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

——————— Wed, 24 Jan 2024 21:13:14 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 43 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—2—100
total time           187.67               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             6436<=6436           subtour              2188.0               
connectivity cuts    1250.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1243                 n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
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—2—100

RING
1  ---  4 | cost [196.0]
1  --- 100 | cost [0.0]
2  --- 12 | cost [91.0]
2  --- 100 | cost [98.0]
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
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 --> 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 --> 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 --> 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

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 24 Jan 2024 21:16:39 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 44 hubs —— 1-2-3-12-13-22-21-30-29-38-39-48-47-57-56-65-74-73-83-84-85-86-87-88-79-78-69-70-71-62-53-52-51-42-43-34-35-26-25-16-6-5-4-100-1
total time           175.38               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             6436<=6436           Master/SP costs      6436/0               
Master time          175.38               SP time              0.0                  
subtour              1600.0               connectivity cuts    1819.0               
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       1819                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—3—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  ---  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 --- 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 --> 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 --> 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

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1