------------------------------------------------------------
                            α=5.0 —— st70 —— 70 nodes       
------------------------------------------------------------

——————— Wed, 24 Jan 2024 15:10:20 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 59 hubs —— 1—23—47—37—58—50—5—10—52—60—51—65—56—67—48—54—33—12—34—21—17—9—40—61—39—45—46—27—68—44—30—20—14—28—49—26—8—3—32—42—18—4—2—7—19—24—15—57—63—22—59—38—69—31—70—13—29—36—71
total time           394.04               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3122.67<=3122.95     subtour              113.0                
connectivity cuts    70.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:70                 
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     3.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—23—47—37—58—50—5—10—52—60—51—65—56—67—48—54—33—12—34—21—17—9—40—61—39—45—46—27—68—44—30—20—14—28—49—26—8—3—32—42—18—4—2—7—19—24—15—57—63—22—59—38—69—31—70—13—29—36—71

RING
1  --- 23 | cost [45.0]
1  --- 71 | cost [0.0]
2  ---  4 | cost [45.0]
2  ---  7 | cost [25.0]
3  ---  8 | cost [60.0]
3  --- 32 | cost [30.0]
4  --- 18 | cost [20.0]
5  --- 10 | cost [30.0]
5  --- 50 | cost [55.0]
7  --- 19 | cost [55.0]
8  --- 26 | cost [40.0]
9  --- 17 | cost [80.0]
9  --- 40 | cost [55.0]
10 --- 52 | cost [30.0]
12 --- 33 | cost [50.0]
12 --- 34 | cost [40.0]
13 --- 29 | cost [10.0]
13 --- 70 | cost [30.0]
14 --- 20 | cost [35.0]
14 --- 28 | cost [70.0]
15 --- 24 | cost [20.0]
15 --- 57 | cost [35.0]
17 --- 21 | cost [70.0]
18 --- 42 | cost [30.0]
19 --- 24 | cost [100.0]
20 --- 30 | cost [35.0]
21 --- 34 | cost [5.0]
22 --- 59 | cost [30.0]
22 --- 63 | cost [20.0]
23 --- 47 | cost [45.0]
26 --- 49 | cost [45.0]
27 --- 46 | cost [30.0]
27 --- 68 | cost [105.0]
28 --- 49 | cost [70.0]
29 --- 36 | cost [60.0]
30 --- 44 | cost [75.0]
31 --- 69 | cost [10.0]
31 --- 70 | cost [30.0]
32 --- 42 | cost [65.0]
33 --- 54 | cost [50.0]
36 --- 71 | cost [20.0]
37 --- 47 | cost [50.0]
37 --- 58 | cost [5.0]
38 --- 59 | cost [40.0]
38 --- 69 | cost [45.0]
39 --- 45 | cost [35.0]
39 --- 61 | cost [45.0]
40 --- 61 | cost [25.0]
44 --- 68 | cost [20.0]
45 --- 46 | cost [75.0]
48 --- 54 | cost [65.0]
48 --- 67 | cost [25.0]
50 --- 58 | cost [45.0]
51 --- 60 | cost [80.0]
51 --- 65 | cost [50.0]
52 --- 60 | cost [45.0]
56 --- 65 | cost [40.0]
56 --- 67 | cost [40.0]
57 --- 63 | cost [70.0]

STAR
6  --> 42 | cost [45.0]
11 --> 56 | cost [45.0]
16 --> 47 | cost [30.0]
25 --> 45 | cost [40.0]
35 --> 69 | cost [60.0]
41 --> 42 | cost [45.0]
43 --> 17 | cost [20.0]
53 -->  5 | cost [45.0]
55 --> 49 | cost [40.0]
62 --> 54 | cost [55.0]
64 --> 65 | cost [100.0]
66 --> 22 | cost [30.0]

BACKUP RING
1  --- 47 | cost [0.65]
2  --- 18 | cost [0.6]
2  --- 19 | cost [0.65]
3  --- 26 | cost [0.9500000000000001]
3  --- 42 | cost [0.7000000000000001]
4  ---  7 | cost [0.6]
4  --- 42 | cost [0.55]
5  --- 52 | cost [0.55]
5  --- 58 | cost [0.75]
7  --- 24 | cost [1.1500000000000001]
8  --- 32 | cost [0.65]
8  --- 49 | cost [0.7000000000000001]
9  --- 21 | cost [1.0]
9  --- 61 | cost [0.65]
10 --- 50 | cost [0.45]
10 --- 60 | cost [0.75]
12 --- 21 | cost [0.4]
12 --- 54 | cost [0.9500000000000001]
13 --- 31 | cost [0.3]
13 --- 36 | cost [0.65]
14 --- 30 | cost [0.5]
14 --- 49 | cost [1.3]
15 --- 19 | cost [1.1500000000000001]
15 --- 63 | cost [1.05]
17 --- 34 | cost [0.75]
17 --- 40 | cost [1.3]
18 --- 32 | cost [0.65]
20 --- 28 | cost [0.9500000000000001]
20 --- 44 | cost [1.0]
22 --- 38 | cost [0.4]
22 --- 57 | cost [0.9]
23 --- 37 | cost [1.0]
24 --- 57 | cost [0.35000000000000003]
26 --- 28 | cost [0.55]
27 --- 44 | cost [1.2]
27 --- 45 | cost [0.9]
29 --- 70 | cost [0.3]
29 --- 71 | cost [0.7000000000000001]
30 --- 68 | cost [0.85]
31 --- 38 | cost [0.5]
33 --- 34 | cost [0.7000000000000001]
33 --- 48 | cost [0.9500000000000001]
37 --- 50 | cost [0.5]
39 --- 40 | cost [0.6]
39 --- 46 | cost [1.1]
45 --- 61 | cost [0.5]
46 --- 68 | cost [1.35]
47 --- 58 | cost [0.5]
48 --- 56 | cost [0.65]
51 --- 52 | cost [0.85]
51 --- 56 | cost [0.45]
54 --- 67 | cost [0.65]
59 --- 63 | cost [0.3]
59 --- 69 | cost [0.5]
60 --- 65 | cost [1.25]
65 --- 67 | cost [0.8]
69 --- 70 | cost [0.4]

BACKUP STAR
6  --> 18 | cost [0.5]
11 --> 48 | cost [0.45]
16 -->  1 | cost [0.45]
25 --> 39 | cost [0.55]
35 --> 31 | cost [0.65]
41 --> 17 | cost [0.7000000000000001]
43 --> 68 | cost [0.75]
53 --> 10 | cost [0.75]
55 --> 26 | cost [0.8]
62 --> 33 | cost [0.9]
64 --> 56 | cost [1.35]
66 --> 63 | cost [0.3]

B = 1.85
i★ = 18
j★ = 42
k★ = 32

       
——————— Wed, 24 Jan 2024 15:11:53 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 56 hubs —— 1-16-47-37-58-50-5-10-52-60-51-65-56-67-48-54-33-12-21-17-9-40-61-39-45-46-27-68-44-30-20-14-28-49-26-8-3-32-42-18-4-2-7-19-24-57-63-22-59-38-69-31-70-13-23-71-1
total time           54.42                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3122.95<=3122.95     Master/SP costs      3110/12.95           
Master time          53.7                 SP time              0.73                 
subtour              1155.0               connectivity cuts    1680.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            9.0                  SP method            poly                 
tildeV               2:70                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1772                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—16—47—37—58—50—5—10—52—60—51—65—56—67—48—54—33—12—21—17—9—40—61—39—45—46—27—68—44—30—20—14—28—49—26—8—3—32—42—18—4—2—7—19—24—57—63—22—59—38—69—31—70—13—23—71

RING
1  --- 16 | cost [45.0]
1  --- 71 | cost [0.0]
2  ---  4 | cost [45.0]
2  ---  7 | cost [25.0]
3  ---  8 | cost [60.0]
3  --- 32 | cost [30.0]
4  --- 18 | cost [20.0]
5  --- 10 | cost [30.0]
5  --- 50 | cost [55.0]
7  --- 19 | cost [55.0]
8  --- 26 | cost [40.0]
9  --- 17 | cost [80.0]
9  --- 40 | cost [55.0]
10 --- 52 | cost [30.0]
12 --- 21 | cost [40.0]
12 --- 33 | cost [50.0]
13 --- 23 | cost [60.0]
13 --- 70 | cost [30.0]
14 --- 20 | cost [35.0]
14 --- 28 | cost [70.0]
16 --- 47 | cost [30.0]
17 --- 21 | cost [70.0]
18 --- 42 | cost [30.0]
19 --- 24 | cost [100.0]
20 --- 30 | cost [35.0]
22 --- 59 | cost [30.0]
22 --- 63 | cost [20.0]
23 --- 71 | cost [45.0]
24 --- 57 | cost [35.0]
26 --- 49 | cost [45.0]
27 --- 46 | cost [30.0]
27 --- 68 | cost [105.0]
28 --- 49 | cost [70.0]
30 --- 44 | cost [75.0]
31 --- 69 | cost [10.0]
31 --- 70 | cost [30.0]
32 --- 42 | cost [65.0]
33 --- 54 | cost [50.0]
37 --- 47 | cost [50.0]
37 --- 58 | cost [5.0]
38 --- 59 | cost [40.0]
38 --- 69 | cost [45.0]
39 --- 45 | cost [35.0]
39 --- 61 | cost [45.0]
40 --- 61 | cost [25.0]
44 --- 68 | cost [20.0]
45 --- 46 | cost [75.0]
48 --- 54 | cost [65.0]
48 --- 67 | cost [25.0]
50 --- 58 | cost [45.0]
51 --- 60 | cost [80.0]
51 --- 65 | cost [50.0]
52 --- 60 | cost [45.0]
56 --- 65 | cost [40.0]
56 --- 67 | cost [40.0]
57 --- 63 | cost [70.0]

STAR
6  --> 42 | cost [45.0]
11 --> 56 | cost [45.0]
15 --> 24 | cost [20.0]
25 --> 45 | cost [40.0]
29 --> 13 | cost [10.0]
34 --> 21 | cost [5.0]
35 --> 69 | cost [60.0]
36 -->  1 | cost [20.0]
41 --> 42 | cost [45.0]
43 --> 17 | cost [20.0]
53 -->  5 | cost [45.0]
55 --> 49 | cost [40.0]
62 --> 54 | cost [55.0]
64 --> 65 | cost [100.0]
66 --> 63 | cost [30.0]

BACKUP RING
1  --- 47 | cost [0.65]
2  --- 18 | cost [0.6]
2  --- 19 | cost [0.65]
3  --- 26 | cost [0.9500000000000001]
3  --- 42 | cost [0.7000000000000001]
4  ---  7 | cost [0.6]
4  --- 42 | cost [0.55]
5  --- 52 | cost [0.55]
5  --- 58 | cost [0.75]
7  --- 24 | cost [1.1500000000000001]
8  --- 32 | cost [0.65]
8  --- 49 | cost [0.7000000000000001]
9  --- 21 | cost [1.0]
9  --- 61 | cost [0.65]
10 --- 50 | cost [0.45]
10 --- 60 | cost [0.75]
12 --- 17 | cost [0.9500000000000001]
12 --- 54 | cost [0.9500000000000001]
13 --- 31 | cost [0.3]
13 --- 71 | cost [0.75]
14 --- 30 | cost [0.5]
14 --- 49 | cost [1.3]
16 --- 37 | cost [0.6]
17 --- 40 | cost [1.3]
18 --- 32 | cost [0.65]
19 --- 57 | cost [1.3]
20 --- 28 | cost [0.9500000000000001]
20 --- 44 | cost [1.0]
21 --- 33 | cost [0.7000000000000001]
22 --- 38 | cost [0.4]
22 --- 57 | cost [0.9]
23 --- 70 | cost [0.9]
24 --- 63 | cost [1.05]
26 --- 28 | cost [0.55]
27 --- 44 | cost [1.2]
27 --- 45 | cost [0.9]
30 --- 68 | cost [0.85]
31 --- 38 | cost [0.5]
33 --- 48 | cost [0.9500000000000001]
37 --- 50 | cost [0.5]
39 --- 40 | cost [0.6]
39 --- 46 | cost [1.1]
45 --- 61 | cost [0.5]
46 --- 68 | cost [1.35]
47 --- 58 | cost [0.5]
48 --- 56 | cost [0.65]
51 --- 52 | cost [0.85]
51 --- 56 | cost [0.45]
54 --- 67 | cost [0.65]
59 --- 63 | cost [0.3]
59 --- 69 | cost [0.5]
60 --- 65 | cost [1.25]
65 --- 67 | cost [0.8]
69 --- 70 | cost [0.4]

BACKUP STAR
6  --> 18 | cost [0.5]
11 --> 48 | cost [0.45]
15 --> 57 | cost [0.35000000000000003]
25 --> 39 | cost [0.55]
29 --> 70 | cost [0.3]
34 --> 12 | cost [0.4]
35 --> 31 | cost [0.65]
41 --> 17 | cost [0.7000000000000001]
43 --> 68 | cost [0.75]
53 --> 10 | cost [0.75]
55 --> 26 | cost [0.8]
62 --> 33 | cost [0.9]
64 --> 56 | cost [1.35]
66 --> 22 | cost [0.3]

B = 1.85
i★ = 18
j★ = 42
k★ = 32