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

——————— Sun, 28 Jan 2024 21:50:27 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 43 hubs —— 1—32—11—38—9—49—10—30—34—50—16—2—29—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           753.06               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2243.75<=2243.75     subtour              108.0                
connectivity cuts    616.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       4582                 n lazycuts edges     1.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—32—11—38—9—49—10—30—34—50—16—2—29—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  --- 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]
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  --> 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]
43 -->  7 | cost [60.0]

BACKUP RING
1  --- 11 | cost [0.6]
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]
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]
51 --- 52 | cost [0.7000000000000001]

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]
43 --> 24 | cost [0.6]

B = 1.25
i★ = 41
j★ = 19
k★ = 42

       
——————— Sun, 28 Jan 2024 22:51:03 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 43 hubs —— 1-32-11-38-9-49-10-30-34-50-16-2-29-20-35-3-28-31-26-8-48-7-23-24-14-25-13-41-19-42-44-45-15-37-17-4-18-47-12-46-51-27-52-1
total time           3603.33 (TL 3600)    gap                  0.031                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2173.79<=2243.75     Master/SP costs      2015/228.75          
Master time          3594.07              SP time              9.26                 
subtour              10181.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            760.0                SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       318838               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—32—11—38—9—49—10—30—34—50—16—2—29—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  --- 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]
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]
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  --- 11 | cost [0.6]
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]
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]
51 --- 52 | cost [0.7000000000000001]

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

       
——————— Mon, 04 Mar 2024 11:17:40 ————————— 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           685.35               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2243.75<=2243.75     subtour              83.0                 
connectivity cuts    781.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       5807                 n lazycuts edges     2.0                  
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  --> 27 | 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  --> 48 | 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

       
——————— Mon, 04 Mar 2024 11:39:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 43 hubs —— 1-32-11-38-9-49-10-30-34-50-16-2-29-20-35-3-28-31-26-8-48-7-23-24-14-25-13-41-19-42-44-45-15-37-17-4-18-47-12-46-51-27-52-1
total time           1286.56              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2243.75<=2243.75     Master/SP costs      2015/228.75          
Master time          1279.03              SP time              7.53                 
subtour              4968.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            467.0                SP method            poly                 
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       247392               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—32—11—38—9—49—10—30—34—50—16—2—29—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  --- 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]
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]
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  --- 11 | cost [0.6]
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]
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]
51 --- 52 | cost [0.7000000000000001]

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

       
——————— Thu, 11 Apr 2024 10:40:37 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
       
——————— Sat, 13 Apr 2024 11:38:51 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false