------------------------------------------------------------
                          α=3.0 —— rd100 —— 100 nodes       
------------------------------------------------------------

——————— Fri, 19 Jan 2024 05:46:23 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 101 hubs —— 1—18—62—87—15—63—86—97—67—13—49—21—75—82—85—14—12—4—32—9—26—74—20—78—3—33—10—27—92—17—72—70—38—54—73—50—46—56—19—37—28—93—77—95—59—76—58—89—2—23—35—29—44—100—39—96—55—40—43—25—24—42—7—34—41—22—5—61—11—52—45—16—31—84—88—66—98—94—6—79—53—99—47—57—36—64—91—81—80—30—48—65—90—51—83—68—71—8—69—60—101
total time           1635.87              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             23797.83<=23797.83   subtour              473.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—18—62—87—15—63—86—97—67—13—49—21—75—82—85—14—12—4—32—9—26—74—20—78—3—33—10—27—92—17—72—70—38—54—73—50—46—56—19—37—28—93—77—95—59—76—58—89—2—23—35—29—44—100—39—96—55—40—43—25—24—42—7—34—41—22—5—61—11—52—45—16—31—84—88—66—98—94—6—79—53—99—47—57—36—64—91—81—80—30—48—65—90—51—83—68—71—8—69—60—101

RING
1  --- 18 | cost [264.0]
2  --- 23 | cost [261.0]
2  --- 89 | cost [324.0]
3  --- 33 | cost [345.0]
3  --- 78 | cost [486.0]
4  --- 12 | cost [360.0]
4  --- 32 | cost [126.0]
5  --- 22 | cost [279.0]
5  --- 61 | cost [150.0]
6  --- 79 | cost [138.0]
6  --- 94 | cost [363.0]
7  --- 34 | cost [171.0]
7  --- 42 | cost [219.0]
8  --- 69 | cost [183.0]
8  --- 71 | cost [378.0]
9  --- 26 | cost [126.0]
9  --- 32 | cost [360.0]
10 --- 27 | cost [357.0]
10 --- 33 | cost [123.0]
11 --- 52 | cost [534.0]
11 --- 61 | cost [243.0]
12 --- 14 | cost [144.0]
13 --- 49 | cost [264.0]
13 --- 67 | cost [177.0]
14 --- 85 | cost [123.0]
15 --- 63 | cost [90.0]
15 --- 87 | cost [360.0]
16 --- 31 | cost [375.0]
16 --- 45 | cost [306.0]
17 --- 72 | cost [162.0]
17 --- 92 | cost [450.0]
18 --- 62 | cost [201.0]
19 --- 37 | cost [282.0]
19 --- 56 | cost [264.0]
20 --- 74 | cost [57.0]
20 --- 78 | cost [117.0]
21 --- 49 | cost [105.0]
21 --- 75 | cost [75.0]
22 --- 41 | cost [150.0]
23 --- 35 | cost [750.0]
24 --- 25 | cost [198.0]
24 --- 42 | cost [204.0]
25 --- 43 | cost [126.0]
26 --- 74 | cost [117.0]
27 --- 92 | cost [111.0]
28 --- 37 | cost [108.0]
28 --- 93 | cost [267.0]
29 --- 35 | cost [174.0]
29 --- 44 | cost [258.0]
30 --- 48 | cost [237.0]
30 --- 80 | cost [252.0]
31 --- 84 | cost [162.0]
34 --- 41 | cost [291.0]
36 --- 57 | cost [300.0]
36 --- 64 | cost [408.0]
38 --- 54 | cost [213.0]
38 --- 70 | cost [261.0]
39 --- 96 | cost [120.0]
39 --- 100 | cost [486.0]
40 --- 43 | cost [363.0]
40 --- 55 | cost [357.0]
44 --- 100 | cost [219.0]
45 --- 52 | cost [378.0]
46 --- 50 | cost [15.0]
46 --- 56 | cost [75.0]
47 --- 57 | cost [300.0]
47 --- 99 | cost [276.0]
48 --- 65 | cost [309.0]
50 --- 73 | cost [81.0]
51 --- 83 | cost [102.0]
51 --- 90 | cost [126.0]
53 --- 79 | cost [195.0]
53 --- 99 | cost [144.0]
54 --- 73 | cost [240.0]
55 --- 96 | cost [348.0]
58 --- 76 | cost [288.0]
58 --- 89 | cost [729.0]
59 --- 76 | cost [390.0]
59 --- 95 | cost [57.0]
60 --- 69 | cost [249.0]
60 --- 101 | cost [66.0]
62 --- 87 | cost [252.0]
63 --- 86 | cost [45.0]
64 --- 91 | cost [417.0]
65 --- 90 | cost [288.0]
66 --- 88 | cost [306.0]
66 --- 98 | cost [216.0]
67 --- 97 | cost [96.0]
68 --- 71 | cost [423.0]
68 --- 83 | cost [243.0]
70 --- 72 | cost [171.0]
75 --- 82 | cost [108.0]
77 --- 93 | cost [132.0]
77 --- 95 | cost [156.0]
80 --- 81 | cost [201.0]
81 --- 91 | cost [387.0]
82 --- 85 | cost [123.0]
84 --- 88 | cost [57.0]
86 --- 97 | cost [39.0]
94 --- 98 | cost [228.0]

STAR

BACKUP RING
1  --- 62 | cost [2.82]
2  --- 35 | cost [9.51]
2  --- 58 | cost [9.24]
3  --- 10 | cost [3.9]
3  --- 20 | cost [5.76]
4  ---  9 | cost [4.86]
4  --- 14 | cost [4.3500000000000005]
5  --- 11 | cost [3.54]
5  --- 41 | cost [3.84]
6  --- 53 | cost [1.77]
6  --- 98 | cost [5.67]
7  --- 24 | cost [4.2]
7  --- 41 | cost [3.18]
8  --- 60 | cost [1.02]
8  --- 68 | cost [5.1000000000000005]
9  --- 74 | cost [2.43]
10 --- 92 | cost [4.41]
11 --- 45 | cost [9.09]
12 --- 32 | cost [3.42]
12 --- 85 | cost [1.23]
13 --- 21 | cost [3.54]
13 --- 97 | cost [2.7]
14 --- 82 | cost [2.31]
15 --- 62 | cost [3.33]
15 --- 86 | cost [1.29]
16 --- 52 | cost [5.61]
16 --- 84 | cost [5.37]
17 --- 27 | cost [5.61]
17 --- 70 | cost [3.3000000000000003]
18 --- 87 | cost [4.32]
19 --- 28 | cost [3.87]
19 --- 46 | cost [2.52]
20 --- 26 | cost [1.56]
21 --- 82 | cost [1.26]
22 --- 34 | cost [3.7800000000000002]
22 --- 61 | cost [3.45]
23 --- 29 | cost [9.0]
23 --- 89 | cost [4.83]
24 --- 43 | cost [1.35]
25 --- 40 | cost [4.71]
25 --- 42 | cost [3.27]
26 --- 32 | cost [3.69]
27 --- 33 | cost [4.11]
28 --- 77 | cost [2.22]
29 --- 100 | cost [2.82]
30 --- 65 | cost [4.23]
30 --- 81 | cost [3.6]
31 --- 45 | cost [5.1000000000000005]
31 --- 88 | cost [1.77]
33 --- 78 | cost [3.45]
34 --- 42 | cost [3.84]
35 --- 44 | cost [2.91]
36 --- 47 | cost [4.92]
36 --- 91 | cost [6.66]
37 --- 56 | cost [3.3000000000000003]
37 --- 93 | cost [3.27]
38 --- 72 | cost [2.0100000000000002]
38 --- 73 | cost [3.33]
39 --- 44 | cost [6.63]
39 --- 55 | cost [3.36]
40 --- 96 | cost [6.36]
43 --- 55 | cost [6.24]
46 --- 73 | cost [0.87]
47 --- 53 | cost [2.97]
48 --- 80 | cost [2.31]
48 --- 90 | cost [5.25]
49 --- 67 | cost [2.61]
49 --- 75 | cost [1.1400000000000001]
50 --- 54 | cost [3.0300000000000002]
50 --- 56 | cost [0.84]
51 --- 65 | cost [2.49]
51 --- 68 | cost [3.27]
52 --- 61 | cost [7.74]
54 --- 70 | cost [4.3500000000000005]
57 --- 64 | cost [6.15]
57 --- 99 | cost [5.76]
58 --- 59 | cost [6.15]
59 --- 77 | cost [1.44]
63 --- 87 | cost [3.87]
63 --- 97 | cost [0.24]
64 --- 81 | cost [7.26]
66 --- 84 | cost [3.48]
66 --- 94 | cost [4.41]
67 --- 86 | cost [1.2]
69 --- 71 | cost [5.46]
69 --- 101 | cost [3.09]
71 --- 83 | cost [6.2700000000000005]
72 --- 92 | cost [5.97]
74 --- 78 | cost [1.62]
75 --- 85 | cost [2.31]
76 --- 89 | cost [9.69]
76 --- 95 | cost [4.2]
79 --- 94 | cost [4.83]
79 --- 99 | cost [2.07]
80 --- 91 | cost [4.62]
83 --- 90 | cost [2.16]
88 --- 98 | cost [5.07]
93 --- 95 | cost [2.67]
96 --- 100 | cost [5.25]

BACKUP STAR

B = 9.69
i★ = 76
j★ = 58
k★ = 89

       
——————— Fri, 19 Jan 2024 05:52:10 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-18-62-87-15-63-86-97-67-13-49-21-75-82-85-14-12-4-32-9-26-74-20-78-3-33-10-27-92-17-72-70-38-54-73-50-46-56-19-37-28-93-77-95-59-76-58-89-2-23-35-29-44-100-39-96-55-40-43-25-24-42-7-34-41-22-5-61-11-52-45-16-31-84-88-66-98-94-6-79-53-99-47-57-36-64-91-81-80-30-48-65-90-51-83-68-71-8-69-60-101-1
total time           271.44               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             23797.83<=23797.83   Master/SP costs      23730/67.83          
Master time          267.55               SP time              3.89                 
subtour              6584.0               connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            14.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       3701                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—18—62—87—15—63—86—97—67—13—49—21—75—82—85—14—12—4—32—9—26—74—20—78—3—33—10—27—92—17—72—70—38—54—73—50—46—56—19—37—28—93—77—95—59—76—58—89—2—23—35—29—44—100—39—96—55—40—43—25—24—42—7—34—41—22—5—61—11—52—45—16—31—84—88—66—98—94—6—79—53—99—47—57—36—64—91—81—80—30—48—65—90—51—83—68—71—8—69—60—101

RING
1  --- 18 | cost [264.0]
2  --- 23 | cost [261.0]
2  --- 89 | cost [324.0]
3  --- 33 | cost [345.0]
3  --- 78 | cost [486.0]
4  --- 12 | cost [360.0]
4  --- 32 | cost [126.0]
5  --- 22 | cost [279.0]
5  --- 61 | cost [150.0]
6  --- 79 | cost [138.0]
6  --- 94 | cost [363.0]
7  --- 34 | cost [171.0]
7  --- 42 | cost [219.0]
8  --- 69 | cost [183.0]
8  --- 71 | cost [378.0]
9  --- 26 | cost [126.0]
9  --- 32 | cost [360.0]
10 --- 27 | cost [357.0]
10 --- 33 | cost [123.0]
11 --- 52 | cost [534.0]
11 --- 61 | cost [243.0]
12 --- 14 | cost [144.0]
13 --- 49 | cost [264.0]
13 --- 67 | cost [177.0]
14 --- 85 | cost [123.0]
15 --- 63 | cost [90.0]
15 --- 87 | cost [360.0]
16 --- 31 | cost [375.0]
16 --- 45 | cost [306.0]
17 --- 72 | cost [162.0]
17 --- 92 | cost [450.0]
18 --- 62 | cost [201.0]
19 --- 37 | cost [282.0]
19 --- 56 | cost [264.0]
20 --- 74 | cost [57.0]
20 --- 78 | cost [117.0]
21 --- 49 | cost [105.0]
21 --- 75 | cost [75.0]
22 --- 41 | cost [150.0]
23 --- 35 | cost [750.0]
24 --- 25 | cost [198.0]
24 --- 42 | cost [204.0]
25 --- 43 | cost [126.0]
26 --- 74 | cost [117.0]
27 --- 92 | cost [111.0]
28 --- 37 | cost [108.0]
28 --- 93 | cost [267.0]
29 --- 35 | cost [174.0]
29 --- 44 | cost [258.0]
30 --- 48 | cost [237.0]
30 --- 80 | cost [252.0]
31 --- 84 | cost [162.0]
34 --- 41 | cost [291.0]
36 --- 57 | cost [300.0]
36 --- 64 | cost [408.0]
38 --- 54 | cost [213.0]
38 --- 70 | cost [261.0]
39 --- 96 | cost [120.0]
39 --- 100 | cost [486.0]
40 --- 43 | cost [363.0]
40 --- 55 | cost [357.0]
44 --- 100 | cost [219.0]
45 --- 52 | cost [378.0]
46 --- 50 | cost [15.0]
46 --- 56 | cost [75.0]
47 --- 57 | cost [300.0]
47 --- 99 | cost [276.0]
48 --- 65 | cost [309.0]
50 --- 73 | cost [81.0]
51 --- 83 | cost [102.0]
51 --- 90 | cost [126.0]
53 --- 79 | cost [195.0]
53 --- 99 | cost [144.0]
54 --- 73 | cost [240.0]
55 --- 96 | cost [348.0]
58 --- 76 | cost [288.0]
58 --- 89 | cost [729.0]
59 --- 76 | cost [390.0]
59 --- 95 | cost [57.0]
60 --- 69 | cost [249.0]
60 --- 101 | cost [66.0]
62 --- 87 | cost [252.0]
63 --- 86 | cost [45.0]
64 --- 91 | cost [417.0]
65 --- 90 | cost [288.0]
66 --- 88 | cost [306.0]
66 --- 98 | cost [216.0]
67 --- 97 | cost [96.0]
68 --- 71 | cost [423.0]
68 --- 83 | cost [243.0]
70 --- 72 | cost [171.0]
75 --- 82 | cost [108.0]
77 --- 93 | cost [132.0]
77 --- 95 | cost [156.0]
80 --- 81 | cost [201.0]
81 --- 91 | cost [387.0]
82 --- 85 | cost [123.0]
84 --- 88 | cost [57.0]
86 --- 97 | cost [39.0]
94 --- 98 | cost [228.0]

STAR

BACKUP RING
1  --- 62 | cost [2.82]
2  --- 35 | cost [9.51]
2  --- 58 | cost [9.24]
3  --- 10 | cost [3.9]
3  --- 20 | cost [5.76]
4  ---  9 | cost [4.86]
4  --- 14 | cost [4.3500000000000005]
5  --- 11 | cost [3.54]
5  --- 41 | cost [3.84]
6  --- 53 | cost [1.77]
6  --- 98 | cost [5.67]
7  --- 24 | cost [4.2]
7  --- 41 | cost [3.18]
8  --- 60 | cost [1.02]
8  --- 68 | cost [5.1000000000000005]
9  --- 74 | cost [2.43]
10 --- 92 | cost [4.41]
11 --- 45 | cost [9.09]
12 --- 32 | cost [3.42]
12 --- 85 | cost [1.23]
13 --- 21 | cost [3.54]
13 --- 97 | cost [2.7]
14 --- 82 | cost [2.31]
15 --- 62 | cost [3.33]
15 --- 86 | cost [1.29]
16 --- 52 | cost [5.61]
16 --- 84 | cost [5.37]
17 --- 27 | cost [5.61]
17 --- 70 | cost [3.3000000000000003]
18 --- 87 | cost [4.32]
19 --- 28 | cost [3.87]
19 --- 46 | cost [2.52]
20 --- 26 | cost [1.56]
21 --- 82 | cost [1.26]
22 --- 34 | cost [3.7800000000000002]
22 --- 61 | cost [3.45]
23 --- 29 | cost [9.0]
23 --- 89 | cost [4.83]
24 --- 43 | cost [1.35]
25 --- 40 | cost [4.71]
25 --- 42 | cost [3.27]
26 --- 32 | cost [3.69]
27 --- 33 | cost [4.11]
28 --- 77 | cost [2.22]
29 --- 100 | cost [2.82]
30 --- 65 | cost [4.23]
30 --- 81 | cost [3.6]
31 --- 45 | cost [5.1000000000000005]
31 --- 88 | cost [1.77]
33 --- 78 | cost [3.45]
34 --- 42 | cost [3.84]
35 --- 44 | cost [2.91]
36 --- 47 | cost [4.92]
36 --- 91 | cost [6.66]
37 --- 56 | cost [3.3000000000000003]
37 --- 93 | cost [3.27]
38 --- 72 | cost [2.0100000000000002]
38 --- 73 | cost [3.33]
39 --- 44 | cost [6.63]
39 --- 55 | cost [3.36]
40 --- 96 | cost [6.36]
43 --- 55 | cost [6.24]
46 --- 73 | cost [0.87]
47 --- 53 | cost [2.97]
48 --- 80 | cost [2.31]
48 --- 90 | cost [5.25]
49 --- 67 | cost [2.61]
49 --- 75 | cost [1.1400000000000001]
50 --- 54 | cost [3.0300000000000002]
50 --- 56 | cost [0.84]
51 --- 65 | cost [2.49]
51 --- 68 | cost [3.27]
52 --- 61 | cost [7.74]
54 --- 70 | cost [4.3500000000000005]
57 --- 64 | cost [6.15]
57 --- 99 | cost [5.76]
58 --- 59 | cost [6.15]
59 --- 77 | cost [1.44]
63 --- 87 | cost [3.87]
63 --- 97 | cost [0.24]
64 --- 81 | cost [7.26]
66 --- 84 | cost [3.48]
66 --- 94 | cost [4.41]
67 --- 86 | cost [1.2]
69 --- 71 | cost [5.46]
69 --- 101 | cost [3.09]
71 --- 83 | cost [6.2700000000000005]
72 --- 92 | cost [5.97]
74 --- 78 | cost [1.62]
75 --- 85 | cost [2.31]
76 --- 89 | cost [9.69]
76 --- 95 | cost [4.2]
79 --- 94 | cost [4.83]
79 --- 99 | cost [2.07]
80 --- 91 | cost [4.62]
83 --- 90 | cost [2.16]
88 --- 98 | cost [5.07]
93 --- 95 | cost [2.67]
96 --- 100 | cost [5.25]

BACKUP STAR

B = 9.69
i★ = 76
j★ = 58
k★ = 89