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

——————— Mon, 22 Jan 2024 09:56:38 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 27 hubs —— 1—3—20—26—24—19—95—87—66—83—80—89—58—38—41—43—47—49—50—48—104—21—30—103—5—8—106
total time           3640.21 (TL 3600)    gap                  0.953                
blossom time         0                    nb blossom           0.0                  
LB <= UB             43362.46<=923816.75  subtour              1828.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:105                
2-opt strategy       0                                                              
explored_nodes       63                   n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—3—20—26—24—19—95—87—66—83—80—89—58—38—41—43—47—49—50—48—104—21—30—103—5—8—106

RING
1  ---  3 | cost [927.0]
3  --- 20 | cost [1497.0]
5  ---  8 | cost [1761.0]
5  --- 103 | cost [3213.0]
8  --- 106 | cost [1794.0]
19 --- 24 | cost [117.0]
19 --- 95 | cost [7023.0]
20 --- 26 | cost [1041.0]
21 --- 30 | cost [444.0]
21 --- 104 | cost [1722.0]
24 --- 26 | cost [483.0]
30 --- 103 | cost [474.0]
38 --- 41 | cost [1962.0]
38 --- 58 | cost [2247.0]
41 --- 43 | cost [201.0]
43 --- 47 | cost [510.0]
47 --- 49 | cost [969.0]
48 --- 50 | cost [189.0]
48 --- 104 | cost [816.0]
49 --- 50 | cost [414.0]
58 --- 89 | cost [3048.0]
66 --- 83 | cost [3258.0]
66 --- 87 | cost [1149.0]
80 --- 83 | cost [1032.0]
80 --- 89 | cost [942.0]
87 --- 95 | cost [1032.0]

STAR
2  -->  1 | cost [217.0]
4  -->  3 | cost [6349.0]
6  -->  1 | cost [1050.0]
7  -->  1 | cost [1267.0]
9  -->  1 | cost [4879.0]
10 -->  1 | cost [2093.0]
11 -->  1 | cost [2317.0]
12 -->  1 | cost [3416.0]
13 -->  1 | cost [8925.0]
14 -->  1 | cost [8589.0]
15 -->  1 | cost [3311.0]
16 -->  1 | cost [5341.0]
17 -->  1 | cost [5922.0]
18 -->  3 | cost [4004.0]
22 -->  1 | cost [4270.0]
23 --> 21 | cost [1239.0]
25 -->  3 | cost [4242.0]
27 -->  1 | cost [5411.0]
28 -->  1 | cost [4837.0]
29 -->  1 | cost [4494.0]
31 -->  3 | cost [4851.0]
32 -->  1 | cost [5509.0]
33 -->  1 | cost [5943.0]
34 -->  5 | cost [4816.0]
35 -->  5 | cost [5012.0]
36 -->  1 | cost [7588.0]
37 -->  1 | cost [8029.0]
39 -->  3 | cost [9625.0]
40 -->  1 | cost [8540.0]
42 -->  5 | cost [8414.0]
44 -->  3 | cost [8582.0]
45 -->  1 | cost [9219.0]
46 -->  5 | cost [9394.0]
51 -->  1 | cost [10409.0]
52 -->  1 | cost [10780.0]
53 -->  1 | cost [11186.0]
54 -->  1 | cost [10836.0]
55 -->  1 | cost [10528.0]
56 -->  1 | cost [10969.0]
57 --> 104 | cost [3262.0]
59 -->  1 | cost [11711.0]
60 -->  1 | cost [14861.0]
61 -->  1 | cost [14805.0]
62 -->  1 | cost [13531.0]
63 -->  3 | cost [12705.0]
64 -->  1 | cost [14322.0]
65 -->  5 | cost [13398.0]
67 -->  1 | cost [14910.0]
68 -->  1 | cost [15120.0]
69 -->  1 | cost [15596.0]
70 -->  1 | cost [15848.0]
71 -->  1 | cost [15274.0]
72 -->  1 | cost [15582.0]
73 -->  1 | cost [15771.0]
74 -->  1 | cost [16023.0]
75 -->  1 | cost [16282.0]
76 -->  5 | cost [15596.0]
77 -->  1 | cost [15855.0]
78 -->  1 | cost [15883.0]
79 -->  1 | cost [16072.0]
81 -->  1 | cost [16492.0]
82 --> 47 | cost [7014.0]
84 -->  1 | cost [16408.0]
85 -->  1 | cost [16926.0]
86 -->  1 | cost [17157.0]
88 -->  5 | cost [16478.0]
90 -->  1 | cost [18606.0]
91 -->  1 | cost [18851.0]
92 -->  1 | cost [19068.0]
93 -->  1 | cost [19292.0]
94 --> 19 | cost [16317.0]
96 -->  1 | cost [19901.0]
97 -->  1 | cost [20118.0]
98 -->  1 | cost [20496.0]
99 -->  1 | cost [20699.0]
100 -->  5 | cost [19684.0]
101 -->  1 | cost [20944.0]
102 -->  1 | cost [21168.0]
105 -->  1 | cost [12201.0]

BACKUP RING
1  --- 20 | cost [18.72]
3  --- 26 | cost [19.02]
5  --- 30 | cost [34.2]
5  --- 106 | cost [34.53]
8  --- 103 | cost [15.780000000000001]
19 --- 26 | cost [5.19]
19 --- 87 | cost [61.35]
20 --- 24 | cost [5.58]
21 --- 48 | cost [24.03]
21 --- 103 | cost [2.52]
24 --- 95 | cost [69.09]
30 --- 104 | cost [12.84]
38 --- 43 | cost [19.32]
38 --- 89 | cost [47.160000000000004]
41 --- 47 | cost [5.5200000000000005]
41 --- 58 | cost [9.48]
43 --- 49 | cost [14.52]
47 --- 50 | cost [6.42]
48 --- 49 | cost [3.54]
50 --- 104 | cost [9.99]
58 --- 80 | cost [22.47]
66 --- 80 | cost [22.29]
66 --- 95 | cost [21.48]
83 --- 87 | cost [33.78]
83 --- 89 | cost [15.75]

BACKUP STAR
4  -->  5 | cost [4.97]
18 --> 26 | cost [4.97]
23 --> 20 | cost [2.73]
25 --> 26 | cost [2.24]
31 --> 30 | cost [3.92]
34 --> 38 | cost [21.490000000000002]
35 --> 38 | cost [19.81]
39 --> 38 | cost [4.9]
42 --> 43 | cost [6.65]
44 --> 47 | cost [4.41]
46 --> 43 | cost [4.41]
57 --> 58 | cost [11.06]
63 --> 58 | cost [22.19]
65 --> 66 | cost [4.97]
76 --> 80 | cost [2.17]
82 --> 83 | cost [3.0100000000000002]
88 --> 87 | cost [4.9]
94 --> 95 | cost [4.9]
100 --> 95 | cost [11.41]

B = 91.59
i★ = 8
j★ = 5
k★ = 103

       
——————— Mon, 22 Jan 2024 10:09:10 ————————— 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           657.6                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             43810.32<=43810.32   Master/SP costs      43137/673.32         
Master time          651.73               SP time              5.86                 
subtour              13063.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            15.0                 SP method            poly                 
tildeV               2:105                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       6250                 
F                    31.0                 
                                          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