------------------------------------------------------------
                           α=7.0 —— eil76 —— 76 nodes       
------------------------------------------------------------

——————— Mon, 08 Jan 2024 08:02:59 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—73—77
total time           13.83                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2458<=2458           subtour              143.0                
connectivity cuts    54.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—73—77

RING
1  --- 73 | cost [35.0]
3  --- 44 | cost [21.0]
3  --- 51 | cost [70.0]
6  --- 51 | cost [42.0]
6  --- 68 | cost [35.0]
8  --- 35 | cost [35.0]
8  --- 46 | cost [35.0]
9  --- 32 | cost [49.0]
9  --- 39 | cost [28.0]
10 --- 38 | cost [49.0]
10 --- 72 | cost [56.0]
11 --- 38 | cost [56.0]
11 --- 53 | cost [56.0]
29 --- 45 | cost [28.0]
29 --- 48 | cost [42.0]
32 --- 44 | cost [35.0]
34 --- 52 | cost [28.0]
34 --- 67 | cost [35.0]
35 --- 53 | cost [49.0]
36 --- 69 | cost [49.0]
36 --- 71 | cost [49.0]
39 --- 72 | cost [35.0]
41 --- 42 | cost [28.0]
41 --- 43 | cost [28.0]
42 --- 43 | cost [35.0]
45 --- 48 | cost [63.0]
46 --- 52 | cost [35.0]
67 --- 76 | cost [35.0]
68 --- 75 | cost [28.0]
69 --- 71 | cost [63.0]
73 --- 77 | cost [35.0]
75 --- 76 | cost [21.0]

STAR
2  --> 68 | cost [21.0]
4  --> 75 | cost [15.0]
5  --> 29 | cost [21.0]
7  --> 35 | cost [15.0]
12 --> 72 | cost [27.0]
13 --> 52 | cost [27.0]
14 --> 53 | cost [21.0]
15 --> 29 | cost [30.0]
16 --> 51 | cost [27.0]
17 --> 51 | cost [18.0]
18 --> 32 | cost [39.0]
19 --> 35 | cost [21.0]
20 --> 71 | cost [33.0]
21 --> 48 | cost [27.0]
22 -->  1 | cost [30.0]
23 --> 43 | cost [30.0]
24 -->  3 | cost [42.0]
25 -->  9 | cost [30.0]
26 --> 67 | cost [18.0]
27 --> 52 | cost [12.0]
28 --> 73 | cost [33.0]
30 --> 48 | cost [21.0]
31 --> 10 | cost [39.0]
33 --> 73 | cost [15.0]
37 --> 36 | cost [24.0]
40 --> 32 | cost [27.0]
47 --> 48 | cost [18.0]
49 -->  3 | cost [33.0]
50 --> 32 | cost [24.0]
54 -->  8 | cost [39.0]
55 -->  9 | cost [57.0]
56 --> 41 | cost [30.0]
57 --> 29 | cost [39.0]
58 --> 72 | cost [15.0]
59 --> 11 | cost [45.0]
60 --> 71 | cost [15.0]
61 --> 69 | cost [42.0]
62 --> 73 | cost [15.0]
63 -->  1 | cost [24.0]
64 --> 42 | cost [27.0]
65 --> 38 | cost [15.0]
66 --> 11 | cost [21.0]
70 --> 71 | cost [24.0]
74 --> 48 | cost [24.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:03:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 33 hubs —— 1-43-23-49-3-44-32-9-39-72-10-38-11-53-35-8-46-34-67-76-75-4-45-29-5-37-36-47-21-28-62-73-77-1
total time           22.31                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2504<=2504           Master/SP costs      2504/0               
Master time          22.31                SP time              0.0                  
subtour              134.0                connectivity cuts    127.0                
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       44                   
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—43—23—49—3—44—32—9—39—72—10—38—11—53—35—8—46—34—67—76—75—4—45—29—5—37—36—47—21—28—62—73—77

RING
1  --- 43 | cost [49.0]
1  --- 77 | cost [0.0]
3  --- 44 | cost [21.0]
3  --- 49 | cost [77.0]
4  --- 45 | cost [49.0]
4  --- 75 | cost [35.0]
5  --- 29 | cost [49.0]
5  --- 37 | cost [49.0]
8  --- 35 | cost [35.0]
8  --- 46 | cost [35.0]
9  --- 32 | cost [49.0]
9  --- 39 | cost [28.0]
10 --- 38 | cost [49.0]
10 --- 72 | cost [56.0]
11 --- 38 | cost [56.0]
11 --- 53 | cost [56.0]
21 --- 28 | cost [63.0]
21 --- 47 | cost [42.0]
23 --- 43 | cost [70.0]
23 --- 49 | cost [70.0]
28 --- 62 | cost [42.0]
29 --- 45 | cost [28.0]
32 --- 44 | cost [35.0]
34 --- 46 | cost [14.0]
34 --- 67 | cost [35.0]
35 --- 53 | cost [49.0]
36 --- 37 | cost [56.0]
36 --- 47 | cost [42.0]
39 --- 72 | cost [35.0]
62 --- 73 | cost [35.0]
67 --- 76 | cost [35.0]
73 --- 77 | cost [35.0]
75 --- 76 | cost [21.0]

STAR
2  --> 62 | cost [24.0]
6  --> 75 | cost [24.0]
7  --> 35 | cost [15.0]
12 --> 72 | cost [27.0]
13 -->  8 | cost [36.0]
14 --> 53 | cost [21.0]
15 -->  5 | cost [24.0]
16 --> 49 | cost [27.0]
17 --> 76 | cost [24.0]
18 --> 32 | cost [39.0]
19 --> 35 | cost [21.0]
20 --> 37 | cost [18.0]
22 --> 62 | cost [24.0]
24 --> 49 | cost [21.0]
25 -->  9 | cost [30.0]
26 --> 76 | cost [18.0]
27 --> 45 | cost [18.0]
30 --> 45 | cost [24.0]
31 --> 10 | cost [39.0]
33 --> 73 | cost [15.0]
40 --> 44 | cost [27.0]
41 --> 43 | cost [12.0]
42 --> 43 | cost [15.0]
48 --> 47 | cost [18.0]
50 --> 32 | cost [24.0]
51 -->  3 | cost [30.0]
52 --> 34 | cost [12.0]
54 -->  8 | cost [39.0]
55 -->  9 | cost [57.0]
56 --> 23 | cost [18.0]
57 -->  5 | cost [36.0]
58 --> 72 | cost [15.0]
59 --> 11 | cost [45.0]
60 --> 37 | cost [36.0]
61 --> 28 | cost [30.0]
63 -->  1 | cost [24.0]
64 --> 43 | cost [42.0]
65 --> 38 | cost [15.0]
66 --> 11 | cost [21.0]
68 --> 75 | cost [12.0]
69 --> 36 | cost [21.0]
70 --> 37 | cost [27.0]
71 --> 36 | cost [21.0]
74 --> 28 | cost [18.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 14:33:32 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—73—77
total time           14.34                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2391<=2391           subtour              154.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1915                 n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—73—77

RING
1  --- 73 | cost [35.0]
3  --- 40 | cost [70.0]
3  --- 44 | cost [21.0]
5  --- 15 | cost [56.0]
5  --- 37 | cost [49.0]
8  --- 46 | cost [35.0]
8  --- 52 | cost [49.0]
9  --- 39 | cost [28.0]
9  --- 72 | cost [63.0]
11 --- 38 | cost [56.0]
11 --- 65 | cost [49.0]
15 --- 37 | cost [63.0]
21 --- 36 | cost [70.0]
21 --- 47 | cost [42.0]
32 --- 40 | cost [63.0]
32 --- 44 | cost [35.0]
36 --- 47 | cost [42.0]
38 --- 65 | cost [35.0]
39 --- 72 | cost [35.0]
41 --- 42 | cost [28.0]
41 --- 43 | cost [28.0]
42 --- 43 | cost [35.0]
46 --- 52 | cost [35.0]
68 --- 75 | cost [28.0]
68 --- 76 | cost [49.0]
73 --- 77 | cost [35.0]
75 --- 76 | cost [21.0]

STAR
2  --> 68 | cost [21.0]
4  --> 75 | cost [15.0]
6  --> 68 | cost [15.0]
7  -->  8 | cost [21.0]
10 --> 38 | cost [21.0]
12 --> 40 | cost [15.0]
13 --> 52 | cost [27.0]
14 --> 11 | cost [33.0]
16 -->  3 | cost [27.0]
17 --> 40 | cost [21.0]
18 --> 32 | cost [39.0]
19 -->  8 | cost [24.0]
20 --> 37 | cost [18.0]
22 -->  1 | cost [30.0]
23 --> 43 | cost [30.0]
24 -->  3 | cost [42.0]
25 -->  9 | cost [30.0]
26 --> 76 | cost [18.0]
27 --> 52 | cost [12.0]
28 --> 21 | cost [27.0]
29 -->  5 | cost [21.0]
30 --> 68 | cost [27.0]
31 --> 72 | cost [48.0]
33 --> 73 | cost [15.0]
34 --> 46 | cost [6.0]
35 -->  8 | cost [15.0]
45 --> 52 | cost [27.0]
48 --> 47 | cost [18.0]
49 -->  3 | cost [33.0]
50 --> 32 | cost [24.0]
51 -->  3 | cost [30.0]
53 --> 11 | cost [24.0]
54 -->  8 | cost [39.0]
55 -->  9 | cost [57.0]
56 --> 41 | cost [30.0]
57 --> 15 | cost [12.0]
58 --> 72 | cost [15.0]
59 --> 11 | cost [45.0]
60 --> 36 | cost [36.0]
61 --> 21 | cost [33.0]
62 --> 73 | cost [15.0]
63 -->  1 | cost [24.0]
64 --> 42 | cost [27.0]
66 --> 11 | cost [21.0]
67 --> 76 | cost [15.0]
69 --> 36 | cost [21.0]
70 --> 37 | cost [27.0]
71 --> 36 | cost [21.0]
74 --> 21 | cost [24.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 15:07:32 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 33 hubs —— 1-43-23-49-3-44-32-9-39-72-10-38-11-53-35-8-46-34-67-76-75-4-45-29-5-37-36-47-21-28-62-73-77-1
total time           2011.6               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2504<=2504           Master/SP costs      2504/0               
Master time          2011.6               SP time              0.0                  
subtour              73496.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       38499                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—43—23—49—3—44—32—9—39—72—10—38—11—53—35—8—46—34—67—76—75—4—45—29—5—37—36—47—21—28—62—73—77

RING
1  --- 43 | cost [49.0]
3  --- 44 | cost [21.0]
3  --- 49 | cost [77.0]
4  --- 45 | cost [49.0]
4  --- 75 | cost [35.0]
5  --- 29 | cost [49.0]
5  --- 37 | cost [49.0]
8  --- 35 | cost [35.0]
8  --- 46 | cost [35.0]
9  --- 32 | cost [49.0]
9  --- 39 | cost [28.0]
10 --- 38 | cost [49.0]
10 --- 72 | cost [56.0]
11 --- 38 | cost [56.0]
11 --- 53 | cost [56.0]
21 --- 28 | cost [63.0]
21 --- 47 | cost [42.0]
23 --- 43 | cost [70.0]
23 --- 49 | cost [70.0]
28 --- 62 | cost [42.0]
29 --- 45 | cost [28.0]
32 --- 44 | cost [35.0]
34 --- 46 | cost [14.0]
34 --- 67 | cost [35.0]
35 --- 53 | cost [49.0]
36 --- 37 | cost [56.0]
36 --- 47 | cost [42.0]
39 --- 72 | cost [35.0]
62 --- 73 | cost [35.0]
67 --- 76 | cost [35.0]
73 --- 77 | cost [35.0]
75 --- 76 | cost [21.0]

STAR
2  --> 62 | cost [24.0]
6  --> 75 | cost [24.0]
7  --> 35 | cost [15.0]
12 --> 72 | cost [27.0]
13 -->  8 | cost [36.0]
14 --> 53 | cost [21.0]
15 -->  5 | cost [24.0]
16 --> 49 | cost [27.0]
17 --> 76 | cost [24.0]
18 --> 32 | cost [39.0]
19 --> 35 | cost [21.0]
20 --> 37 | cost [18.0]
22 --> 62 | cost [24.0]
24 --> 49 | cost [21.0]
25 -->  9 | cost [30.0]
26 --> 67 | cost [18.0]
27 --> 45 | cost [18.0]
30 --> 45 | cost [24.0]
31 --> 10 | cost [39.0]
33 --> 73 | cost [15.0]
40 --> 32 | cost [27.0]
41 --> 43 | cost [12.0]
42 --> 43 | cost [15.0]
48 --> 47 | cost [18.0]
50 --> 32 | cost [24.0]
51 -->  3 | cost [30.0]
52 --> 34 | cost [12.0]
54 -->  8 | cost [39.0]
55 -->  9 | cost [57.0]
56 --> 23 | cost [18.0]
57 -->  5 | cost [36.0]
58 --> 72 | cost [15.0]
59 --> 11 | cost [45.0]
60 --> 36 | cost [36.0]
61 --> 28 | cost [30.0]
63 -->  1 | cost [24.0]
64 --> 43 | cost [42.0]
65 --> 38 | cost [15.0]
66 --> 11 | cost [21.0]
68 --> 75 | cost [12.0]
69 --> 36 | cost [21.0]
70 --> 37 | cost [27.0]
71 --> 36 | cost [21.0]
74 --> 28 | cost [18.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1