------------------------------------------------------------
                          α=7.0 —— rd100 —— 100 nodes       
------------------------------------------------------------

——————— Wed, 31 Jan 2024 01:46:57 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 53 hubs —— 1—15—63—97—86—21—82—4—32—78—20—74—33—10—27—17—72—38—73—50—46—56—28—77—59—76—66—84—31—98—94—79—53—47—57—45—44—100—39—55—40—42—7—34—61—5—81—80—65—51—8—60—101
total time           3632.95 (TL 3600)    gap                  0.207                
blossom time         0                    nb blossom           0.0                  
LB <= UB             41057.61<=51776.8    subtour              221.0                
connectivity cuts    172.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—15—63—97—86—21—82—4—32—78—20—74—33—10—27—17—72—38—73—50—46—56—28—77—59—76—66—84—31—98—94—79—53—47—57—45—44—100—39—55—40—42—7—34—61—5—81—80—65—51—8—60—101

RING
1  --- 15 | cost [910.0]
4  --- 32 | cost [294.0]
4  --- 82 | cost [560.0]
5  --- 61 | cost [350.0]
5  --- 81 | cost [896.0]
7  --- 34 | cost [399.0]
7  --- 42 | cost [511.0]
8  --- 51 | cost [1302.0]
8  --- 60 | cost [238.0]
10 --- 27 | cost [833.0]
10 --- 33 | cost [287.0]
15 --- 63 | cost [210.0]
17 --- 27 | cost [1309.0]
17 --- 72 | cost [378.0]
20 --- 74 | cost [133.0]
20 --- 78 | cost [273.0]
21 --- 82 | cost [294.0]
21 --- 86 | cost [609.0]
28 --- 56 | cost [896.0]
28 --- 77 | cost [518.0]
31 --- 84 | cost [378.0]
31 --- 98 | cost [1001.0]
32 --- 78 | cost [658.0]
33 --- 74 | cost [973.0]
34 --- 61 | cost [756.0]
38 --- 72 | cost [469.0]
38 --- 73 | cost [777.0]
39 --- 55 | cost [784.0]
39 --- 100 | cost [1134.0]
40 --- 42 | cost [616.0]
40 --- 55 | cost [833.0]
44 --- 45 | cost [973.0]
44 --- 100 | cost [511.0]
45 --- 57 | cost [1519.0]
46 --- 50 | cost [35.0]
46 --- 56 | cost [175.0]
47 --- 53 | cost [693.0]
47 --- 57 | cost [700.0]
50 --- 73 | cost [189.0]
51 --- 65 | cost [581.0]
53 --- 79 | cost [455.0]
59 --- 76 | cost [910.0]
59 --- 77 | cost [336.0]
60 --- 101 | cost [154.0]
63 --- 97 | cost [56.0]
65 --- 80 | cost [420.0]
66 --- 76 | cost [476.0]
66 --- 84 | cost [812.0]
79 --- 94 | cost [1127.0]
80 --- 81 | cost [469.0]
86 --- 97 | cost [91.0]
94 --- 98 | cost [532.0]

STAR
2  --> 84 | cost [711.0]
3  --> 10 | cost [390.0]
6  --> 79 | cost [138.0]
9  --> 74 | cost [243.0]
11 --> 61 | cost [243.0]
12 --> 82 | cost [237.0]
13 --> 97 | cost [270.0]
14 --> 82 | cost [231.0]
16 --> 98 | cost [354.0]
18 -->  1 | cost [264.0]
19 --> 46 | cost [252.0]
22 -->  5 | cost [279.0]
23 --> 84 | cost [546.0]
24 --> 42 | cost [204.0]
25 --> 42 | cost [327.0]
26 --> 74 | cost [117.0]
29 --> 100 | cost [282.0]
30 --> 80 | cost [252.0]
35 --> 44 | cost [291.0]
36 --> 47 | cost [492.0]
37 --> 28 | cost [108.0]
41 --> 34 | cost [291.0]
43 --> 42 | cost [198.0]
48 --> 80 | cost [231.0]
49 --> 21 | cost [105.0]
52 --> 45 | cost [378.0]
54 --> 38 | cost [213.0]
58 --> 76 | cost [288.0]
62 -->  1 | cost [282.0]
64 --> 47 | cost [606.0]
67 --> 97 | cost [96.0]
68 --> 51 | cost [327.0]
69 -->  8 | cost [183.0]
70 --> 38 | cost [261.0]
71 --> 60 | cost [384.0]
75 --> 21 | cost [75.0]
83 --> 51 | cost [102.0]
85 --> 82 | cost [123.0]
87 --> 15 | cost [360.0]
88 --> 84 | cost [57.0]
89 --> 84 | cost [663.0]
90 --> 51 | cost [126.0]
91 --> 65 | cost [360.0]
92 --> 50 | cost [246.0]
93 --> 77 | cost [132.0]
95 --> 59 | cost [57.0]
96 --> 39 | cost [120.0]
99 --> 53 | cost [144.0]

BACKUP RING
1  --- 63 | cost [11.13]
4  --- 21 | cost [7.140000000000001]
4  --- 78 | cost [8.33]
5  --- 34 | cost [9.8]
5  --- 80 | cost [13.09]
7  --- 40 | cost [4.97]
7  --- 61 | cost [11.48]
8  --- 65 | cost [18.2]
8  --- 101 | cost [3.85]
10 --- 17 | cost [19.6]
10 --- 74 | cost [12.25]
15 --- 97 | cost [2.66]
17 --- 38 | cost [5.18]
20 --- 32 | cost [9.03]
20 --- 33 | cost [8.47]
21 --- 97 | cost [6.79]
27 --- 33 | cost [9.59]
27 --- 72 | cost [16.45]
28 --- 46 | cost [10.43]
28 --- 59 | cost [8.33]
31 --- 66 | cost [6.65]
31 --- 94 | cost [14.98]
32 --- 82 | cost [7.28]
34 --- 42 | cost [8.96]
38 --- 50 | cost [9.59]
39 --- 40 | cost [13.09]
39 --- 44 | cost [15.47]
42 --- 55 | cost [14.07]
44 --- 57 | cost [22.68]
45 --- 47 | cost [19.95]
45 --- 100 | cost [11.76]
46 --- 73 | cost [2.0300000000000002]
47 --- 79 | cost [10.85]
50 --- 56 | cost [1.96]
51 --- 60 | cost [15.4]
51 --- 80 | cost [9.59]
53 --- 57 | cost [13.370000000000001]
53 --- 94 | cost [7.98]
55 --- 100 | cost [19.04]
56 --- 77 | cost [13.93]
59 --- 66 | cost [11.83]
61 --- 81 | cost [12.46]
63 --- 86 | cost [1.05]
65 --- 81 | cost [6.86]
72 --- 73 | cost [11.69]
74 --- 78 | cost [3.7800000000000002]
76 --- 77 | cost [12.11]
76 --- 84 | cost [10.01]
79 --- 98 | cost [16.17]
82 --- 86 | cost [8.68]
84 --- 98 | cost [12.6]

BACKUP STAR
2  --> 31 | cost [8.22]
3  --> 33 | cost [3.45]
6  --> 53 | cost [1.77]
9  --> 20 | cost [2.79]
11 -->  5 | cost [3.54]
12 --> 32 | cost [3.42]
13 --> 86 | cost [2.88]
14 --> 21 | cost [3.06]
16 --> 45 | cost [3.06]
19 --> 56 | cost [2.64]
22 --> 61 | cost [3.45]
23 --> 31 | cost [6.18]
24 -->  7 | cost [4.2]
25 --> 40 | cost [4.71]
26 --> 20 | cost [1.56]
29 --> 44 | cost [2.58]
30 --> 81 | cost [3.6]
35 --> 100 | cost [4.17]
36 --> 57 | cost [3.0]
37 --> 77 | cost [3.18]
41 -->  7 | cost [3.18]
43 --> 40 | cost [3.63]
48 --> 65 | cost [3.09]
49 --> 82 | cost [2.13]
52 --> 100 | cost [4.29]
54 --> 73 | cost [2.4]
58 --> 84 | cost [3.93]
64 --> 57 | cost [6.15]
67 --> 63 | cost [1.1400000000000001]
68 -->  8 | cost [5.1000000000000005]
69 --> 60 | cost [2.49]
70 --> 72 | cost [1.71]
71 -->  8 | cost [3.7800000000000002]
75 --> 82 | cost [1.08]
83 --> 65 | cost [3.09]
85 --> 21 | cost [2.2800000000000002]
87 --> 86 | cost [3.81]
88 --> 31 | cost [1.77]
89 --> 31 | cost [8.13]
90 --> 65 | cost [2.88]
91 --> 81 | cost [3.87]
92 --> 27 | cost [1.11]
93 --> 59 | cost [2.31]
95 --> 77 | cost [1.56]
96 --> 55 | cost [3.48]
99 --> 79 | cost [2.07]

B = 30.950000000000003
i★ = 31
j★ = 84
k★ = 66

       
——————— Wed, 31 Jan 2024 02:48:05 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 50 hubs —— 1-60-8-51-90-65-80-81-5-61-34-7-42-40-55-96-39-100-44-45-16-31-84-88-66-98-94-53-6-95-77-28-56-46-50-73-38-17-74-20-78-32-4-82-21-86-97-63-15-101-1
total time           3604.21 (TL 3600)    gap                  0.088                
blossom time         0                    nb blossom           0.0                  
LB <= UB             41394.88<=45407.96   Master/SP costs      41726/3681.96        
Master time          3227.14              SP time              377.07               
subtour              2801.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            2350.0               SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       109250               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—60—8—51—90—65—80—81—5—61—34—7—42—40—55—96—39—100—44—45—16—31—84—88—66—98—94—53—6—95—77—28—56—46—50—73—38—17—74—20—78—32—4—82—21—86—97—63—15—101

RING
1  --- 60 | cost [154.0]
1  --- 101 | cost [0.0]
4  --- 32 | cost [294.0]
4  --- 82 | cost [560.0]
5  --- 61 | cost [350.0]
5  --- 81 | cost [896.0]
6  --- 53 | cost [413.0]
6  --- 95 | cost [1183.0]
7  --- 34 | cost [399.0]
7  --- 42 | cost [511.0]
8  --- 51 | cost [1302.0]
8  --- 60 | cost [238.0]
15 --- 63 | cost [210.0]
15 --- 101 | cost [910.0]
16 --- 31 | cost [875.0]
16 --- 45 | cost [714.0]
17 --- 38 | cost [518.0]
17 --- 74 | cost [1470.0]
20 --- 74 | cost [133.0]
20 --- 78 | cost [273.0]
21 --- 82 | cost [294.0]
21 --- 86 | cost [609.0]
28 --- 56 | cost [896.0]
28 --- 77 | cost [518.0]
31 --- 84 | cost [378.0]
32 --- 78 | cost [658.0]
34 --- 61 | cost [756.0]
38 --- 73 | cost [777.0]
39 --- 96 | cost [280.0]
39 --- 100 | cost [1134.0]
40 --- 42 | cost [616.0]
40 --- 55 | cost [833.0]
44 --- 45 | cost [973.0]
44 --- 100 | cost [511.0]
46 --- 50 | cost [35.0]
46 --- 56 | cost [175.0]
50 --- 73 | cost [189.0]
51 --- 90 | cost [294.0]
53 --- 94 | cost [798.0]
55 --- 96 | cost [812.0]
63 --- 97 | cost [56.0]
65 --- 80 | cost [420.0]
65 --- 90 | cost [672.0]
66 --- 88 | cost [714.0]
66 --- 98 | cost [504.0]
77 --- 95 | cost [364.0]
80 --- 81 | cost [469.0]
84 --- 88 | cost [133.0]
86 --- 97 | cost [91.0]
94 --- 98 | cost [532.0]

STAR
2  --> 84 | cost [711.0]
3  -->  4 | cost [441.0]
9  --> 74 | cost [243.0]
10 --> 78 | cost [468.0]
11 --> 61 | cost [243.0]
12 --> 82 | cost [237.0]
13 --> 97 | cost [270.0]
14 --> 82 | cost [231.0]
18 -->  1 | cost [264.0]
19 --> 46 | cost [252.0]
22 -->  5 | cost [279.0]
23 --> 84 | cost [546.0]
24 --> 42 | cost [204.0]
25 --> 42 | cost [327.0]
26 --> 74 | cost [117.0]
27 --> 56 | cost [273.0]
29 --> 44 | cost [258.0]
30 --> 80 | cost [252.0]
33 --> 78 | cost [345.0]
35 --> 44 | cost [291.0]
36 --> 61 | cost [669.0]
37 --> 28 | cost [108.0]
41 --> 34 | cost [291.0]
43 --> 42 | cost [198.0]
47 --> 53 | cost [297.0]
48 --> 80 | cost [231.0]
49 --> 21 | cost [105.0]
52 --> 100 | cost [429.0]
54 --> 38 | cost [213.0]
57 --> 16 | cost [570.0]
58 --> 88 | cost [345.0]
59 --> 95 | cost [57.0]
62 -->  1 | cost [282.0]
64 --> 90 | cost [762.0]
67 --> 97 | cost [96.0]
68 --> 51 | cost [327.0]
69 -->  8 | cost [183.0]
70 --> 38 | cost [261.0]
71 --> 60 | cost [384.0]
72 --> 38 | cost [201.0]
75 --> 21 | cost [75.0]
76 --> 66 | cost [204.0]
79 -->  6 | cost [138.0]
83 --> 51 | cost [102.0]
85 --> 82 | cost [123.0]
87 --> 15 | cost [360.0]
89 --> 88 | cost [687.0]
91 --> 65 | cost [360.0]
92 --> 50 | cost [246.0]
93 --> 77 | cost [132.0]
99 --> 53 | cost [144.0]

BACKUP RING
1  ---  8 | cost [3.85]
4  --- 21 | cost [7.140000000000001]
4  --- 78 | cost [8.33]
5  --- 34 | cost [9.8]
5  --- 80 | cost [13.09]
6  --- 77 | cost [14.07]
6  --- 94 | cost [8.47]
7  --- 40 | cost [4.97]
7  --- 61 | cost [11.48]
8  --- 90 | cost [11.48]
15 --- 97 | cost [2.66]
16 --- 44 | cost [16.8]
16 --- 84 | cost [12.530000000000001]
17 --- 20 | cost [15.47]
17 --- 73 | cost [9.66]
20 --- 32 | cost [9.03]
21 --- 97 | cost [6.79]
28 --- 46 | cost [10.43]
28 --- 95 | cost [8.05]
31 --- 45 | cost [11.9]
31 --- 88 | cost [4.13]
32 --- 82 | cost [7.28]
34 --- 42 | cost [8.96]
38 --- 50 | cost [9.59]
38 --- 74 | cost [19.18]
39 --- 44 | cost [15.47]
39 --- 55 | cost [7.84]
40 --- 96 | cost [14.84]
42 --- 55 | cost [14.07]
45 --- 100 | cost [11.76]
46 --- 73 | cost [2.0300000000000002]
50 --- 56 | cost [1.96]
51 --- 60 | cost [15.4]
51 --- 65 | cost [5.8100000000000005]
53 --- 95 | cost [14.91]
53 --- 98 | cost [13.23]
56 --- 77 | cost [13.93]
61 --- 81 | cost [12.46]
63 --- 86 | cost [1.05]
63 --- 101 | cost [11.13]
65 --- 81 | cost [6.86]
66 --- 84 | cost [8.120000000000001]
66 --- 94 | cost [10.290000000000001]
74 --- 78 | cost [3.7800000000000002]
80 --- 90 | cost [10.92]
82 --- 86 | cost [8.68]
88 --- 98 | cost [11.83]
96 --- 100 | cost [12.25]

BACKUP STAR
2  --> 88 | cost [7.53]
3  --> 78 | cost [4.86]
9  --> 20 | cost [2.79]
10 -->  6 | cost [4.71]
11 -->  5 | cost [3.54]
12 --> 32 | cost [3.42]
13 --> 86 | cost [2.88]
14 --> 21 | cost [3.06]
19 --> 56 | cost [2.64]
22 --> 61 | cost [3.45]
23 --> 88 | cost [5.97]
24 -->  7 | cost [4.2]
25 --> 40 | cost [4.71]
26 --> 20 | cost [1.56]
27 --> 50 | cost [2.85]
29 --> 100 | cost [2.82]
30 --> 81 | cost [3.6]
33 --> 20 | cost [3.63]
35 --> 100 | cost [4.17]
36 -->  5 | cost [6.78]
37 --> 77 | cost [3.18]
41 -->  7 | cost [3.18]
43 --> 40 | cost [3.63]
47 --> 94 | cost [4.65]
48 --> 65 | cost [3.09]
49 --> 82 | cost [2.13]
52 --> 45 | cost [3.7800000000000002]
54 --> 73 | cost [2.4]
57 --> 53 | cost [5.73]
58 --> 84 | cost [3.93]
59 --> 77 | cost [1.44]
64 --> 81 | cost [7.26]
67 --> 63 | cost [1.1400000000000001]
68 --> 90 | cost [3.99]
69 --> 60 | cost [2.49]
70 --> 17 | cost [3.3000000000000003]
71 -->  8 | cost [3.7800000000000002]
72 --> 17 | cost [1.62]
75 --> 82 | cost [1.08]
76 --> 98 | cost [3.54]
79 --> 53 | cost [1.95]
83 --> 90 | cost [2.16]
85 --> 21 | cost [2.2800000000000002]
87 --> 86 | cost [3.81]
89 --> 84 | cost [6.63]
91 --> 81 | cost [3.87]
92 --> 46 | cost [2.58]
93 --> 28 | cost [2.67]
99 -->  6 | cost [2.73]

B = 20.12
i★ = 5
j★ = 61
k★ = 34