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

——————— Mon, 22 Jan 2024 05:51:12 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 42 hubs —— 1—8—71—68—51—83—65—61—41—40—7—96—39—45—76—66—2—44—23—77—79—33—73—38—70—74—9—32—12—85—82—75—4—21—99—49—67—15—87—62—60—101
total time           3638.06 (TL 3600)    gap                  0.68                 
blossom time         0                    nb blossom           0.0                  
LB <= UB             37166.81<=116022.05  subtour              2102.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       615                  n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—8—71—68—51—83—65—61—41—40—7—96—39—45—76—66—2—44—23—77—79—33—73—38—70—74—9—32—12—85—82—75—4—21—99—49—67—15—87—62—60—101

RING
1  ---  8 | cost [275.0]
2  --- 44 | cost [1710.0]
2  --- 66 | cost [1765.0]
4  --- 21 | cost [510.0]
4  --- 75 | cost [390.0]
7  --- 40 | cost [355.0]
7  --- 96 | cost [1310.0]
8  --- 71 | cost [630.0]
9  --- 32 | cost [600.0]
9  --- 74 | cost [405.0]
12 --- 32 | cost [570.0]
12 --- 85 | cost [205.0]
15 --- 67 | cost [310.0]
15 --- 87 | cost [600.0]
21 --- 99 | cost [1790.0]
23 --- 44 | cost [1300.0]
23 --- 77 | cost [2480.0]
33 --- 73 | cost [1210.0]
33 --- 79 | cost [780.0]
38 --- 70 | cost [435.0]
38 --- 73 | cost [555.0]
39 --- 45 | cost [1635.0]
39 --- 96 | cost [200.0]
40 --- 41 | cost [880.0]
41 --- 61 | cost [660.0]
45 --- 76 | cost [1470.0]
49 --- 67 | cost [435.0]
49 --- 99 | cost [1645.0]
51 --- 68 | cost [545.0]
51 --- 83 | cost [170.0]
60 --- 62 | cost [560.0]
60 --- 101 | cost [110.0]
61 --- 65 | cost [1380.0]
62 --- 87 | cost [420.0]
65 --- 83 | cost [515.0]
66 --- 76 | cost [340.0]
68 --- 71 | cost [705.0]
70 --- 74 | cost [1580.0]
75 --- 82 | cost [180.0]
77 --- 79 | cost [1185.0]
82 --- 85 | cost [205.0]

STAR
3  --> 33 | cost [575.0]
5  --> 41 | cost [640.0]
6  --> 99 | cost [455.0]
10 --> 99 | cost [800.0]
11 --> 41 | cost [1045.0]
13 --> 67 | cost [295.0]
14 -->  1 | cost [1390.0]
16 --> 44 | cost [1200.0]
17 -->  1 | cost [3680.0]
18 --> 62 | cost [335.0]
19 --> 99 | cost [1915.0]
20 -->  1 | cost [2580.0]
22 --> 41 | cost [250.0]
24 -->  7 | cost [700.0]
25 -->  7 | cost [890.0]
26 -->  1 | cost [2560.0]
27 -->  1 | cost [3280.0]
28 --> 99 | cost [1490.0]
29 --> 96 | cost [800.0]
30 --> 41 | cost [925.0]
31 --> 44 | cost [1350.0]
34 -->  7 | cost [285.0]
35 -->  1 | cost [4785.0]
36 -->  7 | cost [1900.0]
37 --> 99 | cost [1620.0]
42 -->  7 | cost [365.0]
43 -->  1 | cost [3955.0]
46 --> 99 | cost [1650.0]
47 -->  8 | cost [2595.0]
48 --> 41 | cost [1315.0]
50 --> 99 | cost [1645.0]
52 --> 44 | cost [865.0]
53 --> 99 | cost [240.0]
54 --> 38 | cost [355.0]
55 --> 96 | cost [580.0]
56 --> 99 | cost [1545.0]
57 --> 96 | cost [2240.0]
58 --> 44 | cost [2165.0]
59 --> 99 | cost [1375.0]
63 -->  1 | cost [795.0]
64 -->  8 | cost [1670.0]
69 -->  8 | cost [305.0]
72 -->  1 | cost [3920.0]
78 -->  1 | cost [2390.0]
80 --> 41 | cost [1150.0]
81 --> 41 | cost [1005.0]
84 --> 44 | cost [1510.0]
86 -->  1 | cost [865.0]
88 --> 44 | cost [1590.0]
89 --> 23 | cost [805.0]
90 --> 51 | cost [210.0]
91 --> 65 | cost [600.0]
92 --> 99 | cost [1435.0]
93 --> 77 | cost [220.0]
94 --> 44 | cost [1935.0]
95 --> 99 | cost [1285.0]
97 -->  1 | cost [830.0]
98 --> 44 | cost [1775.0]
100 --> 44 | cost [365.0]

BACKUP RING
1  --- 71 | cost [6.55]
2  --- 23 | cost [4.3500000000000005]
2  --- 76 | cost [18.45]
4  --- 82 | cost [4.0]
4  --- 99 | cost [15.55]
7  --- 39 | cost [11.55]
7  --- 41 | cost [5.3]
8  --- 68 | cost [8.5]
9  --- 12 | cost [9.15]
9  --- 70 | cost [17.45]
12 --- 82 | cost [3.95]
15 --- 49 | cost [6.5]
15 --- 62 | cost [5.55]
21 --- 49 | cost [1.75]
21 --- 75 | cost [1.25]
23 --- 79 | cost [28.95]
32 --- 74 | cost [6.8]
32 --- 85 | cost [5.65]
33 --- 38 | cost [15.55]
33 --- 77 | cost [16.7]
38 --- 74 | cost [13.700000000000001]
39 --- 76 | cost [31.0]
40 --- 61 | cost [11.0]
40 --- 96 | cost [10.6]
41 --- 65 | cost [14.35]
44 --- 66 | cost [17.45]
44 --- 77 | cost [27.900000000000002]
45 --- 66 | cost [11.35]
45 --- 96 | cost [17.1]
51 --- 65 | cost [4.15]
51 --- 71 | cost [11.25]
60 --- 87 | cost [9.4]
61 --- 83 | cost [18.95]
62 --- 101 | cost [4.7]
67 --- 87 | cost [8.35]
67 --- 99 | cost [18.5]
68 --- 83 | cost [4.05]
70 --- 73 | cost [9.85]
73 --- 79 | cost [14.200000000000001]
75 --- 85 | cost [3.85]

BACKUP STAR
3  -->  4 | cost [7.3500000000000005]
5  --> 61 | cost [2.5]
6  --> 79 | cost [2.3000000000000003]
10 --> 33 | cost [2.05]
11 --> 61 | cost [4.05]
13 --> 49 | cost [4.4]
16 --> 45 | cost [5.1000000000000005]
18 -->  1 | cost [4.4]
19 --> 73 | cost [4.7]
22 --> 61 | cost [5.75]
24 --> 40 | cost [7.4]
25 --> 40 | cost [7.8500000000000005]
28 --> 77 | cost [3.7]
29 --> 44 | cost [4.3]
30 --> 65 | cost [7.05]
31 --> 66 | cost [4.75]
34 --> 41 | cost [4.8500000000000005]
36 --> 61 | cost [11.15]
37 --> 77 | cost [5.3]
42 --> 40 | cost [4.4]
46 --> 73 | cost [1.45]
47 --> 99 | cost [4.6000000000000005]
48 --> 65 | cost [5.15]
50 --> 73 | cost [1.35]
52 --> 45 | cost [6.3]
53 --> 79 | cost [3.25]
54 --> 73 | cost [4.0]
55 --> 39 | cost [5.6000000000000005]
56 --> 73 | cost [2.7]
57 --> 99 | cost [9.6]
58 --> 76 | cost [4.8]
59 --> 77 | cost [2.4]
64 --> 99 | cost [12.3]
69 --> 60 | cost [4.15]
80 --> 65 | cost [3.0]
81 --> 65 | cost [4.9]
84 --> 66 | cost [5.8]
88 --> 66 | cost [5.1000000000000005]
89 -->  2 | cost [5.4]
90 --> 83 | cost [3.6]
91 --> 51 | cost [7.8500000000000005]
92 --> 73 | cost [4.3500000000000005]
93 --> 76 | cost [8.950000000000001]
94 --> 66 | cost [7.3500000000000005]
95 --> 77 | cost [2.6]
98 --> 66 | cost [3.6]
100 --> 39 | cost [8.1]

B = 55.25000000000001
i★ = 2
j★ = 44
k★ = 23

       
——————— Mon, 22 Jan 2024 06:52:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 75 hubs —— 1-71-8-69-90-81-91-48-80-83-65-43-42-41-34-22-61-7-40-55-39-96-29-35-44-45-31-84-23-2-89-58-88-66-98-16-57-47-99-53-94-59-77-93-28-37-19-46-50-73-54-38-72-17-26-74-20-78-33-3-4-32-12-85-82-75-21-49-67-97-63-15-62-18-101-1
total time           3610.65 (TL 3600)    gap                  0.227                
blossom time         0                    nb blossom           0.0                  
LB <= UB             35663.75<=46108.8    Master/SP costs      45185/923.8          
Master time          3593.48              SP time              17.17                
subtour              44930.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            57.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       20945                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—71—8—69—90—81—91—48—80—83—65—43—42—41—34—22—61—7—40—55—39—96—29—35—44—45—31—84—23—2—89—58—88—66—98—16—57—47—99—53—94—59—77—93—28—37—19—46—50—73—54—38—72—17—26—74—20—78—33—3—4—32—12—85—82—75—21—49—67—97—63—15—62—18—101

RING
1  --- 71 | cost [655.0]
2  --- 23 | cost [435.0]
2  --- 89 | cost [540.0]
3  ---  4 | cost [735.0]
3  --- 33 | cost [575.0]
4  --- 32 | cost [210.0]
7  --- 40 | cost [355.0]
7  --- 61 | cost [820.0]
8  --- 69 | cost [305.0]
8  --- 71 | cost [630.0]
12 --- 32 | cost [570.0]
12 --- 85 | cost [205.0]
15 --- 62 | cost [555.0]
15 --- 63 | cost [150.0]
16 --- 57 | cost [950.0]
16 --- 98 | cost [590.0]
17 --- 26 | cost [1135.0]
17 --- 72 | cost [270.0]
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 --- 34 | cost [630.0]
22 --- 61 | cost [575.0]
23 --- 84 | cost [910.0]
26 --- 74 | cost [195.0]
28 --- 37 | cost [180.0]
28 --- 93 | cost [445.0]
29 --- 35 | cost [290.0]
29 --- 96 | cost [800.0]
31 --- 45 | cost [850.0]
31 --- 84 | cost [270.0]
33 --- 78 | cost [575.0]
34 --- 41 | cost [485.0]
35 --- 44 | cost [485.0]
38 --- 54 | cost [355.0]
38 --- 72 | cost [335.0]
39 --- 55 | cost [560.0]
39 --- 96 | cost [200.0]
40 --- 55 | cost [595.0]
41 --- 42 | cost [670.0]
42 --- 43 | cost [330.0]
43 --- 65 | cost [2380.0]
44 --- 45 | cost [695.0]
46 --- 50 | cost [25.0]
47 --- 57 | cost [500.0]
47 --- 99 | cost [460.0]
48 --- 80 | cost [385.0]
48 --- 91 | cost [1100.0]
49 --- 67 | cost [435.0]
50 --- 73 | cost [135.0]
53 --- 94 | cost [570.0]
53 --- 99 | cost [240.0]
54 --- 73 | cost [400.0]
58 --- 88 | cost [575.0]
58 --- 89 | cost [1215.0]
59 --- 77 | cost [240.0]
59 --- 94 | cost [860.0]
63 --- 97 | cost [40.0]
65 --- 83 | cost [515.0]
66 --- 88 | cost [510.0]
66 --- 98 | cost [360.0]
67 --- 97 | cost [160.0]
69 --- 90 | cost [675.0]
75 --- 82 | cost [180.0]
77 --- 93 | cost [220.0]
80 --- 83 | cost [745.0]
81 --- 90 | cost [930.0]
81 --- 91 | cost [645.0]
82 --- 85 | cost [205.0]

STAR
5  --> 61 | cost [250.0]
6  --> 53 | cost [295.0]
9  --> 26 | cost [210.0]
10 --> 33 | cost [205.0]
11 --> 61 | cost [405.0]
13 --> 67 | cost [295.0]
14 --> 85 | cost [205.0]
24 --> 43 | cost [225.0]
25 --> 43 | cost [210.0]
27 --> 50 | cost [475.0]
30 --> 48 | cost [395.0]
36 --> 57 | cost [500.0]
51 --> 83 | cost [170.0]
52 --> 45 | cost [630.0]
56 --> 46 | cost [125.0]
60 -->  1 | cost [110.0]
64 --> 91 | cost [695.0]
68 --> 83 | cost [405.0]
70 --> 72 | cost [285.0]
76 --> 66 | cost [340.0]
79 --> 53 | cost [325.0]
86 --> 97 | cost [65.0]
87 --> 62 | cost [420.0]
92 --> 50 | cost [410.0]
95 --> 59 | cost [95.0]
100 --> 44 | cost [365.0]

BACKUP RING
1  ---  8 | cost [2.75]
2  --- 58 | cost [15.4]
2  --- 84 | cost [11.85]
3  --- 32 | cost [8.6]
3  --- 78 | cost [8.1]
4  --- 12 | cost [6.0]
4  --- 33 | cost [9.35]
7  --- 22 | cost [7.55]
7  --- 55 | cost [9.3]
8  --- 90 | cost [8.2]
12 --- 82 | cost [3.95]
15 --- 18 | cost [8.45]
15 --- 97 | cost [1.9000000000000001]
16 --- 47 | cost [11.15]
16 --- 66 | cost [7.0]
17 --- 38 | cost [3.7]
17 --- 74 | cost [10.5]
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 --- 41 | cost [2.5]
23 --- 31 | cost [10.3]
23 --- 89 | cost [8.05]
26 --- 72 | cost [13.65]
28 --- 77 | cost [3.7]
29 --- 39 | cost [8.5]
29 --- 44 | cost [4.3]
31 --- 44 | cost [13.5]
32 --- 85 | cost [5.65]
34 --- 42 | cost [6.4]
34 --- 61 | cost [5.4]
35 --- 45 | cost [11.450000000000001]
35 --- 96 | cost [10.6]
37 --- 46 | cost [6.4]
37 --- 93 | cost [5.45]
38 --- 73 | cost [5.55]
39 --- 40 | cost [9.35]
40 --- 61 | cost [11.0]
41 --- 43 | cost [9.8]
42 --- 65 | cost [20.95]
43 --- 83 | cost [27.95]
45 --- 84 | cost [10.9]
46 --- 73 | cost [1.45]
47 --- 53 | cost [4.95]
48 --- 81 | cost [7.15]
48 --- 83 | cost [6.65]
49 --- 75 | cost [1.9000000000000001]
49 --- 97 | cost [4.7]
50 --- 54 | cost [5.05]
53 --- 59 | cost [11.55]
54 --- 72 | cost [6.9]
55 --- 96 | cost [5.8]
57 --- 98 | cost [12.15]
57 --- 99 | cost [9.6]
58 --- 66 | cost [7.0]
59 --- 93 | cost [3.85]
62 --- 63 | cost [6.8]
62 --- 101 | cost [4.7]
63 --- 67 | cost [1.9000000000000001]
65 --- 80 | cost [3.0]
69 --- 71 | cost [9.1]
69 --- 81 | cost [15.4]
74 --- 78 | cost [2.7]
75 --- 85 | cost [3.85]
77 --- 94 | cost [10.5]
80 --- 91 | cost [7.7]
88 --- 89 | cost [11.450000000000001]
88 --- 98 | cost [8.45]
90 --- 91 | cost [6.6000000000000005]
94 --- 99 | cost [8.0]

BACKUP STAR
5  --> 22 | cost [4.65]
6  --> 99 | cost [4.55]
9  --> 74 | cost [4.05]
10 -->  3 | cost [6.5]
11 --> 34 | cost [7.9]
13 --> 49 | cost [4.4]
14 --> 12 | cost [2.4]
24 --> 42 | cost [3.4]
25 --> 42 | cost [5.45]
27 --> 46 | cost [4.9]
30 --> 80 | cost [4.2]
36 --> 47 | cost [8.2]
51 --> 90 | cost [2.1]
52 --> 57 | cost [8.15]
56 --> 50 | cost [1.4000000000000001]
64 --> 47 | cost [10.1]
68 --> 90 | cost [6.65]
70 --> 38 | cost [4.3500000000000005]
76 --> 58 | cost [4.8]
79 --> 99 | cost [3.45]
86 --> 63 | cost [0.75]
87 --> 15 | cost [6.0]
92 --> 46 | cost [4.3]
95 --> 77 | cost [2.6]
100 --> 29 | cost [4.7]

B = 29.799999999999997
i★ = 42
j★ = 43
k★ = 65