | cost [0.7000000000000001]
14 --- 23 | cost [0.8]
15 --- 17 | cost [0.55]
15 --- 44 | cost [0.3]
17 --- 18 | cost [0.7000000000000001]
19 --- 44 | cost [0.85]
20 --- 29 | cost [0.5]
21 --- 34 | cost [0.45]
23 --- 48 | cost [0.45]
24 --- 25 | cost [0.7000000000000001]
25 --- 41 | cost [1.05]
26 --- 28 | cost [0.8]
26 --- 48 | cost [0.65]
27 --- 46 | cost [0.45]
28 --- 35 | cost [0.9500000000000001]
29 --- 50 | cost [0.55]
30 --- 49 | cost [0.5]
30 --- 50 | cost [0.5]
32 --- 38 | cost [0.65]
37 --- 45 | cost [0.7000000000000001]
38 --- 49 | cost [0.4]
41 --- 42 | cost [0.65]
42 --- 45 | cost [0.9]
46 --- 47 | cost [0.5]
51 --- 52 | cost [0.7000000000000001]

BACKUP STAR
5  --> 49 | cost [0.4]
6  --> 48 | cost [0.45]
16 -->  9 | cost [0.4]
33 --> 10 | cost [0.6]
36 -->  3 | cost [0.6]
39 --> 30 | cost [0.6]
40 --> 41 | cost [0.6]
43 --> 24 | cost [0.6]

B = 1.25
i★ = 41
j★ = 19
k★ = 42

       
——————— Sun, 07 Jan 2024 13:01:02 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 43 hubs —— 1-27-46-12-47-18-4-17-37-15-45-44-42-19-41-13-25-14-24-43-7-23-48-8-26-31-28-3-35-20-29-2-16-50-34-30-10-49-9-38-11-32-52-1
total time           3604.54 (TL 3600)    gap                  0.052                
blossom time         396.83               nb blossom           92908.0              
LB <= UB             2136.49<=2253.75     Master/SP costs      2025/228.75          
Master time          3595.82              SP time              8.72                 
subtour              11670.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            851.0                SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       113818               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—27—46—12—47—18—4—17—37—15—45—44—42—19—41—13—25—14—24—43—7—23—48—8—26—31—28—3—35—20—29—2—16—50—34—30—10—49—9—38—11—32—52

RING
1  --- 27 | cost [40.0]
1  --- 52 | cost [0.0]
2  --- 16 | cost [45.0]
2  --- 29 | cost [45.0]
3  --- 28 | cost [45.0]
3  --- 35 | cost [50.0]
4  --- 17 | cost [40.0]
4  --- 18 | cost [40.0]
7  --- 23 | cost [30.0]
7  --- 43 | cost [60.0]
8  --- 26 | cost [35.0]
8  --- 48 | cost [45.0]
9  --- 38 | cost [35.0]
9  --- 49 | cost [30.0]
10 --- 30 | cost [45.0]
10 --- 49 | cost [40.0]
11 --- 32 | cost [30.0]
11 --- 38 | cost [35.0]
12 --- 46 | cost [35.0]
12 --- 47 | cost [30.0]
13 --- 25 | cost [65.0]
13 --- 41 | cost [45.0]
14 --- 24 | cost [55.0]
14 --- 25 | cost [30.0]
15 --- 37 | cost [35.0]
15 --- 45 | cost [35.0]
16 --- 50 | cost [30.0]
17 --- 37 | cost [25.0]
18 --- 47 | cost [40.0]
19 --- 41 | cost [25.0]
19 --- 42 | cost [45.0]
20 --- 29 | cost [50.0]
20 --- 35 | cost [35.0]
23 --- 48 | cost [45.0]
24 --- 43 | cost [60.0]
26 --- 31 | cost [50.0]
27 --- 46 | cost [45.0]
28 --- 31 | cost [30.0]
30 --- 34 | cost [35.0]
32 --- 52 | cost [30.0]
34 --- 50 | cost [30.0]
42 --- 44 | cost [50.0]
44 --- 45 | cost [50.0]

STAR
5  --> 38 | cost [35.0]
6  --> 48 | cost [45.0]
21 --> 29 | cost [35.0]
22 -->  1 | cost [35.0]
33 --> 45 | cost [35.0]
36 --> 35 | cost [30.0]
39 --> 10 | cost [50.0]
40 --> 19 | cost [55.0]
51 --> 46 | cost [10.0]

BACKUP RING
1  --- 46 | cost [0.7000000000000001]
2  --- 20 | cost [0.6]
2  --- 50 | cost [0.7000000000000001]
3  --- 20 | cost [0.4]
3  --- 31 | cost [0.8]
4  --- 37 | cost [0.65]
4  --- 47 | cost [0.4]
7  --- 24 | cost [0.7000000000000001]
7  --- 48 | cost [0.55]
8  --- 23 | cost [0.8]
8  --- 31 | cost [0.45]
9  --- 10 | cost [0.6]
9  --- 11 | cost [0.65]
10 --- 34 | cost [0.8]
11 --- 52 | cost [0.6]
12 --- 18 | cost [0.7000000000000001]
12 --- 27 | cost [0.8]
13 --- 14 | cost [0.9]
13 --- 19 | cost [0.7000000000000001]
14 --- 43 | cost [1.1500000000000001]
15 --- 17 | cost [0.55]
15 --- 44 | cost [0.3]
16 --- 29 | cost [0.45]
16 --- 34 | cost [0.6]
17 --- 18 | cost [0.7000000000000001]
19 --- 44 | cost [0.85]
23 --- 43 | cost [0.65]
24 --- 25 | cost [0.7000000000000001]
25 --- 41 | cost [1.05]
26 --- 28 | cost [0.8]
26 --- 48 | cost [0.65]
28 --- 35 | cost [0.9500000000000001]
29 --- 35 | cost [0.8]
30 --- 49 | cost [0.5]
30 --- 50 | cost [0.5]
32 --- 38 | cost [0.65]
37 --- 45 | cost [0.7000000000000001]
38 --- 49 | cost [0.4]
41 --- 42 | cost [0.65]
42 --- 45 | cost [0.9]
46 --- 47 | cost [0.5]

BACKUP STAR
5  --> 49 | cost [0.4]
6  --> 27 | cost [0.45]
21 --> 50 | cost [0.4]
33 --> 10 | cost [0.6]
36 -->  3 | cost [0.6]
39 --> 30 | cost [0.6]
40 --> 41 | cost [0.6]
51 --> 12 | cost [0.4]

B = 1.25
i★ = 41
j★ = 19
k★ = 42