------------------------------------------------------------
                         α=3.0 —— lin105 —— 105 nodes       
------------------------------------------------------------

——————— Fri, 19 Jan 2024 10:40:06 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 106 hubs —— 1—3—8—9—5—4—13—14—34—35—38—39—60—61—65—66—87—88—94—95—100—99—98—90—89—93—102—101—97—96—92—91—85—84—83—82—78—71—68—67—64—72—77—79—86—80—76—73—81—75—74—69—70—63—62—105—59—56—55—50—48—45—49—40—104—44—47—51—54—57—58—53—52—46—43—41—42—37—36—26—25—18—17—16—27—24—19—12—20—23—28—33—32—31—30—29—22—21—103—15—11—10—7—6—2—106
total time           2517.97              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             43288.46<=43289.04   subtour              1824.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:105                
2-opt strategy       0                                                              
explored_nodes       17                   n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—3—8—9—5—4—13—14—34—35—38—39—60—61—65—66—87—88—94—95—100—99—98—90—89—93—102—101—97—96—92—91—85—84—83—82—78—71—68—67—64—72—77—79—86—80—76—73—81—75—74—69—70—63—62—105—59—56—55—50—48—45—49—40—104—44—47—51—54—57—58—53—52—46—43—41—42—37—36—26—25—18—17—16—27—24—19—12—20—23—28—33—32—31—30—29—22—21—103—15—11—10—7—6—2—106

RING
1  ---  3 | cost [927.0]
2  ---  6 | cost [357.0]
2  --- 106 | cost [93.0]
3  ---  8 | cost [876.0]
4  ---  5 | cost [213.0]
4  --- 13 | cost [921.0]
5  ---  9 | cost [1461.0]
6  ---  7 | cost [93.0]
7  --- 10 | cost [354.0]
8  ---  9 | cost [306.0]
10 --- 11 | cost [96.0]
11 --- 15 | cost [480.0]
12 --- 19 | cost [681.0]
12 --- 20 | cost [591.0]
13 --- 14 | cost [213.0]
14 --- 34 | cost [1149.0]
15 --- 103 | cost [300.0]
16 --- 17 | cost [306.0]
16 --- 27 | cost [552.0]
17 --- 18 | cost [273.0]
18 --- 25 | cost [117.0]
19 --- 24 | cost [117.0]
20 --- 23 | cost [117.0]
21 --- 22 | cost [93.0]
21 --- 103 | cost [252.0]
22 --- 29 | cost [96.0]
23 --- 28 | cost [96.0]
24 --- 27 | cost [96.0]
25 --- 26 | cost [96.0]
26 --- 36 | cost [852.0]
28 --- 33 | cost [477.0]
29 --- 30 | cost [300.0]
30 --- 31 | cost [168.0]
31 --- 32 | cost [108.0]
32 --- 33 | cost [594.0]
34 --- 35 | cost [210.0]
35 --- 38 | cost [849.0]
36 --- 37 | cost [306.0]
37 --- 42 | cost [921.0]
38 --- 39 | cost [210.0]
39 --- 60 | cost [1758.0]
40 --- 49 | cost [435.0]
40 --- 104 | cost [597.0]
41 --- 42 | cost [306.0]
41 --- 43 | cost [201.0]
43 --- 46 | cost [189.0]
44 --- 47 | cost [189.0]
44 --- 104 | cost [702.0]
45 --- 48 | cost [189.0]
45 --- 49 | cost [390.0]
46 --- 52 | cost [189.0]
47 --- 51 | cost [189.0]
48 --- 50 | cost [189.0]
50 --- 55 | cost [189.0]
51 --- 54 | cost [189.0]
52 --- 53 | cost [189.0]
53 --- 58 | cost [189.0]
54 --- 57 | cost [189.0]
55 --- 56 | cost [189.0]
56 --- 59 | cost [468.0]
57 --- 58 | cost [474.0]
59 --- 105 | cost [561.0]
60 --- 61 | cost [213.0]
61 --- 65 | cost [846.0]
62 --- 63 | cost [306.0]
62 --- 105 | cost [876.0]
63 --- 70 | cost [921.0]
64 --- 67 | cost [582.0]
64 --- 72 | cost [591.0]
65 --- 66 | cost [213.0]
66 --- 87 | cost [1149.0]
67 --- 68 | cost [105.0]
68 --- 71 | cost [159.0]
69 --- 70 | cost [306.0]
69 --- 74 | cost [183.0]
71 --- 78 | cost [261.0]
72 --- 77 | cost [117.0]
73 --- 76 | cost [117.0]
73 --- 81 | cost [519.0]
74 --- 75 | cost [117.0]
75 --- 81 | cost [93.0]
76 --- 80 | cost [93.0]
77 --- 79 | cost [93.0]
78 --- 82 | cost [93.0]
79 --- 86 | cost [480.0]
80 --- 86 | cost [588.0]
82 --- 83 | cost [129.0]
83 --- 84 | cost [189.0]
84 --- 85 | cost [330.0]
85 --- 91 | cost [855.0]
87 --- 88 | cost [210.0]
88 --- 94 | cost [849.0]
89 --- 90 | cost [306.0]
89 --- 93 | cost [936.0]
90 --- 98 | cost [948.0]
91 --- 92 | cost [93.0]
92 --- 96 | cost [357.0]
93 --- 102 | cost [1242.0]
94 --- 95 | cost [210.0]
95 --- 100 | cost [489.0]
96 --- 97 | cost [93.0]
97 --- 101 | cost [354.0]
98 --- 99 | cost [306.0]
99 --- 100 | cost [1647.0]
101 --- 102 | cost [96.0]

STAR

BACKUP RING
1  ---  8 | cost [17.94]
2  ---  7 | cost [4.5]
3  ---  9 | cost [11.64]
4  ---  9 | cost [16.65]
4  --- 14 | cost [10.35]
5  ---  8 | cost [17.61]
5  --- 13 | cost [8.46]
6  --- 10 | cost [4.47]
6  --- 106 | cost [4.5]
7  --- 11 | cost [4.5]
10 --- 15 | cost [5.64]
11 --- 103 | cost [7.8]
12 --- 23 | cost [7.05]
12 --- 24 | cost [7.8]
13 --- 34 | cost [12.3]
14 --- 35 | cost [12.27]
15 --- 21 | cost [3.33]
16 --- 18 | cost [1.8]
16 --- 24 | cost [4.92]
17 --- 25 | cost [3.48]
17 --- 27 | cost [7.92]
18 --- 26 | cost [2.13]
19 --- 20 | cost [5.46]
19 --- 27 | cost [2.13]
20 --- 28 | cost [2.13]
21 --- 29 | cost [1.8900000000000001]
22 --- 30 | cost [3.69]
22 --- 103 | cost [3.0]
23 --- 33 | cost [5.67]
25 --- 36 | cost [9.48]
26 --- 37 | cost [9.03]
28 --- 32 | cost [5.8500000000000005]
29 --- 31 | cost [3.6]
30 --- 32 | cost [2.7600000000000002]
31 --- 33 | cost [5.61]
34 --- 38 | cost [9.21]
35 --- 39 | cost [9.21]
36 --- 42 | cost [9.93]
37 --- 41 | cost [9.48]
38 --- 60 | cost [18.42]
39 --- 61 | cost [18.45]
40 --- 44 | cost [9.09]
40 --- 45 | cost [3.66]
41 --- 46 | cost [3.84]
42 --- 43 | cost [2.85]
43 --- 52 | cost [3.7800000000000002]
44 --- 51 | cost [3.7800000000000002]
45 --- 50 | cost [3.7800000000000002]
46 --- 53 | cost [3.7800000000000002]
47 --- 54 | cost [3.7800000000000002]
47 --- 104 | cost [8.67]
48 --- 49 | cost [3.54]
48 --- 55 | cost [3.7800000000000002]
49 --- 104 | cost [9.6]
50 --- 56 | cost [3.7800000000000002]
51 --- 57 | cost [3.7800000000000002]
52 --- 58 | cost [3.7800000000000002]
53 --- 57 | cost [5.1000000000000005]
54 --- 58 | cost [5.1000000000000005]
55 --- 59 | cost [6.24]
56 --- 105 | cost [5.5200000000000005]
59 --- 62 | cost [14.31]
60 --- 65 | cost [9.21]
61 --- 66 | cost [9.21]
62 --- 70 | cost [9.93]
63 --- 69 | cost [9.48]
63 --- 105 | cost [11.64]
64 --- 68 | cost [6.75]
64 --- 77 | cost [7.05]
65 --- 87 | cost [12.3]
66 --- 88 | cost [12.27]
67 --- 71 | cost [2.52]
67 --- 72 | cost [4.2]
68 --- 78 | cost [3.63]
69 --- 75 | cost [2.94]
70 --- 74 | cost [2.7600000000000002]
71 --- 82 | cost [3.54]
72 --- 79 | cost [2.1]
73 --- 75 | cost [4.89]
73 --- 80 | cost [2.1]
74 --- 81 | cost [2.1]
76 --- 81 | cost [4.83]
76 --- 86 | cost [6.63]
77 --- 86 | cost [5.67]
78 --- 83 | cost [2.19]
79 --- 80 | cost [5.43]
82 --- 84 | cost [2.64]
83 --- 85 | cost [2.37]
84 --- 91 | cost [11.55]
85 --- 92 | cost [9.48]
87 --- 94 | cost [9.21]
88 --- 95 | cost [9.21]
89 --- 98 | cost [9.21]
89 --- 102 | cost [21.72]
90 --- 93 | cost [11.94]
90 --- 99 | cost [9.21]
91 --- 96 | cost [4.5]
92 --- 97 | cost [4.5]
93 --- 101 | cost [11.790000000000001]
94 --- 100 | cost [5.43]
95 --- 99 | cost [14.61]
96 --- 101 | cost [4.47]
97 --- 102 | cost [4.5]
98 --- 100 | cost [19.53]

BACKUP STAR

B = 21.72
i★ = 89
j★ = 93
k★ = 102

       
——————— Fri, 19 Jan 2024 10:52:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 106 hubs —— 1-2-6-7-10-11-15-103-21-22-29-30-31-32-33-28-23-20-12-19-24-27-16-17-18-25-26-36-37-42-41-43-46-52-53-58-57-54-51-47-44-104-40-49-45-48-50-55-56-59-105-62-63-70-69-74-75-81-73-76-80-86-79-77-72-64-67-68-71-78-82-83-84-85-91-92-96-97-101-102-93-89-90-98-99-100-95-94-88-87-66-65-61-60-39-38-35-34-14-13-4-5-9-8-3-106-1
total time           673.8                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             43289.04<=43289.04   Master/SP costs      43137/152.04         
Master time          665.95               SP time              7.85                 
subtour              20496.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            9.0                  SP method            poly                 
tildeV               2:105                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       7236                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—6—7—10—11—15—103—21—22—29—30—31—32—33—28—23—20—12—19—24—27—16—17—18—25—26—36—37—42—41—43—46—52—53—58—57—54—51—47—44—104—40—49—45—48—50—55—56—59—105—62—63—70—69—74—75—81—73—76—80—86—79—77—72—64—67—68—71—78—82—83—84—85—91—92—96—97—101—102—93—89—90—98—99—100—95—94—88—87—66—65—61—60—39—38—35—34—14—13—4—5—9—8—3—106

RING
1  ---  2 | cost [93.0]
2  ---  6 | cost [357.0]
3  ---  8 | cost [876.0]
3  --- 106 | cost [927.0]
4  ---  5 | cost [213.0]
4  --- 13 | cost [921.0]
5  ---  9 | cost [1461.0]
6  ---  7 | cost [93.0]
7  --- 10 | cost [354.0]
8  ---  9 | cost [306.0]
10 --- 11 | cost [96.0]
11 --- 15 | cost [480.0]
12 --- 19 | cost [681.0]
12 --- 20 | cost [591.0]
13 --- 14 | cost [213.0]
14 --- 34 | cost [1149.0]
15 --- 103 | cost [300.0]
16 --- 17 | cost [306.0]
16 --- 27 | cost [552.0]
17 --- 18 | cost [273.0]
18 --- 25 | cost [117.0]
19 --- 24 | cost [117.0]
20 --- 23 | cost [117.0]
21 --- 22 | cost [93.0]
21 --- 103 | cost [252.0]
22 --- 29 | cost [96.0]
23 --- 28 | cost [96.0]
24 --- 27 | cost [96.0]
25 --- 26 | cost [96.0]
26 --- 36 | cost [852.0]
28 --- 33 | cost [477.0]
29 --- 30 | cost [300.0]
30 --- 31 | cost [168.0]
31 --- 32 | cost [108.0]
32 --- 33 | cost [594.0]
34 --- 35 | cost [210.0]
35 --- 38 | cost [849.0]
36 --- 37 | cost [306.0]
37 --- 42 | cost [921.0]
38 --- 39 | cost [210.0]
39 --- 60 | cost [1758.0]
40 --- 49 | cost [435.0]
40 --- 104 | cost [597.0]
41 --- 42 | cost [306.0]
41 --- 43 | cost [201.0]
43 --- 46 | cost [189.0]
44 --- 47 | cost [189.0]
44 --- 104 | cost [702.0]
45 --- 48 | cost [189.0]
45 --- 49 | cost [390.0]
46 --- 52 | cost [189.0]
47 --- 51 | cost [189.0]
48 --- 50 | cost [189.0]
50 --- 55 | cost [189.0]
51 --- 54 | cost [189.0]
52 --- 53 | cost [189.0]
53 --- 58 | cost [189.0]
54 --- 57 | cost [189.0]
55 --- 56 | cost [189.0]
56 --- 59 | cost [468.0]
57 --- 58 | cost [474.0]
59 --- 105 | cost [561.0]
60 --- 61 | cost [213.0]
61 --- 65 | cost [846.0]
62 --- 63 | cost [306.0]
62 --- 105 | cost [876.0]
63 --- 70 | cost [921.0]
64 --- 67 | cost [582.0]
64 --- 72 | cost [591.0]
65 --- 66 | cost [213.0]
66 --- 87 | cost [1149.0]
67 --- 68 | cost [105.0]
68 --- 71 | cost [159.0]
69 --- 70 | cost [306.0]
69 --- 74 | cost [183.0]
71 --- 78 | cost [261.0]
72 --- 77 | cost [117.0]
73 --- 76 | cost [117.0]
73 --- 81 | cost [519.0]
74 --- 75 | cost [117.0]
75 --- 81 | cost [93.0]
76 --- 80 | cost [93.0]
77 --- 79 | cost [93.0]
78 --- 82 | cost [93.0]
79 --- 86 | cost [480.0]
80 --- 86 | cost [588.0]
82 --- 83 | cost [129.0]
83 --- 84 | cost [189.0]
84 --- 85 | cost [330.0]
85 --- 91 | cost [855.0]
87 --- 88 | cost [210.0]
88 --- 94 | cost [849.0]
89 --- 90 | cost [306.0]
89 --- 93 | cost [936.0]
90 --- 98 | cost [948.0]
91 --- 92 | cost [93.0]
92 --- 96 | cost [357.0]
93 --- 102 | cost [1242.0]
94 --- 95 | cost [210.0]
95 --- 100 | cost [489.0]
96 --- 97 | cost [93.0]
97 --- 101 | cost [354.0]
98 --- 99 | cost [306.0]
99 --- 100 | cost [1647.0]
101 --- 102 | cost [96.0]

STAR

BACKUP RING
1  ---  6 | cost [4.5]
2  ---  7 | cost [4.5]
3  ---  9 | cost [11.64]
4  ---  9 | cost [16.65]
4  --- 14 | cost [10.35]
5  ---  8 | cost [17.61]
5  --- 13 | cost [8.46]
6  --- 10 | cost [4.47]
7  --- 11 | cost [4.5]
8  --- 106 | cost [17.94]
10 --- 15 | cost [5.64]
11 --- 103 | cost [7.8]
12 --- 23 | cost [7.05]
12 --- 24 | cost [7.8]
13 --- 34 | cost [12.3]
14 --- 35 | cost [12.27]
15 --- 21 | cost [3.33]
16 --- 18 | cost [1.8]
16 --- 24 | cost [4.92]
17 --- 25 | cost [3.48]
17 --- 27 | cost [7.92]
18 --- 26 | cost [2.13]
19 --- 20 | cost [5.46]
19 --- 27 | cost [2.13]
20 --- 28 | cost [2.13]
21 --- 29 | cost [1.8900000000000001]
22 --- 30 | cost [3.69]
22 --- 103 | cost [3.0]
23 --- 33 | cost [5.67]
25 --- 36 | cost [9.48]
26 --- 37 | cost [9.03]
28 --- 32 | cost [5.8500000000000005]
29 --- 31 | cost [3.6]
30 --- 32 | cost [2.7600000000000002]
31 --- 33 | cost [5.61]
34 --- 38 | cost [9.21]
35 --- 39 | cost [9.21]
36 --- 42 | cost [9.93]
37 --- 41 | cost [9.48]
38 --- 60 | cost [18.42]
39 --- 61 | cost [18.45]
40 --- 44 | cost [9.09]
40 --- 45 | cost [3.66]
41 --- 46 | cost [3.84]
42 --- 43 | cost [2.85]
43 --- 52 | cost [3.7800000000000002]
44 --- 51 | cost [3.7800000000000002]
45 --- 50 | cost [3.7800000000000002]
46 --- 53 | cost [3.7800000000000002]
47 --- 54 | cost [3.7800000000000002]
47 --- 104 | cost [8.67]
48 --- 49 | cost [3.54]
48 --- 55 | cost [3.7800000000000002]
49 --- 104 | cost [9.6]
50 --- 56 | cost [3.7800000000000002]
51 --- 57 | cost [3.7800000000000002]
52 --- 58 | cost [3.7800000000000002]
53 --- 57 | cost [5.1000000000000005]
54 --- 58 | cost [5.1000000000000005]
55 --- 59 | cost [6.24]
56 --- 105 | cost [5.5200000000000005]
59 --- 62 | cost [14.31]
60 --- 65 | cost [9.21]
61 --- 66 | cost [9.21]
62 --- 70 | cost [9.93]
63 --- 69 | cost [9.48]
63 --- 105 | cost [11.64]
64 --- 68 | cost [6.75]
64 --- 77 | cost [7.05]
65 --- 87 | cost [12.3]
66 --- 88 | cost [12.27]
67 --- 71 | cost [2.52]
67 --- 72 | cost [4.2]
68 --- 78 | cost [3.63]
69 --- 75 | cost [2.94]
70 --- 74 | cost [2.7600000000000002]
71 --- 82 | cost [3.54]
72 --- 79 | cost [2.1]
73 --- 75 | cost [4.89]
73 --- 80 | cost [2.1]
74 --- 81 | cost [2.1]
76 --- 81 | cost [4.83]
76 --- 86 | cost [6.63]
77 --- 86 | cost [5.67]
78 --- 83 | cost [2.19]
79 --- 80 | cost [5.43]
82 --- 84 | cost [2.64]
83 --- 85 | cost [2.37]
84 --- 91 | cost [11.55]
85 --- 92 | cost [9.48]
87 --- 94 | cost [9.21]
88 --- 95 | cost [9.21]
89 --- 98 | cost [9.21]
89 --- 102 | cost [21.72]
90 --- 93 | cost [11.94]
90 --- 99 | cost [9.21]
91 --- 96 | cost [4.5]
92 --- 97 | cost [4.5]
93 --- 101 | cost [11.790000000000001]
94 --- 100 | cost [5.43]
95 --- 99 | cost [14.61]
96 --- 101 | cost [4.47]
97 --- 102 | cost [4.5]
98 --- 100 | cost [19.53]

BACKUP STAR

B = 21.72
i★ = 89
j★ = 93
k★ = 102