------------------------------------------------------------
                          α=5.0 —— rd100 —— 100 nodes       
------------------------------------------------------------

——————— Sun, 28 Jan 2024 02:57:10 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 82 hubs —— 1—60—8—71—68—83—51—65—80—81—91—64—36—57—47—99—53—6—94—98—16—45—52—11—61—5—22—41—34—7—42—43—40—55—96—39—100—44—29—35—23—2—89—84—31—66—76—59—77—28—37—19—46—50—73—54—38—72—17—92—27—10—33—78—20—74—26—9—32—4—85—82—75—21—49—67—97—63—15—62—18—101
total time           2951.59              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             38528.3<=38531.5     subtour              369.0                
connectivity cuts    194.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       199                  n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—60—8—71—68—83—51—65—80—81—91—64—36—57—47—99—53—6—94—98—16—45—52—11—61—5—22—41—34—7—42—43—40—55—96—39—100—44—29—35—23—2—89—84—31—66—76—59—77—28—37—19—46—50—73—54—38—72—17—92—27—10—33—78—20—74—26—9—32—4—85—82—75—21—49—67—97—63—15—62—18—101

RING
1  --- 60 | cost [110.0]
1  --- 101 | cost [0.0]
2  --- 23 | cost [435.0]
2  --- 89 | cost [540.0]
4  --- 32 | cost [210.0]
4  --- 85 | cost [520.0]
5  --- 22 | cost [465.0]
5  --- 61 | cost [250.0]
6  --- 53 | cost [295.0]
6  --- 94 | cost [605.0]
7  --- 34 | cost [285.0]
7  --- 42 | cost [365.0]
8  --- 60 | cost [170.0]
8  --- 71 | cost [630.0]
9  --- 26 | cost [210.0]
9  --- 32 | cost [600.0]
10 --- 27 | cost [595.0]
10 --- 33 | cost [205.0]
11 --- 52 | cost [890.0]
11 --- 61 | cost [405.0]
15 --- 62 | cost [555.0]
15 --- 63 | cost [150.0]
16 --- 45 | cost [510.0]
16 --- 98 | cost [590.0]
17 --- 72 | cost [270.0]
17 --- 92 | cost [750.0]
18 --- 62 | cost [335.0]
18 --- 101 | cost [440.0]
19 --- 37 | cost [470.0]
19 --- 46 | cost [420.0]
20 --- 74 | cost [95.0]
20 --- 78 | cost [195.0]
21 --- 49 | cost [175.0]
21 --- 75 | cost [125.0]
22 --- 41 | cost [250.0]
23 --- 35 | cost [1250.0]
26 --- 74 | cost [195.0]
27 --- 92 | cost [185.0]
28 --- 37 | cost [180.0]
28 --- 77 | cost [370.0]
29 --- 35 | cost [290.0]
29 --- 44 | cost [430.0]
31 --- 66 | cost [475.0]
31 --- 84 | cost [270.0]
33 --- 78 | cost [575.0]
34 --- 41 | cost [485.0]
36 --- 57 | cost [500.0]
36 --- 64 | cost [680.0]
38 --- 54 | cost [355.0]
38 --- 72 | cost [335.0]
39 --- 96 | cost [200.0]
39 --- 100 | cost [810.0]
40 --- 43 | cost [605.0]
40 --- 55 | cost [595.0]
42 --- 43 | cost [330.0]
44 --- 100 | cost [365.0]
45 --- 52 | cost [630.0]
46 --- 50 | cost [25.0]
47 --- 57 | cost [500.0]
47 --- 99 | cost [460.0]
49 --- 67 | cost [435.0]
50 --- 73 | cost [135.0]
51 --- 65 | cost [415.0]
51 --- 83 | cost [170.0]
53 --- 99 | cost [240.0]
54 --- 73 | cost [400.0]
55 --- 96 | cost [580.0]
59 --- 76 | cost [650.0]
59 --- 77 | cost [240.0]
63 --- 97 | cost [40.0]
64 --- 91 | cost [695.0]
65 --- 80 | cost [300.0]
66 --- 76 | cost [340.0]
67 --- 97 | cost [160.0]
68 --- 71 | cost [705.0]
68 --- 83 | cost [405.0]
75 --- 82 | cost [180.0]
80 --- 81 | cost [335.0]
81 --- 91 | cost [645.0]
82 --- 85 | cost [205.0]
84 --- 89 | cost [1105.0]
94 --- 98 | cost [380.0]

STAR
3  --> 33 | cost [575.0]
12 --> 85 | cost [205.0]
13 --> 67 | cost [295.0]
14 --> 85 | cost [205.0]
24 --> 43 | cost [225.0]
25 --> 43 | cost [210.0]
30 --> 80 | cost [420.0]
48 --> 80 | cost [385.0]
56 --> 46 | cost [125.0]
58 --> 76 | cost [480.0]
69 -->  8 | cost [305.0]
70 --> 72 | cost [285.0]
79 -->  6 | cost [230.0]
86 --> 97 | cost [65.0]
87 --> 62 | cost [420.0]
88 --> 84 | cost [95.0]
90 --> 51 | cost [210.0]
93 --> 77 | cost [220.0]
95 --> 59 | cost [95.0]

BACKUP RING
1  ---  8 | cost [2.75]
2  --- 35 | cost [15.85]
2  --- 84 | cost [11.85]
4  ---  9 | cost [8.1]
4  --- 82 | cost [4.0]
5  --- 11 | cost [5.9]
5  --- 41 | cost [6.4]
6  --- 98 | cost [9.450000000000001]
6  --- 99 | cost [4.55]
7  --- 41 | cost [5.3]
7  --- 43 | cost [6.75]
8  --- 68 | cost [8.5]
9  --- 74 | cost [4.05]
10 --- 78 | cost [7.8]
10 --- 92 | cost [7.3500000000000005]
11 --- 45 | cost [15.15]
15 --- 18 | cost [8.45]
15 --- 97 | cost [1.9000000000000001]
16 --- 52 | cost [9.35]
16 --- 94 | cost [7.45]
17 --- 27 | cost [9.35]
17 --- 38 | cost [3.7]
19 --- 28 | cost [6.45]
19 --- 50 | cost [4.45]
20 --- 26 | cost [2.6]
20 --- 33 | cost [6.05]
21 --- 67 | cost [5.1000000000000005]
21 --- 82 | cost [2.1]
22 --- 34 | cost [6.3]
22 --- 61 | cost [5.75]
23 --- 29 | cost [15.0]
23 --- 89 | cost [8.05]
26 --- 32 | cost [6.15]
27 --- 33 | cost [6.8500000000000005]
28 --- 59 | cost [5.95]
29 --- 100 | cost [4.7]
31 --- 76 | cost [7.3]
31 --- 89 | cost [13.55]
32 --- 85 | cost [5.65]
34 --- 42 | cost [6.4]
35 --- 44 | cost [4.8500000000000005]
36 --- 47 | cost [8.2]
36 --- 91 | cost [11.1]
37 --- 46 | cost [6.4]
37 --- 77 | cost [5.3]
38 --- 73 | cost [5.55]
39 --- 44 | cost [11.05]
39 --- 55 | cost [5.6000000000000005]
40 --- 42 | cost [4.4]
40 --- 96 | cost [10.6]
43 --- 55 | cost [10.4]
45 --- 98 | cost [10.950000000000001]
46 --- 73 | cost [1.45]
47 --- 53 | cost [4.95]
49 --- 75 | cost [1.9000000000000001]
49 --- 97 | cost [4.7]
50 --- 54 | cost [5.05]
51 --- 68 | cost [5.45]
51 --- 80 | cost [6.8500000000000005]
52 --- 61 | cost [12.9]
53 --- 94 | cost [5.7]
54 --- 72 | cost [6.9]
57 --- 64 | cost [10.25]
57 --- 99 | cost [9.6]
59 --- 66 | cost [8.45]
60 --- 71 | cost [6.4]
62 --- 63 | cost [6.8]
62 --- 101 | cost [4.7]
63 --- 67 | cost [1.9000000000000001]
64 --- 81 | cost [12.1]
65 --- 81 | cost [4.9]
65 --- 83 | cost [5.15]
66 --- 84 | cost [5.8]
71 --- 83 | cost [10.450000000000001]
72 --- 92 | cost [9.950000000000001]
74 --- 78 | cost [2.7]
75 --- 85 | cost [3.85]
76 --- 77 | cost [8.65]
80 --- 91 | cost [7.7]
96 --- 100 | cost [8.75]

BACKUP STAR
3  --> 10 | cost [6.5]
12 --> 82 | cost [3.95]
13 --> 49 | cost [4.4]
14 --> 82 | cost [3.85]
24 --> 42 | cost [3.4]
25 --> 42 | cost [5.45]
30 --> 81 | cost [6.0]
48 --> 65 | cost [5.15]
56 --> 50 | cost [1.4000000000000001]
58 --> 84 | cost [6.55]
69 --> 60 | cost [4.15]
70 --> 38 | cost [4.3500000000000005]
79 --> 53 | cost [3.25]
86 --> 63 | cost [0.75]
87 --> 15 | cost [6.0]
88 --> 31 | cost [2.95]
90 --> 83 | cost [3.6]
93 --> 59 | cost [3.85]
95 --> 77 | cost [2.6]

B = 16.5
i★ = 31
j★ = 84
k★ = 89

       
——————— Sun, 28 Jan 2024 03:06:02 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 82 hubs —— 1-60-8-71-68-83-51-65-80-81-91-64-36-57-47-99-53-6-94-98-16-45-52-11-61-5-22-41-34-7-42-43-40-55-96-39-100-44-29-35-23-2-89-84-31-66-76-59-77-28-37-19-46-50-73-54-38-72-17-92-27-10-33-78-20-74-26-9-32-4-85-82-75-21-49-67-97-63-15-62-18-101-1
total time           467.17               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             38530<=38531.5       Master/SP costs      38020/511.5          
Master time          459.6                SP time              7.58                 
subtour              12722.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            40.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       13146                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—60—8—71—68—83—51—65—80—81—91—64—36—57—47—99—53—6—94—98—16—45—52—11—61—5—22—41—34—7—42—43—40—55—96—39—100—44—29—35—23—2—89—84—31—66—76—59—77—28—37—19—46—50—73—54—38—72—17—92—27—10—33—78—20—74—26—9—32—4—85—82—75—21—49—67—97—63—15—62—18—101

RING
1  --- 60 | cost [110.0]
1  --- 101 | cost [0.0]
2  --- 23 | cost [435.0]
2  --- 89 | cost [540.0]
4  --- 32 | cost [210.0]
4  --- 85 | cost [520.0]
5  --- 22 | cost [465.0]
5  --- 61 | cost [250.0]
6  --- 53 | cost [295.0]
6  --- 94 | cost [605.0]
7  --- 34 | cost [285.0]
7  --- 42 | cost [365.0]
8  --- 60 | cost [170.0]
8  --- 71 | cost [630.0]
9  --- 26 | cost [210.0]
9  --- 32 | cost [600.0]
10 --- 27 | cost [595.0]
10 --- 33 | cost [205.0]
11 --- 52 | cost [890.0]
11 --- 61 | cost [405.0]
15 --- 62 | cost [555.0]
15 --- 63 | cost [150.0]
16 --- 45 | cost [510.0]
16 --- 98 | cost [590.0]
17 --- 72 | cost [270.0]
17 --- 92 | cost [750.0]
18 --- 62 | cost [335.0]
18 --- 101 | cost [440.0]
19 --- 37 | cost [470.0]
19 --- 46 | cost [420.0]
20 --- 74 | cost [95.0]
20 --- 78 | cost [195.0]
21 --- 49 | cost [175.0]
21 --- 75 | cost [125.0]
22 --- 41 | cost [250.0]
23 --- 35 | cost [1250.0]
26 --- 74 | cost [195.0]
27 --- 92 | cost [185.0]
28 --- 37 | cost [180.0]
28 --- 77 | cost [370.0]
29 --- 35 | cost [290.0]
29 --- 44 | cost [430.0]
31 --- 66 | cost [475.0]
31 --- 84 | cost [270.0]
33 --- 78 | cost [575.0]
34 --- 41 | cost [485.0]
36 --- 57 | cost [500.0]
36 --- 64 | cost [680.0]
38 --- 54 | cost [355.0]
38 --- 72 | cost [335.0]
39 --- 96 | cost [200.0]
39 --- 100 | cost [810.0]
40 --- 43 | cost [605.0]
40 --- 55 | cost [595.0]
42 --- 43 | cost [330.0]
44 --- 100 | cost [365.0]
45 --- 52 | cost [630.0]
46 --- 50 | cost [25.0]
47 --- 57 | cost [500.0]
47 --- 99 | cost [460.0]
49 --- 67 | cost [435.0]
50 --- 73 | cost [135.0]
51 --- 65 | cost [415.0]
51 --- 83 | cost [170.0]
53 --- 99 | cost [240.0]
54 --- 73 | cost [400.0]
55 --- 96 | cost [580.0]
59 --- 76 | cost [650.0]
59 --- 77 | cost [240.0]
63 --- 97 | cost [40.0]
64 --- 91 | cost [695.0]
65 --- 80 | cost [300.0]
66 --- 76 | cost [340.0]
67 --- 97 | cost [160.0]
68 --- 71 | cost [705.0]
68 --- 83 | cost [405.0]
75 --- 82 | cost [180.0]
80 --- 81 | cost [335.0]
81 --- 91 | cost [645.0]
82 --- 85 | cost [205.0]
84 --- 89 | cost [1105.0]
94 --- 98 | cost [380.0]

STAR
3  --> 33 | cost [575.0]
12 --> 85 | cost [205.0]
13 --> 67 | cost [295.0]
14 --> 85 | cost [205.0]
24 --> 43 | cost [225.0]
25 --> 43 | cost [210.0]
30 --> 80 | cost [420.0]
48 --> 80 | cost [385.0]
56 --> 46 | cost [125.0]
58 --> 76 | cost [480.0]
69 -->  8 | cost [305.0]
70 --> 72 | cost [285.0]
79 -->  6 | cost [230.0]
86 --> 97 | cost [65.0]
87 --> 62 | cost [420.0]
88 --> 84 | cost [95.0]
90 --> 51 | cost [210.0]
93 --> 77 | cost [220.0]
95 --> 59 | cost [95.0]

BACKUP RING
1  ---  8 | cost [2.75]
2  --- 35 | cost [15.85]
2  --- 84 | cost [11.85]
4  ---  9 | cost [8.1]
4  --- 82 | cost [4.0]
5  --- 11 | cost [5.9]
5  --- 41 | cost [6.4]
6  --- 98 | cost [9.450000000000001]
6  --- 99 | cost [4.55]
7  --- 41 | cost [5.3]
7  --- 43 | cost [6.75]
8  --- 68 | cost [8.5]
9  --- 74 | cost [4.05]
10 --- 78 | cost [7.8]
10 --- 92 | cost [7.3500000000000005]
11 --- 45 | cost [15.15]
15 --- 18 | cost [8.45]
15 --- 97 | cost [1.9000000000000001]
16 --- 52 | cost [9.35]
16 --- 94 | cost [7.45]
17 --- 27 | cost [9.35]
17 --- 38 | cost [3.7]
19 --- 28 | cost [6.45]
19 --- 50 | cost [4.45]
20 --- 26 | cost [2.6]
20 --- 33 | cost [6.05]
21 --- 67 | cost [5.1000000000000005]
21 --- 82 | cost [2.1]
22 --- 34 | cost [6.3]
22 --- 61 | cost [5.75]
23 --- 29 | cost [15.0]
23 --- 89 | cost [8.05]
26 --- 32 | cost [6.15]
27 --- 33 | cost [6.8500000000000005]
28 --- 59 | cost [5.95]
29 --- 100 | cost [4.7]
31 --- 76 | cost [7.3]
31 --- 89 | cost [13.55]
32 --- 85 | cost [5.65]
34 --- 42 | cost [6.4]
35 --- 44 | cost [4.8500000000000005]
36 --- 47 | cost [8.2]
36 --- 91 | cost [11.1]
37 --- 46 | cost [6.4]
37 --- 77 | cost [5.3]
38 --- 73 | cost [5.55]
39 --- 44 | cost [11.05]
39 --- 55 | cost [5.6000000000000005]
40 --- 42 | cost [4.4]
40 --- 96 | cost [10.6]
43 --- 55 | cost [10.4]
45 --- 98 | cost [10.950000000000001]
46 --- 73 | cost [1.45]
47 --- 53 | cost [4.95]
49 --- 75 | cost [1.9000000000000001]
49 --- 97 | cost [4.7]
50 --- 54 | cost [5.05]
51 --- 68 | cost [5.45]
51 --- 80 | cost [6.8500000000000005]
52 --- 61 | cost [12.9]
53 --- 94 | cost [5.7]
54 --- 72 | cost [6.9]
57 --- 64 | cost [10.25]
57 --- 99 | cost [9.6]
59 --- 66 | cost [8.45]
60 --- 71 | cost [6.4]
62 --- 63 | cost [6.8]
62 --- 101 | cost [4.7]
63 --- 67 | cost [1.9000000000000001]
64 --- 81 | cost [12.1]
65 --- 81 | cost [4.9]
65 --- 83 | cost [5.15]
66 --- 84 | cost [5.8]
71 --- 83 | cost [10.450000000000001]
72 --- 92 | cost [9.950000000000001]
74 --- 78 | cost [2.7]
75 --- 85 | cost [3.85]
76 --- 77 | cost [8.65]
80 --- 91 | cost [7.7]
96 --- 100 | cost [8.75]

BACKUP STAR
3  --> 10 | cost [6.5]
12 --> 82 | cost [3.95]
13 --> 49 | cost [4.4]
14 --> 82 | cost [3.85]
24 --> 42 | cost [3.4]
25 --> 42 | cost [5.45]
30 --> 81 | cost [6.0]
48 --> 65 | cost [5.15]
56 --> 50 | cost [1.4000000000000001]
58 --> 84 | cost [6.55]
69 --> 60 | cost [4.15]
70 --> 38 | cost [4.3500000000000005]
79 --> 53 | cost [3.25]
86 --> 63 | cost [0.75]
87 --> 15 | cost [6.0]
88 --> 31 | cost [2.95]
90 --> 83 | cost [3.6]
93 --> 59 | cost [3.85]
95 --> 77 | cost [2.6]

B = 16.5
i★ = 31
j★ = 84
k★ = 89