------------------------------------------------------------
                           α=5.0 —— rat99 —— 99 nodes       
------------------------------------------------------------

——————— Sun, 21 Jan 2024 10:14:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—2—100
total time           3634.67 (TL 3600)    gap                  0.097                
blossom time         0                    nb blossom           0.0                  
LB <= UB             5865.28<=6494.9      subtour              3594.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:99                 
2-opt strategy       0                                                              
explored_nodes       847                  n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—100

RING
1  ---  2 | cost [70.0]
2  --- 100 | cost [70.0]
3  ---  4 | cost [55.0]
3  --- 12 | cost [35.0]
4  --- 14 | cost [75.0]
5  ---  6 | cost [45.0]
5  --- 14 | cost [60.0]
6  ---  7 | cost [55.0]
7  ---  8 | cost [50.0]
8  ---  9 | cost [50.0]
9  --- 18 | cost [100.0]
12 --- 13 | cost [65.0]
13 --- 22 | cost [70.0]
15 --- 16 | cost [50.0]
15 --- 23 | cost [70.0]
16 --- 17 | cost [65.0]
17 --- 18 | cost [50.0]
19 --- 20 | cost [65.0]
19 --- 28 | cost [95.0]
20 --- 21 | cost [90.0]
21 --- 22 | cost [30.0]
23 --- 24 | cost [50.0]
24 --- 25 | cost [45.0]
25 --- 26 | cost [50.0]
26 --- 35 | cost [60.0]
28 --- 37 | cost [45.0]
29 --- 30 | cost [55.0]
29 --- 37 | cost [45.0]
30 --- 31 | cost [60.0]
31 --- 32 | cost [55.0]
32 --- 41 | cost [45.0]
33 --- 34 | cost [60.0]
33 --- 42 | cost [60.0]
34 --- 43 | cost [30.0]
35 --- 36 | cost [55.0]
36 --- 44 | cost [65.0]
39 --- 40 | cost [30.0]
39 --- 48 | cost [20.0]
40 --- 41 | cost [70.0]
42 --- 43 | cost [40.0]
44 --- 45 | cost [80.0]
45 --- 54 | cost [65.0]
46 --- 47 | cost [40.0]
46 --- 55 | cost [75.0]
47 --- 48 | cost [75.0]
49 --- 50 | cost [70.0]
49 --- 58 | cost [60.0]
50 --- 51 | cost [60.0]
51 --- 52 | cost [45.0]
52 --- 53 | cost [40.0]
53 --- 54 | cost [70.0]
55 --- 56 | cost [90.0]
56 --- 57 | cost [40.0]
57 --- 58 | cost [65.0]
61 --- 62 | cost [45.0]
61 --- 70 | cost [80.0]
62 --- 63 | cost [80.0]
63 --- 72 | cost [100.0]
65 --- 66 | cost [55.0]
65 --- 74 | cost [75.0]
66 --- 67 | cost [65.0]
67 --- 68 | cost [25.0]
68 --- 78 | cost [70.0]
70 --- 71 | cost [35.0]
71 --- 80 | cost [50.0]
72 --- 81 | cost [65.0]
73 --- 74 | cost [85.0]
73 --- 82 | cost [90.0]
76 --- 77 | cost [60.0]
76 --- 85 | cost [50.0]
77 --- 78 | cost [50.0]
80 --- 81 | cost [65.0]
82 --- 83 | cost [60.0]
83 --- 91 | cost [80.0]
85 --- 86 | cost [55.0]
86 --- 95 | cost [40.0]
87 --- 88 | cost [40.0]
87 --- 97 | cost [75.0]
88 --- 89 | cost [75.0]
89 --- 90 | cost [40.0]
90 --- 99 | cost [50.0]
91 --- 92 | cost [35.0]
92 --- 93 | cost [60.0]
93 --- 94 | cost [65.0]
94 --- 95 | cost [90.0]
97 --- 98 | cost [65.0]
98 --- 99 | cost [45.0]

STAR
10 -->  2 | cost [55.0]
11 --> 12 | cost [30.0]
27 --> 35 | cost [65.0]
38 --> 99 | cost [640.0]
59 --> 58 | cost [40.0]
60 --> 51 | cost [70.0]
64 --> 65 | cost [70.0]
69 --> 70 | cost [45.0]
75 --> 76 | cost [65.0]
79 --> 78 | cost [70.0]
84 --> 85 | cost [50.0]
96 --> 97 | cost [55.0]

BACKUP RING
1  --- 100 | cost [0.0]
3  --- 13 | cost [0.9500000000000001]
3  --- 14 | cost [1.0]
4  ---  5 | cost [0.75]
4  --- 12 | cost [0.8]
5  ---  7 | cost [0.9500000000000001]
6  ---  8 | cost [1.0]
6  --- 14 | cost [0.85]
7  ---  9 | cost [1.0]
8  --- 18 | cost [1.35]
9  --- 17 | cost [1.25]
12 --- 22 | cost [1.3]
13 --- 21 | cost [0.9]
15 --- 17 | cost [1.1500000000000001]
15 --- 24 | cost [0.85]
16 --- 18 | cost [1.1]
16 --- 23 | cost [1.05]
19 --- 21 | cost [1.25]
19 --- 37 | cost [1.4000000000000001]
20 --- 22 | cost [1.1]
20 --- 28 | cost [1.45]
23 --- 25 | cost [0.85]
24 --- 26 | cost [0.85]
25 --- 35 | cost [1.1]
26 --- 36 | cost [1.1500000000000001]
28 --- 29 | cost [0.65]
29 --- 31 | cost [1.0]
30 --- 32 | cost [1.1]
30 --- 37 | cost [0.9500000000000001]
31 --- 41 | cost [0.9500000000000001]
32 --- 40 | cost [1.05]
33 --- 43 | cost [0.65]
34 --- 42 | cost [0.65]
35 --- 44 | cost [0.8]
36 --- 45 | cost [1.25]
39 --- 41 | cost [1.0]
39 --- 47 | cost [0.9]
40 --- 48 | cost [0.45]
44 --- 54 | cost [1.45]
45 --- 53 | cost [0.85]
46 --- 48 | cost [1.05]
46 --- 56 | cost [1.4000000000000001]
47 --- 55 | cost [0.85]
49 --- 51 | cost [1.1]
49 --- 57 | cost [0.9]
50 --- 52 | cost [1.05]
50 --- 58 | cost [1.3]
51 --- 53 | cost [0.8]
52 --- 54 | cost [1.05]
55 --- 57 | cost [1.1]
56 --- 58 | cost [0.9500000000000001]
61 --- 63 | cost [1.25]
61 --- 71 | cost [0.9500000000000001]
62 --- 70 | cost [0.9]
62 --- 72 | cost [1.05]
63 --- 81 | cost [1.6500000000000001]
65 --- 67 | cost [1.1500000000000001]
65 --- 73 | cost [1.6]
66 --- 68 | cost [0.9]
66 --- 74 | cost [0.75]
67 --- 78 | cost [0.9500000000000001]
68 --- 77 | cost [0.75]
70 --- 80 | cost [0.6]
71 --- 81 | cost [0.85]
72 --- 80 | cost [0.9]
73 --- 83 | cost [1.05]
74 --- 82 | cost [1.75]
76 --- 78 | cost [1.1]
76 --- 86 | cost [1.05]
77 --- 85 | cost [0.85]
82 --- 91 | cost [0.85]
83 --- 92 | cost [1.05]
85 --- 95 | cost [0.9]
86 --- 94 | cost [1.2]
87 --- 89 | cost [1.0]
87 --- 98 | cost [1.3]
88 --- 90 | cost [1.1500000000000001]
88 --- 97 | cost [0.9]
89 --- 99 | cost [0.7000000000000001]
90 --- 98 | cost [0.85]
91 --- 93 | cost [0.7000000000000001]
92 --- 94 | cost [1.1]
93 --- 95 | cost [1.3]
97 --- 99 | cost [0.9500000000000001]

BACKUP STAR
10 -->  1 | cost [0.85]
11 -->  2 | cost [0.55]
27 --> 26 | cost [0.8]
38 --> 39 | cost [0.45]
59 --> 49 | cost [0.9]
60 --> 49 | cost [0.8]
64 --> 56 | cost [0.9500000000000001]
69 --> 78 | cost [0.6]
75 --> 74 | cost [0.7000000000000001]
79 --> 88 | cost [0.7000000000000001]
84 --> 76 | cost [0.7000000000000001]
96 --> 95 | cost [0.75]

B = 2.05
i★ = 87
j★ = 97
k★ = 98

       
——————— Sun, 21 Jan 2024 11:15:47 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 83 hubs —— 1-2-3-12-13-22-21-20-19-28-37-38-39-48-47-46-55-56-57-58-49-50-51-52-53-54-63-72-81-80-75-73-82-91-92-93-84-85-76-99-90-89-98-97-96-95-86-87-66-67-68-77-78-71-70-61-43-34-33-42-32-31-30-41-45-44-36-35-26-25-24-23-15-16-17-18-9-8-7-6-5-4-100-1
total time           3610.3 (TL 3600)     gap                  0.204                
blossom time         0                    nb blossom           0.0                  
LB <= UB             5798.75<=7287.1      Master/SP costs      7160/127.1           
Master time          3605.31              SP time              4.99                 
subtour              43435.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            12.0                 SP method            poly                 
tildeV               2:99                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       11087                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—3—12—13—22—21—20—19—28—37—38—39—48—47—46—55—56—57—58—49—50—51—52—53—54—63—72—81—80—75—73—82—91—92—93—84—85—76—99—90—89—98—97—96—95—86—87—66—67—68—77—78—71—70—61—43—34—33—42—32—31—30—41—45—44—36—35—26—25—24—23—15—16—17—18—9—8—7—6—5—4—100

RING
1  ---  2 | cost [70.0]
2  ---  3 | cost [45.0]
3  --- 12 | cost [35.0]
4  ---  5 | cost [75.0]
4  --- 100 | cost [140.0]
5  ---  6 | cost [45.0]
6  ---  7 | cost [55.0]
7  ---  8 | cost [50.0]
8  ---  9 | cost [50.0]
9  --- 18 | cost [100.0]
12 --- 13 | cost [65.0]
13 --- 22 | cost [70.0]
15 --- 16 | cost [50.0]
15 --- 23 | cost [70.0]
16 --- 17 | cost [65.0]
17 --- 18 | cost [50.0]
19 --- 20 | cost [65.0]
19 --- 28 | cost [95.0]
20 --- 21 | cost [90.0]
21 --- 22 | cost [30.0]
23 --- 24 | cost [50.0]
24 --- 25 | cost [45.0]
25 --- 26 | cost [50.0]
26 --- 35 | cost [60.0]
28 --- 37 | cost [45.0]
30 --- 31 | cost [60.0]
30 --- 41 | cost [140.0]
31 --- 32 | cost [55.0]
32 --- 42 | cost [90.0]
33 --- 34 | cost [60.0]
33 --- 42 | cost [60.0]
34 --- 43 | cost [30.0]
35 --- 36 | cost [55.0]
36 --- 44 | cost [65.0]
37 --- 38 | cost [85.0]
38 --- 39 | cost [45.0]
39 --- 48 | cost [20.0]
41 --- 45 | cost [205.0]
43 --- 61 | cost [250.0]
44 --- 45 | cost [80.0]
46 --- 47 | cost [40.0]
46 --- 55 | cost [75.0]
47 --- 48 | cost [75.0]
49 --- 50 | cost [70.0]
49 --- 58 | cost [60.0]
50 --- 51 | cost [60.0]
51 --- 52 | cost [45.0]
52 --- 53 | cost [40.0]
53 --- 54 | cost [70.0]
54 --- 63 | cost [95.0]
55 --- 56 | cost [90.0]
56 --- 57 | cost [40.0]
57 --- 58 | cost [65.0]
61 --- 70 | cost [80.0]
63 --- 72 | cost [100.0]
66 --- 67 | cost [65.0]
66 --- 87 | cost [260.0]
67 --- 68 | cost [25.0]
68 --- 77 | cost [75.0]
70 --- 71 | cost [35.0]
71 --- 78 | cost [120.0]
72 --- 81 | cost [65.0]
73 --- 75 | cost [110.0]
73 --- 82 | cost [90.0]
75 --- 80 | cost [245.0]
76 --- 85 | cost [50.0]
76 --- 99 | cost [285.0]
77 --- 78 | cost [50.0]
80 --- 81 | cost [65.0]
82 --- 91 | cost [85.0]
84 --- 85 | cost [50.0]
84 --- 93 | cost [110.0]
86 --- 87 | cost [55.0]
86 --- 95 | cost [40.0]
89 --- 90 | cost [40.0]
89 --- 98 | cost [85.0]
90 --- 99 | cost [50.0]
91 --- 92 | cost [35.0]
92 --- 93 | cost [60.0]
95 --- 96 | cost [75.0]
96 --- 97 | cost [55.0]
97 --- 98 | cost [65.0]

STAR
10 -->  2 | cost [55.0]
11 --> 12 | cost [30.0]
14 -->  5 | cost [60.0]
27 --> 35 | cost [65.0]
29 --> 37 | cost [45.0]
40 --> 39 | cost [30.0]
59 --> 58 | cost [40.0]
60 --> 51 | cost [70.0]
62 --> 61 | cost [45.0]
64 --> 56 | cost [95.0]
65 --> 66 | cost [55.0]
69 --> 70 | cost [45.0]
74 --> 66 | cost [75.0]
79 --> 78 | cost [70.0]
83 --> 82 | cost [60.0]
88 --> 87 | cost [40.0]
94 --> 93 | cost [65.0]

BACKUP RING
1  ---  3 | cost [1.1500000000000001]
2  --- 12 | cost [0.65]
3  --- 13 | cost [0.9500000000000001]
4  ---  6 | cost [1.2]
5  ---  7 | cost [0.9500000000000001]
5  --- 100 | cost [2.15]
6  ---  8 | cost [1.0]
7  ---  9 | cost [1.0]
8  --- 18 | cost [1.35]
9  --- 17 | cost [1.25]
12 --- 22 | cost [1.3]
13 --- 21 | cost [0.9]
15 --- 17 | cost [1.1500000000000001]
15 --- 24 | cost [0.85]
16 --- 18 | cost [1.1]
16 --- 23 | cost [1.05]
19 --- 21 | cost [1.25]
19 --- 37 | cost [1.4000000000000001]
20 --- 22 | cost [1.1]
20 --- 28 | cost [1.45]
23 --- 25 | cost [0.85]
24 --- 26 | cost [0.85]
25 --- 35 | cost [1.1]
26 --- 36 | cost [1.1500000000000001]
28 --- 38 | cost [1.3]
30 --- 32 | cost [1.1]
30 --- 45 | cost [3.35]
31 --- 41 | cost [0.9500000000000001]
31 --- 42 | cost [1.45]
32 --- 33 | cost [0.6]
33 --- 43 | cost [0.65]
34 --- 42 | cost [0.65]
34 --- 61 | cost [2.8000000000000003]
35 --- 44 | cost [0.8]
36 --- 45 | cost [1.25]
37 --- 39 | cost [1.25]
38 --- 48 | cost [0.55]
39 --- 47 | cost [0.9]
41 --- 44 | cost [1.75]
43 --- 70 | cost [3.3000000000000003]
46 --- 48 | cost [1.05]
46 --- 56 | cost [1.4000000000000001]
47 --- 55 | cost [0.85]
49 --- 51 | cost [1.1]
49 --- 57 | cost [0.9]
50 --- 52 | cost [1.05]
50 --- 58 | cost [1.3]
51 --- 53 | cost [0.8]
52 --- 54 | cost [1.05]
53 --- 63 | cost [1.05]
54 --- 72 | cost [1.95]
55 --- 57 | cost [1.1]
56 --- 58 | cost [0.9500000000000001]
61 --- 71 | cost [0.9500000000000001]
63 --- 81 | cost [1.6500000000000001]
66 --- 68 | cost [0.9]
66 --- 86 | cost [2.35]
67 --- 77 | cost [0.9500000000000001]
67 --- 87 | cost [2.15]
68 --- 78 | cost [0.7000000000000001]
70 --- 78 | cost [0.9500000000000001]
71 --- 77 | cost [1.7]
72 --- 80 | cost [0.9]
73 --- 80 | cost [3.5]
73 --- 91 | cost [1.7]
75 --- 81 | cost [3.0500000000000003]
75 --- 82 | cost [1.75]
76 --- 84 | cost [0.7000000000000001]
76 --- 90 | cost [2.65]
82 --- 92 | cost [1.2]
84 --- 92 | cost [1.6]
85 --- 93 | cost [1.4000000000000001]
85 --- 99 | cost [2.5]
86 --- 96 | cost [1.1]
87 --- 95 | cost [0.65]
89 --- 97 | cost [0.85]
89 --- 99 | cost [0.7000000000000001]
90 --- 98 | cost [0.85]
91 --- 93 | cost [0.7000000000000001]
95 --- 97 | cost [0.9500000000000001]
96 --- 98 | cost [1.0]

BACKUP STAR
10 -->  1 | cost [0.85]
11 -->  2 | cost [0.55]
14 -->  4 | cost [0.75]
27 --> 26 | cost [0.8]
29 --> 30 | cost [0.55]
40 --> 48 | cost [0.45]
59 --> 49 | cost [0.9]
60 --> 49 | cost [0.8]
62 --> 63 | cost [0.8]
64 --> 55 | cost [1.1]
65 --> 56 | cost [0.65]
69 --> 78 | cost [0.6]
74 --> 75 | cost [0.7000000000000001]
79 --> 80 | cost [0.75]
83 --> 84 | cost [0.8]
88 --> 89 | cost [0.75]
94 --> 95 | cost [0.9]

B = 4.1000000000000005
i★ = 43
j★ = 61
k★ = 70