------------------------------------------------------------
                        α=7.0 —— kroD100 —— 100 nodes       
------------------------------------------------------------

——————— Fri, 19 Jan 2024 04:16:55 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—50—101
total time           3371.1               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             101984.53<=101987.19 subtour              299.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       256                  n lazycuts edges     1.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—50—101

RING
1  --- 50 | cost [651.0]
4  --- 44 | cost [1015.0]
4  --- 93 | cost [1246.0]
6  --- 18 | cost [1533.0]
6  --- 83 | cost [420.0]
7  --- 61 | cost [1967.0]
7  --- 67 | cost [2422.0]
8  --- 52 | cost [602.0]
8  --- 66 | cost [616.0]
9  --- 26 | cost [2226.0]
9  --- 55 | cost [1463.0]
16 --- 54 | cost [1673.0]
16 --- 63 | cost [1029.0]
17 --- 70 | cost [2506.0]
17 --- 90 | cost [385.0]
18 --- 59 | cost [1666.0]
19 --- 37 | cost [826.0]
19 --- 100 | cost [1365.0]
21 --- 47 | cost [1526.0]
21 --- 95 | cost [2219.0]
24 --- 84 | cost [2205.0]
24 --- 88 | cost [707.0]
26 --- 87 | cost [84.0]
31 --- 78 | cost [693.0]
31 --- 99 | cost [413.0]
37 --- 51 | cost [700.0]
38 --- 52 | cost [1477.0]
38 --- 66 | cost [679.0]
40 --- 59 | cost [1106.0]
40 --- 83 | cost [217.0]
41 --- 84 | cost [952.0]
41 --- 88 | cost [1974.0]
44 --- 60 | cost [1351.0]
45 --- 78 | cost [2051.0]
45 --- 99 | cost [1491.0]
47 --- 56 | cost [2975.0]
50 --- 101 | cost [651.0]
51 --- 100 | cost [798.0]
54 --- 91 | cost [98.0]
55 --- 87 | cost [1288.0]
56 --- 95 | cost [826.0]
60 --- 93 | cost [1883.0]
61 --- 74 | cost [1211.0]
63 --- 91 | cost [1022.0]
67 --- 74 | cost [3164.0]
70 --- 89 | cost [1582.0]
89 --- 90 | cost [1330.0]

STAR
2  --> 100 | cost [306.0]
3  --> 83 | cost [285.0]
5  --> 83 | cost [1041.0]
10 -->  9 | cost [609.0]
11 --> 90 | cost [576.0]
12 --> 47 | cost [690.0]
13 --> 88 | cost [408.0]
14 --> 45 | cost [729.0]
15 --> 63 | cost [828.0]
20 -->  9 | cost [825.0]
22 --> 70 | cost [1566.0]
23 --> 66 | cost [1071.0]
25 -->  9 | cost [930.0]
27 --> 24 | cost [186.0]
28 --> 47 | cost [750.0]
29 --> 67 | cost [1620.0]
30 --> 100 | cost [390.0]
32 --> 17 | cost [1020.0]
33 --> 45 | cost [495.0]
34 --> 38 | cost [513.0]
35 --> 51 | cost [708.0]
36 --> 67 | cost [375.0]
39 --> 91 | cost [690.0]
42 --> 89 | cost [1281.0]
43 -->  4 | cost [756.0]
46 --> 52 | cost [726.0]
48 --> 100 | cost [912.0]
49 --> 70 | cost [513.0]
53 --> 60 | cost [597.0]
57 --> 31 | cost [654.0]
58 --> 67 | cost [1881.0]
62 --> 37 | cost [528.0]
64 --> 59 | cost [723.0]
65 --> 78 | cost [912.0]
68 --> 45 | cost [669.0]
69 --> 63 | cost [1323.0]
71 -->  4 | cost [606.0]
72 --> 31 | cost [1026.0]
73 --> 91 | cost [1047.0]
75 --> 67 | cost [144.0]
76 --> 78 | cost [1107.0]
77 --> 54 | cost [489.0]
79 --> 88 | cost [381.0]
80 --> 78 | cost [747.0]
81 --> 38 | cost [567.0]
82 --> 18 | cost [1098.0]
85 --> 59 | cost [444.0]
86 --> 16 | cost [1104.0]
92 --> 19 | cost [921.0]
94 --> 17 | cost [555.0]
96 --> 16 | cost [945.0]
97 --> 17 | cost [1041.0]
98 --> 70 | cost [750.0]

BACKUP RING
1  --- 101 | cost [0.0]
4  --- 60 | cost [23.59]
6  --- 40 | cost [2.87]
6  --- 59 | cost [12.11]
7  --- 74 | cost [18.55]
8  --- 38 | cost [12.950000000000001]
9  --- 87 | cost [22.82]
16 --- 91 | cost [17.64]
17 --- 89 | cost [17.080000000000002]
18 --- 40 | cost [17.5]
18 --- 83 | cost [19.46]
19 --- 51 | cost [9.94]
21 --- 56 | cost [16.59]
24 --- 41 | cost [17.71]
26 --- 55 | cost [12.81]
31 --- 45 | cost [19.04]
37 --- 100 | cost [14.63]
44 --- 93 | cost [10.85]
47 --- 95 | cost [36.61]
52 --- 66 | cost [9.17]
54 --- 63 | cost [9.31]
59 --- 83 | cost [12.88]
61 --- 67 | cost [40.04]
70 --- 90 | cost [22.75]
78 --- 99 | cost [8.47]
84 --- 88 | cost [26.39]

BACKUP STAR
2  --> 51 | cost [5.64]
3  --> 40 | cost [3.63]
5  --> 40 | cost [11.34]
10 --> 26 | cost [9.69]
11 --> 89 | cost [6.0]
12 --> 21 | cost [12.3]
13 --> 24 | cost [6.87]
14 --> 99 | cost [11.790000000000001]
15 --> 54 | cost [9.03]
20 --> 18 | cost [10.26]
22 --> 89 | cost [17.61]
23 -->  8 | cost [10.92]
25 --> 18 | cost [9.42]
27 --> 88 | cost [3.9]
28 --> 21 | cost [9.84]
29 --> 74 | cost [25.47]
30 --> 51 | cost [6.12]
32 --> 90 | cost [11.82]
33 --> 99 | cost [10.5]
34 --> 66 | cost [7.47]
35 --> 37 | cost [7.71]
36 -->  7 | cost [13.89]
39 --> 54 | cost [7.32]
42 --> 70 | cost [15.96]
43 --> 91 | cost [7.68]
46 -->  8 | cost [8.58]
48 --> 19 | cost [9.6]
49 --> 89 | cost [9.99]
53 --> 44 | cost [9.0]
57 --> 99 | cost [7.59]
58 --> 74 | cost [24.12]
62 --> 51 | cost [7.95]
64 --> 16 | cost [10.17]
65 --> 45 | cost [9.75]
68 --> 99 | cost [11.34]
69 --> 84 | cost [14.4]
71 --> 93 | cost [8.700000000000001]
72 --> 99 | cost [11.73]
73 --> 54 | cost [10.83]
75 -->  7 | cost [10.14]
76 --> 31 | cost [12.15]
77 --> 91 | cost [4.92]
79 --> 24 | cost [6.87]
80 --> 31 | cost [9.21]
81 --> 66 | cost [7.5600000000000005]
82 --> 47 | cost [16.830000000000002]
85 --> 18 | cost [5.64]
86 --> 63 | cost [14.85]
92 --> 55 | cost [11.85]
94 --> 90 | cost [7.0200000000000005]
96 --> 63 | cost [13.41]
97 --> 90 | cost [11.91]
98 --> 17 | cost [10.38]

B = 92.17
i★ = 7
j★ = 67
k★ = 74

       
——————— Fri, 19 Jan 2024 05:18:29 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 52 hubs —— 1-50-13-79-88-24-41-73-91-54-77-43-44-60-62-19-37-51-100-2-3-83-40-6-9-26-10-95-21-25-82-68-14-33-99-31-76-61-7-67-36-58-22-70-49-98-17-90-11-66-8-101-1
total time           3607.21 (TL 3600)    gap                  0.175                
blossom time         0                    nb blossom           0.0                  
LB <= UB             109107.02<=132242    Master/SP costs      131521/721           
Master time          3601.02              SP time              6.19                 
subtour              41013.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            20.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       24334                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—50—13—79—88—24—41—73—91—54—77—43—44—60—62—19—37—51—100—2—3—83—40—6—9—26—10—95—21—25—82—68—14—33—99—31—76—61—7—67—36—58—22—70—49—98—17—90—11—66—8—101

RING
1  --- 50 | cost [651.0]
2  ---  3 | cost [6951.0]
2  --- 100 | cost [714.0]
3  --- 83 | cost [665.0]
6  ---  9 | cost [3290.0]
6  --- 40 | cost [287.0]
7  --- 61 | cost [1967.0]
7  --- 67 | cost [2422.0]
8  --- 66 | cost [616.0]
8  --- 101 | cost [4795.0]
9  --- 26 | cost [2226.0]
10 --- 26 | cost [2261.0]
10 --- 95 | cost [3136.0]
11 --- 66 | cost [3423.0]
11 --- 90 | cost [1344.0]
13 --- 50 | cost [3171.0]
13 --- 79 | cost [525.0]
14 --- 33 | cost [679.0]
14 --- 68 | cost [147.0]
17 --- 90 | cost [385.0]
17 --- 98 | cost [2422.0]
19 --- 37 | cost [826.0]
19 --- 62 | cost [1904.0]
21 --- 25 | cost [3731.0]
21 --- 95 | cost [2219.0]
22 --- 58 | cost [2926.0]
22 --- 70 | cost [3654.0]
24 --- 41 | cost [1771.0]
24 --- 88 | cost [707.0]
25 --- 82 | cost [2660.0]
31 --- 76 | cost [2835.0]
31 --- 99 | cost [413.0]
33 --- 99 | cost [2450.0]
36 --- 58 | cost [3612.0]
36 --- 67 | cost [875.0]
37 --- 51 | cost [700.0]
40 --- 83 | cost [217.0]
41 --- 73 | cost [2695.0]
43 --- 44 | cost [2660.0]
43 --- 77 | cost [1022.0]
44 --- 60 | cost [1351.0]
49 --- 70 | cost [1197.0]
49 --- 98 | cost [574.0]
51 --- 100 | cost [798.0]
54 --- 77 | cost [1141.0]
54 --- 91 | cost [98.0]
60 --- 62 | cost [2695.0]
61 --- 76 | cost [3367.0]
68 --- 82 | cost [4053.0]
73 --- 91 | cost [2443.0]
79 --- 88 | cost [889.0]

STAR
4  --> 44 | cost [435.0]
5  -->  3 | cost [804.0]
12 --> 21 | cost [1230.0]
15 --> 54 | cost [903.0]
16 --> 54 | cost [717.0]
18 -->  6 | cost [657.0]
20 --> 25 | cost [105.0]
23 --> 66 | cost [1071.0]
27 --> 24 | cost [186.0]
28 --> 21 | cost [984.0]
29 --> 58 | cost [732.0]
30 --> 100 | cost [390.0]
32 --> 17 | cost [1020.0]
34 --> 66 | cost [747.0]
35 --> 51 | cost [708.0]
38 --> 66 | cost [291.0]
39 --> 73 | cost [450.0]
42 --> 22 | cost [1191.0]
45 --> 33 | cost [495.0]
46 -->  8 | cost [858.0]
47 --> 21 | cost [654.0]
48 -->  2 | cost [606.0]
52 -->  8 | cost [258.0]
53 --> 60 | cost [597.0]
55 --> 26 | cost [549.0]
56 --> 95 | cost [354.0]
57 --> 31 | cost [654.0]
59 --> 40 | cost [474.0]
63 --> 54 | cost [399.0]
64 --> 77 | cost [783.0]
65 --> 14 | cost [615.0]
69 --> 54 | cost [1638.0]
71 --> 43 | cost [681.0]
72 --> 31 | cost [1026.0]
74 --> 61 | cost [519.0]
75 --> 67 | cost [144.0]
78 --> 31 | cost [297.0]
80 --> 76 | cost [405.0]
81 --> 66 | cost [756.0]
84 --> 41 | cost [408.0]
85 -->  6 | cost [810.0]
86 --> 14 | cost [1308.0]
87 --> 26 | cost [36.0]
89 --> 90 | cost [570.0]
92 --> 19 | cost [921.0]
93 --> 44 | cost [465.0]
94 --> 17 | cost [555.0]
96 --> 14 | cost [1464.0]
97 --> 17 | cost [1041.0]

BACKUP RING
1  --- 13 | cost [25.55]
2  --- 51 | cost [13.16]
2  --- 83 | cost [74.55]
3  --- 40 | cost [8.47]
3  --- 100 | cost [68.60000000000001]
6  --- 26 | cost [53.97]
6  --- 83 | cost [4.2]
7  --- 36 | cost [32.410000000000004]
7  --- 76 | cost [42.56]
8  --- 11 | cost [39.480000000000004]
9  --- 10 | cost [14.21]
9  --- 40 | cost [34.44]
10 --- 21 | cost [22.68]
11 --- 17 | cost [16.17]
13 --- 88 | cost [9.52]
14 --- 82 | cost [39.550000000000004]
14 --- 99 | cost [27.51]
17 --- 49 | cost [24.150000000000002]
19 --- 51 | cost [9.94]
19 --- 60 | cost [45.57]
21 --- 82 | cost [48.86]
22 --- 36 | cost [61.25]
22 --- 49 | cost [47.39]
24 --- 73 | cost [44.52]
24 --- 79 | cost [16.03]
25 --- 68 | cost [65.45]
25 --- 95 | cost [53.83]
26 --- 95 | cost [34.37]
31 --- 33 | cost [28.28]
31 --- 61 | cost [59.29]
33 --- 68 | cost [5.32]
37 --- 62 | cost [12.32]
37 --- 100 | cost [14.63]
41 --- 88 | cost [19.740000000000002]
41 --- 91 | cost [45.43]
43 --- 54 | cost [18.34]
43 --- 60 | cost [39.83]
44 --- 62 | cost [40.32]
44 --- 77 | cost [35.980000000000004]
50 --- 79 | cost [36.68]
54 --- 73 | cost [25.27]
58 --- 67 | cost [43.89]
58 --- 70 | cost [64.68]
61 --- 67 | cost [40.04]
66 --- 90 | cost [47.46]
66 --- 101 | cost [42.56]
70 --- 98 | cost [17.5]
76 --- 99 | cost [32.2]
77 --- 91 | cost [11.48]
90 --- 98 | cost [24.57]

BACKUP STAR
4  --> 43 | cost [7.5600000000000005]
5  --> 83 | cost [10.41]
12 --> 82 | cost [19.86]
15 --> 91 | cost [9.03]
16 --> 77 | cost [7.5600000000000005]
18 --> 40 | cost [7.5]
20 -->  9 | cost [8.25]
23 -->  8 | cost [10.92]
27 --> 88 | cost [3.9]
28 --> 95 | cost [15.51]
29 --> 36 | cost [12.450000000000001]
30 --> 51 | cost [6.12]
32 --> 90 | cost [11.82]
34 --> 50 | cost [9.09]
35 --> 37 | cost [7.71]
38 -->  8 | cost [5.55]
39 --> 91 | cost [6.9]
42 --> 11 | cost [14.46]
45 --> 99 | cost [6.390000000000001]
46 --> 66 | cost [10.950000000000001]
47 --> 10 | cost [13.8]
48 --> 100 | cost [9.120000000000001]
52 --> 66 | cost [3.93]
53 --> 44 | cost [9.0]
55 -->  9 | cost [6.2700000000000005]
56 --> 21 | cost [7.11]
57 --> 99 | cost [7.59]
59 -->  6 | cost [5.19]
63 --> 91 | cost [4.38]
64 --> 43 | cost [9.27]
65 --> 68 | cost [6.390000000000001]
69 --> 91 | cost [16.59]
71 --> 44 | cost [10.17]
72 --> 76 | cost [11.28]
74 -->  7 | cost [7.95]
75 --> 36 | cost [4.7700000000000005]
78 --> 99 | cost [3.63]
80 --> 31 | cost [9.21]
81 -->  8 | cost [9.57]
84 --> 24 | cost [9.450000000000001]
85 --> 40 | cost [8.25]
86 --> 68 | cost [13.59]
87 -->  9 | cost [9.78]
89 --> 11 | cost [6.0]
92 -->  2 | cost [11.64]
93 --> 60 | cost [8.07]
94 --> 90 | cost [7.0200000000000005]
96 --> 68 | cost [15.18]
97 --> 98 | cost [10.620000000000001]

B = 103.0
i★ = 25
j★ = 21
k★ = 95