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

——————— Sat, 06 Jan 2024 11:03:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 57 hubs —— 1—36—29—13—70—31—69—38—59—22—63—57—15—24—19—7—2—4—18—42—32—3—8—26—49—28—14—20—30—44—68—27—46—45—40—9—17—21—34—12—33—54—48—67—56—65—51—60—52—10—5—50—58—37—47—23—71
total time           10.97                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3110<=3110           subtour              541.0                
connectivity cuts    294.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       484                  n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—36—29—13—70—31—69—38—59—22—63—57—15—24—19—7—2—4—18—42—32—3—8—26—49—28—14—20—30—44—68—27—46—45—40—9—17—21—34—12—33—54—48—67—56—65—51—60—52—10—5—50—58—37—47—23—71

RING
1  --- 36 | cost [20.0]
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]
23 --- 71 | 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]
37 --- 47 | cost [50.0]
37 --- 58 | cost [5.0]
38 --- 59 | cost [40.0]
38 --- 69 | cost [45.0]
40 --- 45 | cost [45.0]
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 --> 48 | cost [45.0]
16 --> 47 | cost [30.0]
25 --> 45 | cost [40.0]
35 --> 69 | cost [60.0]
39 --> 45 | cost [35.0]
41 --> 42 | cost [45.0]
43 --> 17 | cost [20.0]
53 -->  5 | cost [45.0]
55 --> 49 | cost [40.0]
61 --> 40 | cost [25.0]
62 --> 54 | cost [55.0]
64 --> 65 | cost [100.0]
66 --> 63 | cost [30.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 06 Jan 2024 11:04:34 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 56 hubs —— 1-23-13-29-70-31-69-38-59-22-63-57-24-19-7-2-4-18-42-32-3-8-26-49-28-14-20-30-44-68-27-46-45-40-9-17-21-34-12-33-54-48-67-56-65-51-60-52-10-5-50-58-37-47-16-71-1
total time           25.91                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3110<=3110           Master/SP costs      3110/0               
Master time          25.91                SP time              0.0                  
subtour              721.0                connectivity cuts    1071.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1073                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—23—13—29—70—31—69—38—59—22—63—57—24—19—7—2—4—18—42—32—3—8—26—49—28—14—20—30—44—68—27—46—45—40—9—17—21—34—12—33—54—48—67—56—65—51—60—52—10—5—50—58—37—47—16—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 --- 23 | cost [60.0]
13 --- 29 | cost [10.0]
14 --- 20 | cost [35.0]
14 --- 28 | cost [70.0]
16 --- 47 | cost [30.0]
16 --- 71 | cost [45.0]
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]
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]
29 --- 70 | cost [30.0]
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]
40 --- 45 | cost [45.0]
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 --> 67 | cost [45.0]
15 --> 24 | cost [20.0]
25 --> 45 | cost [40.0]
35 --> 69 | cost [60.0]
36 -->  1 | cost [20.0]
39 --> 45 | cost [35.0]
41 --> 42 | cost [45.0]
43 --> 17 | cost [20.0]
53 -->  5 | cost [45.0]
55 --> 49 | cost [40.0]
61 --> 40 | cost [25.0]
62 --> 54 | cost [55.0]
64 --> 65 | cost [100.0]
66 --> 63 | cost [30.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 08:03:16 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 57 hubs —— 1—36—29—13—70—31—69—38—59—22—63—57—15—24—19—7—2—4—18—42—32—3—8—26—49—28—14—20—30—44—68—27—46—45—40—9—17—21—34—12—33—54—48—67—56—65—51—60—52—10—5—50—58—37—47—23—71
total time           12.82                gap                  0.0                  
blossom time         0.41                 nb blossom           55.0                 
LB <= UB             3110<=3110           subtour              535.0                
connectivity cuts    295.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       490                  n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—36—29—13—70—31—69—38—59—22—63—57—15—24—19—7—2—4—18—42—32—3—8—26—49—28—14—20—30—44—68—27—46—45—40—9—17—21—34—12—33—54—48—67—56—65—51—60—52—10—5—50—58—37—47—23—71

RING
1  --- 36 | cost [20.0]
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]
23 --- 71 | 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]
37 --- 47 | cost [50.0]
37 --- 58 | cost [5.0]
38 --- 59 | cost [40.0]
38 --- 69 | cost [45.0]
40 --- 45 | cost [45.0]
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 --> 48 | cost [45.0]
16 --> 47 | cost [30.0]
25 --> 45 | cost [40.0]
35 --> 69 | cost [60.0]
39 --> 45 | cost [35.0]
41 --> 42 | cost [45.0]
43 --> 17 | cost [20.0]
53 -->  5 | cost [45.0]
55 --> 49 | cost [40.0]
61 --> 40 | cost [25.0]
62 --> 54 | cost [55.0]
64 --> 65 | cost [100.0]
66 --> 63 | cost [30.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 08:04:18 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 56 hubs —— 1-23-13-29-70-31-69-38-59-22-63-57-24-19-7-2-4-18-42-32-3-8-26-49-28-14-20-30-44-68-27-46-45-40-9-17-21-34-12-33-54-48-67-56-65-51-60-52-10-5-50-58-37-47-16-71-1
total time           32.25                gap                  0.0                  
blossom time         1.14                 nb blossom           2.0                  
LB <= UB             3110<=3110           Master/SP costs      3110/0               
Master time          32.25                SP time              0.0                  
subtour              721.0                connectivity cuts    1071.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1073                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—23—13—29—70—31—69—38—59—22—63—57—24—19—7—2—4—18—42—32—3—8—26—49—28—14—20—30—44—68—27—46—45—40—9—17—21—34—12—33—54—48—67—56—65—51—60—52—10—5—50—58—37—47—16—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 --- 23 | cost [60.0]
13 --- 29 | cost [10.0]
14 --- 20 | cost [35.0]
14 --- 28 | cost [70.0]
16 --- 47 | cost [30.0]
16 --- 71 | cost [45.0]
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]
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]
29 --- 70 | cost [30.0]
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]
40 --- 45 | cost [45.0]
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 --> 67 | cost [45.0]
15 --> 24 | cost [20.0]
25 --> 45 | cost [40.0]
35 --> 69 | cost [60.0]
36 -->  1 | cost [20.0]
39 --> 45 | cost [35.0]
41 --> 42 | cost [45.0]
43 --> 17 | cost [20.0]
53 -->  5 | cost [45.0]
55 --> 49 | cost [40.0]
61 --> 40 | cost [25.0]
62 --> 54 | cost [55.0]
64 --> 65 | cost [100.0]
66 --> 63 | cost [30.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1