------------------------------------------------------------
                            α=7.0 —— st70 —— 70 nodes       
------------------------------------------------------------

——————— Sat, 06 Jan 2024 11:05:13 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 31 hubs —— 1—16—37—58—50—51—56—67—54—33—34—61—40—9—68—44—14—28—8—32—18—4—2—24—57—63—59—69—31—29—71
total time           13.48                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3402<=3402           subtour              88.0                 
connectivity cuts    82.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—16—37—58—50—51—56—67—54—33—34—61—40—9—68—44—14—28—8—32—18—4—2—24—57—63—59—69—31—29—71

RING
1  --- 16 | cost [63.0]
1  --- 71 | cost [0.0]
2  ---  4 | cost [63.0]
2  --- 24 | cost [140.0]
4  --- 18 | cost [28.0]
8  --- 28 | cost [28.0]
8  --- 32 | cost [91.0]
9  --- 40 | cost [77.0]
9  --- 68 | cost [126.0]
14 --- 28 | cost [98.0]
14 --- 44 | cost [112.0]
16 --- 37 | cost [84.0]
18 --- 32 | cost [91.0]
24 --- 57 | cost [49.0]
29 --- 31 | cost [49.0]
29 --- 71 | cost [98.0]
31 --- 69 | cost [14.0]
33 --- 34 | cost [98.0]
33 --- 54 | cost [70.0]
34 --- 61 | cost [161.0]
37 --- 58 | cost [7.0]
40 --- 61 | cost [35.0]
44 --- 68 | cost [28.0]
50 --- 51 | cost [112.0]
50 --- 58 | cost [63.0]
51 --- 56 | cost [63.0]
54 --- 67 | cost [91.0]
56 --- 67 | cost [56.0]
57 --- 63 | cost [98.0]
59 --- 63 | cost [42.0]
59 --- 69 | cost [70.0]

STAR
3  --> 32 | cost [18.0]
5  --> 50 | cost [33.0]
6  --> 18 | cost [30.0]
7  -->  2 | cost [15.0]
10 --> 50 | cost [27.0]
11 --> 56 | cost [27.0]
12 --> 34 | cost [24.0]
13 --> 29 | cost [6.0]
15 --> 24 | cost [12.0]
17 --> 34 | cost [45.0]
19 -->  2 | cost [39.0]
20 --> 14 | cost [21.0]
21 --> 34 | cost [3.0]
22 --> 63 | cost [12.0]
23 -->  1 | cost [27.0]
25 --> 40 | cost [51.0]
26 -->  8 | cost [24.0]
27 --> 40 | cost [39.0]
30 --> 14 | cost [30.0]
35 --> 69 | cost [36.0]
36 -->  1 | cost [12.0]
38 --> 59 | cost [24.0]
39 --> 61 | cost [27.0]
41 --> 18 | cost [42.0]
42 --> 18 | cost [18.0]
43 --> 68 | cost [45.0]
45 --> 40 | cost [27.0]
46 --> 40 | cost [42.0]
47 --> 16 | cost [18.0]
48 --> 67 | cost [15.0]
49 -->  8 | cost [42.0]
52 --> 50 | cost [39.0]
53 --> 50 | cost [60.0]
55 -->  8 | cost [63.0]
60 --> 33 | cost [30.0]
62 --> 54 | cost [33.0]
64 --> 56 | cost [81.0]
65 --> 56 | cost [24.0]
66 --> 63 | cost [18.0]
70 --> 31 | cost [18.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 06 Jan 2024 11:05:54 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 31 hubs —— 1-29-31-69-59-63-57-24-2-4-18-32-8-28-14-44-68-9-40-61-34-33-54-67-56-51-50-58-37-16-71-1
total time           14.51                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3402<=3402           Master/SP costs      3402/0               
Master time          14.51                SP time              0.0                  
subtour              249.0                connectivity cuts    100.0                
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       1                    
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—29—31—69—59—63—57—24—2—4—18—32—8—28—14—44—68—9—40—61—34—33—54—67—56—51—50—58—37—16—71

RING
1  --- 29 | cost [98.0]
1  --- 71 | cost [0.0]
2  ---  4 | cost [63.0]
2  --- 24 | cost [140.0]
4  --- 18 | cost [28.0]
8  --- 28 | cost [28.0]
8  --- 32 | cost [91.0]
9  --- 40 | cost [77.0]
9  --- 68 | cost [126.0]
14 --- 28 | cost [98.0]
14 --- 44 | cost [112.0]
16 --- 37 | cost [84.0]
16 --- 71 | cost [63.0]
18 --- 32 | cost [91.0]
24 --- 57 | cost [49.0]
29 --- 31 | cost [49.0]
31 --- 69 | cost [14.0]
33 --- 34 | cost [98.0]
33 --- 54 | cost [70.0]
34 --- 61 | cost [161.0]
37 --- 58 | cost [7.0]
40 --- 61 | cost [35.0]
44 --- 68 | cost [28.0]
50 --- 51 | cost [112.0]
50 --- 58 | cost [63.0]
51 --- 56 | cost [63.0]
54 --- 67 | cost [91.0]
56 --- 67 | cost [56.0]
57 --- 63 | cost [98.0]
59 --- 63 | cost [42.0]
59 --- 69 | cost [70.0]

STAR
3  --> 32 | cost [18.0]
5  --> 50 | cost [33.0]
6  --> 18 | cost [30.0]
7  -->  2 | cost [15.0]
10 --> 50 | cost [27.0]
11 --> 67 | cost [27.0]
12 --> 34 | cost [24.0]
13 --> 29 | cost [6.0]
15 --> 24 | cost [12.0]
17 --> 34 | cost [45.0]
19 -->  2 | cost [39.0]
20 --> 14 | cost [21.0]
21 --> 34 | cost [3.0]
22 --> 63 | cost [12.0]
23 -->  1 | cost [27.0]
25 --> 40 | cost [51.0]
26 -->  8 | cost [24.0]
27 --> 40 | cost [39.0]
30 --> 14 | cost [30.0]
35 --> 69 | cost [36.0]
36 -->  1 | cost [12.0]
38 --> 59 | cost [24.0]
39 --> 61 | cost [27.0]
41 --> 18 | cost [42.0]
42 --> 18 | cost [18.0]
43 --> 68 | cost [45.0]
45 --> 40 | cost [27.0]
46 --> 40 | cost [42.0]
47 --> 16 | cost [18.0]
48 --> 67 | cost [15.0]
49 --> 28 | cost [42.0]
52 --> 50 | cost [39.0]
53 --> 50 | cost [60.0]
55 -->  8 | cost [63.0]
60 --> 33 | cost [30.0]
62 --> 54 | cost [33.0]
64 --> 56 | cost [81.0]
65 --> 56 | cost [24.0]
66 --> 63 | cost [18.0]
70 --> 31 | cost [18.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 08:05:01 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 31 hubs —— 1—16—37—58—50—51—56—67—54—33—34—61—40—9—68—44—14—28—8—32—18—4—2—24—57—63—59—69—31—29—71
total time           14.65                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3402<=3402           subtour              88.0                 
connectivity cuts    82.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—16—37—58—50—51—56—67—54—33—34—61—40—9—68—44—14—28—8—32—18—4—2—24—57—63—59—69—31—29—71

RING
1  --- 16 | cost [63.0]
1  --- 71 | cost [0.0]
2  ---  4 | cost [63.0]
2  --- 24 | cost [140.0]
4  --- 18 | cost [28.0]
8  --- 28 | cost [28.0]
8  --- 32 | cost [91.0]
9  --- 40 | cost [77.0]
9  --- 68 | cost [126.0]
14 --- 28 | cost [98.0]
14 --- 44 | cost [112.0]
16 --- 37 | cost [84.0]
18 --- 32 | cost [91.0]
24 --- 57 | cost [49.0]
29 --- 31 | cost [49.0]
29 --- 71 | cost [98.0]
31 --- 69 | cost [14.0]
33 --- 34 | cost [98.0]
33 --- 54 | cost [70.0]
34 --- 61 | cost [161.0]
37 --- 58 | cost [7.0]
40 --- 61 | cost [35.0]
44 --- 68 | cost [28.0]
50 --- 51 | cost [112.0]
50 --- 58 | cost [63.0]
51 --- 56 | cost [63.0]
54 --- 67 | cost [91.0]
56 --- 67 | cost [56.0]
57 --- 63 | cost [98.0]
59 --- 63 | cost [42.0]
59 --- 69 | cost [70.0]

STAR
3  --> 32 | cost [18.0]
5  --> 50 | cost [33.0]
6  --> 18 | cost [30.0]
7  -->  2 | cost [15.0]
10 --> 50 | cost [27.0]
11 --> 56 | cost [27.0]
12 --> 34 | cost [24.0]
13 --> 29 | cost [6.0]
15 --> 24 | cost [12.0]
17 --> 34 | cost [45.0]
19 -->  2 | cost [39.0]
20 --> 14 | cost [21.0]
21 --> 34 | cost [3.0]
22 --> 63 | cost [12.0]
23 -->  1 | cost [27.0]
25 --> 40 | cost [51.0]
26 -->  8 | cost [24.0]
27 --> 40 | cost [39.0]
30 --> 14 | cost [30.0]
35 --> 69 | cost [36.0]
36 -->  1 | cost [12.0]
38 --> 59 | cost [24.0]
39 --> 61 | cost [27.0]
41 --> 18 | cost [42.0]
42 --> 18 | cost [18.0]
43 --> 68 | cost [45.0]
45 --> 40 | cost [27.0]
46 --> 40 | cost [42.0]
47 --> 16 | cost [18.0]
48 --> 67 | cost [15.0]
49 -->  8 | cost [42.0]
52 --> 50 | cost [39.0]
53 --> 50 | cost [60.0]
55 -->  8 | cost [63.0]
60 --> 33 | cost [30.0]
62 --> 54 | cost [33.0]
64 --> 56 | cost [81.0]
65 --> 56 | cost [24.0]
66 --> 63 | cost [18.0]
70 --> 31 | cost [18.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 08:05:46 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 31 hubs —— 1-29-31-69-59-63-57-24-2-4-18-32-8-28-14-44-68-9-40-61-34-33-54-67-56-51-50-58-37-16-71-1
total time           15.48                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3402<=3402           Master/SP costs      3402/0               
Master time          15.48                SP time              0.0                  
subtour              249.0                connectivity cuts    100.0                
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       1                    
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—29—31—69—59—63—57—24—2—4—18—32—8—28—14—44—68—9—40—61—34—33—54—67—56—51—50—58—37—16—71

RING
1  --- 29 | cost [98.0]
1  --- 71 | cost [0.0]
2  ---  4 | cost [63.0]
2  --- 24 | cost [140.0]
4  --- 18 | cost [28.0]
8  --- 28 | cost [28.0]
8  --- 32 | cost [91.0]
9  --- 40 | cost [77.0]
9  --- 68 | cost [126.0]
14 --- 28 | cost [98.0]
14 --- 44 | cost [112.0]
16 --- 37 | cost [84.0]
16 --- 71 | cost [63.0]
18 --- 32 | cost [91.0]
24 --- 57 | cost [49.0]
29 --- 31 | cost [49.0]
31 --- 69 | cost [14.0]
33 --- 34 | cost [98.0]
33 --- 54 | cost [70.0]
34 --- 61 | cost [161.0]
37 --- 58 | cost [7.0]
40 --- 61 | cost [35.0]
44 --- 68 | cost [28.0]
50 --- 51 | cost [112.0]
50 --- 58 | cost [63.0]
51 --- 56 | cost [63.0]
54 --- 67 | cost [91.0]
56 --- 67 | cost [56.0]
57 --- 63 | cost [98.0]
59 --- 63 | cost [42.0]
59 --- 69 | cost [70.0]

STAR
3  --> 32 | cost [18.0]
5  --> 50 | cost [33.0]
6  --> 18 | cost [30.0]
7  -->  2 | cost [15.0]
10 --> 50 | cost [27.0]
11 --> 67 | cost [27.0]
12 --> 34 | cost [24.0]
13 --> 29 | cost [6.0]
15 --> 24 | cost [12.0]
17 --> 34 | cost [45.0]
19 -->  2 | cost [39.0]
20 --> 14 | cost [21.0]
21 --> 34 | cost [3.0]
22 --> 63 | cost [12.0]
23 -->  1 | cost [27.0]
25 --> 40 | cost [51.0]
26 -->  8 | cost [24.0]
27 --> 40 | cost [39.0]
30 --> 14 | cost [30.0]
35 --> 69 | cost [36.0]
36 -->  1 | cost [12.0]
38 --> 59 | cost [24.0]
39 --> 61 | cost [27.0]
41 --> 18 | cost [42.0]
42 --> 18 | cost [18.0]
43 --> 68 | cost [45.0]
45 --> 40 | cost [27.0]
46 --> 40 | cost [42.0]
47 --> 16 | cost [18.0]
48 --> 67 | cost [15.0]
49 --> 28 | cost [42.0]
52 --> 50 | cost [39.0]
53 --> 50 | cost [60.0]
55 -->  8 | cost [63.0]
60 --> 33 | cost [30.0]
62 --> 54 | cost [33.0]
64 --> 56 | cost [81.0]
65 --> 56 | cost [24.0]
66 --> 63 | cost [18.0]
70 --> 31 | cost [18.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1