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

——————— Mon, 08 Jan 2024 08:30:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 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
total time           36.74                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             6436<=6436           subtour              316.0                
connectivity cuts    139.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       31                   n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
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

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:31:51 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 43 hubs —— 1-4-5-6-16-25-26-35-34-43-42-51-52-53-62-71-70-69-78-79-88-87-86-85-84-83-73-74-65-56-57-47-48-39-38-29-30-21-22-13-12-2-100-1
total time           35.15                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             6436<=6436           Master/SP costs      6436/0               
Master time          35.15                SP time              0.0                  
subtour              314.0                connectivity cuts    144.0                
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       119                  
F                    0.0                  
                                          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—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 --> 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

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 21:32:05 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—2—100
total time           3356.78              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             6162<=6162           subtour              15948.0              
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       81793                n lazycuts edges     6.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—100

RING
1  ---  2 | cost [98.0]
2  --- 100 | cost [98.0]
13 --- 14 | cost [112.0]
13 --- 22 | cost [98.0]
14 --- 15 | cost [119.0]
15 --- 16 | cost [70.0]
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 --- 47 | cost [126.0]
42 --- 43 | cost [56.0]
42 --- 51 | cost [147.0]
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 --- 66 | cost [77.0]
66 --- 67 | cost [91.0]
67 --- 68 | cost [35.0]
68 --- 78 | cost [98.0]
69 --- 70 | cost [63.0]
69 --- 78 | cost [84.0]
70 --- 71 | cost [49.0]
83 --- 91 | cost [112.0]
83 --- 93 | cost [112.0]
86 --- 87 | cost [77.0]
86 --- 95 | cost [56.0]
87 --- 95 | cost [91.0]
90 --- 98 | cost [119.0]
90 --- 99 | cost [70.0]
91 --- 93 | cost [98.0]
98 --- 99 | cost [63.0]

STAR
3  -->  2 | cost [27.0]
4  --> 14 | cost [45.0]
5  --> 14 | cost [36.0]
6  --> 14 | cost [51.0]
7  --> 16 | cost [78.0]
8  --> 16 | cost [87.0]
9  --> 16 | cost [90.0]
10 -->  2 | cost [33.0]
11 -->  2 | cost [33.0]
12 -->  2 | cost [39.0]
17 --> 16 | cost [39.0]
18 --> 16 | cost [66.0]
19 --> 30 | cost [75.0]
20 --> 21 | cost [54.0]
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]
48 --> 39 | cost [12.0]
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 --> 67 | cost [54.0]
60 --> 51 | cost [42.0]
61 --> 62 | cost [27.0]
63 --> 62 | cost [48.0]
64 --> 65 | cost [42.0]
72 --> 71 | cost [39.0]
73 --> 83 | cost [63.0]
74 --> 66 | cost [45.0]
75 --> 66 | cost [48.0]
76 --> 68 | cost [60.0]
77 --> 78 | cost [30.0]
79 --> 78 | cost [42.0]
80 --> 71 | cost [30.0]
81 --> 71 | cost [51.0]
82 --> 83 | cost [36.0]
84 --> 83 | cost [48.0]
85 --> 86 | cost [33.0]
88 --> 87 | cost [24.0]
89 --> 90 | cost [24.0]
92 --> 91 | cost [21.0]
94 --> 93 | cost [39.0]
96 --> 95 | cost [45.0]
97 --> 98 | cost [39.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 22:32:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 48 hubs —— 1-19-37-38-39-48-49-56-66-74-82-91-93-76-85-86-90-99-89-88-79-80-71-62-53-52-51-42-33-34-26-25-27-18-9-8-7-6-16-15-24-22-13-12-11-3-2-100-1
total time           3606.2 (TL 3600)     gap                  0.225                
blossom time         0                    nb blossom           0.0                  
LB <= UB             5989<=7731           Master/SP costs      7731/0               
Master time          3606.2               SP time              0.0                  
subtour              27589.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       16424                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—19—37—38—39—48—49—56—66—74—82—91—93—76—85—86—90—99—89—88—79—80—71—62—53—52—51—42—33—34—26—25—27—18—9—8—7—6—16—15—24—22—13—12—11—3—2—100

RING
1  --- 19 | cost [343.0]
2  ---  3 | cost [63.0]
2  --- 100 | cost [98.0]
3  --- 11 | cost [77.0]
6  ---  7 | cost [77.0]
6  --- 16 | cost [161.0]
7  ---  8 | cost [70.0]
8  ---  9 | cost [70.0]
9  --- 18 | cost [140.0]
11 --- 12 | cost [42.0]
12 --- 13 | cost [91.0]
13 --- 22 | cost [98.0]
15 --- 16 | cost [70.0]
15 --- 24 | cost [119.0]
18 --- 27 | cost [154.0]
19 --- 37 | cost [196.0]
22 --- 24 | cost [154.0]
25 --- 26 | cost [70.0]
25 --- 27 | cost [168.0]
26 --- 34 | cost [161.0]
33 --- 34 | cost [84.0]
33 --- 42 | cost [84.0]
37 --- 38 | cost [119.0]
38 --- 39 | cost [63.0]
39 --- 48 | cost [28.0]
42 --- 51 | cost [147.0]
48 --- 49 | cost [147.0]
49 --- 56 | cost [182.0]
51 --- 52 | cost [63.0]
52 --- 53 | cost [56.0]
53 --- 62 | cost [147.0]
56 --- 66 | cost [147.0]
62 --- 71 | cost [119.0]
66 --- 74 | cost [105.0]
71 --- 80 | cost [70.0]
74 --- 82 | cost [245.0]
76 --- 85 | cost [70.0]
76 --- 93 | cost [245.0]
79 --- 80 | cost [105.0]
79 --- 88 | cost [98.0]
82 --- 91 | cost [119.0]
85 --- 86 | cost [77.0]
86 --- 90 | cost [273.0]
88 --- 89 | cost [105.0]
89 --- 99 | cost [98.0]
90 --- 99 | cost [70.0]
91 --- 93 | cost [98.0]

STAR
4  --> 16 | cost [120.0]
5  -->  7 | cost [57.0]
10 -->  2 | cost [33.0]
14 -->  6 | cost [51.0]
17 --> 18 | cost [30.0]
20 --> 19 | cost [39.0]
21 --> 22 | cost [18.0]
23 --> 24 | cost [30.0]
28 --> 37 | cost [27.0]
29 --> 37 | cost [27.0]
30 --> 37 | cost [57.0]
31 --> 33 | cost [63.0]
32 --> 33 | cost [36.0]
35 --> 27 | cost [39.0]
36 --> 27 | cost [48.0]
40 --> 39 | cost [18.0]
41 --> 42 | cost [42.0]
43 --> 34 | cost [18.0]
44 --> 34 | cost [39.0]
45 --> 53 | cost [51.0]
46 --> 38 | cost [54.0]
47 --> 48 | cost [45.0]
50 --> 51 | cost [36.0]
54 --> 53 | cost [42.0]
55 --> 56 | cost [54.0]
57 --> 56 | cost [24.0]
58 --> 49 | cost [36.0]
59 --> 49 | cost [54.0]
60 --> 51 | cost [42.0]
61 --> 62 | cost [27.0]
63 --> 62 | cost [48.0]
64 --> 74 | cost [57.0]
65 --> 66 | cost [33.0]
67 --> 66 | cost [39.0]
68 --> 76 | cost [60.0]
69 --> 71 | cost [48.0]
70 --> 71 | cost [21.0]
72 --> 71 | cost [39.0]
73 --> 74 | cost [51.0]
75 --> 76 | cost [39.0]
77 --> 76 | cost [36.0]
78 --> 80 | cost [60.0]
81 --> 80 | cost [39.0]
83 --> 82 | cost [36.0]
84 --> 85 | cost [30.0]
87 --> 88 | cost [24.0]
92 --> 91 | cost [21.0]
94 --> 93 | cost [39.0]
95 --> 86 | cost [24.0]
96 --> 86 | cost [66.0]
97 --> 89 | cost [51.0]
98 --> 99 | cost [27.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1