------------------------------------------------------------
                            α=5.0 —— gr96 —— 96 nodes       
------------------------------------------------------------

——————— Thu, 18 Jan 2024 07:04:51 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 64 hubs —— 1—29—2—4—5—6—8—7—9—10—12—13—14—15—16—19—17—18—21—20—26—28—27—24—23—22—63—62—64—66—67—68—94—93—92—75—77—76—72—71—74—90—79—56—57—58—54—53—47—50—43—40—45—11—33—34—35—38—37—36—32—31—30—97
total time           3632.0 (TL 3600)     gap                  0.334                
blossom time         0                    nb blossom           0.0                  
LB <= UB             2371.72<=3563.5      subtour              1905.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:96                 
2-opt strategy       0                                                              
explored_nodes       1033                 n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—29—2—4—5—6—8—7—9—10—12—13—14—15—16—19—17—18—21—20—26—28—27—24—23—22—63—62—64—66—67—68—94—93—92—75—77—76—72—71—74—90—79—56—57—58—54—53—47—50—43—40—45—11—33—34—35—38—37—36—32—31—30—97

RING
1  --- 29 | cost [40.0]
2  ---  4 | cost [40.0]
2  --- 29 | cost [50.0]
4  ---  5 | cost [10.0]
5  ---  6 | cost [5.0]
6  ---  8 | cost [10.0]
7  ---  8 | cost [10.0]
7  ---  9 | cost [20.0]
9  --- 10 | cost [20.0]
10 --- 12 | cost [15.0]
11 --- 33 | cost [50.0]
11 --- 45 | cost [50.0]
12 --- 13 | cost [20.0]
13 --- 14 | cost [10.0]
14 --- 15 | cost [15.0]
15 --- 16 | cost [35.0]
16 --- 19 | cost [65.0]
17 --- 18 | cost [15.0]
17 --- 19 | cost [15.0]
18 --- 21 | cost [35.0]
20 --- 21 | cost [30.0]
20 --- 26 | cost [85.0]
22 --- 23 | cost [30.0]
22 --- 63 | cost [100.0]
23 --- 24 | cost [15.0]
24 --- 27 | cost [45.0]
26 --- 28 | cost [30.0]
27 --- 28 | cost [25.0]
30 --- 31 | cost [5.0]
30 --- 97 | cost [30.0]
31 --- 32 | cost [10.0]
32 --- 36 | cost [15.0]
33 --- 34 | cost [30.0]
34 --- 35 | cost [10.0]
35 --- 38 | cost [20.0]
36 --- 37 | cost [5.0]
37 --- 38 | cost [15.0]
40 --- 43 | cost [20.0]
40 --- 45 | cost [40.0]
43 --- 50 | cost [25.0]
47 --- 50 | cost [40.0]
47 --- 53 | cost [40.0]
53 --- 54 | cost [35.0]
54 --- 58 | cost [20.0]
56 --- 57 | cost [0.0]
56 --- 79 | cost [120.0]
57 --- 58 | cost [25.0]
62 --- 63 | cost [15.0]
62 --- 64 | cost [30.0]
64 --- 66 | cost [20.0]
66 --- 67 | cost [10.0]
67 --- 68 | cost [0.0]
68 --- 94 | cost [60.0]
71 --- 72 | cost [5.0]
71 --- 74 | cost [45.0]
72 --- 76 | cost [35.0]
74 --- 90 | cost [70.0]
75 --- 77 | cost [20.0]
75 --- 92 | cost [70.0]
76 --- 77 | cost [20.0]
79 --- 90 | cost [180.0]
92 --- 93 | cost [30.0]
93 --- 94 | cost [35.0]

STAR
3  -->  2 | cost [25.0]
25 --> 24 | cost [25.0]
39 --> 40 | cost [15.0]
41 --> 40 | cost [10.0]
42 --> 40 | cost [15.0]
44 --> 40 | cost [30.0]
46 --> 11 | cost [55.0]
48 --> 47 | cost [10.0]
49 --> 43 | cost [5.0]
51 --> 40 | cost [50.0]
52 --> 40 | cost [50.0]
55 --> 40 | cost [60.0]
59 --> 57 | cost [35.0]
60 --> 62 | cost [25.0]
61 --> 62 | cost [10.0]
65 --> 66 | cost [40.0]
69 --> 71 | cost [70.0]
70 --> 71 | cost [60.0]
73 --> 72 | cost [15.0]
78 --> 74 | cost [35.0]
80 --> 40 | cost [225.0]
81 --> 74 | cost [70.0]
82 --> 74 | cost [60.0]
83 --> 74 | cost [75.0]
84 --> 74 | cost [25.0]
85 --> 74 | cost [25.0]
86 --> 71 | cost [75.0]
87 --> 74 | cost [45.0]
88 --> 74 | cost [50.0]
89 --> 90 | cost [10.0]
91 --> 74 | cost [85.0]
95 --> 93 | cost [50.0]
96 --> 94 | cost [50.0]

BACKUP RING
1  ---  2 | cost [0.8]
2  ---  5 | cost [0.5]
4  ---  6 | cost [0.15]
4  --- 29 | cost [0.75]
5  ---  8 | cost [0.15]
6  ---  7 | cost [0.1]
7  --- 10 | cost [0.4]
8  ---  9 | cost [0.25]
9  --- 12 | cost [0.35000000000000003]
10 --- 13 | cost [0.35000000000000003]
11 --- 34 | cost [0.85]
11 --- 40 | cost [0.85]
12 --- 14 | cost [0.2]
13 --- 15 | cost [0.25]
14 --- 16 | cost [0.5]
15 --- 19 | cost [0.9500000000000001]
16 --- 17 | cost [0.5]
17 --- 21 | cost [0.4]
18 --- 19 | cost [0.1]
18 --- 20 | cost [0.1]
20 --- 28 | cost [1.1]
21 --- 26 | cost [0.55]
22 --- 24 | cost [0.45]
22 --- 62 | cost [1.1]
23 --- 27 | cost [0.45]
23 --- 63 | cost [0.75]
24 --- 28 | cost [0.65]
26 --- 27 | cost [0.3]
30 --- 32 | cost [0.15]
31 --- 36 | cost [0.25]
31 --- 97 | cost [0.35000000000000003]
32 --- 37 | cost [0.2]
33 --- 35 | cost [0.45]
33 --- 45 | cost [0.3]
34 --- 38 | cost [0.35000000000000003]
35 --- 37 | cost [0.2]
36 --- 38 | cost [0.2]
40 --- 50 | cost [0.45]
43 --- 45 | cost [0.35000000000000003]
43 --- 47 | cost [0.6]
47 --- 54 | cost [0.45]
50 --- 53 | cost [0.25]
53 --- 58 | cost [0.4]
54 --- 57 | cost [0.45]
56 --- 58 | cost [0.25]
56 --- 90 | cost [1.55]
57 --- 79 | cost [1.2]
62 --- 66 | cost [0.5]
63 --- 64 | cost [0.2]
64 --- 67 | cost [0.3]
66 --- 68 | cost [0.1]
67 --- 94 | cost [0.6]
68 --- 93 | cost [0.75]
71 --- 76 | cost [0.45]
71 --- 90 | cost [1.1]
72 --- 74 | cost [0.4]
72 --- 77 | cost [0.45]
74 --- 79 | cost [1.7]
75 --- 76 | cost [0.2]
75 --- 93 | cost [0.8]
77 --- 92 | cost [0.5]
92 --- 94 | cost [0.6]

BACKUP STAR
3  -->  4 | cost [0.45]
25 --> 23 | cost [0.35000000000000003]
39 --> 43 | cost [0.3]
41 --> 43 | cost [0.15]
42 --> 43 | cost [0.05]
44 --> 45 | cost [0.2]
46 --> 47 | cost [0.25]
48 --> 53 | cost [0.45]
49 --> 50 | cost [0.2]
51 --> 50 | cost [0.3]
52 --> 50 | cost [0.15]
55 --> 53 | cost [0.2]
59 --> 56 | cost [0.35000000000000003]
60 --> 58 | cost [0.35000000000000003]
61 --> 63 | cost [0.25]
65 --> 64 | cost [0.45]
69 --> 56 | cost [0.25]
70 --> 56 | cost [0.4]
73 --> 71 | cost [0.2]
78 --> 77 | cost [0.3]
80 --> 79 | cost [1.1500000000000001]
81 --> 90 | cost [0.8]
82 --> 90 | cost [0.7000000000000001]
83 --> 90 | cost [0.65]
84 --> 75 | cost [0.45]
85 --> 75 | cost [0.4]
86 --> 74 | cost [0.3]
87 --> 90 | cost [0.25]
88 --> 90 | cost [0.35000000000000003]
89 --> 74 | cost [0.65]
91 --> 90 | cost [0.35000000000000003]
95 --> 94 | cost [0.55]
96 --> 66 | cost [0.8]

B = 5.35
i★ = 71
j★ = 74
k★ = 90

       
——————— Thu, 18 Jan 2024 07:19:32 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 73 hubs —— 1-30-31-32-36-37-35-34-33-44-40-41-42-43-49-50-52-55-57-69-70-81-82-83-91-90-89-87-86-85-74-75-73-72-76-77-92-93-94-67-66-64-63-62-61-60-59-58-54-47-48-25-24-23-26-22-21-19-20-17-16-15-14-12-10-9-7-6-5-4-2-29-97-1
total time           810.2                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2389.7<=2389.7       Master/SP costs      2375.35/14.35        
Master time          799.72               SP time              10.48                
subtour              13205.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            27.0                 SP method            poly                 
tildeV               2:96                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       15363                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—30—31—32—36—37—35—34—33—44—40—41—42—43—49—50—52—55—57—69—70—81—82—83—91—90—89—87—86—85—74—75—73—72—76—77—92—93—94—67—66—64—63—62—61—60—59—58—54—47—48—25—24—23—26—22—21—19—20—17—16—15—14—12—10—9—7—6—5—4—2—29—97

RING
1  --- 30 | cost [30.0]
2  ---  4 | cost [40.0]
2  --- 29 | cost [50.0]
4  ---  5 | cost [10.0]
5  ---  6 | cost [5.0]
6  ---  7 | cost [10.0]
7  ---  9 | cost [20.0]
9  --- 10 | cost [20.0]
10 --- 12 | cost [15.0]
12 --- 14 | cost [20.0]
14 --- 15 | cost [15.0]
15 --- 16 | cost [35.0]
16 --- 17 | cost [50.0]
17 --- 20 | cost [10.0]
19 --- 20 | cost [5.0]
19 --- 21 | cost [30.0]
21 --- 22 | cost [35.0]
22 --- 26 | cost [20.0]
23 --- 24 | cost [15.0]
23 --- 26 | cost [30.0]
24 --- 25 | cost [25.0]
25 --- 48 | cost [50.0]
29 --- 97 | cost [40.0]
30 --- 31 | cost [5.0]
31 --- 32 | cost [10.0]
32 --- 36 | cost [15.0]
33 --- 34 | cost [30.0]
33 --- 44 | cost [25.0]
34 --- 35 | cost [10.0]
35 --- 37 | cost [20.0]
36 --- 37 | cost [5.0]
40 --- 41 | cost [10.0]
40 --- 44 | cost [30.0]
41 --- 42 | cost [5.0]
42 --- 43 | cost [5.0]
43 --- 49 | cost [5.0]
47 --- 48 | cost [10.0]
47 --- 54 | cost [45.0]
49 --- 50 | cost [20.0]
50 --- 52 | cost [15.0]
52 --- 55 | cost [15.0]
54 --- 58 | cost [20.0]
55 --- 57 | cost [35.0]
57 --- 69 | cost [25.0]
58 --- 59 | cost [35.0]
59 --- 60 | cost [35.0]
60 --- 61 | cost [25.0]
61 --- 62 | cost [10.0]
62 --- 63 | cost [15.0]
63 --- 64 | cost [20.0]
64 --- 66 | cost [20.0]
66 --- 67 | cost [10.0]
67 --- 94 | cost [60.0]
69 --- 70 | cost [25.0]
70 --- 81 | cost [50.0]
72 --- 73 | cost [15.0]
72 --- 76 | cost [35.0]
73 --- 75 | cost [20.0]
74 --- 75 | cost [20.0]
74 --- 85 | cost [25.0]
76 --- 77 | cost [20.0]
77 --- 92 | cost [50.0]
81 --- 82 | cost [15.0]
82 --- 83 | cost [20.0]
83 --- 91 | cost [40.0]
85 --- 86 | cost [5.0]
86 --- 87 | cost [20.0]
87 --- 89 | cost [20.0]
89 --- 90 | cost [10.0]
90 --- 91 | cost [35.0]
92 --- 93 | cost [30.0]
93 --- 94 | cost [35.0]

STAR
3  -->  2 | cost [25.0]
8  -->  6 | cost [10.0]
11 --> 33 | cost [50.0]
13 --> 14 | cost [10.0]
18 --> 19 | cost [10.0]
27 --> 26 | cost [30.0]
28 --> 26 | cost [30.0]
38 --> 37 | cost [15.0]
39 --> 40 | cost [15.0]
45 --> 44 | cost [20.0]
46 --> 47 | cost [25.0]
51 --> 55 | cost [15.0]
53 --> 52 | cost [15.0]
56 --> 57 | cost [0.0]
65 --> 66 | cost [40.0]
68 --> 67 | cost [0.0]
71 --> 72 | cost [5.0]
78 --> 85 | cost [20.0]
79 --> 69 | cost [100.0]
80 --> 83 | cost [145.0]
84 --> 86 | cost [15.0]
88 --> 86 | cost [20.0]
95 --> 93 | cost [50.0]
96 --> 94 | cost [50.0]

BACKUP RING
1  --- 31 | cost [0.35000000000000003]
2  ---  5 | cost [0.5]
2  --- 97 | cost [0.8]
4  ---  6 | cost [0.15]
4  --- 29 | cost [0.75]
5  ---  7 | cost [0.15]
6  ---  9 | cost [0.3]
7  --- 10 | cost [0.4]
9  --- 12 | cost [0.35000000000000003]
10 --- 14 | cost [0.4]
12 --- 15 | cost [0.4]
14 --- 16 | cost [0.5]
15 --- 17 | cost [0.8]
16 --- 20 | cost [0.55]
17 --- 19 | cost [0.15]
19 --- 22 | cost [0.55]
20 --- 21 | cost [0.3]
21 --- 26 | cost [0.55]
22 --- 23 | cost [0.3]
23 --- 25 | cost [0.35000000000000003]
24 --- 26 | cost [0.45]
24 --- 48 | cost [0.75]
25 --- 47 | cost [0.6]
30 --- 32 | cost [0.15]
31 --- 36 | cost [0.25]
32 --- 37 | cost [0.2]
33 --- 35 | cost [0.45]
33 --- 40 | cost [0.5]
34 --- 37 | cost [0.35000000000000003]
34 --- 44 | cost [0.35000000000000003]
35 --- 36 | cost [0.2]
40 --- 42 | cost [0.15]
41 --- 43 | cost [0.15]
41 --- 44 | cost [0.35000000000000003]
42 --- 49 | cost [0.1]
43 --- 50 | cost [0.25]
47 --- 58 | cost [0.65]
48 --- 54 | cost [0.45]
49 --- 52 | cost [0.3]
50 --- 55 | cost [0.3]
52 --- 57 | cost [0.5]
54 --- 59 | cost [0.55]
55 --- 69 | cost [0.5]
57 --- 70 | cost [0.4]
58 --- 60 | cost [0.35000000000000003]
59 --- 61 | cost [0.35000000000000003]
60 --- 62 | cost [0.25]
61 --- 63 | cost [0.25]
62 --- 64 | cost [0.3]
63 --- 66 | cost [0.4]
64 --- 67 | cost [0.3]
66 --- 94 | cost [0.65]
67 --- 93 | cost [0.75]
69 --- 81 | cost [0.7000000000000001]
70 --- 82 | cost [0.5]
72 --- 75 | cost [0.3]
72 --- 77 | cost [0.45]
73 --- 74 | cost [0.25]
73 --- 76 | cost [0.35000000000000003]
74 --- 86 | cost [0.3]
75 --- 85 | cost [0.4]
76 --- 92 | cost [0.55]
77 --- 93 | cost [0.65]
81 --- 83 | cost [0.2]
82 --- 91 | cost [0.55]
83 --- 90 | cost [0.65]
85 --- 87 | cost [0.2]
86 --- 89 | cost [0.35000000000000003]
87 --- 90 | cost [0.25]
89 --- 91 | cost [0.45]
92 --- 94 | cost [0.6]

BACKUP STAR
3  -->  4 | cost [0.45]
8  -->  7 | cost [0.1]
11 --> 44 | cost [0.6]
13 --> 12 | cost [0.2]
18 --> 20 | cost [0.1]
27 --> 23 | cost [0.45]
28 --> 22 | cost [0.5]
38 --> 35 | cost [0.2]
39 --> 41 | cost [0.2]
45 --> 33 | cost [0.3]
46 --> 50 | cost [0.3]
51 --> 52 | cost [0.2]
53 --> 55 | cost [0.2]
56 --> 58 | cost [0.25]
65 --> 64 | cost [0.45]
68 --> 66 | cost [0.1]
71 --> 73 | cost [0.2]
78 --> 86 | cost [0.2]
79 --> 70 | cost [1.05]
80 --> 81 | cost [1.5]
84 --> 85 | cost [0.15]
88 --> 85 | cost [0.25]
95 --> 94 | cost [0.55]
96 --> 66 | cost [0.8]

B = 2.05
i★ = 82
j★ = 83
k★ = 91