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

——————— Sun, 28 Jan 2024 04:07:06 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 46 hubs —— 1—15—63—97—86—21—82—4—32—78—20—74—17—38—50—73—46—56—28—77—59—76—88—66—98—94—53—47—57—52—100—39—55—40—42—7—34—61—5—81—80—65—51—8—60—101
total time           3633.57 (TL 3600)    gap                  0.069                
blossom time         0                    nb blossom           0.0                  
LB <= UB             40646.16<=43678.93   subtour              21.0                 
connectivity cuts    135.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       11                   n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—15—63—97—86—21—82—4—32—78—20—74—17—38—50—73—46—56—28—77—59—76—88—66—98—94—53—47—57—52—100—39—55—40—42—7—34—61—5—81—80—65—51—8—60—101

RING
1  --- 15 | cost [910.0]
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]
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]
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]
32 --- 78 | cost [658.0]
34 --- 61 | cost [756.0]
38 --- 50 | cost [959.0]
39 --- 55 | cost [784.0]
39 --- 100 | cost [1134.0]
40 --- 42 | cost [616.0]
40 --- 55 | cost [833.0]
46 --- 56 | cost [175.0]
46 --- 73 | cost [203.0]
47 --- 53 | cost [693.0]
47 --- 57 | cost [700.0]
50 --- 73 | cost [189.0]
51 --- 65 | cost [581.0]
52 --- 57 | cost [1141.0]
52 --- 100 | cost [1001.0]
53 --- 94 | cost [798.0]
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 --- 88 | cost [714.0]
66 --- 98 | cost [504.0]
76 --- 88 | cost [875.0]
80 --- 81 | cost [469.0]
86 --- 97 | cost [91.0]
94 --- 98 | cost [532.0]

STAR
2  --> 88 | cost [753.0]
3  -->  4 | cost [441.0]
6  --> 53 | cost [177.0]
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]
16 --> 98 | cost [354.0]
18 -->  1 | cost [264.0]
19 --> 46 | cost [252.0]
22 -->  5 | cost [279.0]
23 --> 88 | cost [597.0]
24 --> 42 | cost [204.0]
25 --> 42 | cost [327.0]
26 --> 74 | cost [117.0]
27 --> 56 | cost [273.0]
29 --> 100 | cost [282.0]
30 --> 80 | cost [252.0]
31 --> 66 | cost [285.0]
33 --> 78 | cost [345.0]
35 --> 100 | cost [417.0]
36 --> 57 | cost [300.0]
37 --> 28 | cost [108.0]
41 --> 34 | cost [291.0]
43 --> 42 | cost [198.0]
44 --> 100 | cost [219.0]
45 --> 52 | cost [378.0]
48 --> 80 | cost [231.0]
49 --> 21 | cost [105.0]
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 -->  8 | cost [378.0]
72 --> 17 | cost [162.0]
75 --> 21 | cost [75.0]
79 --> 53 | cost [195.0]
83 --> 51 | cost [102.0]
84 --> 88 | cost [57.0]
85 --> 82 | cost [123.0]
87 --> 15 | cost [360.0]
89 --> 88 | cost [687.0]
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]
15 --- 97 | cost [2.66]
17 --- 20 | cost [15.47]
17 --- 50 | cost [11.27]
20 --- 32 | cost [9.03]
21 --- 97 | cost [6.79]
28 --- 46 | cost [10.43]
28 --- 59 | cost [8.33]
32 --- 82 | cost [7.28]
34 --- 42 | cost [8.96]
38 --- 73 | cost [7.7700000000000005]
38 --- 74 | cost [19.18]
39 --- 40 | cost [13.09]
39 --- 52 | cost [18.41]
42 --- 55 | cost [14.07]
46 --- 50 | cost [0.35000000000000003]
47 --- 52 | cost [18.13]
47 --- 94 | cost [10.85]
51 --- 60 | cost [15.4]
51 --- 80 | cost [9.59]
53 --- 57 | cost [13.370000000000001]
53 --- 98 | cost [13.23]
55 --- 100 | cost [19.04]
56 --- 73 | cost [3.7800000000000002]
56 --- 77 | cost [13.93]
57 --- 100 | cost [21.42]
59 --- 88 | cost [17.78]
61 --- 81 | cost [12.46]
63 --- 86 | cost [1.05]
65 --- 81 | cost [6.86]
66 --- 76 | cost [4.76]
66 --- 94 | cost [10.290000000000001]
74 --- 78 | cost [3.7800000000000002]
76 --- 77 | cost [12.11]
82 --- 86 | cost [8.68]
88 --- 98 | cost [11.83]

BACKUP STAR
2  --> 66 | cost [10.59]
3  --> 78 | cost [4.86]
6  --> 94 | cost [3.63]
9  --> 20 | cost [2.79]
10 --> 20 | cost [4.74]
11 -->  5 | cost [3.54]
12 --> 32 | cost [3.42]
13 --> 86 | cost [2.88]
14 --> 21 | cost [3.06]
16 --> 66 | cost [4.2]
19 --> 56 | cost [2.64]
22 --> 61 | cost [3.45]
23 --> 66 | cost [8.82]
24 -->  7 | cost [4.2]
25 --> 40 | cost [4.71]
26 --> 20 | cost [1.56]
27 --> 50 | cost [2.85]
29 --> 39 | cost [5.1000000000000005]
30 --> 81 | cost [3.6]
31 --> 88 | cost [1.77]
33 --> 20 | cost [3.63]
35 --> 39 | cost [6.78]
36 --> 47 | cost [4.92]
37 --> 77 | cost [3.18]
41 -->  7 | cost [3.18]
43 --> 40 | cost [3.63]
44 --> 52 | cost [5.19]
45 --> 100 | cost [5.04]
48 --> 65 | cost [3.09]
49 --> 82 | cost [2.13]
54 --> 73 | cost [2.4]
58 --> 88 | cost [3.45]
64 --> 57 | cost [6.15]
67 --> 63 | cost [1.1400000000000001]
68 -->  8 | cost [5.1000000000000005]
69 --> 60 | cost [2.49]
70 --> 17 | cost [3.3000000000000003]
71 --> 60 | cost [3.84]
72 --> 38 | cost [2.0100000000000002]
75 --> 82 | cost [1.08]
79 --> 47 | cost [4.65]
83 --> 65 | cost [3.09]
84 --> 66 | cost [3.48]
85 --> 21 | cost [2.2800000000000002]
87 --> 86 | cost [3.81]
89 --> 76 | cost [9.69]
90 --> 65 | cost [2.88]
91 --> 81 | cost [3.87]
92 --> 46 | cost [2.58]
93 --> 59 | cost [2.31]
95 --> 77 | cost [1.56]
96 --> 55 | cost [3.48]
99 --> 47 | cost [2.7600000000000002]

B = 37.34
i★ = 66
j★ = 88
k★ = 76

       
——————— Sun, 28 Jan 2024 04:18:26 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 48 hubs —— 1-60-8-90-51-65-80-81-5-61-34-7-42-40-55-96-29-44-45-31-84-88-66-98-94-53-6-95-77-28-56-46-50-73-38-17-74-20-78-32-4-82-21-86-97-63-15-101-1
total time           595.82               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             41803.5<=41803.5     Master/SP costs      41044/759.5          
Master time          555.97               SP time              39.85                
subtour              527.0                connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            225.0                SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       57442                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—60—8—90—51—65—80—81—5—61—34—7—42—40—55—96—29—44—45—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  --- 60 | cost [238.0]
8  --- 90 | cost [1148.0]
15 --- 63 | cost [210.0]
15 --- 101 | cost [910.0]
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]
29 --- 44 | cost [602.0]
29 --- 96 | cost [1120.0]
31 --- 45 | cost [1190.0]
31 --- 84 | cost [378.0]
32 --- 78 | cost [658.0]
34 --- 61 | cost [756.0]
38 --- 73 | cost [777.0]
40 --- 42 | cost [616.0]
40 --- 55 | cost [833.0]
44 --- 45 | cost [973.0]
46 --- 50 | cost [35.0]
46 --- 56 | cost [175.0]
50 --- 73 | cost [189.0]
51 --- 65 | cost [581.0]
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]
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]
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]
27 --> 56 | cost [273.0]
30 --> 80 | cost [252.0]
33 --> 78 | cost [345.0]
35 --> 29 | cost [174.0]
36 --> 61 | cost [669.0]
37 --> 28 | cost [108.0]
39 --> 96 | cost [120.0]
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 --> 45 | cost [378.0]
54 --> 38 | cost [213.0]
57 --> 53 | cost [573.0]
58 --> 88 | cost [345.0]
59 --> 95 | cost [57.0]
62 -->  1 | cost [282.0]
64 --> 81 | cost [726.0]
67 --> 97 | cost [96.0]
68 --> 51 | cost [327.0]
69 -->  8 | cost [183.0]
70 --> 38 | cost [261.0]
71 -->  8 | cost [378.0]
72 --> 17 | cost [162.0]
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 --> 84 | cost [663.0]
91 --> 65 | cost [360.0]
92 --> 50 | cost [246.0]
93 --> 77 | cost [132.0]
99 --> 53 | cost [144.0]
100 --> 44 | cost [219.0]

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  --- 51 | cost [13.02]
15 --- 97 | cost [2.66]
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]
29 --- 45 | cost [15.68]
29 --- 55 | cost [19.25]
31 --- 44 | cost [18.900000000000002]
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]
40 --- 96 | cost [14.84]
42 --- 55 | cost [14.07]
44 --- 96 | cost [15.75]
45 --- 84 | cost [15.26]
46 --- 73 | cost [2.0300000000000002]
50 --- 56 | cost [1.96]
51 --- 80 | cost [9.59]
53 --- 95 | cost [14.91]
53 --- 98 | cost [13.23]
56 --- 77 | cost [13.93]
60 --- 90 | cost [13.86]
61 --- 81 | cost [12.46]
63 --- 86 | cost [1.05]
63 --- 101 | cost [11.13]
65 --- 81 | cost [6.86]
65 --- 90 | cost [6.72]
66 --- 84 | cost [8.120000000000001]
66 --- 94 | cost [10.290000000000001]
74 --- 78 | cost [3.7800000000000002]
82 --- 86 | cost [8.68]
88 --- 98 | cost [11.83]

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]
16 --> 45 | 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]
30 --> 81 | cost [3.6]
33 --> 20 | cost [3.63]
35 --> 44 | cost [2.91]
36 -->  5 | cost [6.78]
37 --> 77 | cost [3.18]
39 --> 55 | cost [3.36]
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 --> 44 | cost [5.19]
54 --> 73 | cost [2.4]
57 --> 94 | cost [5.97]
58 --> 84 | cost [3.93]
59 --> 77 | cost [1.44]
64 --> 90 | cost [7.62]
67 --> 63 | cost [1.1400000000000001]
68 --> 90 | cost [3.99]
69 --> 60 | cost [2.49]
70 --> 17 | cost [3.3000000000000003]
71 --> 60 | cost [3.84]
72 --> 38 | cost [2.0100000000000002]
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 --> 88 | cost [6.87]
91 --> 81 | cost [3.87]
92 --> 46 | cost [2.58]
93 --> 28 | cost [2.67]
99 -->  6 | cost [2.73]
100 --> 29 | cost [2.82]

B = 24.5
i★ = 31
j★ = 84
k★ = 88