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

——————— Tue, 30 Jan 2024 05:25:36 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 46 hubs —— 1—4—6—8—17—25—26—35—34—43—42—51—52—53—62—70—71—80—79—89—88—87—95—94—93—83—84—76—75—74—65—56—57—47—48—39—38—29—30—21—22—13—12—3—2—100
total time           3633.57 (TL 3600)    gap                  0.12                 
blossom time         0                    nb blossom           0.0                  
LB <= UB             6428.96<=7309.72     subtour              639.0                
connectivity cuts    238.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:99                 
2-opt strategy       0                                                              
explored_nodes       219                  n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—4—6—8—17—25—26—35—34—43—42—51—52—53—62—70—71—80—79—89—88—87—95—94—93—83—84—76—75—74—65—56—57—47—48—39—38—29—30—21—22—13—12—3—2—100

RING
1  ---  4 | cost [196.0]
1  --- 100 | cost [0.0]
2  ---  3 | cost [63.0]
2  --- 100 | cost [98.0]
3  --- 12 | cost [49.0]
4  ---  6 | cost [168.0]
6  ---  8 | cost [140.0]
8  --- 17 | cost [203.0]
12 --- 13 | cost [91.0]
13 --- 22 | cost [98.0]
17 --- 25 | cost [126.0]
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 --- 70 | cost [126.0]
65 --- 74 | cost [105.0]
70 --- 71 | cost [49.0]
71 --- 80 | cost [70.0]
74 --- 75 | cost [98.0]
75 --- 76 | cost [91.0]
76 --- 84 | cost [98.0]
79 --- 80 | cost [105.0]
79 --- 89 | cost [154.0]
83 --- 84 | cost [112.0]
83 --- 93 | cost [112.0]
87 --- 88 | cost [56.0]
87 --- 95 | cost [91.0]
88 --- 89 | cost [105.0]
93 --- 94 | cost [91.0]
94 --- 95 | cost [126.0]

STAR
5  -->  6 | cost [27.0]
7  -->  8 | cost [30.0]
9  -->  8 | cost [30.0]
10 -->  2 | cost [33.0]
11 --> 12 | cost [18.0]
14 --> 13 | cost [48.0]
15 --> 25 | cost [51.0]
16 --> 25 | cost [42.0]
18 --> 17 | cost [30.0]
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 --> 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 --> 75 | cost [57.0]
68 --> 76 | cost [60.0]
69 --> 70 | cost [27.0]
72 --> 71 | cost [39.0]
73 --> 74 | cost [51.0]
77 --> 76 | cost [36.0]
78 --> 79 | cost [42.0]
81 --> 80 | cost [39.0]
82 --> 83 | cost [36.0]
85 --> 76 | cost [30.0]
86 --> 95 | cost [24.0]
90 --> 89 | cost [24.0]
91 --> 93 | cost [42.0]
92 --> 93 | cost [36.0]
96 --> 95 | cost [45.0]
97 --> 87 | cost [45.0]
98 --> 89 | cost [51.0]
99 --> 89 | cost [42.0]

BACKUP RING
1  ---  6 | cost [3.64]
2  --- 12 | cost [0.91]
3  --- 13 | cost [1.33]
3  --- 100 | cost [1.61]
4  ---  8 | cost [3.08]
6  --- 17 | cost [2.31]
8  --- 25 | cost [2.94]
12 --- 22 | cost [1.82]
13 --- 21 | cost [1.26]
17 --- 26 | cost [1.33]
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 --- 70 | cost [2.73]
56 --- 74 | cost [1.96]
57 --- 65 | cost [1.33]
62 --- 71 | cost [1.19]
65 --- 75 | cost [1.68]
70 --- 80 | cost [0.84]
71 --- 79 | cost [1.68]
74 --- 76 | cost [1.8900000000000001]
75 --- 84 | cost [1.4000000000000001]
76 --- 83 | cost [1.96]
79 --- 88 | cost [0.98]
80 --- 89 | cost [2.24]
83 --- 94 | cost [1.96]
84 --- 93 | cost [1.54]
87 --- 89 | cost [1.4000000000000001]
87 --- 94 | cost [2.24]
88 --- 95 | cost [1.54]
93 --- 95 | cost [1.82]

BACKUP STAR
5  -->  4 | cost [0.45]
7  -->  6 | cost [0.33]
9  --> 17 | cost [0.75]
10 -->  1 | cost [0.51]
11 -->  2 | cost [0.33]
14 -->  4 | cost [0.45]
15 -->  6 | cost [0.63]
16 --> 17 | cost [0.39]
18 -->  8 | 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 --> 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 --> 56 | cost [0.75]
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 --> 76 | cost [0.66]
68 --> 75 | cost [0.6]
69 --> 71 | cost [0.48]
72 --> 80 | cost [0.54]
73 --> 83 | cost [0.63]
77 --> 79 | cost [0.5700000000000001]
78 --> 70 | cost [0.5700000000000001]
81 --> 71 | cost [0.51]
82 --> 93 | cost [0.75]
85 --> 84 | cost [0.3]
86 --> 87 | cost [0.33]
90 --> 88 | cost [0.6900000000000001]
91 --> 83 | cost [0.48]
92 --> 83 | cost [0.63]
96 --> 87 | cost [0.5700000000000001]
97 --> 89 | cost [0.51]
98 --> 87 | cost [0.78]
99 --> 88 | cost [0.81]

B = 3.84
i★ = 53
j★ = 62
k★ = 70

       
——————— Tue, 30 Jan 2024 06:26:55 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 47 hubs —— 1-4-5-6-15-16-25-26-35-34-43-42-51-52-53-62-70-71-80-79-88-89-97-95-94-93-83-84-76-77-68-67-66-65-56-57-47-48-39-38-29-30-21-20-11-2-100-1
total time           3604.9 (TL 3600)     gap                  0.083                
blossom time         0                    nb blossom           0.0                  
LB <= UB             6551.25<=7144.43     Master/SP costs      6557/587.43          
Master time          3214.17              SP time              390.73               
subtour              1996.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            2604.0               SP method            poly                 
tildeV               2:99                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       111717               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—4—5—6—15—16—25—26—35—34—43—42—51—52—53—62—70—71—80—79—88—89—97—95—94—93—83—84—76—77—68—67—66—65—56—57—47—48—39—38—29—30—21—20—11—2—100

RING
1  ---  4 | cost [196.0]
1  --- 100 | cost [0.0]
2  --- 11 | cost [77.0]
2  --- 100 | cost [98.0]
4  ---  5 | cost [105.0]
5  ---  6 | cost [63.0]
6  --- 15 | cost [147.0]
11 --- 20 | cost [133.0]
15 --- 16 | cost [70.0]
16 --- 25 | cost [98.0]
20 --- 21 | cost [126.0]
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 --- 70 | cost [126.0]
65 --- 66 | cost [77.0]
66 --- 67 | cost [91.0]
67 --- 68 | cost [35.0]
68 --- 77 | cost [105.0]
70 --- 71 | cost [49.0]
71 --- 80 | cost [70.0]
76 --- 77 | cost [84.0]
76 --- 84 | cost [98.0]
79 --- 80 | cost [105.0]
79 --- 88 | cost [98.0]
83 --- 84 | cost [112.0]
83 --- 93 | cost [112.0]
88 --- 89 | cost [105.0]
89 --- 97 | cost [119.0]
93 --- 94 | cost [91.0]
94 --- 95 | cost [126.0]
95 --- 97 | cost [133.0]

STAR
3  -->  2 | cost [27.0]
7  -->  6 | cost [33.0]
8  -->  6 | cost [60.0]
9  --> 16 | cost [90.0]
10 -->  2 | cost [33.0]
12 --> 11 | cost [18.0]
13 --> 11 | cost [51.0]
14 -->  5 | cost [36.0]
17 --> 25 | cost [54.0]
18 --> 16 | cost [66.0]
19 --> 20 | cost [39.0]
22 --> 21 | cost [18.0]
23 --> 15 | 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 --> 47 | cost [24.0]
49 --> 57 | cost [54.0]
50 --> 51 | cost [36.0]
54 --> 53 | cost [42.0]
55 --> 56 | cost [54.0]
58 --> 57 | cost [39.0]
59 --> 67 | cost [54.0]
60 --> 51 | cost [42.0]
61 --> 62 | cost [27.0]
63 --> 71 | cost [78.0]
64 --> 65 | cost [42.0]
69 --> 70 | cost [27.0]
72 --> 71 | cost [39.0]
73 --> 83 | cost [63.0]
74 --> 65 | cost [45.0]
75 --> 76 | cost [39.0]
78 --> 77 | cost [30.0]
81 --> 80 | cost [39.0]
82 --> 83 | cost [36.0]
85 --> 76 | cost [30.0]
86 --> 95 | cost [24.0]
87 --> 88 | cost [24.0]
90 --> 89 | cost [24.0]
91 --> 93 | cost [42.0]
92 --> 93 | cost [36.0]
96 --> 97 | cost [33.0]
98 --> 97 | cost [39.0]
99 --> 89 | cost [42.0]

BACKUP RING
1  ---  5 | cost [3.0100000000000002]
2  --- 20 | cost [2.0300000000000002]
4  ---  6 | cost [1.68]
5  --- 15 | cost [1.68]
6  --- 16 | cost [1.61]
11 --- 21 | cost [2.0300000000000002]
11 --- 100 | cost [1.75]
15 --- 25 | cost [1.19]
16 --- 26 | cost [1.54]
20 --- 30 | cost [1.96]
21 --- 29 | cost [1.96]
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 --- 70 | cost [2.73]
56 --- 66 | cost [1.47]
57 --- 65 | cost [1.33]
62 --- 71 | cost [1.19]
65 --- 67 | cost [1.61]
66 --- 68 | cost [1.26]
67 --- 77 | cost [1.33]
68 --- 76 | cost [1.4000000000000001]
70 --- 80 | cost [0.84]
71 --- 79 | cost [1.68]
76 --- 83 | cost [1.96]
77 --- 84 | cost [1.75]
79 --- 89 | cost [1.54]
80 --- 88 | cost [2.0300000000000002]
83 --- 94 | cost [1.96]
84 --- 93 | cost [1.54]
88 --- 97 | cost [1.26]
89 --- 95 | cost [2.24]
93 --- 95 | cost [1.82]
94 --- 97 | cost [2.38]

BACKUP STAR
3  -->  4 | cost [0.33]
7  -->  5 | cost [0.5700000000000001]
8  -->  5 | cost [0.87]
9  -->  6 | cost [0.87]
10 --> 11 | cost [0.36]
12 -->  2 | cost [0.39]
13 --> 21 | cost [0.54]
14 -->  4 | cost [0.45]
17 --> 16 | cost [0.39]
18 --> 25 | cost [0.81]
19 --> 21 | cost [0.75]
22 --> 20 | cost [0.66]
23 --> 25 | cost [0.51]
24 --> 15 | 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 --> 38 | cost [0.54]
49 --> 48 | cost [0.63]
50 --> 42 | cost [0.63]
54 --> 52 | cost [0.63]
55 --> 47 | cost [0.51]
58 --> 56 | cost [0.5700000000000001]
59 --> 57 | cost [0.63]
60 --> 52 | cost [0.5700000000000001]
61 --> 70 | cost [0.48]
63 --> 62 | cost [0.48]
64 --> 56 | cost [0.5700000000000001]
69 --> 68 | cost [0.48]
72 --> 80 | cost [0.54]
73 --> 84 | cost [0.78]
74 --> 66 | cost [0.45]
75 --> 66 | cost [0.48]
78 --> 68 | cost [0.42]
81 --> 71 | cost [0.51]
82 --> 93 | cost [0.75]
85 --> 84 | cost [0.3]
86 --> 88 | cost [0.54]
87 --> 95 | cost [0.39]
90 --> 97 | cost [0.66]
91 --> 83 | cost [0.48]
92 --> 83 | cost [0.63]
96 --> 95 | cost [0.45]
98 --> 89 | cost [0.51]
99 --> 97 | cost [0.5700000000000001]

B = 3.21
i★ = 53
j★ = 62
k★ = 70