<body><meta charset="utf-8"></body><pre>------------------------------------------------------------
                           α=3.0 —— eil51 —— 51 nodes       
------------------------------------------------------------
ILP ——— 52 hubs —— 1—32—11—38—5—49—9—30—10—39—33—45—15—37—17—44—42—19—40—41—13—25—14—18—4—47—12—46—51—27—6—48—23—24—43—7—26—8—31—28—3—36—35—20—29—21—34—50—16—2—22—52
total time           108.03               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1401.78<=1401.78     subtour              59.0                 
connectivity cuts    98.0                 uc strategy          true                 
uc tolerance         0.01                 tildeV               2:51                 
2-opt strategy       0                                                              
explored_nodes       357                  n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                    r_ij                 Euclidian()
          s_ij                 Euclidian()
                                                    <details><summary>Found solution</summary>
RING NODES
1—32—11—38—5—49—9—30—10—39—33—45—15—37—17—44—42—19—40—41—13—25—14—18—4—47—12—46—51—27—6—48—23—24—43—7—26—8—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  --- 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  --- 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 --- 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]
22 --- 52 | 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]
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  --- 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  --- 10 | cost [0.36]
10 --- 33 | 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 --- 34 | cost [0.36]
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 --- 50 | cost [0.24]
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 --- 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 = 0.66
i★ = 26
j★ = 7
k★ = 43
</details>
BD  —— 52 hubs —— 1-32-11-38-5-49-9-30-10-39-33-45-15-37-17-44-42-19-40-41-13-25-14-18-4-47-12-46-51-27-6-48-23-24-43-7-26-8-31-28-3-36-35-20-29-21-34-50-16-2-22-52-1
total time           103.88               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             1401.78<=1401.78     Master/SP costs      1281.0/120.78        
Master time          101.0                SP time              2.88                 
subtour              3154.0               connectivity cuts    2000.0               
uc strategy          true                 uc tolerance         0.01                 
opt. cuts            265.0                SP method            Poly()               
tildeV               2:51                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       10486                
F                    183.0                
                                          o_i                  0                    r_ij                 Euclidian()          
s_ij                 Euclidian()          
<details><summary>Found solution</summary>
RING NODES
1—32—11—38—5—49—9—30—10—39—33—45—15—37—17—44—42—19—40—41—13—25—14—18—4—47—12—46—51—27—6—48—23—24—43—7—26—8—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  --- 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  --- 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 --- 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]
22 --- 52 | 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]
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  --- 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  --- 10 | cost [0.36]
10 --- 33 | 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 --- 34 | cost [0.36]
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 --- 50 | cost [0.24]
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 --- 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 = 0.66
i★ = 26
j★ = 7
k★ = 43
</details>
</details>
</pre>