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

——————— Sat, 06 Jan 2024 11:02:26 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 71 hubs —— 1—23—16—47—37—58—50—51—56—65—64—11—48—67—54—62—33—21—34—12—60—52—10—5—53—6—41—43—17—9—40—61—39—25—45—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
total time           9.84                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2025<=2025           subtour              340.0                
connectivity cuts    148.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       332                  n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—23—16—47—37—58—50—51—56—65—64—11—48—67—54—62—33—21—34—12—60—52—10—5—53—6—41—43—17—9—40—61—39—25—45—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 --- 48 | cost [27.0]
11 --- 64 | cost [72.0]
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]
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 --- 38 | cost [30.0]
31 --- 69 | cost [6.0]
32 --- 42 | cost [39.0]
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 --- 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 --- 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]
54 --- 67 | cost [39.0]
56 --- 65 | cost [24.0]
57 --- 63 | cost [42.0]
63 --- 66 | cost [18.0]
64 --- 65 | cost [60.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 06 Jan 2024 11:03:05 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 71 hubs —— 1-23-16-47-37-58-50-51-56-65-64-11-48-67-54-62-33-21-34-12-60-52-10-5-53-6-41-43-17-9-40-61-39-25-45-46-27-68-44-30-20-14-28-49-55-26-8-3-32-42-18-4-2-7-19-24-15-57-63-66-22-59-38-69-31-35-70-13-29-36-71-1
total time           12.58                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2025<=2025           Master/SP costs      2025/0               
Master time          12.58                SP time              0.0                  
subtour              789.0                connectivity cuts    357.0                
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       510                  
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—23—16—47—37—58—50—51—56—65—64—11—48—67—54—62—33—21—34—12—60—52—10—5—53—6—41—43—17—9—40—61—39—25—45—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—69—31—35—70—13—29—36—71

RING
1  --- 23 | cost [27.0]
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 --- 48 | cost [27.0]
11 --- 64 | cost [72.0]
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]
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]
36 --- 71 | cost [12.0]
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 --- 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]
54 --- 67 | cost [39.0]
56 --- 65 | cost [24.0]
57 --- 63 | cost [42.0]
63 --- 66 | cost [18.0]
64 --- 65 | cost [60.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 08:01:49 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 71 hubs —— 1—23—16—47—37—58—50—51—56—65—64—11—48—67—54—62—33—21—34—12—60—52—10—5—53—6—41—43—17—9—40—61—39—25—45—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
total time           12.08                gap                  0.0                  
blossom time         0.87                 nb blossom           136.0                
LB <= UB             2025<=2025           subtour              369.0                
connectivity cuts    153.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       389                  n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—23—16—47—37—58—50—51—56—65—64—11—48—67—54—62—33—21—34—12—60—52—10—5—53—6—41—43—17—9—40—61—39—25—45—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 --- 48 | cost [27.0]
11 --- 64 | cost [72.0]
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]
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 --- 38 | cost [30.0]
31 --- 69 | cost [6.0]
32 --- 42 | cost [39.0]
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 --- 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 --- 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]
54 --- 67 | cost [39.0]
56 --- 65 | cost [24.0]
57 --- 63 | cost [42.0]
63 --- 66 | cost [18.0]
64 --- 65 | cost [60.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 08:02:34 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 71 hubs —— 1-23-16-47-37-58-50-51-56-65-64-11-48-67-54-62-33-21-34-12-60-52-10-5-53-6-41-43-17-9-40-61-39-25-45-46-27-68-44-30-20-14-28-49-55-26-8-3-32-42-18-4-2-7-19-24-15-57-63-66-22-59-38-69-31-35-70-13-29-36-71-1
total time           14.79                gap                  0.0                  
blossom time         0.89                 nb blossom           6.0                  
LB <= UB             2025<=2025           Master/SP costs      2025/0               
Master time          14.79                SP time              0.0                  
subtour              789.0                connectivity cuts    356.0                
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       479                  
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—23—16—47—37—58—50—51—56—65—64—11—48—67—54—62—33—21—34—12—60—52—10—5—53—6—41—43—17—9—40—61—39—25—45—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—69—31—35—70—13—29—36—71

RING
1  --- 23 | cost [27.0]
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 --- 48 | cost [27.0]
11 --- 64 | cost [72.0]
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]
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]
36 --- 71 | cost [12.0]
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 --- 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]
54 --- 67 | cost [39.0]
56 --- 65 | cost [24.0]
57 --- 63 | cost [42.0]
63 --- 66 | cost [18.0]
64 --- 65 | cost [60.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1