------------------------------------------------------------
                        α=3.0 —— kroA100 —— 100 nodes       
------------------------------------------------------------

——————— Sat, 27 Jan 2024 18:43:34 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 101 hubs —— 1—63—6—49—90—19—75—92—8—42—89—31—80—56—97—4—65—26—66—70—22—94—16—88—53—79—18—24—38—99—36—84—10—72—21—74—59—17—15—11—32—45—91—98—23—77—60—62—35—86—27—12—20—57—9—7—55—83—34—29—46—43—3—14—71—41—100—48—30—96—78—52—5—37—33—76—13—95—82—39—85—68—73—50—44—2—54—40—64—69—81—25—87—51—61—58—67—28—93—47—101
total time           834.64               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             64632.93<=64632.93   subtour              203.0                
connectivity cuts    49.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       78                   n lazycuts edges     6.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—63—6—49—90—19—75—92—8—42—89—31—80—56—97—4—65—26—66—70—22—94—16—88—53—79—18—24—38—99—36—84—10—72—21—74—59—17—15—11—32—45—91—98—23—77—60—62—35—86—27—12—20—57—9—7—55—83—34—29—46—43—3—14—71—41—100—48—30—96—78—52—5—37—33—76—13—95—82—39—85—68—73—50—44—2—54—40—64—69—81—25—87—51—61—58—67—28—93—47—101

RING
1  --- 63 | cost [864.0]
1  --- 101 | cost [0.0]
2  --- 44 | cost [771.0]
2  --- 54 | cost [993.0]
3  --- 14 | cost [663.0]
3  --- 43 | cost [513.0]
4  --- 65 | cost [441.0]
4  --- 97 | cost [972.0]
5  --- 37 | cost [207.0]
5  --- 52 | cost [777.0]
6  --- 49 | cost [141.0]
6  --- 63 | cost [471.0]
7  ---  9 | cost [150.0]
7  --- 55 | cost [792.0]
8  --- 42 | cost [744.0]
8  --- 92 | cost [618.0]
9  --- 57 | cost [300.0]
10 --- 72 | cost [810.0]
10 --- 84 | cost [420.0]
11 --- 15 | cost [339.0]
11 --- 32 | cost [606.0]
12 --- 20 | cost [462.0]
12 --- 27 | cost [408.0]
13 --- 76 | cost [309.0]
13 --- 95 | cost [648.0]
14 --- 71 | cost [804.0]
15 --- 17 | cost [39.0]
16 --- 88 | cost [174.0]
16 --- 94 | cost [483.0]
17 --- 59 | cost [1074.0]
18 --- 24 | cost [543.0]
18 --- 79 | cost [690.0]
19 --- 75 | cost [702.0]
19 --- 90 | cost [1128.0]
20 --- 57 | cost [612.0]
21 --- 72 | cost [456.0]
21 --- 74 | cost [198.0]
22 --- 70 | cost [558.0]
22 --- 94 | cost [402.0]
23 --- 77 | cost [1146.0]
23 --- 98 | cost [324.0]
24 --- 38 | cost [288.0]
25 --- 81 | cost [153.0]
25 --- 87 | cost [1020.0]
26 --- 65 | cost [849.0]
26 --- 66 | cost [969.0]
27 --- 86 | cost [243.0]
28 --- 67 | cost [903.0]
28 --- 93 | cost [144.0]
29 --- 34 | cost [903.0]
29 --- 46 | cost [444.0]
30 --- 48 | cost [1281.0]
30 --- 96 | cost [921.0]
31 --- 80 | cost [261.0]
31 --- 89 | cost [564.0]
32 --- 45 | cost [666.0]
33 --- 37 | cost [1224.0]
33 --- 76 | cost [276.0]
34 --- 83 | cost [438.0]
35 --- 62 | cost [975.0]
35 --- 86 | cost [423.0]
36 --- 84 | cost [966.0]
36 --- 99 | cost [900.0]
38 --- 99 | cost [939.0]
39 --- 82 | cost [2043.0]
39 --- 85 | cost [1116.0]
40 --- 54 | cost [312.0]
40 --- 64 | cost [240.0]
41 --- 71 | cost [249.0]
41 --- 100 | cost [555.0]
42 --- 89 | cost [540.0]
43 --- 46 | cost [594.0]
44 --- 50 | cost [486.0]
45 --- 91 | cost [537.0]
47 --- 93 | cost [1599.0]
47 --- 101 | cost [1287.0]
48 --- 100 | cost [756.0]
49 --- 90 | cost [624.0]
50 --- 73 | cost [540.0]
51 --- 61 | cost [558.0]
51 --- 87 | cost [438.0]
52 --- 78 | cost [120.0]
53 --- 79 | cost [669.0]
53 --- 88 | cost [690.0]
55 --- 83 | cost [69.0]
56 --- 80 | cost [843.0]
56 --- 97 | cost [648.0]
58 --- 61 | cost [975.0]
58 --- 67 | cost [1035.0]
59 --- 74 | cost [267.0]
60 --- 62 | cost [453.0]
60 --- 77 | cost [573.0]
64 --- 69 | cost [891.0]
66 --- 70 | cost [1200.0]
68 --- 73 | cost [801.0]
68 --- 85 | cost [459.0]
69 --- 81 | cost [909.0]
75 --- 92 | cost [1074.0]
78 --- 96 | cost [204.0]
82 --- 95 | cost [735.0]
91 --- 98 | cost [297.0]

STAR

BACKUP RING
1  ---  6 | cost [11.91]
2  --- 40 | cost [10.11]
2  --- 50 | cost [12.48]
3  --- 46 | cost [4.17]
3  --- 71 | cost [12.030000000000001]
4  --- 26 | cost [12.51]
4  --- 56 | cost [15.0]
5  --- 33 | cost [14.25]
5  --- 78 | cost [7.26]
6  --- 90 | cost [7.47]
7  --- 57 | cost [2.79]
7  --- 83 | cost [8.1]
8  --- 75 | cost [13.71]
8  --- 89 | cost [12.48]
9  --- 20 | cost [8.43]
9  --- 55 | cost [8.94]
10 --- 21 | cost [12.6]
10 --- 36 | cost [13.23]
11 --- 17 | cost [3.45]
11 --- 45 | cost [11.1]
12 --- 57 | cost [7.23]
12 --- 86 | cost [5.58]
13 --- 33 | cost [3.0300000000000002]
13 --- 82 | cost [12.0]
14 --- 41 | cost [10.32]
14 --- 43 | cost [11.370000000000001]
15 --- 32 | cost [8.4]
15 --- 59 | cost [11.1]
16 --- 22 | cost [2.1]
16 --- 53 | cost [7.68]
17 --- 74 | cost [10.620000000000001]
18 --- 38 | cost [8.31]
18 --- 53 | cost [12.99]
19 --- 49 | cost [12.96]
19 --- 92 | cost [17.31]
20 --- 27 | cost [5.43]
21 --- 59 | cost [4.53]
22 --- 66 | cost [16.47]
23 --- 60 | cost [10.35]
23 --- 91 | cost [5.76]
24 --- 79 | cost [11.58]
24 --- 99 | cost [11.91]
25 --- 51 | cost [7.62]
25 --- 69 | cost [10.41]
26 --- 70 | cost [20.07]
27 --- 35 | cost [5.34]
28 --- 47 | cost [17.13]
28 --- 58 | cost [9.09]
29 --- 43 | cost [10.14]
29 --- 83 | cost [13.08]
30 --- 78 | cost [10.56]
30 --- 100 | cost [19.32]
31 --- 42 | cost [6.87]
31 --- 56 | cost [11.01]
32 --- 91 | cost [6.45]
34 --- 46 | cost [9.33]
34 --- 55 | cost [5.07]
35 --- 60 | cost [13.92]
36 --- 38 | cost [6.84]
37 --- 52 | cost [9.78]
37 --- 76 | cost [14.88]
39 --- 68 | cost [14.67]
39 --- 95 | cost [23.82]
40 --- 69 | cost [10.92]
41 --- 48 | cost [12.99]
42 --- 92 | cost [13.41]
44 --- 54 | cost [13.89]
44 --- 73 | cost [6.99]
45 --- 98 | cost [6.42]
48 --- 96 | cost [13.56]
49 --- 63 | cost [6.0600000000000005]
50 --- 68 | cost [9.6]
51 --- 58 | cost [13.05]
52 --- 96 | cost [3.18]
54 --- 64 | cost [5.43]
61 --- 67 | cost [17.91]
61 --- 87 | cost [9.72]
62 --- 77 | cost [6.63]
62 --- 86 | cost [9.24]
64 --- 81 | cost [17.97]
65 --- 66 | cost [3.45]
65 --- 97 | cost [14.01]
67 --- 93 | cost [10.41]
70 --- 94 | cost [9.39]
71 --- 100 | cost [3.63]
72 --- 74 | cost [6.45]
72 --- 84 | cost [9.42]
73 --- 85 | cost [12.36]
75 --- 90 | cost [12.48]
76 --- 95 | cost [7.8]
77 --- 98 | cost [13.65]
79 --- 88 | cost [7.7700000000000005]
80 --- 89 | cost [7.59]
80 --- 97 | cost [14.91]
81 --- 87 | cost [11.55]
82 --- 85 | cost [24.03]
84 --- 99 | cost [17.79]
88 --- 94 | cost [4.83]
93 --- 101 | cost [12.39]

BACKUP STAR

B = 24.03
i★ = 82
j★ = 39
k★ = 85

       
——————— Sat, 27 Jan 2024 18:48:46 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-63-6-49-90-19-75-92-8-42-89-31-80-56-97-4-65-26-66-70-22-94-16-88-53-79-18-24-38-99-36-84-10-72-21-74-59-17-15-11-32-45-91-98-23-77-60-62-35-86-27-12-20-57-9-7-55-83-34-29-46-43-3-14-71-41-100-48-30-96-78-52-5-37-33-76-13-95-82-39-85-68-73-50-44-2-54-40-64-69-81-25-87-51-61-58-67-28-93-47-101-1
total time           248.46               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             64632.93<=64632.93   Master/SP costs      63888/744.93         
Master time          244.2                SP time              4.26                 
subtour              2747.0               connectivity cuts    1959.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            21.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       2083                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—63—6—49—90—19—75—92—8—42—89—31—80—56—97—4—65—26—66—70—22—94—16—88—53—79—18—24—38—99—36—84—10—72—21—74—59—17—15—11—32—45—91—98—23—77—60—62—35—86—27—12—20—57—9—7—55—83—34—29—46—43—3—14—71—41—100—48—30—96—78—52—5—37—33—76—13—95—82—39—85—68—73—50—44—2—54—40—64—69—81—25—87—51—61—58—67—28—93—47—101

RING
1  --- 63 | cost [864.0]
1  --- 101 | cost [0.0]
2  --- 44 | cost [771.0]
2  --- 54 | cost [993.0]
3  --- 14 | cost [663.0]
3  --- 43 | cost [513.0]
4  --- 65 | cost [441.0]
4  --- 97 | cost [972.0]
5  --- 37 | cost [207.0]
5  --- 52 | cost [777.0]
6  --- 49 | cost [141.0]
6  --- 63 | cost [471.0]
7  ---  9 | cost [150.0]
7  --- 55 | cost [792.0]
8  --- 42 | cost [744.0]
8  --- 92 | cost [618.0]
9  --- 57 | cost [300.0]
10 --- 72 | cost [810.0]
10 --- 84 | cost [420.0]
11 --- 15 | cost [339.0]
11 --- 32 | cost [606.0]
12 --- 20 | cost [462.0]
12 --- 27 | cost [408.0]
13 --- 76 | cost [309.0]
13 --- 95 | cost [648.0]
14 --- 71 | cost [804.0]
15 --- 17 | cost [39.0]
16 --- 88 | cost [174.0]
16 --- 94 | cost [483.0]
17 --- 59 | cost [1074.0]
18 --- 24 | cost [543.0]
18 --- 79 | cost [690.0]
19 --- 75 | cost [702.0]
19 --- 90 | cost [1128.0]
20 --- 57 | cost [612.0]
21 --- 72 | cost [456.0]
21 --- 74 | cost [198.0]
22 --- 70 | cost [558.0]
22 --- 94 | cost [402.0]
23 --- 77 | cost [1146.0]
23 --- 98 | cost [324.0]
24 --- 38 | cost [288.0]
25 --- 81 | cost [153.0]
25 --- 87 | cost [1020.0]
26 --- 65 | cost [849.0]
26 --- 66 | cost [969.0]
27 --- 86 | cost [243.0]
28 --- 67 | cost [903.0]
28 --- 93 | cost [144.0]
29 --- 34 | cost [903.0]
29 --- 46 | cost [444.0]
30 --- 48 | cost [1281.0]
30 --- 96 | cost [921.0]
31 --- 80 | cost [261.0]
31 --- 89 | cost [564.0]
32 --- 45 | cost [666.0]
33 --- 37 | cost [1224.0]
33 --- 76 | cost [276.0]
34 --- 83 | cost [438.0]
35 --- 62 | cost [975.0]
35 --- 86 | cost [423.0]
36 --- 84 | cost [966.0]
36 --- 99 | cost [900.0]
38 --- 99 | cost [939.0]
39 --- 82 | cost [2043.0]
39 --- 85 | cost [1116.0]
40 --- 54 | cost [312.0]
40 --- 64 | cost [240.0]
41 --- 71 | cost [249.0]
41 --- 100 | cost [555.0]
42 --- 89 | cost [540.0]
43 --- 46 | cost [594.0]
44 --- 50 | cost [486.0]
45 --- 91 | cost [537.0]
47 --- 93 | cost [1599.0]
47 --- 101 | cost [1287.0]
48 --- 100 | cost [756.0]
49 --- 90 | cost [624.0]
50 --- 73 | cost [540.0]
51 --- 61 | cost [558.0]
51 --- 87 | cost [438.0]
52 --- 78 | cost [120.0]
53 --- 79 | cost [669.0]
53 --- 88 | cost [690.0]
55 --- 83 | cost [69.0]
56 --- 80 | cost [843.0]
56 --- 97 | cost [648.0]
58 --- 61 | cost [975.0]
58 --- 67 | cost [1035.0]
59 --- 74 | cost [267.0]
60 --- 62 | cost [453.0]
60 --- 77 | cost [573.0]
64 --- 69 | cost [891.0]
66 --- 70 | cost [1200.0]
68 --- 73 | cost [801.0]
68 --- 85 | cost [459.0]
69 --- 81 | cost [909.0]
75 --- 92 | cost [1074.0]
78 --- 96 | cost [204.0]
82 --- 95 | cost [735.0]
91 --- 98 | cost [297.0]

STAR

BACKUP RING
1  ---  6 | cost [11.91]
2  --- 40 | cost [10.11]
2  --- 50 | cost [12.48]
3  --- 46 | cost [4.17]
3  --- 71 | cost [12.030000000000001]
4  --- 26 | cost [12.51]
4  --- 56 | cost [15.0]
5  --- 33 | cost [14.25]
5  --- 78 | cost [7.26]
6  --- 90 | cost [7.47]
7  --- 57 | cost [2.79]
7  --- 83 | cost [8.1]
8  --- 75 | cost [13.71]
8  --- 89 | cost [12.48]
9  --- 20 | cost [8.43]
9  --- 55 | cost [8.94]
10 --- 21 | cost [12.6]
10 --- 36 | cost [13.23]
11 --- 17 | cost [3.45]
11 --- 45 | cost [11.1]
12 --- 57 | cost [7.23]
12 --- 86 | cost [5.58]
13 --- 33 | cost [3.0300000000000002]
13 --- 82 | cost [12.0]
14 --- 41 | cost [10.32]
14 --- 43 | cost [11.370000000000001]
15 --- 32 | cost [8.4]
15 --- 59 | cost [11.1]
16 --- 22 | cost [2.1]
16 --- 53 | cost [7.68]
17 --- 74 | cost [10.620000000000001]
18 --- 38 | cost [8.31]
18 --- 53 | cost [12.99]
19 --- 49 | cost [12.96]
19 --- 92 | cost [17.31]
20 --- 27 | cost [5.43]
21 --- 59 | cost [4.53]
22 --- 66 | cost [16.47]
23 --- 60 | cost [10.35]
23 --- 91 | cost [5.76]
24 --- 79 | cost [11.58]
24 --- 99 | cost [11.91]
25 --- 51 | cost [7.62]
25 --- 69 | cost [10.41]
26 --- 70 | cost [20.07]
27 --- 35 | cost [5.34]
28 --- 47 | cost [17.13]
28 --- 58 | cost [9.09]
29 --- 43 | cost [10.14]
29 --- 83 | cost [13.08]
30 --- 78 | cost [10.56]
30 --- 100 | cost [19.32]
31 --- 42 | cost [6.87]
31 --- 56 | cost [11.01]
32 --- 91 | cost [6.45]
34 --- 46 | cost [9.33]
34 --- 55 | cost [5.07]
35 --- 60 | cost [13.92]
36 --- 38 | cost [6.84]
37 --- 52 | cost [9.78]
37 --- 76 | cost [14.88]
39 --- 68 | cost [14.67]
39 --- 95 | cost [23.82]
40 --- 69 | cost [10.92]
41 --- 48 | cost [12.99]
42 --- 92 | cost [13.41]
44 --- 54 | cost [13.89]
44 --- 73 | cost [6.99]
45 --- 98 | cost [6.42]
48 --- 96 | cost [13.56]
49 --- 63 | cost [6.0600000000000005]
50 --- 68 | cost [9.6]
51 --- 58 | cost [13.05]
52 --- 96 | cost [3.18]
54 --- 64 | cost [5.43]
61 --- 67 | cost [17.91]
61 --- 87 | cost [9.72]
62 --- 77 | cost [6.63]
62 --- 86 | cost [9.24]
64 --- 81 | cost [17.97]
65 --- 66 | cost [3.45]
65 --- 97 | cost [14.01]
67 --- 93 | cost [10.41]
70 --- 94 | cost [9.39]
71 --- 100 | cost [3.63]
72 --- 74 | cost [6.45]
72 --- 84 | cost [9.42]
73 --- 85 | cost [12.36]
75 --- 90 | cost [12.48]
76 --- 95 | cost [7.8]
77 --- 98 | cost [13.65]
79 --- 88 | cost [7.7700000000000005]
80 --- 89 | cost [7.59]
80 --- 97 | cost [14.91]
81 --- 87 | cost [11.55]
82 --- 85 | cost [24.03]
84 --- 99 | cost [17.79]
88 --- 94 | cost [4.83]
93 --- 101 | cost [12.39]

BACKUP STAR

B = 24.03
i★ = 82
j★ = 39
k★ = 85