------------------------------------------------------------
                        α=3.0 —— kroC100 —— 100 nodes       
------------------------------------------------------------

——————— Sat, 27 Jan 2024 21:36:26 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 101 hubs —— 1—85—27—15—13—79—64—20—42—55—67—47—31—65—80—77—30—68—35—2—54—6—75—22—8—17—25—90—34—58—98—88—28—39—38—71—56—43—5—86—72—83—62—50—95—94—91—76—70—23—21—89—41—59—73—3—69—60—4—93—99—19—92—10—14—36—57—74—100—33—45—81—97—96—87—52—11—84—48—66—44—63—51—16—37—9—78—82—7—26—61—32—24—46—29—18—49—12—40—53—101
total time           856                  gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             62981.7<=62981.7     subtour              169.0                
connectivity cuts    33.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—85—27—15—13—79—64—20—42—55—67—47—31—65—80—77—30—68—35—2—54—6—75—22—8—17—25—90—34—58—98—88—28—39—38—71—56—43—5—86—72—83—62—50—95—94—91—76—70—23—21—89—41—59—73—3—69—60—4—93—99—19—92—10—14—36—57—74—100—33—45—81—97—96—87—52—11—84—48—66—44—63—51—16—37—9—78—82—7—26—61—32—24—46—29—18—49—12—40—53—101

RING
1  --- 85 | cost [648.0]
1  --- 101 | cost [0.0]
2  --- 35 | cost [228.0]
2  --- 54 | cost [1497.0]
3  --- 69 | cost [1245.0]
3  --- 73 | cost [54.0]
4  --- 60 | cost [774.0]
4  --- 93 | cost [870.0]
5  --- 43 | cost [510.0]
5  --- 86 | cost [756.0]
6  --- 54 | cost [327.0]
6  --- 75 | cost [804.0]
7  --- 26 | cost [1113.0]
7  --- 82 | cost [1023.0]
8  --- 17 | cost [924.0]
8  --- 22 | cost [384.0]
9  --- 37 | cost [1083.0]
9  --- 78 | cost [249.0]
10 --- 14 | cost [789.0]
10 --- 92 | cost [204.0]
11 --- 52 | cost [81.0]
11 --- 84 | cost [285.0]
12 --- 40 | cost [672.0]
12 --- 49 | cost [1179.0]
13 --- 15 | cost [702.0]
13 --- 79 | cost [390.0]
14 --- 36 | cost [630.0]
15 --- 27 | cost [750.0]
16 --- 37 | cost [993.0]
16 --- 51 | cost [471.0]
17 --- 25 | cost [306.0]
18 --- 29 | cost [321.0]
18 --- 49 | cost [321.0]
19 --- 92 | cost [318.0]
19 --- 99 | cost [300.0]
20 --- 42 | cost [729.0]
20 --- 64 | cost [75.0]
21 --- 23 | cost [1062.0]
21 --- 89 | cost [1107.0]
22 --- 75 | cost [501.0]
23 --- 70 | cost [1011.0]
24 --- 32 | cost [456.0]
24 --- 46 | cost [978.0]
25 --- 90 | cost [288.0]
26 --- 61 | cost [513.0]
27 --- 85 | cost [771.0]
28 --- 39 | cost [285.0]
28 --- 88 | cost [609.0]
29 --- 46 | cost [804.0]
30 --- 68 | cost [417.0]
30 --- 77 | cost [1152.0]
31 --- 47 | cost [261.0]
31 --- 65 | cost [777.0]
32 --- 61 | cost [717.0]
33 --- 45 | cost [321.0]
33 --- 100 | cost [147.0]
34 --- 58 | cost [996.0]
34 --- 90 | cost [270.0]
35 --- 68 | cost [459.0]
36 --- 57 | cost [126.0]
38 --- 39 | cost [345.0]
38 --- 71 | cost [258.0]
40 --- 53 | cost [1107.0]
41 --- 59 | cost [855.0]
41 --- 89 | cost [639.0]
42 --- 55 | cost [327.0]
43 --- 56 | cost [1017.0]
44 --- 63 | cost [327.0]
44 --- 66 | cost [570.0]
45 --- 81 | cost [237.0]
47 --- 67 | cost [501.0]
48 --- 66 | cost [867.0]
48 --- 84 | cost [453.0]
50 --- 62 | cost [855.0]
50 --- 95 | cost [927.0]
51 --- 63 | cost [366.0]
52 --- 87 | cost [1344.0]
53 --- 101 | cost [96.0]
55 --- 67 | cost [648.0]
56 --- 71 | cost [591.0]
57 --- 74 | cost [186.0]
58 --- 98 | cost [618.0]
59 --- 73 | cost [417.0]
60 --- 69 | cost [1716.0]
62 --- 83 | cost [132.0]
64 --- 79 | cost [876.0]
65 --- 80 | cost [771.0]
70 --- 76 | cost [348.0]
72 --- 83 | cost [570.0]
72 --- 86 | cost [1173.0]
74 --- 100 | cost [360.0]
76 --- 91 | cost [708.0]
77 --- 80 | cost [582.0]
78 --- 82 | cost [348.0]
81 --- 97 | cost [360.0]
87 --- 96 | cost [846.0]
88 --- 98 | cost [546.0]
91 --- 94 | cost [387.0]
93 --- 99 | cost [1044.0]
94 --- 95 | cost [369.0]
96 --- 97 | cost [1527.0]

STAR

BACKUP RING
1  --- 27 | cost [13.86]
2  ---  6 | cost [16.56]
2  --- 68 | cost [6.2700000000000005]
3  --- 59 | cost [3.9]
3  --- 60 | cost [23.7]
4  --- 69 | cost [19.95]
4  --- 99 | cost [14.91]
5  --- 56 | cost [6.57]
5  --- 72 | cost [14.97]
6  --- 22 | cost [13.02]
7  --- 61 | cost [16.26]
7  --- 78 | cost [10.8]
8  --- 25 | cost [12.09]
8  --- 75 | cost [7.890000000000001]
9  --- 16 | cost [12.81]
9  --- 82 | cost [5.37]
10 --- 19 | cost [4.74]
10 --- 36 | cost [7.17]
11 --- 48 | cost [7.08]
11 --- 87 | cost [13.68]
12 --- 18 | cost [13.74]
12 --- 53 | cost [15.66]
13 --- 27 | cost [11.85]
13 --- 64 | cost [12.030000000000001]
14 --- 57 | cost [6.75]
14 --- 92 | cost [9.51]
15 --- 79 | cost [7.3500000000000005]
15 --- 85 | cost [9.27]
16 --- 63 | cost [3.63]
17 --- 22 | cost [12.42]
17 --- 90 | cost [5.55]
18 --- 46 | cost [9.39]
19 --- 93 | cost [10.86]
20 --- 55 | cost [5.76]
20 --- 79 | cost [9.06]
21 --- 41 | cost [17.22]
21 --- 70 | cost [12.450000000000001]
23 --- 76 | cost [13.23]
23 --- 89 | cost [17.7]
24 --- 29 | cost [12.870000000000001]
24 --- 61 | cost [9.66]
25 --- 34 | cost [5.3100000000000005]
26 --- 32 | cost [7.68]
26 --- 82 | cost [9.48]
28 --- 38 | cost [3.27]
28 --- 98 | cost [10.620000000000001]
29 --- 49 | cost [6.18]
30 --- 35 | cost [8.64]
30 --- 80 | cost [14.73]
31 --- 67 | cost [3.9]
31 --- 80 | cost [12.93]
32 --- 46 | cost [13.26]
33 --- 74 | cost [4.65]
33 --- 81 | cost [3.5100000000000002]
34 --- 98 | cost [11.88]
35 --- 54 | cost [17.28]
36 --- 74 | cost [3.09]
37 --- 51 | cost [14.4]
37 --- 78 | cost [13.17]
38 --- 56 | cost [5.3100000000000005]
39 --- 71 | cost [4.68]
39 --- 88 | cost [7.95]
40 --- 49 | cost [18.42]
40 --- 101 | cost [11.370000000000001]
41 --- 73 | cost [12.72]
42 --- 64 | cost [7.05]
42 --- 67 | cost [9.6]
43 --- 71 | cost [14.34]
43 --- 86 | cost [11.31]
44 --- 48 | cost [9.450000000000001]
44 --- 51 | cost [6.390000000000001]
45 --- 97 | cost [5.64]
45 --- 100 | cost [4.68]
47 --- 55 | cost [8.1]
47 --- 65 | cost [10.32]
50 --- 83 | cost [8.790000000000001]
50 --- 94 | cost [12.66]
52 --- 84 | cost [3.54]
52 --- 96 | cost [9.21]
54 --- 75 | cost [7.08]
57 --- 100 | cost [4.32]
58 --- 88 | cost [10.200000000000001]
58 --- 90 | cost [11.82]
59 --- 89 | cost [10.950000000000001]
60 --- 93 | cost [16.41]
62 --- 72 | cost [6.69]
62 --- 95 | cost [17.580000000000002]
63 --- 66 | cost [8.07]
65 --- 77 | cost [12.0]
66 --- 84 | cost [12.51]
68 --- 77 | cost [13.59]
69 --- 73 | cost [12.84]
70 --- 91 | cost [7.08]
76 --- 94 | cost [7.62]
81 --- 96 | cost [17.82]
83 --- 86 | cost [16.17]
87 --- 97 | cost [21.45]
91 --- 95 | cost [5.76]
92 --- 99 | cost [3.18]

BACKUP STAR

B = 23.7
i★ = 3
j★ = 69
k★ = 60

       
——————— Sat, 27 Jan 2024 21:45:01 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-85-27-15-13-79-64-20-42-55-67-47-31-65-80-77-30-68-35-2-54-6-75-22-8-17-25-90-34-58-98-88-28-39-38-71-56-43-5-86-72-83-62-50-95-94-91-76-70-23-21-89-41-59-73-3-69-60-4-93-99-19-92-10-14-36-57-74-100-33-45-81-97-96-87-52-11-84-48-66-44-63-51-16-37-9-78-82-7-26-61-32-24-46-29-18-49-12-40-53-101-1
total time           451.71               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             62976<=62981.7       Master/SP costs      62247/734.7          
Master time          446.08               SP time              5.64                 
subtour              8121.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            32.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       3670                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—85—27—15—13—79—64—20—42—55—67—47—31—65—80—77—30—68—35—2—54—6—75—22—8—17—25—90—34—58—98—88—28—39—38—71—56—43—5—86—72—83—62—50—95—94—91—76—70—23—21—89—41—59—73—3—69—60—4—93—99—19—92—10—14—36—57—74—100—33—45—81—97—96—87—52—11—84—48—66—44—63—51—16—37—9—78—82—7—26—61—32—24—46—29—18—49—12—40—53—101

RING
1  --- 85 | cost [648.0]
2  --- 35 | cost [228.0]
2  --- 54 | cost [1497.0]
3  --- 69 | cost [1245.0]
3  --- 73 | cost [54.0]
4  --- 60 | cost [774.0]
4  --- 93 | cost [870.0]
5  --- 43 | cost [510.0]
5  --- 86 | cost [756.0]
6  --- 54 | cost [327.0]
6  --- 75 | cost [804.0]
7  --- 26 | cost [1113.0]
7  --- 82 | cost [1023.0]
8  --- 17 | cost [924.0]
8  --- 22 | cost [384.0]
9  --- 37 | cost [1083.0]
9  --- 78 | cost [249.0]
10 --- 14 | cost [789.0]
10 --- 92 | cost [204.0]
11 --- 52 | cost [81.0]
11 --- 84 | cost [285.0]
12 --- 40 | cost [672.0]
12 --- 49 | cost [1179.0]
13 --- 15 | cost [702.0]
13 --- 79 | cost [390.0]
14 --- 36 | cost [630.0]
15 --- 27 | cost [750.0]
16 --- 37 | cost [993.0]
16 --- 51 | cost [471.0]
17 --- 25 | cost [306.0]
18 --- 29 | cost [321.0]
18 --- 49 | cost [321.0]
19 --- 92 | cost [318.0]
19 --- 99 | cost [300.0]
20 --- 42 | cost [729.0]
20 --- 64 | cost [75.0]
21 --- 23 | cost [1062.0]
21 --- 89 | cost [1107.0]
22 --- 75 | cost [501.0]
23 --- 70 | cost [1011.0]
24 --- 32 | cost [456.0]
24 --- 46 | cost [978.0]
25 --- 90 | cost [288.0]
26 --- 61 | cost [513.0]
27 --- 85 | cost [771.0]
28 --- 39 | cost [285.0]
28 --- 88 | cost [609.0]
29 --- 46 | cost [804.0]
30 --- 68 | cost [417.0]
30 --- 77 | cost [1152.0]
31 --- 47 | cost [261.0]
31 --- 65 | cost [777.0]
32 --- 61 | cost [717.0]
33 --- 45 | cost [321.0]
33 --- 100 | cost [147.0]
34 --- 58 | cost [996.0]
34 --- 90 | cost [270.0]
35 --- 68 | cost [459.0]
36 --- 57 | cost [126.0]
38 --- 39 | cost [345.0]
38 --- 71 | cost [258.0]
40 --- 53 | cost [1107.0]
41 --- 59 | cost [855.0]
41 --- 89 | cost [639.0]
42 --- 55 | cost [327.0]
43 --- 56 | cost [1017.0]
44 --- 63 | cost [327.0]
44 --- 66 | cost [570.0]
45 --- 81 | cost [237.0]
47 --- 67 | cost [501.0]
48 --- 66 | cost [867.0]
48 --- 84 | cost [453.0]
50 --- 62 | cost [855.0]
50 --- 95 | cost [927.0]
51 --- 63 | cost [366.0]
52 --- 87 | cost [1344.0]
53 --- 101 | cost [96.0]
55 --- 67 | cost [648.0]
56 --- 71 | cost [591.0]
57 --- 74 | cost [186.0]
58 --- 98 | cost [618.0]
59 --- 73 | cost [417.0]
60 --- 69 | cost [1716.0]
62 --- 83 | cost [132.0]
64 --- 79 | cost [876.0]
65 --- 80 | cost [771.0]
70 --- 76 | cost [348.0]
72 --- 83 | cost [570.0]
72 --- 86 | cost [1173.0]
74 --- 100 | cost [360.0]
76 --- 91 | cost [708.0]
77 --- 80 | cost [582.0]
78 --- 82 | cost [348.0]
81 --- 97 | cost [360.0]
87 --- 96 | cost [846.0]
88 --- 98 | cost [546.0]
91 --- 94 | cost [387.0]
93 --- 99 | cost [1044.0]
94 --- 95 | cost [369.0]
96 --- 97 | cost [1527.0]

STAR

BACKUP RING
1  --- 27 | cost [13.86]
2  ---  6 | cost [16.56]
2  --- 68 | cost [6.2700000000000005]
3  --- 59 | cost [3.9]
3  --- 60 | cost [23.7]
4  --- 69 | cost [19.95]
4  --- 99 | cost [14.91]
5  --- 56 | cost [6.57]
5  --- 72 | cost [14.97]
6  --- 22 | cost [13.02]
7  --- 61 | cost [16.26]
7  --- 78 | cost [10.8]
8  --- 25 | cost [12.09]
8  --- 75 | cost [7.890000000000001]
9  --- 16 | cost [12.81]
9  --- 82 | cost [5.37]
10 --- 19 | cost [4.74]
10 --- 36 | cost [7.17]
11 --- 48 | cost [7.08]
11 --- 87 | cost [13.68]
12 --- 18 | cost [13.74]
12 --- 53 | cost [15.66]
13 --- 27 | cost [11.85]
13 --- 64 | cost [12.030000000000001]
14 --- 57 | cost [6.75]
14 --- 92 | cost [9.51]
15 --- 79 | cost [7.3500000000000005]
15 --- 85 | cost [9.27]
16 --- 63 | cost [3.63]
17 --- 22 | cost [12.42]
17 --- 90 | cost [5.55]
18 --- 46 | cost [9.39]
19 --- 93 | cost [10.86]
20 --- 55 | cost [5.76]
20 --- 79 | cost [9.06]
21 --- 41 | cost [17.22]
21 --- 70 | cost [12.450000000000001]
23 --- 76 | cost [13.23]
23 --- 89 | cost [17.7]
24 --- 29 | cost [12.870000000000001]
24 --- 61 | cost [9.66]
25 --- 34 | cost [5.3100000000000005]
26 --- 32 | cost [7.68]
26 --- 82 | cost [9.48]
28 --- 38 | cost [3.27]
28 --- 98 | cost [10.620000000000001]
29 --- 49 | cost [6.18]
30 --- 35 | cost [8.64]
30 --- 80 | cost [14.73]
31 --- 67 | cost [3.9]
31 --- 80 | cost [12.93]
32 --- 46 | cost [13.26]
33 --- 74 | cost [4.65]
33 --- 81 | cost [3.5100000000000002]
34 --- 98 | cost [11.88]
35 --- 54 | cost [17.28]
36 --- 74 | cost [3.09]
37 --- 51 | cost [14.4]
37 --- 78 | cost [13.17]
38 --- 56 | cost [5.3100000000000005]
39 --- 71 | cost [4.68]
39 --- 88 | cost [7.95]
40 --- 49 | cost [18.42]
40 --- 101 | cost [11.370000000000001]
41 --- 73 | cost [12.72]
42 --- 64 | cost [7.05]
42 --- 67 | cost [9.6]
43 --- 71 | cost [14.34]
43 --- 86 | cost [11.31]
44 --- 48 | cost [9.450000000000001]
44 --- 51 | cost [6.390000000000001]
45 --- 97 | cost [5.64]
45 --- 100 | cost [4.68]
47 --- 55 | cost [8.1]
47 --- 65 | cost [10.32]
50 --- 83 | cost [8.790000000000001]
50 --- 94 | cost [12.66]
52 --- 84 | cost [3.54]
52 --- 96 | cost [9.21]
54 --- 75 | cost [7.08]
57 --- 100 | cost [4.32]
58 --- 88 | cost [10.200000000000001]
58 --- 90 | cost [11.82]
59 --- 89 | cost [10.950000000000001]
60 --- 93 | cost [16.41]
62 --- 72 | cost [6.69]
62 --- 95 | cost [17.580000000000002]
63 --- 66 | cost [8.07]
65 --- 77 | cost [12.0]
66 --- 84 | cost [12.51]
68 --- 77 | cost [13.59]
69 --- 73 | cost [12.84]
70 --- 91 | cost [7.08]
76 --- 94 | cost [7.62]
81 --- 96 | cost [17.82]
83 --- 86 | cost [16.17]
87 --- 97 | cost [21.45]
91 --- 95 | cost [5.76]
92 --- 99 | cost [3.18]

BACKUP STAR

B = 23.7
i★ = 3
j★ = 69
k★ = 60