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

——————— Sat, 06 Jan 2024 12:11:08 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 39 hubs —— 1—32—11—38—9—49—10—30—34—50—21—29—20—35—3—28—31—8—48—23—24—14—25—13—41—19—42—44—45—15—37—17—4—47—12—46—51—27—52
total time           39.89                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2039.95<=2039.95     subtour              61.0                 
connectivity cuts    31.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       47                   n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—32—11—38—9—49—10—30—34—50—21—29—20—35—3—28—31—8—48—23—24—14—25—13—41—19—42—44—45—15—37—17—4—47—12—46—51—27—52

RING
1  --- 32 | cost [30.0]
1  --- 52 | cost [0.0]
3  --- 28 | cost [45.0]
3  --- 35 | cost [50.0]
4  --- 17 | cost [40.0]
4  --- 47 | cost [40.0]
8  --- 31 | cost [45.0]
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]
19 --- 41 | cost [25.0]
19 --- 42 | cost [45.0]
20 --- 29 | cost [50.0]
20 --- 35 | cost [35.0]
21 --- 29 | cost [35.0]
21 --- 50 | cost [40.0]
23 --- 24 | cost [45.0]
23 --- 48 | cost [45.0]
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
2  --> 29 | cost [45.0]
5  --> 38 | cost [35.0]
6  --> 48 | cost [45.0]
7  --> 23 | cost [30.0]
16 --> 50 | cost [30.0]
18 --> 47 | cost [40.0]
22 -->  1 | cost [35.0]
26 -->  8 | cost [35.0]
33 --> 45 | cost [35.0]
36 --> 35 | cost [30.0]
39 --> 10 | cost [50.0]
40 --> 19 | cost [55.0]
43 --> 24 | cost [60.0]

BACKUP RING
1  --- 11 | cost [0.6]
3  --- 20 | cost [0.4]
3  --- 31 | cost [0.8]
4  --- 12 | cost [0.65]
4  --- 37 | cost [0.65]
8  --- 23 | cost [0.8]
8  --- 28 | cost [0.65]
9  --- 10 | cost [0.6]
9  --- 11 | cost [0.65]
10 --- 34 | cost [0.8]
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 --- 47 | cost [0.45]
19 --- 44 | cost [0.85]
20 --- 21 | cost [0.85]
21 --- 34 | cost [0.45]
24 --- 25 | cost [0.7000000000000001]
24 --- 48 | cost [0.85]
25 --- 41 | cost [1.05]
27 --- 46 | cost [0.45]
28 --- 35 | cost [0.9500000000000001]
29 --- 35 | cost [0.8]
29 --- 50 | cost [0.55]
30 --- 49 | cost [0.5]
30 --- 50 | cost [0.5]
31 --- 48 | cost [0.9]
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
2  --> 11 | cost [0.55]
5  --> 49 | cost [0.4]
6  --> 27 | cost [0.45]
7  --> 48 | cost [0.55]
16 -->  9 | cost [0.4]
18 -->  4 | cost [0.4]
26 --> 31 | cost [0.5]
33 --> 10 | cost [0.6]
36 -->  3 | cost [0.6]
39 --> 30 | cost [0.6]
40 --> 41 | cost [0.6]
43 --> 23 | cost [0.65]

B = 1.4500000000000002
i★ = 14
j★ = 24
k★ = 23

       
——————— Sat, 06 Jan 2024 12:11:52 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 40 hubs —— 1-32-11-38-9-49-10-30-34-50-21-29-20-35-3-28-31-8-48-23-24-14-25-13-41-19-42-44-45-15-37-17-4-18-47-12-46-51-27-52-1
total time           16                   gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2039.95<=2039.95     Master/SP costs      1995/44.95           
Master time          15.64                SP time              0.36                 
subtour              811.0                connectivity cuts    1295.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            21.0                 SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       2290                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—32—11—38—9—49—10—30—34—50—21—29—20—35—3—28—31—8—48—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]
3  --- 28 | cost [45.0]
3  --- 35 | cost [50.0]
4  --- 17 | cost [40.0]
4  --- 18 | cost [40.0]
8  --- 31 | cost [45.0]
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 --- 29 | cost [50.0]
20 --- 35 | cost [35.0]
21 --- 29 | cost [35.0]
21 --- 50 | cost [40.0]
23 --- 24 | cost [45.0]
23 --- 48 | cost [45.0]
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
2  --> 29 | cost [45.0]
5  --> 38 | cost [35.0]
6  --> 27 | cost [45.0]
7  --> 23 | cost [30.0]
16 --> 50 | cost [30.0]
22 -->  1 | cost [35.0]
26 -->  8 | cost [35.0]
33 --> 45 | cost [35.0]
36 --> 35 | cost [30.0]
39 --> 10 | cost [50.0]
40 --> 19 | cost [55.0]
43 --> 24 | cost [60.0]

BACKUP RING
1  --- 11 | cost [0.6]
3  --- 20 | cost [0.4]
3  --- 31 | cost [0.8]
4  --- 37 | cost [0.65]
4  --- 47 | cost [0.4]
8  --- 23 | cost [0.8]
8  --- 28 | cost [0.65]
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 --- 21 | cost [0.85]
21 --- 34 | cost [0.45]
24 --- 25 | cost [0.7000000000000001]
24 --- 48 | cost [0.85]
25 --- 41 | cost [1.05]
27 --- 46 | cost [0.45]
28 --- 35 | cost [0.9500000000000001]
29 --- 35 | cost [0.8]
29 --- 50 | cost [0.55]
30 --- 49 | cost [0.5]
30 --- 50 | cost [0.5]
31 --- 48 | cost [0.9]
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
2  --> 11 | cost [0.55]
5  --> 49 | cost [0.4]
6  --> 48 | cost [0.45]
7  --> 48 | cost [0.55]
16 -->  9 | cost [0.4]
26 --> 31 | cost [0.5]
33 --> 10 | cost [0.6]
36 -->  3 | cost [0.6]
39 --> 30 | cost [0.6]
40 --> 41 | cost [0.6]
43 --> 23 | cost [0.65]

B = 1.4500000000000002
i★ = 14
j★ = 24
k★ = 23

       
——————— Sun, 07 Jan 2024 09:19:31 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 39 hubs —— 1—27—51—46—12—47—4—17—37—15—45—44—42—19—41—13—25—14—24—23—48—8—31—28—3—35—20—29—21—50—34—30—10—49—9—38—11—32—52
total time           47.46                gap                  0.0                  
blossom time         0.22                 nb blossom           38.0                 
LB <= UB             2039.95<=2039.95     subtour              61.0                 
connectivity cuts    27.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       63                   n lazycuts edges     0.0                  
F                    31.0                 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—48—8—31—28—3—35—20—29—21—50—34—30—10—49—9—38—11—32—52

RING
1  --- 27 | cost [40.0]
1  --- 52 | cost [0.0]
3  --- 28 | cost [45.0]
3  --- 35 | cost [50.0]
4  --- 17 | cost [40.0]
4  --- 47 | cost [40.0]
8  --- 31 | cost [45.0]
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]
19 --- 41 | cost [25.0]
19 --- 42 | cost [45.0]
20 --- 29 | cost [50.0]
20 --- 35 | cost [35.0]
21 --- 29 | cost [35.0]
21 --- 50 | cost [40.0]
23 --- 24 | cost [45.0]
23 --- 48 | cost [45.0]
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
2  --> 29 | cost [45.0]
5  --> 38 | cost [35.0]
6  --> 48 | cost [45.0]
7  --> 23 | cost [30.0]
16 --> 50 | cost [30.0]
18 -->  4 | cost [40.0]
22 -->  1 | cost [35.0]
26 -->  8 | cost [35.0]
33 --> 45 | cost [35.0]
36 --> 35 | cost [30.0]
39 --> 10 | cost [50.0]
40 --> 19 | cost [55.0]
43 --> 24 | cost [60.0]

BACKUP RING
1  --- 51 | cost [0.7000000000000001]
3  --- 20 | cost [0.4]
3  --- 31 | cost [0.8]
4  --- 12 | cost [0.65]
4  --- 37 | cost [0.65]
8  --- 23 | cost [0.8]
8  --- 28 | cost [0.65]
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]
17 --- 47 | cost [0.45]
19 --- 44 | cost [0.85]
20 --- 21 | cost [0.85]
21 --- 34 | cost [0.45]
24 --- 25 | cost [0.7000000000000001]
24 --- 48 | cost [0.85]
25 --- 41 | cost [1.05]
27 --- 46 | cost [0.45]
28 --- 35 | cost [0.9500000000000001]
29 --- 35 | cost [0.8]
29 --- 50 | cost [0.55]
30 --- 49 | cost [0.5]
30 --- 50 | cost [0.5]
31 --- 48 | cost [0.9]
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
2  --> 11 | cost [0.55]
5  --> 49 | cost [0.4]
6  --> 27 | cost [0.45]
7  --> 48 | cost [0.55]
16 -->  9 | cost [0.4]
18 --> 47 | cost [0.4]
26 --> 31 | cost [0.5]
33 --> 10 | cost [0.6]
36 -->  3 | cost [0.6]
39 --> 30 | cost [0.6]
40 --> 41 | cost [0.6]
43 --> 23 | cost [0.65]

B = 1.4500000000000002
i★ = 14
j★ = 24
k★ = 23

       
——————— Sun, 07 Jan 2024 09:20:26 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 40 hubs —— 1-32-11-38-9-49-10-30-34-50-21-29-20-35-3-28-31-8-48-23-24-14-25-13-41-19-42-44-45-15-37-17-4-18-47-12-46-51-27-52-1
total time           22.06                gap                  0.0                  
blossom time         1.87                 nb blossom           302.0                
LB <= UB             2039.95<=2039.95     Master/SP costs      1995/44.95           
Master time          21.65                SP time              0.41                 
subtour              633.0                connectivity cuts    1262.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            23.0                 SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       2362                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—32—11—38—9—49—10—30—34—50—21—29—20—35—3—28—31—8—48—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]
3  --- 28 | cost [45.0]
3  --- 35 | cost [50.0]
4  --- 17 | cost [40.0]
4  --- 18 | cost [40.0]
8  --- 31 | cost [45.0]
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 --- 29 | cost [50.0]
20 --- 35 | cost [35.0]
21 --- 29 | cost [35.0]
21 --- 50 | cost [40.0]
23 --- 24 | cost [45.0]
23 --- 48 | cost [45.0]
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
2  --> 29 | cost [45.0]
5  --> 38 | cost [35.0]
6  --> 27 | cost [45.0]
7  --> 23 | cost [30.0]
16 --> 50 | cost [30.0]
22 -->  1 | cost [35.0]
26 -->  8 | cost [35.0]
33 --> 45 | cost [35.0]
36 --> 35 | cost [30.0]
39 --> 10 | cost [50.0]
40 --> 19 | cost [55.0]
43 --> 24 | cost [60.0]

BACKUP RING
1  --- 11 | cost [0.6]
3  --- 20 | cost [0.4]
3  --- 31 | cost [0.8]
4  --- 37 | cost [0.65]
4  --- 47 | cost [0.4]
8  --- 23 | cost [0.8]
8  --- 28 | cost [0.65]
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 --- 21 | cost [0.85]
21 --- 34 | cost [0.45]
24 --- 25 | cost [0.7000000000000001]
24 --- 48 | cost [0.85]
25 --- 41 | cost [1.05]
27 --- 46 | cost [0.45]
28 --- 35 | cost [0.9500000000000001]
29 --- 35 | cost [0.8]
29 --- 50 | cost [0.55]
30 --- 49 | cost [0.5]
30 --- 50 | cost [0.5]
31 --- 48 | cost [0.9]
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
2  --> 11 | cost [0.55]
5  --> 49 | cost [0.4]
6  --> 48 | cost [0.45]
7  --> 48 | cost [0.55]
16 -->  9 | cost [0.4]
26 --> 31 | cost [0.5]
33 --> 10 | cost [0.6]
36 -->  3 | cost [0.6]
39 --> 30 | cost [0.6]
40 --> 41 | cost [0.6]
43 --> 23 | cost [0.65]

B = 1.4500000000000002
i★ = 14
j★ = 24
k★ = 23