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

——————— Mon, 29 Jan 2024 12:39:36 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 34 hubs —— 1—29—31—69—59—63—57—24—2—4—18—32—8—28—14—44—68—9—40—61—34—21—33—54—67—56—51—52—10—50—58—37—16—71
total time           3613.45 (TL 3600)    gap                  0.096                
blossom time         0                    nb blossom           0.0                  
LB <= UB             3507.42<=3880.88     subtour              48.0                 
connectivity cuts    703.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:70                 
2-opt strategy       0                                                              
explored_nodes       1160                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
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—21—33—54—67—56—51—52—10—50—58—37—16—71

RING
1  --- 29 | cost [98.0]
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]
10 --- 50 | cost [63.0]
10 --- 52 | cost [42.0]
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]
21 --- 33 | cost [98.0]
21 --- 34 | cost [7.0]
24 --- 57 | cost [49.0]
29 --- 31 | cost [49.0]
31 --- 69 | cost [14.0]
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 --- 58 | cost [63.0]
51 --- 52 | cost [119.0]
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  --> 10 | cost [18.0]
6  --> 18 | cost [30.0]
7  --> 32 | cost [30.0]
11 --> 67 | cost [27.0]
12 --> 21 | cost [24.0]
13 --> 29 | cost [6.0]
15 --> 24 | cost [12.0]
17 --> 21 | cost [42.0]
19 -->  2 | cost [39.0]
20 --> 14 | cost [21.0]
22 --> 63 | cost [12.0]
23 -->  1 | cost [27.0]
25 --> 40 | cost [51.0]
26 -->  8 | cost [24.0]
27 -->  9 | cost [42.0]
30 --> 44 | cost [45.0]
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]
53 --> 10 | cost [45.0]
55 -->  8 | cost [63.0]
60 --> 52 | cost [27.0]
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
1  --- 31 | cost [1.4000000000000001]
2  --- 18 | cost [0.84]
2  --- 57 | cost [1.61]
4  --- 24 | cost [1.68]
4  --- 32 | cost [0.98]
8  --- 14 | cost [1.19]
8  --- 18 | cost [1.75]
9  --- 44 | cost [1.61]
9  --- 61 | cost [0.91]
10 --- 51 | cost [1.33]
10 --- 58 | cost [1.12]
14 --- 68 | cost [1.33]
16 --- 58 | cost [0.91]
21 --- 54 | cost [1.54]
21 --- 61 | cost [1.68]
24 --- 63 | cost [1.47]
28 --- 32 | cost [1.12]
28 --- 44 | cost [1.75]
29 --- 69 | cost [0.63]
31 --- 59 | cost [0.84]
33 --- 34 | cost [0.98]
33 --- 67 | cost [1.12]
34 --- 40 | cost [1.82]
37 --- 50 | cost [0.7000000000000001]
37 --- 71 | cost [1.47]
40 --- 68 | cost [1.96]
50 --- 52 | cost [0.91]
51 --- 67 | cost [1.19]
52 --- 56 | cost [1.61]
54 --- 56 | cost [1.4000000000000001]
57 --- 59 | cost [1.26]
63 --- 69 | cost [1.12]

BACKUP STAR
3  -->  8 | cost [0.36]
5  --> 50 | cost [0.33]
6  -->  4 | cost [0.42]
7  -->  2 | cost [0.15]
11 --> 56 | cost [0.27]
12 --> 34 | cost [0.24]
13 --> 31 | cost [0.18]
15 --> 57 | cost [0.21]
17 --> 34 | cost [0.45]
19 --> 24 | cost [0.6]
20 --> 28 | cost [0.5700000000000001]
22 --> 59 | cost [0.18]
25 --> 61 | cost [0.54]
26 --> 28 | cost [0.33]
27 --> 40 | cost [0.39]
30 --> 14 | cost [0.3]
35 --> 31 | cost [0.39]
38 --> 69 | cost [0.27]
39 --> 40 | cost [0.36]
41 -->  4 | cost [0.54]
42 -->  4 | cost [0.33]
43 -->  9 | cost [0.51]
45 --> 61 | cost [0.3]
46 -->  9 | cost [0.5700000000000001]
47 --> 37 | cost [0.3]
48 --> 54 | cost [0.39]
49 -->  8 | cost [0.42]
53 --> 52 | cost [0.5700000000000001]
55 --> 28 | cost [0.66]
60 --> 33 | cost [0.3]
62 --> 33 | cost [0.54]
64 --> 51 | cost [0.87]
65 --> 51 | cost [0.3]
66 --> 59 | cost [0.33]
70 --> 29 | cost [0.18]

B = 2.36
i★ = 51
j★ = 56
k★ = 67

       
——————— Mon, 29 Jan 2024 13:40:19 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 35 hubs —— 1-16-37-58-50-10-52-51-56-67-54-33-21-34-61-40-9-68-44-30-14-28-8-32-18-4-2-24-57-63-59-69-31-29-71-1
total time           3603.42 (TL 3600)    gap                  0.102                
blossom time         0                    nb blossom           0.0                  
LB <= UB             3501.3<=3898.88      Master/SP costs      3467/431.88          
Master time          3451.45              SP time              151.98               
subtour              2109.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            5728.0               SP method            poly                 
tildeV               2:70                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       298152               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—16—37—58—50—10—52—51—56—67—54—33—21—34—61—40—9—68—44—30—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]
10 --- 50 | cost [63.0]
10 --- 52 | cost [42.0]
14 --- 28 | cost [98.0]
14 --- 30 | cost [70.0]
16 --- 37 | cost [84.0]
18 --- 32 | cost [91.0]
21 --- 33 | cost [98.0]
21 --- 34 | cost [7.0]
24 --- 57 | cost [49.0]
29 --- 31 | cost [49.0]
29 --- 71 | cost [98.0]
30 --- 44 | cost [105.0]
31 --- 69 | cost [14.0]
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 --- 58 | cost [63.0]
51 --- 52 | cost [119.0]
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  --> 10 | cost [18.0]
6  --> 18 | cost [30.0]
7  --> 32 | cost [30.0]
11 --> 67 | cost [27.0]
12 --> 21 | cost [24.0]
13 --> 29 | cost [6.0]
15 --> 24 | cost [12.0]
17 --> 21 | cost [42.0]
19 -->  2 | cost [39.0]
20 --> 30 | cost [21.0]
22 --> 63 | cost [12.0]
23 -->  1 | cost [27.0]
25 --> 40 | cost [51.0]
26 -->  8 | cost [24.0]
27 -->  9 | cost [42.0]
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]
53 --> 10 | cost [45.0]
55 -->  8 | cost [63.0]
60 --> 52 | cost [27.0]
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
1  --- 37 | cost [1.47]
2  --- 18 | cost [0.84]
2  --- 57 | cost [1.61]
4  --- 24 | cost [1.68]
4  --- 32 | cost [0.98]
8  --- 14 | cost [1.19]
8  --- 18 | cost [1.75]
9  --- 44 | cost [1.61]
9  --- 61 | cost [0.91]
10 --- 51 | cost [1.33]
10 --- 58 | cost [1.12]
14 --- 44 | cost [1.12]
16 --- 58 | cost [0.91]
21 --- 54 | cost [1.54]
21 --- 61 | cost [1.68]
24 --- 63 | cost [1.47]
28 --- 30 | cost [1.68]
28 --- 32 | cost [1.12]
29 --- 69 | cost [0.63]
30 --- 68 | cost [1.19]
31 --- 59 | cost [0.84]
31 --- 71 | cost [1.4000000000000001]
33 --- 34 | cost [0.98]
33 --- 67 | cost [1.12]
34 --- 40 | cost [1.82]
37 --- 50 | cost [0.7000000000000001]
40 --- 68 | cost [1.96]
50 --- 52 | cost [0.91]
51 --- 67 | cost [1.19]
52 --- 56 | cost [1.61]
54 --- 56 | cost [1.4000000000000001]
57 --- 59 | cost [1.26]
63 --- 69 | cost [1.12]

BACKUP STAR
3  -->  8 | cost [0.36]
5  --> 50 | cost [0.33]
6  -->  4 | cost [0.42]
7  -->  2 | cost [0.15]
11 --> 56 | cost [0.27]
12 --> 34 | cost [0.24]
13 --> 31 | cost [0.18]
15 --> 57 | cost [0.21]
17 --> 34 | cost [0.45]
19 --> 24 | cost [0.6]
20 --> 14 | cost [0.21]
22 --> 59 | cost [0.18]
25 --> 61 | cost [0.54]
26 --> 28 | cost [0.33]
27 --> 40 | cost [0.39]
35 --> 31 | cost [0.39]
38 --> 69 | cost [0.27]
39 --> 40 | cost [0.36]
41 -->  4 | cost [0.54]
42 -->  4 | cost [0.33]
43 -->  9 | cost [0.51]
45 --> 61 | cost [0.3]
46 -->  9 | cost [0.5700000000000001]
47 --> 37 | cost [0.3]
48 --> 54 | cost [0.39]
49 -->  8 | cost [0.42]
53 --> 52 | cost [0.5700000000000001]
55 --> 28 | cost [0.66]
60 --> 33 | cost [0.3]
62 --> 33 | cost [0.54]
64 --> 51 | cost [0.87]
65 --> 51 | cost [0.3]
66 --> 59 | cost [0.33]
70 --> 29 | cost [0.18]

B = 2.36
i★ = 51
j★ = 56
k★ = 67