------------------------------------------------------------
                           α=7.0 —— rat99 —— 99 nodes       
------------------------------------------------------------

——————— Sat, 27 Jan 2024 18:15:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 44 hubs —— 1—2—3—12—13—22—21—30—29—38—39—48—49—58—57—56—65—74—73—83—84—85—86—87—88—79—78—69—70—71—62—53—52—42—43—34—35—26—25—16—6—5—4—100
total time           3634.46 (TL 3600)    gap                  0.027                
blossom time         0                    nb blossom           0.0                  
LB <= UB             6418.02<=6593.28     subtour              254.0                
connectivity cuts    292.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:99                 
2-opt strategy       0                                                              
explored_nodes       290                  n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—3—12—13—22—21—30—29—38—39—48—49—58—57—56—65—74—73—83—84—85—86—87—88—79—78—69—70—71—62—53—52—42—43—34—35—26—25—16—6—5—4—100

RING
1  ---  2 | cost [98.0]
1  --- 100 | cost [0.0]
2  ---  3 | cost [63.0]
3  --- 12 | cost [49.0]
4  ---  5 | cost [105.0]
4  --- 100 | cost [196.0]
5  ---  6 | cost [63.0]
6  --- 16 | cost [161.0]
12 --- 13 | cost [91.0]
13 --- 22 | cost [98.0]
16 --- 25 | cost [98.0]
21 --- 22 | cost [42.0]
21 --- 30 | cost [126.0]
25 --- 26 | cost [70.0]
26 --- 35 | cost [84.0]
29 --- 30 | cost [77.0]
29 --- 38 | cost [119.0]
34 --- 35 | cost [119.0]
34 --- 43 | cost [42.0]
38 --- 39 | cost [63.0]
39 --- 48 | cost [28.0]
42 --- 43 | cost [56.0]
42 --- 52 | cost [161.0]
48 --- 49 | cost [147.0]
49 --- 58 | cost [84.0]
52 --- 53 | cost [56.0]
53 --- 62 | cost [147.0]
56 --- 57 | cost [56.0]
56 --- 65 | cost [91.0]
57 --- 58 | cost [91.0]
62 --- 71 | cost [119.0]
65 --- 74 | cost [105.0]
69 --- 70 | cost [63.0]
69 --- 78 | cost [84.0]
70 --- 71 | cost [49.0]
73 --- 74 | cost [119.0]
73 --- 83 | cost [147.0]
78 --- 79 | cost [98.0]
79 --- 88 | cost [98.0]
83 --- 84 | cost [112.0]
84 --- 85 | cost [70.0]
85 --- 86 | cost [77.0]
86 --- 87 | cost [77.0]
87 --- 88 | cost [56.0]

STAR
7  -->  6 | cost [33.0]
8  -->  6 | cost [60.0]
9  -->  6 | cost [87.0]
10 -->  2 | cost [33.0]
11 --> 12 | cost [18.0]
14 -->  5 | cost [36.0]
15 --> 16 | cost [30.0]
17 --> 16 | cost [39.0]
18 --> 16 | cost [66.0]
19 --> 30 | cost [75.0]
20 --> 21 | cost [54.0]
23 --> 22 | cost [42.0]
24 --> 25 | cost [27.0]
27 --> 35 | cost [39.0]
28 --> 29 | cost [39.0]
31 --> 30 | cost [36.0]
32 --> 42 | cost [54.0]
33 --> 34 | cost [36.0]
36 --> 35 | cost [33.0]
37 --> 29 | cost [27.0]
40 --> 39 | cost [18.0]
41 --> 42 | cost [42.0]
44 --> 34 | cost [39.0]
45 --> 53 | cost [51.0]
46 --> 38 | cost [54.0]
47 --> 48 | cost [45.0]
50 --> 49 | cost [42.0]
51 --> 52 | cost [27.0]
54 --> 53 | cost [42.0]
55 --> 56 | cost [54.0]
59 --> 58 | cost [24.0]
60 --> 49 | cost [48.0]
61 --> 62 | cost [27.0]
63 --> 62 | cost [48.0]
64 --> 65 | cost [42.0]
66 --> 65 | cost [33.0]
67 --> 69 | cost [57.0]
68 --> 78 | cost [42.0]
72 --> 71 | cost [39.0]
75 --> 74 | cost [42.0]
76 --> 85 | cost [30.0]
77 --> 78 | cost [30.0]
80 --> 71 | cost [30.0]
81 --> 71 | cost [51.0]
82 --> 83 | cost [36.0]
89 --> 88 | cost [45.0]
90 --> 88 | cost [69.0]
91 --> 83 | cost [48.0]
92 --> 83 | cost [63.0]
93 --> 83 | cost [48.0]
94 --> 86 | cost [72.0]
95 --> 86 | cost [24.0]
96 --> 87 | cost [57.0]
97 --> 87 | cost [45.0]
98 --> 87 | cost [78.0]
99 --> 88 | cost [81.0]

BACKUP RING
1  ---  3 | cost [1.61]
2  --- 12 | cost [0.91]
3  --- 13 | cost [1.33]
4  ---  6 | cost [1.68]
5  --- 16 | cost [2.0300000000000002]
5  --- 100 | cost [3.0100000000000002]
6  --- 25 | cost [2.59]
12 --- 22 | cost [1.82]
13 --- 21 | cost [1.26]
16 --- 26 | cost [1.54]
21 --- 29 | cost [1.96]
22 --- 30 | cost [1.68]
25 --- 35 | cost [1.54]
26 --- 34 | cost [1.61]
29 --- 39 | cost [1.61]
30 --- 38 | cost [1.75]
34 --- 42 | cost [0.91]
35 --- 43 | cost [1.61]
38 --- 48 | cost [0.77]
39 --- 49 | cost [1.68]
42 --- 53 | cost [2.0300000000000002]
43 --- 52 | cost [1.75]
48 --- 58 | cost [2.17]
49 --- 57 | cost [1.26]
52 --- 62 | cost [1.75]
53 --- 71 | cost [2.66]
56 --- 58 | cost [1.33]
56 --- 74 | cost [1.96]
57 --- 65 | cost [1.33]
62 --- 70 | cost [1.26]
65 --- 73 | cost [2.24]
69 --- 71 | cost [1.12]
69 --- 79 | cost [1.54]
70 --- 78 | cost [1.33]
73 --- 84 | cost [1.82]
74 --- 83 | cost [2.38]
78 --- 88 | cost [1.68]
79 --- 87 | cost [1.54]
83 --- 85 | cost [1.82]
84 --- 86 | cost [1.33]
85 --- 87 | cost [1.4000000000000001]
86 --- 88 | cost [1.26]

BACKUP STAR
7  -->  5 | cost [0.5700000000000001]
8  -->  5 | cost [0.87]
9  --> 16 | cost [0.9]
10 -->  1 | cost [0.51]
11 -->  2 | cost [0.33]
14 -->  4 | cost [0.45]
15 --> 25 | cost [0.51]
17 --> 25 | cost [0.54]
18 --> 25 | cost [0.81]
19 --> 21 | cost [0.75]
20 --> 12 | cost [0.66]
23 --> 25 | cost [0.51]
24 --> 26 | cost [0.51]
27 --> 26 | cost [0.48]
28 --> 30 | cost [0.54]
31 --> 21 | cost [0.5700000000000001]
32 --> 30 | cost [0.66]
33 --> 42 | cost [0.36]
36 --> 34 | cost [0.66]
37 --> 38 | cost [0.51]
40 --> 48 | cost [0.27]
41 --> 39 | cost [0.6]
44 --> 43 | cost [0.42]
45 --> 52 | cost [0.6]
46 --> 48 | cost [0.63]
47 --> 38 | cost [0.48]
50 --> 42 | cost [0.63]
51 --> 53 | cost [0.48]
54 --> 52 | cost [0.63]
55 --> 57 | cost [0.66]
59 --> 49 | cost [0.54]
60 --> 52 | cost [0.5700000000000001]
61 --> 70 | cost [0.48]
63 --> 53 | cost [0.63]
64 --> 56 | cost [0.5700000000000001]
66 --> 74 | cost [0.45]
67 --> 78 | cost [0.5700000000000001]
68 --> 69 | cost [0.48]
72 --> 70 | cost [0.6]
75 --> 84 | cost [0.6]
76 --> 84 | cost [0.42]
77 --> 85 | cost [0.51]
80 --> 70 | cost [0.36]
81 --> 70 | cost [0.6900000000000001]
82 --> 73 | cost [0.54]
89 --> 87 | cost [0.6]
90 --> 79 | cost [0.84]
91 --> 84 | cost [0.9]
92 --> 84 | cost [0.96]
93 --> 84 | cost [0.66]
94 --> 83 | cost [0.84]
95 --> 87 | cost [0.39]
96 --> 86 | cost [0.66]
97 --> 88 | cost [0.54]
98 --> 88 | cost [0.81]
99 --> 87 | cost [0.9]

B = 4.880000000000001
i★ = 73
j★ = 83
k★ = 84

       
——————— Sat, 27 Jan 2024 18:29:11 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 44 hubs —— 1-4-5-6-16-25-26-35-34-43-42-51-52-53-62-71-70-69-78-79-88-87-86-85-84-83-73-74-65-56-57-47-48-39-38-29-30-21-22-13-12-3-2-100-1
total time           748.93               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             6587.28<=6587.28     Master/SP costs      6436/151.28          
Master time          723.64               SP time              25.29                
subtour              739.0                connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            173.0                SP method            poly                 
tildeV               2:99                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       63489                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—4—5—6—16—25—26—35—34—43—42—51—52—53—62—71—70—69—78—79—88—87—86—85—84—83—73—74—65—56—57—47—48—39—38—29—30—21—22—13—12—3—2—100

RING
1  ---  4 | cost [196.0]
2  ---  3 | cost [63.0]
2  --- 100 | cost [98.0]
3  --- 12 | cost [49.0]
4  ---  5 | cost [105.0]
5  ---  6 | cost [63.0]
6  --- 16 | cost [161.0]
12 --- 13 | cost [91.0]
13 --- 22 | cost [98.0]
16 --- 25 | cost [98.0]
21 --- 22 | cost [42.0]
21 --- 30 | cost [126.0]
25 --- 26 | cost [70.0]
26 --- 35 | cost [84.0]
29 --- 30 | cost [77.0]
29 --- 38 | cost [119.0]
34 --- 35 | cost [119.0]
34 --- 43 | cost [42.0]
38 --- 39 | cost [63.0]
39 --- 48 | cost [28.0]
42 --- 43 | cost [56.0]
42 --- 51 | cost [147.0]
47 --- 48 | cost [105.0]
47 --- 57 | cost [147.0]
51 --- 52 | cost [63.0]
52 --- 53 | cost [56.0]
53 --- 62 | cost [147.0]
56 --- 57 | cost [56.0]
56 --- 65 | cost [91.0]
62 --- 71 | cost [119.0]
65 --- 74 | cost [105.0]
69 --- 70 | cost [63.0]
69 --- 78 | cost [84.0]
70 --- 71 | cost [49.0]
73 --- 74 | cost [119.0]
73 --- 83 | cost [147.0]
78 --- 79 | cost [98.0]
79 --- 88 | cost [98.0]
83 --- 84 | cost [112.0]
84 --- 85 | cost [70.0]
85 --- 86 | cost [77.0]
86 --- 87 | cost [77.0]
87 --- 88 | cost [56.0]

STAR
7  -->  6 | cost [33.0]
8  -->  6 | cost [60.0]
9  -->  6 | cost [87.0]
10 -->  2 | cost [33.0]
11 --> 12 | cost [18.0]
14 -->  5 | cost [36.0]
15 --> 16 | cost [30.0]
17 --> 16 | cost [39.0]
18 --> 16 | cost [66.0]
19 --> 21 | cost [75.0]
20 --> 21 | cost [54.0]
23 --> 22 | cost [42.0]
24 --> 25 | cost [27.0]
27 --> 35 | cost [39.0]
28 --> 29 | cost [39.0]
31 --> 30 | cost [36.0]
32 --> 42 | cost [54.0]
33 --> 42 | cost [36.0]
36 --> 35 | cost [33.0]
37 --> 29 | cost [27.0]
40 --> 39 | cost [18.0]
41 --> 42 | cost [42.0]
44 --> 34 | cost [39.0]
45 --> 53 | cost [51.0]
46 --> 47 | cost [24.0]
49 --> 57 | cost [54.0]
50 --> 51 | cost [36.0]
54 --> 53 | cost [42.0]
55 --> 47 | cost [51.0]
58 --> 57 | cost [39.0]
59 --> 57 | cost [63.0]
60 --> 51 | cost [42.0]
61 --> 62 | cost [27.0]
63 --> 62 | cost [48.0]
64 --> 65 | cost [42.0]
66 --> 65 | cost [33.0]
67 --> 78 | cost [57.0]
68 --> 78 | cost [42.0]
72 --> 71 | cost [39.0]
75 --> 74 | cost [42.0]
76 --> 85 | cost [30.0]
77 --> 78 | cost [30.0]
80 --> 71 | cost [30.0]
81 --> 71 | cost [51.0]
82 --> 83 | cost [36.0]
89 --> 88 | cost [45.0]
90 --> 88 | cost [69.0]
91 --> 83 | cost [48.0]
92 --> 83 | cost [63.0]
93 --> 83 | cost [48.0]
94 --> 86 | cost [72.0]
95 --> 86 | cost [24.0]
96 --> 87 | cost [57.0]
97 --> 87 | cost [45.0]
98 --> 87 | cost [78.0]
99 --> 88 | cost [81.0]

BACKUP RING
1  ---  5 | cost [3.0100000000000002]
2  --- 12 | cost [0.91]
3  --- 13 | cost [1.33]
3  --- 100 | cost [1.61]
4  ---  6 | cost [1.68]
5  --- 16 | cost [2.0300000000000002]
6  --- 25 | cost [2.59]
12 --- 22 | cost [1.82]
13 --- 21 | cost [1.26]
16 --- 26 | cost [1.54]
21 --- 29 | cost [1.96]
22 --- 30 | cost [1.68]
25 --- 35 | cost [1.54]
26 --- 34 | cost [1.61]
29 --- 39 | cost [1.61]
30 --- 38 | cost [1.75]
34 --- 42 | cost [0.91]
35 --- 43 | cost [1.61]
38 --- 48 | cost [0.77]
39 --- 47 | cost [1.26]
42 --- 52 | cost [1.61]
43 --- 51 | cost [1.82]
47 --- 56 | cost [1.61]
48 --- 57 | cost [1.8900000000000001]
51 --- 53 | cost [1.12]
52 --- 62 | cost [1.75]
53 --- 71 | cost [2.66]
56 --- 74 | cost [1.96]
57 --- 65 | cost [1.33]
62 --- 70 | cost [1.26]
65 --- 73 | cost [2.24]
69 --- 71 | cost [1.12]
69 --- 79 | cost [1.54]
70 --- 78 | cost [1.33]
73 --- 84 | cost [1.82]
74 --- 83 | cost [2.38]
78 --- 88 | cost [1.68]
79 --- 87 | cost [1.54]
83 --- 85 | cost [1.82]
84 --- 86 | cost [1.33]
85 --- 87 | cost [1.4000000000000001]
86 --- 88 | cost [1.26]

BACKUP STAR
7  -->  5 | cost [0.5700000000000001]
8  -->  5 | cost [0.87]
9  --> 16 | cost [0.9]
10 -->  1 | cost [0.51]
11 -->  2 | cost [0.33]
14 -->  4 | cost [0.45]
15 --> 25 | cost [0.51]
17 --> 25 | cost [0.54]
18 --> 25 | cost [0.81]
19 --> 30 | cost [0.75]
20 --> 12 | cost [0.66]
23 --> 25 | cost [0.51]
24 --> 26 | cost [0.51]
27 --> 26 | cost [0.48]
28 --> 30 | cost [0.54]
31 --> 21 | cost [0.5700000000000001]
32 --> 30 | cost [0.66]
33 --> 34 | cost [0.36]
36 --> 34 | cost [0.66]
37 --> 38 | cost [0.51]
40 --> 48 | cost [0.27]
41 --> 39 | cost [0.6]
44 --> 43 | cost [0.42]
45 --> 52 | cost [0.6]
46 --> 38 | cost [0.54]
49 --> 48 | cost [0.63]
50 --> 42 | cost [0.63]
54 --> 52 | cost [0.63]
55 --> 56 | cost [0.54]
58 --> 56 | cost [0.5700000000000001]
59 --> 69 | cost [0.6900000000000001]
60 --> 52 | cost [0.5700000000000001]
61 --> 70 | cost [0.48]
63 --> 53 | cost [0.63]
64 --> 56 | cost [0.5700000000000001]
66 --> 74 | cost [0.45]
67 --> 69 | cost [0.5700000000000001]
68 --> 69 | cost [0.48]
72 --> 70 | cost [0.6]
75 --> 84 | cost [0.6]
76 --> 84 | cost [0.42]
77 --> 85 | cost [0.51]
80 --> 70 | cost [0.36]
81 --> 70 | cost [0.6900000000000001]
82 --> 73 | cost [0.54]
89 --> 87 | cost [0.6]
90 --> 79 | cost [0.84]
91 --> 84 | cost [0.9]
92 --> 84 | cost [0.96]
93 --> 84 | cost [0.66]
94 --> 83 | cost [0.84]
95 --> 87 | cost [0.39]
96 --> 86 | cost [0.66]
97 --> 88 | cost [0.54]
98 --> 88 | cost [0.81]
99 --> 87 | cost [0.9]

B = 4.880000000000001
i★ = 73
j★ = 83
k★ = 84