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

——————— Fri, 19 Jan 2024 08:56:09 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 32 hubs —— 1—15—86—49—75—12—4—32—78—3—99—56—94—98—66—31—44—100—11—34—40—7—41—30—80—90—51—83—68—8—60—101
total time           3651.1 (TL 3600)     gap                  0.262                
blossom time         0                    nb blossom           0.0                  
LB <= UB             37396.39<=50668.11   subtour              321.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—15—86—49—75—12—4—32—78—3—99—56—94—98—66—31—44—100—11—34—40—7—41—30—80—90—51—83—68—8—60—101

RING
1  --- 15 | cost [910.0]
3  --- 78 | cost [1134.0]
3  --- 99 | cost [1148.0]
4  --- 12 | cost [840.0]
4  --- 32 | cost [294.0]
7  --- 40 | cost [497.0]
7  --- 41 | cost [742.0]
8  --- 60 | cost [238.0]
8  --- 68 | cost [1190.0]
11 --- 34 | cost [1106.0]
11 --- 100 | cost [1750.0]
12 --- 75 | cost [798.0]
15 --- 86 | cost [301.0]
30 --- 41 | cost [1295.0]
30 --- 80 | cost [588.0]
31 --- 44 | cost [1890.0]
31 --- 66 | cost [665.0]
32 --- 78 | cost [658.0]
34 --- 40 | cost [798.0]
44 --- 100 | cost [511.0]
49 --- 75 | cost [266.0]
49 --- 86 | cost [616.0]
51 --- 83 | cost [238.0]
51 --- 90 | cost [294.0]
56 --- 94 | cost [2317.0]
56 --- 99 | cost [2163.0]
60 --- 101 | cost [154.0]
66 --- 98 | cost [504.0]
68 --- 83 | cost [567.0]
80 --- 90 | cost [1092.0]
94 --- 98 | cost [532.0]

STAR
2  --> 31 | cost [822.0]
5  --> 11 | cost [354.0]
6  --> 99 | cost [273.0]
9  --> 78 | cost [297.0]
10 --> 78 | cost [468.0]
13 --> 49 | cost [264.0]
14 --> 12 | cost [144.0]
16 --> 98 | cost [354.0]
17 --> 56 | cost [564.0]
18 -->  1 | cost [264.0]
19 --> 56 | cost [264.0]
20 --> 78 | cost [117.0]
21 --> 75 | cost [75.0]
22 --> 41 | cost [150.0]
23 --> 31 | cost [618.0]
24 -->  7 | cost [420.0]
25 --> 40 | cost [471.0]
26 --> 78 | cost [204.0]
27 --> 56 | cost [273.0]
28 --> 56 | cost [384.0]
29 --> 44 | cost [258.0]
33 --> 78 | cost [345.0]
35 --> 44 | cost [291.0]
36 --> 11 | cost [507.0]
37 --> 56 | cost [330.0]
38 --> 56 | cost [492.0]
39 --> 100 | cost [486.0]
42 -->  7 | cost [219.0]
43 --> 40 | cost [363.0]
45 --> 44 | cost [417.0]
46 --> 56 | cost [75.0]
47 --> 99 | cost [276.0]
48 --> 30 | cost [237.0]
50 --> 56 | cost [84.0]
52 --> 100 | cost [429.0]
53 --> 99 | cost [144.0]
54 --> 56 | cost [372.0]
55 --> 40 | cost [357.0]
57 --> 99 | cost [576.0]
58 --> 31 | cost [501.0]
59 --> 98 | cost [480.0]
61 --> 11 | cost [243.0]
62 -->  1 | cost [282.0]
63 --> 86 | cost [45.0]
64 --> 99 | cost [738.0]
65 --> 51 | cost [249.0]
67 --> 86 | cost [120.0]
69 -->  8 | cost [183.0]
70 --> 56 | cost [753.0]
71 -->  8 | cost [378.0]
72 --> 56 | cost [663.0]
73 --> 56 | cost [162.0]
74 --> 78 | cost [162.0]
76 --> 98 | cost [354.0]
77 --> 56 | cost [597.0]
79 --> 99 | cost [207.0]
81 --> 30 | cost [360.0]
82 --> 75 | cost [108.0]
84 --> 31 | cost [162.0]
85 --> 12 | cost [123.0]
87 --> 15 | cost [360.0]
88 --> 31 | cost [177.0]
89 --> 31 | cost [813.0]
91 --> 90 | cost [396.0]
92 --> 56 | cost [267.0]
93 --> 56 | cost [648.0]
95 --> 98 | cost [468.0]
96 --> 100 | cost [525.0]
97 --> 86 | cost [39.0]

BACKUP RING
1  --- 86 | cost [12.11]
3  --- 32 | cost [12.040000000000001]
3  --- 56 | cost [23.38]
4  --- 75 | cost [5.46]
4  --- 78 | cost [8.33]
7  --- 30 | cost [20.37]
7  --- 34 | cost [3.99]
8  --- 83 | cost [13.370000000000001]
8  --- 101 | cost [3.85]
11 --- 40 | cost [17.78]
11 --- 44 | cost [21.91]
12 --- 32 | cost [7.98]
12 --- 49 | cost [10.43]
15 --- 49 | cost [9.1]
30 --- 90 | cost [16.240000000000002]
31 --- 98 | cost [10.01]
31 --- 100 | cost [22.68]
34 --- 100 | cost [21.77]
40 --- 41 | cost [12.32]
41 --- 80 | cost [16.1]
44 --- 66 | cost [24.43]
51 --- 68 | cost [7.63]
51 --- 80 | cost [9.59]
56 --- 98 | cost [25.62]
60 --- 68 | cost [13.790000000000001]
66 --- 94 | cost [10.290000000000001]
75 --- 86 | cost [7.7]
78 --- 99 | cost [20.580000000000002]
83 --- 90 | cost [5.04]
94 --- 99 | cost [11.200000000000001]

BACKUP STAR
2  --> 44 | cost [10.26]
5  --> 41 | cost [3.84]
6  --> 94 | cost [3.63]
9  --> 32 | cost [3.6]
10 -->  3 | cost [3.9]
13 --> 86 | cost [2.88]
14 --> 75 | cost [3.3000000000000003]
16 --> 31 | cost [3.75]
17 --> 78 | cost [7.8]
19 --> 94 | cost [11.28]
20 --> 32 | cost [3.87]
21 --> 49 | cost [1.05]
22 --> 34 | cost [3.7800000000000002]
23 --> 44 | cost [7.8]
24 --> 40 | cost [4.44]
25 -->  7 | cost [5.34]
26 --> 32 | cost [3.69]
27 --> 78 | cost [6.21]
28 --> 94 | cost [7.65]
29 --> 100 | cost [2.82]
33 -->  3 | cost [3.45]
35 --> 100 | cost [4.17]
36 --> 99 | cost [7.44]
37 --> 94 | cost [8.700000000000001]
38 --> 78 | cost [9.6]
39 --> 40 | cost [5.61]
42 --> 40 | cost [2.64]
43 -->  7 | cost [4.05]
45 --> 100 | cost [5.04]
46 --> 78 | cost [8.76]
47 --> 94 | cost [4.65]
48 --> 80 | cost [2.31]
50 --> 78 | cost [8.64]
52 --> 44 | cost [5.19]
53 --> 94 | cost [3.42]
54 --> 78 | cost [10.5]
55 -->  7 | cost [5.58]
57 --> 94 | cost [5.97]
58 --> 66 | cost [4.2]
59 --> 66 | cost [5.07]
61 --> 34 | cost [3.24]
63 --> 15 | cost [0.9]
64 -->  3 | cost [7.41]
65 --> 80 | cost [1.8]
67 --> 15 | cost [1.86]
69 --> 60 | cost [2.49]
70 --> 78 | cost [11.01]
71 --> 60 | cost [3.84]
72 --> 78 | cost [9.3]
73 --> 78 | cost [8.67]
74 --> 32 | cost [4.08]
76 --> 66 | cost [2.04]
77 --> 98 | cost [6.18]
79 --> 94 | cost [4.83]
81 --> 80 | cost [2.0100000000000002]
82 --> 49 | cost [2.13]
84 --> 66 | cost [3.48]
85 --> 75 | cost [2.31]
87 --> 86 | cost [3.81]
88 --> 66 | cost [3.06]
89 --> 66 | cost [9.81]
91 --> 80 | cost [4.62]
92 --> 78 | cost [6.18]
93 --> 66 | cost [6.99]
95 --> 94 | cost [4.8]
96 --> 40 | cost [6.36]
97 --> 15 | cost [1.1400000000000001]

B = 138.67000000000002
i★ = 94
j★ = 56
k★ = 99

       
——————— Fri, 19 Jan 2024 09:57:31 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 45 hubs —— 1-15-63-97-86-21-82-4-32-78-20-74-17-73-50-46-56-28-77-59-76-88-84-31-66-98-94-53-47-57-52-100-39-40-42-7-41-22-5-81-80-65-51-60-101-1
total time           3607.74 (TL 3600)    gap                  0.071                
blossom time         0                    nb blossom           0.0                  
LB <= UB             38641<=41576.36      Master/SP costs      41328/248.36         
Master time          3600.5               SP time              7.24                 
subtour              32246.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            22.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       36732                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—15—63—97—86—21—82—4—32—78—20—74—17—73—50—46—56—28—77—59—76—88—84—31—66—98—94—53—47—57—52—100—39—40—42—7—41—22—5—81—80—65—51—60—101

RING
1  --- 15 | cost [910.0]
4  --- 32 | cost [294.0]
4  --- 82 | cost [560.0]
5  --- 22 | cost [651.0]
5  --- 81 | cost [896.0]
7  --- 41 | cost [742.0]
7  --- 42 | cost [511.0]
15 --- 63 | cost [210.0]
17 --- 73 | cost [966.0]
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]
22 --- 41 | cost [350.0]
28 --- 56 | cost [896.0]
28 --- 77 | cost [518.0]
31 --- 66 | cost [665.0]
31 --- 84 | cost [378.0]
32 --- 78 | cost [658.0]
39 --- 40 | cost [1309.0]
39 --- 100 | cost [1134.0]
40 --- 42 | cost [616.0]
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 --- 60 | cost [1540.0]
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 --- 98 | cost [504.0]
76 --- 88 | cost [875.0]
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]
6  --> 53 | cost [177.0]
8  --> 60 | cost [102.0]
9  --> 74 | cost [243.0]
10 --> 78 | cost [468.0]
11 -->  5 | cost [354.0]
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]
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 --> 100 | cost [282.0]
30 --> 80 | cost [252.0]
33 --> 78 | cost [345.0]
34 -->  7 | cost [171.0]
35 --> 100 | cost [417.0]
36 --> 57 | cost [300.0]
37 --> 28 | cost [108.0]
38 --> 17 | cost [222.0]
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 --> 73 | cost [240.0]
55 --> 39 | cost [336.0]
58 --> 76 | cost [288.0]
61 -->  5 | cost [150.0]
62 -->  1 | cost [282.0]
64 --> 47 | cost [606.0]
67 --> 97 | cost [96.0]
68 --> 51 | cost [327.0]
69 --> 60 | cost [249.0]
70 --> 17 | cost [330.0]
71 --> 60 | cost [384.0]
72 --> 17 | cost [162.0]
75 --> 21 | cost [75.0]
79 --> 53 | cost [195.0]
83 --> 51 | cost [102.0]
85 --> 82 | cost [123.0]
87 --> 15 | cost [360.0]
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  --- 41 | cost [8.96]
5  --- 80 | cost [13.09]
7  --- 22 | cost [10.57]
7  --- 40 | cost [4.97]
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]
22 --- 81 | cost [10.57]
28 --- 46 | cost [10.43]
28 --- 59 | cost [8.33]
31 --- 88 | cost [4.13]
31 --- 98 | cost [10.01]
32 --- 82 | cost [7.28]
39 --- 42 | cost [19.25]
39 --- 52 | cost [18.41]
40 --- 100 | cost [22.54]
41 --- 42 | cost [9.38]
46 --- 73 | cost [2.0300000000000002]
47 --- 52 | cost [18.13]
47 --- 94 | cost [10.85]
50 --- 56 | cost [1.96]
51 --- 80 | cost [9.59]
51 --- 101 | cost [16.87]
53 --- 57 | cost [13.370000000000001]
53 --- 98 | cost [13.23]
56 --- 77 | cost [13.93]
57 --- 100 | cost [21.42]
59 --- 88 | cost [17.78]
60 --- 65 | cost [20.580000000000002]
63 --- 86 | cost [1.05]
65 --- 81 | cost [6.86]
66 --- 84 | cost [8.120000000000001]
66 --- 94 | cost [10.290000000000001]
73 --- 74 | cost [17.990000000000002]
74 --- 78 | cost [3.7800000000000002]
76 --- 77 | cost [12.11]
76 --- 84 | cost [10.01]
82 --- 86 | cost [8.68]

BACKUP STAR
2  --> 88 | cost [7.53]
3  --> 78 | cost [4.86]
6  --> 94 | cost [3.63]
8  -->  1 | cost [1.6500000000000001]
9  --> 20 | cost [2.79]
10 --> 20 | cost [4.74]
11 --> 52 | cost [5.34]
12 --> 32 | cost [3.42]
13 --> 86 | cost [2.88]
14 --> 21 | cost [3.06]
16 --> 31 | cost [3.75]
19 --> 56 | cost [2.64]
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 --> 39 | cost [5.1000000000000005]
30 --> 81 | cost [3.6]
33 --> 20 | cost [3.63]
34 --> 41 | cost [2.91]
35 --> 39 | cost [6.78]
36 --> 47 | cost [4.92]
37 --> 77 | cost [3.18]
38 --> 73 | cost [3.33]
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 --> 46 | cost [3.0]
55 --> 40 | cost [3.5700000000000003]
58 --> 88 | cost [3.45]
61 --> 22 | cost [3.45]
64 --> 57 | cost [6.15]
67 --> 63 | cost [1.1400000000000001]
68 --> 65 | cost [5.5200000000000005]
69 -->  1 | cost [3.09]
70 --> 73 | cost [5.91]
71 -->  1 | cost [3.93]
72 --> 73 | cost [5.01]
75 --> 82 | cost [1.08]
79 --> 47 | cost [4.65]
83 --> 65 | cost [3.09]
85 --> 21 | cost [2.2800000000000002]
87 --> 86 | cost [3.81]
89 --> 88 | cost [6.87]
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 --> 100 | cost [5.25]
99 --> 47 | cost [2.7600000000000002]

B = 35.480000000000004
i★ = 39
j★ = 100
k★ = 52