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

——————— Fri, 19 Jan 2024 06:53:23 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 49 hubs —— 1—60—71—68—83—51—90—80—48—30—41—22—65—91—81—5—61—7—43—40—55—96—39—100—16—2—23—76—45—77—59—56—38—74—33—10—79—99—3—32—14—12—49—13—67—86—63—97—101
total time           3641.75 (TL 3600)    gap                  0.582                
blossom time         0                    nb blossom           0.0                  
LB <= UB             36893.45<=88359.65   subtour              8635.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1232                 n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—60—71—68—83—51—90—80—48—30—41—22—65—91—81—5—61—7—43—40—55—96—39—100—16—2—23—76—45—77—59—56—38—74—33—10—79—99—3—32—14—12—49—13—67—86—63—97—101

RING
1  --- 60 | cost [110.0]
2  --- 16 | cost [1890.0]
2  --- 23 | cost [435.0]
3  --- 32 | cost [860.0]
3  --- 99 | cost [820.0]
5  --- 61 | cost [250.0]
5  --- 81 | cost [640.0]
7  --- 43 | cost [675.0]
7  --- 61 | cost [820.0]
10 --- 33 | cost [205.0]
10 --- 79 | cost [590.0]
12 --- 14 | cost [240.0]
12 --- 49 | cost [745.0]
13 --- 49 | cost [440.0]
13 --- 67 | cost [295.0]
14 --- 32 | cost [755.0]
16 --- 100 | cost [1340.0]
22 --- 41 | cost [250.0]
22 --- 65 | cost [1190.0]
23 --- 76 | cost [1620.0]
30 --- 41 | cost [925.0]
30 --- 48 | cost [395.0]
33 --- 74 | cost [695.0]
38 --- 56 | cost [820.0]
38 --- 74 | cost [1370.0]
39 --- 96 | cost [200.0]
39 --- 100 | cost [810.0]
40 --- 43 | cost [605.0]
40 --- 55 | cost [595.0]
45 --- 76 | cost [1470.0]
45 --- 77 | cost [2125.0]
48 --- 80 | cost [385.0]
51 --- 83 | cost [170.0]
51 --- 90 | cost [210.0]
55 --- 96 | cost [580.0]
56 --- 59 | cost [1195.0]
59 --- 77 | cost [240.0]
60 --- 71 | cost [640.0]
63 --- 86 | cost [75.0]
63 --- 97 | cost [40.0]
65 --- 91 | cost [600.0]
67 --- 86 | cost [200.0]
68 --- 71 | cost [705.0]
68 --- 83 | cost [405.0]
79 --- 99 | cost [345.0]
80 --- 90 | cost [780.0]
81 --- 91 | cost [645.0]
97 --- 101 | cost [830.0]

STAR
4  --> 99 | cost [1555.0]
6  --> 99 | cost [455.0]
8  --> 60 | cost [170.0]
9  --> 32 | cost [600.0]
11 --> 61 | cost [405.0]
15 --> 63 | cost [150.0]
17 --> 32 | cost [1730.0]
18 -->  1 | cost [440.0]
19 --> 99 | cost [1915.0]
20 -->  1 | cost [2580.0]
21 -->  1 | cost [1285.0]
24 --> 43 | cost [225.0]
25 --> 43 | cost [210.0]
26 --> 32 | cost [615.0]
27 --> 99 | cost [1255.0]
28 --> 77 | cost [370.0]
29 --> 40 | cost [1775.0]
31 --> 23 | cost [1030.0]
34 --> 40 | cost [570.0]
35 --> 96 | cost [1060.0]
36 -->  1 | cost [2510.0]
37 -->  1 | cost [4085.0]
42 --> 96 | cost [1500.0]
44 --> 45 | cost [695.0]
46 --> 77 | cost [1110.0]
47 --> 99 | cost [460.0]
50 --> 77 | cost [1130.0]
52 --> 45 | cost [630.0]
53 --> 99 | cost [240.0]
54 --> 77 | cost [1465.0]
57 --> 100 | cost [1530.0]
58 --> 76 | cost [480.0]
62 -->  1 | cost [470.0]
64 -->  1 | cost [1850.0]
66 --> 45 | cost [1135.0]
69 --> 60 | cost [415.0]
70 --> 32 | cost [2250.0]
72 --> 32 | cost [1970.0]
73 --> 77 | cost [1250.0]
75 -->  1 | cost [1405.0]
78 --> 32 | cost [470.0]
82 -->  1 | cost [1440.0]
84 --> 45 | cost [1090.0]
85 -->  1 | cost [1475.0]
87 --> 86 | cost [635.0]
88 --> 23 | cost [995.0]
89 --> 23 | cost [805.0]
92 --> 32 | cost [1500.0]
93 --> 77 | cost [220.0]
94 --> 99 | cost [800.0]
95 --> 59 | cost [95.0]
98 --> 99 | cost [1180.0]

BACKUP RING
1  --- 71 | cost [6.55]
2  --- 76 | cost [18.45]
2  --- 100 | cost [20.7]
3  --- 14 | cost [14.1]
3  --- 79 | cost [8.85]
5  ---  7 | cost [9.5]
5  --- 91 | cost [10.9]
7  --- 40 | cost [3.5500000000000003]
10 --- 74 | cost [8.75]
10 --- 99 | cost [8.0]
12 --- 13 | cost [11.75]
12 --- 32 | cost [5.7]
13 --- 86 | cost [4.8]
14 --- 49 | cost [6.8500000000000005]
16 --- 23 | cost [14.9]
16 --- 39 | cost [21.2]
22 --- 30 | cost [7.3500000000000005]
22 --- 91 | cost [13.65]
23 --- 45 | cost [13.4]
30 --- 80 | cost [4.2]
32 --- 99 | cost [16.6]
33 --- 38 | cost [15.55]
33 --- 79 | cost [7.8]
38 --- 59 | cost [19.85]
39 --- 55 | cost [5.6000000000000005]
40 --- 96 | cost [10.6]
41 --- 48 | cost [13.15]
41 --- 65 | cost [14.35]
43 --- 55 | cost [10.4]
43 --- 61 | cost [14.75]
45 --- 59 | cost [18.900000000000002]
48 --- 90 | cost [8.75]
49 --- 67 | cost [4.3500000000000005]
51 --- 68 | cost [5.45]
51 --- 80 | cost [6.8500000000000005]
56 --- 74 | cost [13.5]
56 --- 77 | cost [9.950000000000001]
60 --- 68 | cost [9.85]
61 --- 81 | cost [8.9]
63 --- 67 | cost [1.9000000000000001]
63 --- 101 | cost [7.95]
65 --- 81 | cost [4.9]
71 --- 83 | cost [10.450000000000001]
76 --- 77 | cost [8.65]
83 --- 90 | cost [3.6]
86 --- 97 | cost [0.65]
96 --- 100 | cost [8.75]

BACKUP STAR
4  --> 32 | cost [2.1]
6  --> 79 | cost [2.3000000000000003]
8  -->  1 | cost [2.75]
9  --> 74 | cost [4.05]
11 -->  5 | cost [5.9]
15 --> 97 | cost [1.9000000000000001]
17 --> 38 | cost [3.7]
19 --> 56 | cost [4.4]
24 -->  7 | cost [7.0]
25 --> 40 | cost [7.8500000000000005]
26 --> 74 | cost [1.95]
27 --> 56 | cost [4.55]
28 --> 59 | cost [5.95]
29 --> 100 | cost [4.7]
31 --> 16 | cost [6.25]
34 -->  7 | cost [2.85]
35 --> 100 | cost [6.95]
42 --> 43 | cost [3.3000000000000003]
44 --> 100 | cost [3.65]
46 --> 56 | cost [1.25]
47 --> 79 | cost [7.75]
50 --> 56 | cost [1.4000000000000001]
52 --> 100 | cost [7.15]
53 --> 79 | cost [3.25]
54 --> 38 | cost [3.5500000000000003]
57 --> 16 | cost [9.5]
58 --> 59 | cost [10.25]
66 --> 76 | cost [3.4]
69 -->  1 | cost [5.15]
70 --> 38 | cost [4.3500000000000005]
72 --> 38 | cost [3.35]
73 --> 56 | cost [2.7]
78 --> 74 | cost [2.7]
84 --> 76 | cost [7.15]
87 --> 14 | cost [6.1000000000000005]
88 --> 76 | cost [6.25]
89 -->  2 | cost [5.4]
92 --> 56 | cost [4.45]
93 --> 59 | cost [3.85]
94 --> 16 | cost [7.45]
95 --> 77 | cost [2.6]
98 --> 16 | cost [5.9]

B = 46.550000000000004
i★ = 3
j★ = 99
k★ = 79

       
——————— Fri, 19 Jan 2024 07:54:42 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 78 hubs —— 1-69-60-15-21-4-85-78-74-33-3-32-10-6-53-57-44-100-45-59-19-54-70-72-38-27-17-50-56-73-46-20-26-12-49-75-86-97-67-13-8-71-90-30-22-24-25-43-7-34-41-42-40-96-39-35-58-84-88-95-77-99-47-98-16-66-94-31-23-89-11-91-51-83-48-81-68-101-1
total time           3609.28 (TL 3600)    gap                  0.485                
blossom time         0                    nb blossom           0.0                  
LB <= UB             35262.5<=68518.6     Master/SP costs      68135/383.6          
Master time          3602.87              SP time              6.41                 
subtour              39869.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            19.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       22177                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—69—60—15—21—4—85—78—74—33—3—32—10—6—53—57—44—100—45—59—19—54—70—72—38—27—17—50—56—73—46—20—26—12—49—75—86—97—67—13—8—71—90—30—22—24—25—43—7—34—41—42—40—96—39—35—58—84—88—95—77—99—47—98—16—66—94—31—23—89—11—91—51—83—48—81—68—101

RING
1  --- 69 | cost [515.0]
3  --- 32 | cost [860.0]
3  --- 33 | cost [575.0]
4  --- 21 | cost [510.0]
4  --- 85 | cost [520.0]
6  --- 10 | cost [785.0]
6  --- 53 | cost [295.0]
7  --- 34 | cost [285.0]
7  --- 43 | cost [675.0]
8  --- 13 | cost [1120.0]
8  --- 71 | cost [630.0]
10 --- 32 | cost [1130.0]
11 --- 89 | cost [3485.0]
11 --- 91 | cost [1385.0]
12 --- 26 | cost [1045.0]
12 --- 49 | cost [745.0]
13 --- 67 | cost [295.0]
15 --- 21 | cost [645.0]
15 --- 60 | cost [655.0]
16 --- 66 | cost [700.0]
16 --- 98 | cost [590.0]
17 --- 27 | cost [935.0]
17 --- 50 | cost [805.0]
19 --- 54 | cost [485.0]
19 --- 59 | cost [1235.0]
20 --- 26 | cost [260.0]
20 --- 46 | cost [1315.0]
22 --- 24 | cost [1115.0]
22 --- 30 | cost [735.0]
23 --- 31 | cost [1030.0]
23 --- 89 | cost [805.0]
24 --- 25 | cost [330.0]
25 --- 43 | cost [210.0]
27 --- 38 | cost [995.0]
30 --- 90 | cost [1160.0]
31 --- 94 | cost [1070.0]
33 --- 74 | cost [695.0]
34 --- 41 | cost [485.0]
35 --- 39 | cost [1130.0]
35 --- 58 | cost [2390.0]
38 --- 72 | cost [335.0]
39 --- 96 | cost [200.0]
40 --- 42 | cost [440.0]
40 --- 96 | cost [1060.0]
41 --- 42 | cost [670.0]
44 --- 57 | cost [1620.0]
44 --- 100 | cost [365.0]
45 --- 59 | cost [1890.0]
45 --- 100 | cost [840.0]
46 --- 73 | cost [145.0]
47 --- 98 | cost [1110.0]
47 --- 99 | cost [460.0]
48 --- 81 | cost [715.0]
48 --- 83 | cost [665.0]
49 --- 75 | cost [190.0]
50 --- 56 | cost [140.0]
51 --- 83 | cost [170.0]
51 --- 91 | cost [785.0]
53 --- 57 | cost [955.0]
54 --- 70 | cost [725.0]
56 --- 73 | cost [270.0]
58 --- 84 | cost [655.0]
60 --- 69 | cost [415.0]
66 --- 94 | cost [735.0]
67 --- 97 | cost [160.0]
68 --- 81 | cost [1410.0]
68 --- 101 | cost [1070.0]
70 --- 72 | cost [285.0]
71 --- 90 | cost [1130.0]
74 --- 78 | cost [270.0]
75 --- 86 | cost [550.0]
77 --- 95 | cost [260.0]
77 --- 99 | cost [1455.0]
78 --- 85 | cost [1035.0]
84 --- 88 | cost [95.0]
86 --- 97 | cost [65.0]
88 --- 95 | cost [1315.0]

STAR
2  --> 23 | cost [435.0]
5  --> 11 | cost [590.0]
9  --> 26 | cost [210.0]
14 --> 85 | cost [205.0]
18 -->  1 | cost [440.0]
28 --> 77 | cost [370.0]
29 --> 35 | cost [290.0]
36 --> 57 | cost [500.0]
37 --> 19 | cost [470.0]
52 --> 45 | cost [630.0]
55 --> 39 | cost [560.0]
61 --> 11 | cost [405.0]
62 -->  1 | cost [470.0]
63 --> 97 | cost [40.0]
64 --> 91 | cost [695.0]
65 --> 51 | cost [415.0]
76 --> 66 | cost [340.0]
79 -->  6 | cost [230.0]
80 --> 81 | cost [335.0]
82 --> 75 | cost [180.0]
87 --> 86 | cost [635.0]
92 --> 27 | cost [185.0]
93 --> 77 | cost [220.0]

BACKUP RING
1  --- 60 | cost [1.1]
3  --- 10 | cost [6.5]
3  --- 74 | cost [10.55]
4  --- 15 | cost [11.55]
4  --- 78 | cost [5.95]
6  --- 32 | cost [18.55]
6  --- 57 | cost [12.35]
7  --- 25 | cost [8.9]
7  --- 41 | cost [5.3]
8  --- 67 | cost [9.200000000000001]
8  --- 90 | cost [8.2]
10 --- 53 | cost [9.0]
11 --- 23 | cost [27.75]
11 --- 51 | cost [20.1]
12 --- 20 | cost [11.65]
12 --- 75 | cost [5.7]
13 --- 71 | cost [17.45]
13 --- 97 | cost [4.5]
15 --- 69 | cost [6.4]
16 --- 47 | cost [11.15]
16 --- 94 | cost [7.45]
17 --- 38 | cost [3.7]
17 --- 56 | cost [9.4]
19 --- 45 | cost [30.7]
19 --- 70 | cost [12.1]
20 --- 73 | cost [12.85]
21 --- 60 | cost [13.0]
21 --- 85 | cost [3.8000000000000003]
22 --- 25 | cost [14.200000000000001]
22 --- 90 | cost [16.6]
23 --- 94 | cost [20.900000000000002]
24 --- 30 | cost [15.85]
24 --- 43 | cost [2.25]
26 --- 46 | cost [14.950000000000001]
26 --- 49 | cost [13.35]
27 --- 50 | cost [4.75]
27 --- 72 | cost [11.75]
30 --- 71 | cost [20.6]
31 --- 66 | cost [4.75]
31 --- 89 | cost [13.55]
32 --- 33 | cost [9.3]
33 --- 78 | cost [5.75]
34 --- 42 | cost [6.4]
34 --- 43 | cost [9.6]
35 --- 84 | cost [17.400000000000002]
35 --- 96 | cost [10.6]
38 --- 70 | cost [4.3500000000000005]
39 --- 40 | cost [9.35]
39 --- 58 | cost [32.55]
40 --- 41 | cost [8.8]
42 --- 96 | cost [15.0]
44 --- 45 | cost [6.95]
44 --- 53 | cost [23.150000000000002]
46 --- 56 | cost [1.25]
47 --- 77 | cost [17.05]
48 --- 51 | cost [7.0]
48 --- 68 | cost [9.65]
49 --- 86 | cost [4.4]
50 --- 73 | cost [1.35]
54 --- 59 | cost [16.95]
54 --- 72 | cost [6.9]
57 --- 100 | cost [15.3]
58 --- 88 | cost [5.75]
59 --- 100 | cost [27.25]
66 --- 98 | cost [3.6]
67 --- 86 | cost [2.0]
74 --- 85 | cost [12.25]
75 --- 97 | cost [5.95]
77 --- 88 | cost [14.9]
81 --- 83 | cost [10.05]
81 --- 101 | cost [20.150000000000002]
83 --- 91 | cost [9.5]
84 --- 95 | cost [14.0]
89 --- 91 | cost [44.75]
95 --- 99 | cost [12.85]
98 --- 99 | cost [11.8]

BACKUP STAR
2  --> 89 | cost [5.4]
5  --> 22 | cost [4.65]
9  --> 74 | cost [4.05]
14 --> 12 | cost [2.4]
28 --> 95 | cost [5.75]
29 --> 44 | cost [4.3]
36 --> 47 | cost [8.2]
37 --> 77 | cost [5.3]
52 --> 100 | cost [7.15]
55 --> 96 | cost [5.8]
61 --> 34 | cost [5.4]
63 --> 86 | cost [0.75]
64 --> 13 | cost [9.950000000000001]
65 --> 90 | cost [4.8]
76 --> 58 | cost [4.8]
79 --> 53 | cost [3.25]
80 --> 48 | cost [3.85]
82 --> 85 | cost [2.05]
87 --> 15 | cost [6.0]
92 --> 50 | cost [4.1]
93 --> 59 | cost [3.85]

B = 54.8
i★ = 89
j★ = 11
k★ = 91