------------------------------------------------------------
                            α=3.0 —— st70 —— 70 nodes       
------------------------------------------------------------

——————— Sat, 27 Jan 2024 10:33:25 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 71 hubs —— 1—36—29—13—70—35—31—69—38—59—22—66—63—57—15—24—19—7—2—4—18—42—32—3—8—26—55—49—28—14—20—30—44—68—27—46—45—25—39—61—40—9—17—43—41—6—53—5—10—52—60—12—34—21—33—62—54—48—67—11—64—65—56—51—50—58—37—47—16—23—71
total time           145.01               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2054.76<=2054.76     subtour              112.0                
connectivity cuts    24.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:70                 
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—36—29—13—70—35—31—69—38—59—22—66—63—57—15—24—19—7—2—4—18—42—32—3—8—26—55—49—28—14—20—30—44—68—27—46—45—25—39—61—40—9—17—43—41—6—53—5—10—52—60—12—34—21—33—62—54—48—67—11—64—65—56—51—50—58—37—47—16—23—71

RING
1  --- 36 | cost [12.0]
1  --- 71 | cost [0.0]
2  ---  4 | cost [27.0]
2  ---  7 | cost [15.0]
3  ---  8 | cost [36.0]
3  --- 32 | cost [18.0]
4  --- 18 | cost [12.0]
5  --- 10 | cost [18.0]
5  --- 53 | cost [27.0]
6  --- 41 | cost [18.0]
6  --- 53 | cost [60.0]
7  --- 19 | cost [33.0]
8  --- 26 | cost [24.0]
9  --- 17 | cost [48.0]
9  --- 40 | cost [33.0]
10 --- 52 | cost [18.0]
11 --- 64 | cost [72.0]
11 --- 67 | cost [27.0]
12 --- 34 | cost [24.0]
12 --- 60 | cost [27.0]
13 --- 29 | cost [6.0]
13 --- 70 | cost [18.0]
14 --- 20 | cost [21.0]
14 --- 28 | cost [42.0]
15 --- 24 | cost [12.0]
15 --- 57 | cost [21.0]
16 --- 23 | cost [30.0]
16 --- 47 | cost [18.0]
17 --- 43 | cost [12.0]
18 --- 42 | cost [18.0]
19 --- 24 | cost [60.0]
20 --- 30 | cost [21.0]
21 --- 33 | cost [42.0]
21 --- 34 | cost [3.0]
22 --- 59 | cost [18.0]
22 --- 66 | cost [18.0]
23 --- 71 | cost [27.0]
25 --- 39 | cost [33.0]
25 --- 45 | cost [24.0]
26 --- 55 | cost [48.0]
27 --- 46 | cost [18.0]
27 --- 68 | cost [63.0]
28 --- 49 | cost [42.0]
29 --- 36 | cost [36.0]
30 --- 44 | cost [45.0]
31 --- 35 | cost [39.0]
31 --- 69 | cost [6.0]
32 --- 42 | cost [39.0]
33 --- 62 | cost [54.0]
35 --- 70 | cost [42.0]
37 --- 47 | cost [30.0]
37 --- 58 | cost [3.0]
38 --- 59 | cost [24.0]
38 --- 69 | cost [27.0]
39 --- 61 | cost [27.0]
40 --- 61 | cost [15.0]
41 --- 43 | cost [33.0]
44 --- 68 | cost [12.0]
45 --- 46 | cost [45.0]
48 --- 54 | cost [39.0]
48 --- 67 | cost [15.0]
49 --- 55 | cost [24.0]
50 --- 51 | cost [48.0]
50 --- 58 | cost [27.0]
51 --- 56 | cost [27.0]
52 --- 60 | cost [27.0]
54 --- 62 | cost [33.0]
56 --- 65 | cost [24.0]
57 --- 63 | cost [42.0]
63 --- 66 | cost [18.0]
64 --- 65 | cost [60.0]

STAR

BACKUP RING
1  --- 29 | cost [0.42]
2  --- 18 | cost [0.36]
2  --- 19 | cost [0.39]
3  --- 26 | cost [0.5700000000000001]
3  --- 42 | cost [0.42]
4  ---  7 | cost [0.36]
4  --- 42 | cost [0.33]
5  ---  6 | cost [0.78]
5  --- 52 | cost [0.33]
6  --- 43 | cost [0.51]
7  --- 24 | cost [0.6900000000000001]
8  --- 32 | cost [0.39]
8  --- 55 | cost [0.63]
9  --- 43 | cost [0.51]
9  --- 61 | cost [0.39]
10 --- 53 | cost [0.45]
10 --- 60 | cost [0.45]
11 --- 48 | cost [0.27]
11 --- 65 | cost [0.36]
12 --- 21 | cost [0.24]
12 --- 52 | cost [0.45]
13 --- 35 | cost [0.54]
13 --- 36 | cost [0.39]
14 --- 30 | cost [0.3]
14 --- 49 | cost [0.78]
15 --- 19 | cost [0.6900000000000001]
15 --- 63 | cost [0.63]
16 --- 37 | cost [0.36]
16 --- 71 | cost [0.27]
17 --- 40 | cost [0.78]
17 --- 41 | cost [0.42]
18 --- 32 | cost [0.39]
20 --- 28 | cost [0.5700000000000001]
20 --- 44 | cost [0.6]
21 --- 62 | cost [0.6900000000000001]
22 --- 38 | cost [0.24]
22 --- 63 | cost [0.12]
23 --- 47 | cost [0.27]
24 --- 57 | cost [0.21]
25 --- 46 | cost [0.5700000000000001]
25 --- 61 | cost [0.54]
26 --- 49 | cost [0.27]
27 --- 44 | cost [0.72]
27 --- 45 | cost [0.54]
28 --- 55 | cost [0.66]
29 --- 70 | cost [0.18]
30 --- 68 | cost [0.51]
31 --- 38 | cost [0.3]
31 --- 70 | cost [0.18]
33 --- 34 | cost [0.42]
33 --- 54 | cost [0.3]
34 --- 60 | cost [0.51]
35 --- 69 | cost [0.36]
37 --- 50 | cost [0.3]
39 --- 40 | cost [0.36]
39 --- 45 | cost [0.21]
41 --- 53 | cost [0.75]
46 --- 68 | cost [0.81]
47 --- 58 | cost [0.3]
48 --- 62 | cost [0.66]
50 --- 56 | cost [0.75]
51 --- 58 | cost [0.72]
51 --- 65 | cost [0.3]
54 --- 67 | cost [0.39]
56 --- 64 | cost [0.81]
57 --- 66 | cost [0.51]
59 --- 66 | cost [0.33]
59 --- 69 | cost [0.3]
64 --- 67 | cost [0.96]

BACKUP STAR

B = 0.96
i★ = 64
j★ = 11
k★ = 67

       
——————— Sat, 27 Jan 2024 10:34:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 71 hubs —— 1-23-16-47-37-58-50-51-56-65-64-11-67-48-54-62-33-34-21-12-60-52-10-5-53-6-41-43-17-9-40-61-39-45-25-46-27-68-44-30-20-14-28-49-55-26-8-3-32-42-18-4-2-7-19-24-15-57-63-66-22-59-38-31-69-35-70-13-29-36-71-1
total time           46.59                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2054.76<=2054.76     Master/SP costs      2025/29.76           
Master time          45.95                SP time              0.65                 
subtour              1637.0               connectivity cuts    1037.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            16.0                 SP method            poly                 
tildeV               2:70                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1073                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—23—16—47—37—58—50—51—56—65—64—11—67—48—54—62—33—34—21—12—60—52—10—5—53—6—41—43—17—9—40—61—39—45—25—46—27—68—44—30—20—14—28—49—55—26—8—3—32—42—18—4—2—7—19—24—15—57—63—66—22—59—38—31—69—35—70—13—29—36—71

RING
1  --- 23 | cost [27.0]
1  --- 71 | cost [0.0]
2  ---  4 | cost [27.0]
2  ---  7 | cost [15.0]
3  ---  8 | cost [36.0]
3  --- 32 | cost [18.0]
4  --- 18 | cost [12.0]
5  --- 10 | cost [18.0]
5  --- 53 | cost [27.0]
6  --- 41 | cost [18.0]
6  --- 53 | cost [60.0]
7  --- 19 | cost [33.0]
8  --- 26 | cost [24.0]
9  --- 17 | cost [48.0]
9  --- 40 | cost [33.0]
10 --- 52 | cost [18.0]
11 --- 64 | cost [72.0]
11 --- 67 | cost [27.0]
12 --- 21 | cost [24.0]
12 --- 60 | cost [27.0]
13 --- 29 | cost [6.0]
13 --- 70 | cost [18.0]
14 --- 20 | cost [21.0]
14 --- 28 | cost [42.0]
15 --- 24 | cost [12.0]
15 --- 57 | cost [21.0]
16 --- 23 | cost [30.0]
16 --- 47 | cost [18.0]
17 --- 43 | cost [12.0]
18 --- 42 | cost [18.0]
19 --- 24 | cost [60.0]
20 --- 30 | cost [21.0]
21 --- 34 | cost [3.0]
22 --- 59 | cost [18.0]
22 --- 66 | cost [18.0]
25 --- 45 | cost [24.0]
25 --- 46 | cost [57.0]
26 --- 55 | cost [48.0]
27 --- 46 | cost [18.0]
27 --- 68 | cost [63.0]
28 --- 49 | cost [42.0]
29 --- 36 | cost [36.0]
30 --- 44 | cost [45.0]
31 --- 38 | cost [30.0]
31 --- 69 | cost [6.0]
32 --- 42 | cost [39.0]
33 --- 34 | cost [42.0]
33 --- 62 | cost [54.0]
35 --- 69 | cost [36.0]
35 --- 70 | cost [42.0]
36 --- 71 | cost [12.0]
37 --- 47 | cost [30.0]
37 --- 58 | cost [3.0]
38 --- 59 | cost [24.0]
39 --- 45 | cost [21.0]
39 --- 61 | cost [27.0]
40 --- 61 | cost [15.0]
41 --- 43 | cost [33.0]
44 --- 68 | cost [12.0]
48 --- 54 | cost [39.0]
48 --- 67 | cost [15.0]
49 --- 55 | cost [24.0]
50 --- 51 | cost [48.0]
50 --- 58 | cost [27.0]
51 --- 56 | cost [27.0]
52 --- 60 | cost [27.0]
54 --- 62 | cost [33.0]
56 --- 65 | cost [24.0]
57 --- 63 | cost [42.0]
63 --- 66 | cost [18.0]
64 --- 65 | cost [60.0]

STAR

BACKUP RING
1  --- 16 | cost [0.27]
2  --- 18 | cost [0.36]
2  --- 19 | cost [0.39]
3  --- 26 | cost [0.5700000000000001]
3  --- 42 | cost [0.42]
4  ---  7 | cost [0.36]
4  --- 42 | cost [0.33]
5  ---  6 | cost [0.78]
5  --- 52 | cost [0.33]
6  --- 43 | cost [0.51]
7  --- 24 | cost [0.6900000000000001]
8  --- 32 | cost [0.39]
8  --- 55 | cost [0.63]
9  --- 43 | cost [0.51]
9  --- 61 | cost [0.39]
10 --- 53 | cost [0.45]
10 --- 60 | cost [0.45]
11 --- 48 | cost [0.27]
11 --- 65 | cost [0.36]
12 --- 34 | cost [0.24]
12 --- 52 | cost [0.45]
13 --- 35 | cost [0.54]
13 --- 36 | cost [0.39]
14 --- 30 | cost [0.3]
14 --- 49 | cost [0.78]
15 --- 19 | cost [0.6900000000000001]
15 --- 63 | cost [0.63]
16 --- 37 | cost [0.36]
17 --- 40 | cost [0.78]
17 --- 41 | cost [0.42]
18 --- 32 | cost [0.39]
20 --- 28 | cost [0.5700000000000001]
20 --- 44 | cost [0.6]
21 --- 33 | cost [0.42]
21 --- 60 | cost [0.51]
22 --- 38 | cost [0.24]
22 --- 63 | cost [0.12]
23 --- 47 | cost [0.27]
24 --- 57 | cost [0.21]
25 --- 27 | cost [0.72]
25 --- 39 | cost [0.33]
26 --- 49 | cost [0.27]
27 --- 44 | cost [0.72]
28 --- 55 | cost [0.66]
29 --- 70 | cost [0.18]
29 --- 71 | cost [0.42]
30 --- 68 | cost [0.51]
31 --- 35 | cost [0.39]
31 --- 59 | cost [0.36]
33 --- 54 | cost [0.3]
34 --- 62 | cost [0.66]
37 --- 50 | cost [0.3]
38 --- 69 | cost [0.27]
39 --- 40 | cost [0.36]
41 --- 53 | cost [0.75]
45 --- 46 | cost [0.45]
45 --- 61 | cost [0.3]
46 --- 68 | cost [0.81]
47 --- 58 | cost [0.3]
48 --- 62 | cost [0.66]
50 --- 56 | cost [0.75]
51 --- 58 | cost [0.72]
51 --- 65 | cost [0.3]
54 --- 67 | cost [0.39]
56 --- 64 | cost [0.81]
57 --- 66 | cost [0.51]
59 --- 66 | cost [0.33]
64 --- 67 | cost [0.96]
69 --- 70 | cost [0.24]

BACKUP STAR

B = 0.96
i★ = 64
j★ = 11
k★ = 67