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

——————— Mon, 08 Jan 2024 11:48:51 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 43 hubs —— 1-2-12-13-22-21-30-29-38-39-48-47-57-56-65-74-73-83-84-85-86-87-88-79-78-69-70-71-62-53-52-51-42-43-34-35-26-25-16-6-5-4-100-1
total time           55.46                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             6470.16<=6470.16     Master/SP costs      6436/34.16           
Master time          50.9                 SP time              4.56                 
subtour              111.0                connectivity cuts    362.0                
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            25.0                 SP method            poly                 
tildeV               2:99                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       732                  
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—12—13—22—21—30—29—38—39—48—47—57—56—65—74—73—83—84—85—86—87—88—79—78—69—70—71—62—53—52—51—42—43—34—35—26—25—16—6—5—4—100

RING
1  ---  2 | cost [98.0]
1  --- 100 | cost [0.0]
2  --- 12 | cost [91.0]
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 --- 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
3  --> 12 | cost [21.0]
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 --> 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 --> 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  --- 12 | cost [1.8900000000000001]
2  --- 13 | cost [1.82]
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 --- 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
3  -->  2 | cost [0.27]
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 --> 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 --> 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

       
——————— Wed, 10 Jan 2024 17:08:26 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 27 hubs —— 1—11—22—16—17—26—35—43—54—60—70—71—81—90—68—83—74—56—64—58—40—46—37—28—19—4—100
total time           3634.34 (TL 3600)    gap                  0.562                
blossom time         0                    nb blossom           0.0                  
LB <= UB             6035.78<=13782.87    subtour              845.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:99                 
2-opt strategy       0                                                              
explored_nodes       134                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—11—22—16—17—26—35—43—54—60—70—71—81—90—68—83—74—56—64—58—40—46—37—28—19—4—100

RING
1  --- 11 | cost [175.0]
4  --- 19 | cost [357.0]
4  --- 100 | cost [196.0]
11 --- 22 | cost [196.0]
16 --- 17 | cost [91.0]
16 --- 22 | cost [245.0]
17 --- 26 | cost [133.0]
19 --- 28 | cost [133.0]
26 --- 35 | cost [84.0]
28 --- 37 | cost [63.0]
35 --- 43 | cost [161.0]
37 --- 46 | cost [196.0]
40 --- 46 | cost [210.0]
40 --- 58 | cost [238.0]
43 --- 54 | cost [245.0]
54 --- 60 | cost [259.0]
56 --- 64 | cost [133.0]
56 --- 74 | cost [196.0]
58 --- 64 | cost [259.0]
60 --- 70 | cost [217.0]
68 --- 83 | cost [329.0]
68 --- 90 | cost [392.0]
70 --- 71 | cost [49.0]
71 --- 81 | cost [119.0]
74 --- 83 | cost [238.0]
81 --- 90 | cost [224.0]

STAR
2  -->  1 | cost [42.0]
3  -->  1 | cost [69.0]
5  -->  1 | cost [129.0]
6  --> 26 | cost [135.0]
7  --> 16 | cost [78.0]
8  -->  1 | cost [213.0]
9  -->  1 | cost [243.0]
10 -->  1 | cost [51.0]
12 -->  1 | cost [81.0]
13 -->  1 | cost [120.0]
14 -->  4 | cost [45.0]
15 -->  1 | cost [174.0]
18 -->  1 | cost [261.0]
20 --> 37 | cost [111.0]
21 --> 37 | cost [105.0]
23 --> 37 | cost [159.0]
24 --> 37 | cost [168.0]
25 --> 26 | cost [30.0]
27 --> 60 | cost [222.0]
29 --> 37 | cost [27.0]
30 --> 37 | cost [57.0]
31 --> 37 | cost [87.0]
32 --> 37 | cost [105.0]
33 --> 26 | cost [78.0]
34 --> 60 | cost [138.0]
36 --> 60 | cost [180.0]
38 --> 37 | cost [51.0]
39 --> 46 | cost [72.0]
41 --> 60 | cost [108.0]
42 --> 60 | cost [102.0]
44 --> 60 | cost [141.0]
45 --> 60 | cost [117.0]
47 --> 46 | cost [24.0]
48 --> 40 | cost [27.0]
49 --> 60 | cost [48.0]
50 --> 60 | cost [51.0]
51 --> 60 | cost [42.0]
52 --> 60 | cost [57.0]
53 --> 60 | cost [69.0]
55 --> 46 | cost [45.0]
57 --> 46 | cost [81.0]
59 --> 60 | cost [54.0]
61 --> 60 | cost [48.0]
62 --> 71 | cost [51.0]
63 --> 60 | cost [105.0]
65 --> 46 | cost [120.0]
66 --> 60 | cost [123.0]
67 --> 60 | cost [105.0]
69 --> 60 | cost [93.0]
72 --> 71 | cost [39.0]
73 --> 46 | cost [204.0]
75 --> 60 | cost [162.0]
76 --> 60 | cost [171.0]
77 --> 90 | cost [135.0]
78 --> 90 | cost [126.0]
79 -->  1 | cost [540.0]
80 --> 68 | cost [93.0]
82 --> 64 | cost [147.0]
84 --> 60 | cost [213.0]
85 --> 90 | cost [144.0]
86 --> 90 | cost [117.0]
87 --> 74 | cost [162.0]
88 --> 90 | cost [69.0]
89 --> 90 | cost [24.0]
91 --> 90 | cost [237.0]
92 --> 90 | cost [231.0]
93 --> 90 | cost [195.0]
94 --> 90 | cost [168.0]
95 --> 71 | cost [174.0]
96 --> 74 | cost [204.0]
97 --> 90 | cost [66.0]
98 --> 90 | cost [51.0]
99 --> 90 | cost [30.0]

BACKUP RING
1  --- 22 | cost [3.64]
4  --- 28 | cost [4.69]
11 --- 16 | cost [3.43]
16 --- 26 | cost [1.54]
17 --- 22 | cost [3.22]
17 --- 35 | cost [1.96]
19 --- 37 | cost [1.96]
19 --- 100 | cost [3.43]
26 --- 43 | cost [2.0300000000000002]
28 --- 46 | cost [2.59]
35 --- 54 | cost [3.08]
37 --- 40 | cost [2.1]
40 --- 64 | cost [3.99]
43 --- 60 | cost [2.8000000000000003]
46 --- 58 | cost [2.66]
54 --- 70 | cost [3.29]
56 --- 58 | cost [1.33]
56 --- 83 | cost [4.34]
60 --- 71 | cost [2.38]
64 --- 74 | cost [1.33]
68 --- 74 | cost [2.0300000000000002]
68 --- 81 | cost [3.08]
70 --- 81 | cost [1.61]
71 --- 90 | cost [3.15]
83 --- 90 | cost [4.97]

BACKUP STAR
6  --> 16 | cost [0.6900000000000001]
7  --> 17 | cost [0.93]
14 --> 11 | cost [0.78]
20 --> 19 | cost [0.39]
21 --> 22 | cost [0.18]
23 --> 22 | cost [0.42]
24 --> 26 | cost [0.51]
25 --> 16 | cost [0.42]
27 --> 35 | cost [0.39]
29 --> 28 | cost [0.39]
30 --> 28 | cost [0.54]
31 --> 22 | cost [0.66]
32 --> 40 | cost [0.63]
33 --> 43 | cost [0.39]
34 --> 43 | cost [0.18]
36 --> 35 | cost [0.33]
38 --> 40 | cost [0.45]
39 --> 40 | cost [0.18]
41 --> 40 | cost [0.42]
42 --> 43 | cost [0.24]
44 --> 43 | cost [0.42]
45 --> 54 | cost [0.39]
47 --> 56 | cost [0.6900000000000001]
48 --> 46 | cost [0.63]
49 --> 58 | cost [0.36]
50 --> 40 | cost [0.51]
51 --> 43 | cost [0.78]
52 --> 54 | cost [0.63]
53 --> 54 | cost [0.42]
55 --> 56 | cost [0.54]
57 --> 56 | cost [0.24]
59 --> 58 | cost [0.24]
61 --> 70 | cost [0.48]
62 --> 70 | cost [0.54]
63 --> 54 | cost [0.5700000000000001]
65 --> 56 | cost [0.39]
66 --> 74 | cost [0.45]
67 --> 68 | cost [0.15]
69 --> 70 | cost [0.27]
72 --> 81 | cost [0.39]
73 --> 74 | cost [0.51]
75 --> 74 | cost [0.42]
76 --> 68 | cost [0.6]
77 --> 68 | cost [0.45]
78 --> 68 | cost [0.42]
80 --> 71 | cost [0.3]
82 --> 83 | cost [0.36]
84 --> 83 | cost [0.48]
85 --> 83 | cost [0.78]
86 --> 83 | cost [0.96]
87 --> 90 | cost [0.84]
88 --> 81 | cost [1.05]
89 --> 81 | cost [0.96]
91 --> 83 | cost [0.48]
92 --> 83 | cost [0.63]
93 --> 83 | cost [0.48]
94 --> 83 | cost [0.84]
95 --> 83 | cost [1.02]
96 --> 90 | cost [0.99]
97 --> 81 | cost [1.44]
98 --> 81 | cost [1.47]
99 --> 81 | cost [1.26]

B = 14.3
i★ = 68
j★ = 90
k★ = 81