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

——————— Mon, 22 Jan 2024 03:19:05 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 68 hubs —— 1—27—88—24—50—34—81—38—66—52—8—7—22—29—86—16—64—15—78—99—76—61—67—36—31—40—85—96—37—35—100—10—87—2—48—51—21—47—28—82—6—19—60—4—71—39—91—54—45—68—14—9—3—83—77—69—84—17—49—98—97—89—90—32—94—79—13—101
total time           3640.25 (TL 3600)    gap                  0.638                
blossom time         0                    nb blossom           0.0                  
LB <= UB             98147.33<=270877.61  subtour              1212.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       535                  n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—27—88—24—50—34—81—38—66—52—8—7—22—29—86—16—64—15—78—99—76—61—67—36—31—40—85—96—37—35—100—10—87—2—48—51—21—47—28—82—6—19—60—4—71—39—91—54—45—68—14—9—3—83—77—69—84—17—49—98—97—89—90—32—94—79—13—101

RING
1  --- 27 | cost [2450.0]
2  --- 48 | cost [1414.0]
2  --- 87 | cost [5789.0]
3  ---  9 | cost [3542.0]
3  --- 83 | cost [665.0]
4  --- 60 | cost [2359.0]
4  --- 71 | cost [1414.0]
6  --- 19 | cost [6461.0]
6  --- 82 | cost [3955.0]
7  ---  8 | cost [5810.0]
7  --- 22 | cost [7966.0]
8  --- 52 | cost [602.0]
9  --- 14 | cost [8582.0]
10 --- 87 | cost [2338.0]
10 --- 100 | cost [8064.0]
13 --- 79 | cost [525.0]
13 --- 101 | cost [2555.0]
14 --- 68 | cost [147.0]
15 --- 64 | cost [4858.0]
15 --- 78 | cost [7301.0]
16 --- 64 | cost [2373.0]
16 --- 86 | cost [2576.0]
17 --- 49 | cost [2415.0]
17 --- 84 | cost [8876.0]
19 --- 60 | cost [4557.0]
21 --- 47 | cost [1526.0]
21 --- 51 | cost [9919.0]
22 --- 29 | cost [4606.0]
24 --- 50 | cost [3255.0]
24 --- 88 | cost [707.0]
27 --- 88 | cost [910.0]
28 --- 47 | cost [1750.0]
28 --- 82 | cost [5509.0]
29 --- 86 | cost [15141.0]
31 --- 36 | cost [9275.0]
31 --- 40 | cost [9436.0]
32 --- 90 | cost [2758.0]
32 --- 94 | cost [1253.0]
34 --- 50 | cost [2121.0]
34 --- 81 | cost [350.0]
35 --- 37 | cost [1799.0]
35 --- 100 | cost [2121.0]
36 --- 67 | cost [875.0]
37 --- 96 | cost [10899.0]
38 --- 66 | cost [679.0]
38 --- 81 | cost [1323.0]
39 --- 71 | cost [2135.0]
39 --- 91 | cost [1610.0]
40 --- 85 | cost [1925.0]
45 --- 54 | cost [8470.0]
45 --- 68 | cost [1561.0]
48 --- 51 | cost [2639.0]
49 --- 98 | cost [574.0]
52 --- 66 | cost [917.0]
54 --- 91 | cost [98.0]
61 --- 67 | cost [4004.0]
61 --- 76 | cost [3367.0]
69 --- 77 | cost [4767.0]
69 --- 84 | cost [3360.0]
76 --- 99 | cost [3220.0]
77 --- 83 | cost [4557.0]
78 --- 99 | cost [847.0]
79 --- 94 | cost [6573.0]
85 --- 96 | cost [3073.0]
89 --- 90 | cost [1330.0]
89 --- 97 | cost [3913.0]
97 --- 98 | cost [2478.0]

STAR
5  -->  3 | cost [804.0]
11 --> 90 | cost [576.0]
12 --> 28 | cost [543.0]
18 --> 85 | cost [564.0]
20 -->  9 | cost [825.0]
23 --> 66 | cost [1071.0]
25 -->  9 | cost [930.0]
26 --> 87 | cost [36.0]
30 --> 100 | cost [390.0]
33 --> 68 | cost [228.0]
41 --> 84 | cost [408.0]
42 --> 89 | cost [1281.0]
43 --> 77 | cost [438.0]
44 -->  4 | cost [435.0]
46 --> 52 | cost [726.0]
53 --> 60 | cost [597.0]
55 --> 87 | cost [552.0]
56 --> 21 | cost [711.0]
57 --> 99 | cost [759.0]
58 --> 29 | cost [732.0]
59 --> 85 | cost [444.0]
62 --> 37 | cost [528.0]
63 --> 54 | cost [399.0]
65 --> 14 | cost [615.0]
70 --> 49 | cost [513.0]
72 --> 76 | cost [1128.0]
73 --> 39 | cost [450.0]
74 --> 61 | cost [519.0]
75 --> 67 | cost [144.0]
80 --> 76 | cost [405.0]
92 --> 19 | cost [921.0]
93 -->  4 | cost [534.0]
95 --> 21 | cost [951.0]

BACKUP RING
1  --- 88 | cost [28.21]
2  --- 10 | cost [77.07000000000001]
2  --- 51 | cost [13.16]
3  --- 14 | cost [75.95]
3  --- 77 | cost [44.730000000000004]
4  --- 19 | cost [68.74]
4  --- 39 | cost [33.88]
6  --- 28 | cost [78.82000000000001]
6  --- 60 | cost [46.76]
7  --- 29 | cost [60.410000000000004]
7  --- 52 | cost [59.99]
8  --- 22 | cost [68.18]
8  --- 66 | cost [6.16]
9  --- 68 | cost [87.01]
9  --- 83 | cost [33.39]
10 --- 35 | cost [89.60000000000001]
13 --- 94 | cost [60.480000000000004]
14 --- 45 | cost [17.01]
15 --- 16 | cost [28.98]
15 --- 99 | cost [81.2]
16 --- 29 | cost [158.41]
17 --- 69 | cost [103.32000000000001]
17 --- 98 | cost [24.22]
19 --- 82 | cost [99.12]
21 --- 28 | cost [22.96]
21 --- 48 | cost [90.86]
22 --- 86 | cost [155.4]
24 --- 27 | cost [4.34]
24 --- 34 | cost [33.74]
31 --- 67 | cost [84.0]
31 --- 85 | cost [75.74]
32 --- 79 | cost [66.99]
32 --- 89 | cost [40.81]
34 --- 38 | cost [11.97]
35 --- 96 | cost [116.06]
36 --- 40 | cost [177.31]
36 --- 61 | cost [46.550000000000004]
37 --- 85 | cost [80.57000000000001]
37 --- 100 | cost [14.63]
38 --- 52 | cost [14.77]
39 --- 54 | cost [17.080000000000002]
40 --- 96 | cost [49.84]
45 --- 91 | cost [85.68]
47 --- 51 | cost [109.41]
47 --- 82 | cost [39.27]
48 --- 87 | cost [50.47]
49 --- 84 | cost [112.07000000000001]
49 --- 97 | cost [29.47]
50 --- 81 | cost [22.75]
50 --- 88 | cost [33.39]
54 --- 68 | cost [74.13]
60 --- 71 | cost [36.68]
61 --- 99 | cost [63.42]
64 --- 78 | cost [75.81]
64 --- 86 | cost [37.24]
66 --- 81 | cost [17.64]
67 --- 76 | cost [66.78]
69 --- 83 | cost [85.89]
71 --- 91 | cost [27.580000000000002]
76 --- 78 | cost [25.830000000000002]
77 --- 84 | cost [52.71]
79 --- 101 | cost [30.66]
87 --- 100 | cost [62.65]
89 --- 98 | cost [27.09]
90 --- 94 | cost [16.38]
90 --- 97 | cost [27.79]

BACKUP STAR
5  --> 83 | cost [10.41]
11 --> 89 | cost [6.0]
12 --> 47 | cost [6.9]
18 -->  6 | cost [6.57]
20 --> 10 | cost [9.450000000000001]
23 -->  8 | cost [10.92]
25 --> 10 | cost [10.41]
26 -->  9 | cost [9.540000000000001]
30 --> 51 | cost [6.12]
33 --> 14 | cost [2.91]
41 --> 24 | cost [7.59]
42 --> 22 | cost [11.91]
43 --> 71 | cost [6.8100000000000005]
44 --> 60 | cost [5.79]
46 -->  8 | cost [8.58]
53 -->  3 | cost [10.200000000000001]
55 -->  9 | cost [6.2700000000000005]
56 --> 28 | cost [11.97]
57 --> 31 | cost [6.54]
58 --> 22 | cost [12.540000000000001]
59 --> 40 | cost [4.74]
62 --> 51 | cost [7.95]
63 --> 91 | cost [4.38]
65 --> 68 | cost [6.390000000000001]
70 --> 89 | cost [6.78]
72 --> 31 | cost [10.26]
73 --> 15 | cost [9.69]
74 -->  7 | cost [7.95]
75 --> 36 | cost [4.7700000000000005]
80 --> 78 | cost [7.47]
92 --> 48 | cost [9.63]
93 --> 60 | cost [8.07]
95 --> 10 | cost [13.44]

B = 177.31
i★ = 36
j★ = 31
k★ = 40

       
——————— Mon, 22 Jan 2024 04:20:43 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 47 hubs —— 1-88-24-41-73-39-91-54-77-53-62-35-51-19-87-26-21-20-25-6-85-18-82-14-68-45-78-99-31-80-76-61-7-75-67-36-58-23-66-38-34-11-90-17-94-50-101-1
total time           3607.56 (TL 3600)    gap                  0.178                
blossom time         0                    nb blossom           0.0                  
LB <= UB             108831.48<=132348.77 Master/SP costs      128298/4050.77       
Master time          3595.53              SP time              12.03                
subtour              30699.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            41.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       26518                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—88—24—41—73—39—91—54—77—53—62—35—51—19—87—26—21—20—25—6—85—18—82—14—68—45—78—99—31—80—76—61—7—75—67—36—58—23—66—38—34—11—90—17—94—50—101

RING
1  --- 88 | cost [2821.0]
6  --- 25 | cost [2478.0]
6  --- 85 | cost [1890.0]
7  --- 61 | cost [1967.0]
7  --- 75 | cost [2366.0]
11 --- 34 | cost [3213.0]
11 --- 90 | cost [1344.0]
14 --- 68 | cost [147.0]
14 --- 82 | cost [3955.0]
17 --- 90 | cost [385.0]
17 --- 94 | cost [1295.0]
18 --- 82 | cost [2562.0]
18 --- 85 | cost [1316.0]
19 --- 51 | cost [994.0]
19 --- 87 | cost [5124.0]
20 --- 21 | cost [3605.0]
20 --- 25 | cost [245.0]
21 --- 26 | cost [3962.0]
23 --- 58 | cost [5187.0]
23 --- 66 | cost [2499.0]
24 --- 41 | cost [1771.0]
24 --- 88 | cost [707.0]
26 --- 87 | cost [84.0]
31 --- 80 | cost [2149.0]
31 --- 99 | cost [413.0]
34 --- 38 | cost [1197.0]
35 --- 51 | cost [1652.0]
35 --- 62 | cost [1981.0]
36 --- 58 | cost [3612.0]
36 --- 67 | cost [875.0]
38 --- 66 | cost [679.0]
39 --- 73 | cost [1050.0]
39 --- 91 | cost [1610.0]
41 --- 73 | cost [2695.0]
45 --- 68 | cost [1561.0]
45 --- 78 | cost [2051.0]
50 --- 94 | cost [3094.0]
50 --- 101 | cost [651.0]
53 --- 62 | cost [2576.0]
53 --- 77 | cost [4900.0]
54 --- 77 | cost [1141.0]
54 --- 91 | cost [98.0]
61 --- 76 | cost [3367.0]
67 --- 75 | cost [336.0]
76 --- 80 | cost [945.0]
78 --- 99 | cost [847.0]

STAR
2  --> 51 | cost [564.0]
3  -->  6 | cost [468.0]
4  --> 77 | cost [1182.0]
5  --> 53 | cost [654.0]
8  --> 66 | cost [264.0]
9  --> 25 | cost [930.0]
10 --> 20 | cost [945.0]
12 --> 21 | cost [1230.0]
13 --> 88 | cost [408.0]
15 --> 54 | cost [903.0]
16 --> 54 | cost [717.0]
22 --> 58 | cost [1254.0]
27 --> 24 | cost [186.0]
28 --> 21 | cost [984.0]
29 --> 58 | cost [732.0]
30 --> 51 | cost [612.0]
32 --> 94 | cost [537.0]
33 --> 68 | cost [228.0]
37 --> 51 | cost [300.0]
40 -->  6 | cost [123.0]
42 --> 23 | cost [639.0]
43 --> 77 | cost [438.0]
44 --> 53 | cost [900.0]
46 --> 66 | cost [1095.0]
47 --> 21 | cost [654.0]
48 --> 19 | cost [960.0]
49 --> 90 | cost [1011.0]
52 --> 66 | cost [393.0]
55 --> 26 | cost [549.0]
56 --> 21 | cost [711.0]
57 --> 31 | cost [654.0]
59 --> 85 | cost [444.0]
60 --> 53 | cost [597.0]
63 --> 54 | cost [399.0]
64 --> 77 | cost [783.0]
65 --> 14 | cost [615.0]
69 --> 54 | cost [1638.0]
70 --> 90 | cost [975.0]
71 --> 39 | cost [915.0]
72 --> 31 | cost [1026.0]
74 --> 61 | cost [519.0]
79 --> 88 | cost [381.0]
81 --> 34 | cost [150.0]
83 -->  6 | cost [180.0]
84 --> 41 | cost [408.0]
86 --> 14 | cost [1308.0]
89 --> 90 | cost [570.0]
92 --> 19 | cost [921.0]
93 --> 53 | cost [1296.0]
95 --> 21 | cost [951.0]
96 --> 85 | cost [1317.0]
97 --> 94 | cost [903.0]
98 --> 17 | cost [1038.0]
100 --> 51 | cost [342.0]

BACKUP RING
1  --- 24 | cost [28.490000000000002]
6  --- 18 | cost [15.33]
6  --- 20 | cost [25.48]
7  --- 67 | cost [24.22]
7  --- 76 | cost [42.56]
11 --- 17 | cost [16.17]
11 --- 38 | cost [29.26]
14 --- 18 | cost [51.52]
14 --- 45 | cost [17.01]
17 --- 50 | cost [38.71]
19 --- 26 | cost [51.870000000000005]
19 --- 35 | cost [25.34]
20 --- 26 | cost [40.46]
21 --- 25 | cost [37.31]
21 --- 87 | cost [40.39]
23 --- 36 | cost [59.78]
23 --- 38 | cost [26.740000000000002]
24 --- 73 | cost [44.52]
25 --- 85 | cost [34.79]
31 --- 76 | cost [28.35]
31 --- 78 | cost [6.93]
34 --- 66 | cost [17.43]
34 --- 90 | cost [43.12]
35 --- 53 | cost [43.4]
36 --- 75 | cost [11.13]
39 --- 41 | cost [36.61]
39 --- 54 | cost [17.080000000000002]
41 --- 88 | cost [19.740000000000002]
45 --- 99 | cost [14.91]
51 --- 62 | cost [18.55]
51 --- 87 | cost [61.11]
53 --- 54 | cost [59.78]
58 --- 66 | cost [75.74]
58 --- 67 | cost [43.89]
61 --- 75 | cost [40.6]
61 --- 80 | cost [43.19]
62 --- 77 | cost [73.78]
68 --- 78 | cost [27.72]
68 --- 82 | cost [40.53]
73 --- 91 | cost [24.43]
77 --- 91 | cost [11.48]
80 --- 99 | cost [24.92]
82 --- 85 | cost [35.35]
90 --- 94 | cost [16.38]
94 --- 101 | cost [35.63]

BACKUP STAR
2  --> 19 | cost [5.8500000000000005]
3  --> 53 | cost [10.200000000000001]
4  --> 53 | cost [12.84]
5  -->  6 | cost [12.06]
8  --> 38 | cost [5.55]
9  --> 20 | cost [8.25]
10 --> 26 | cost [9.69]
12 --> 82 | cost [19.86]
13 --> 24 | cost [6.87]
15 --> 91 | cost [9.03]
16 --> 77 | cost [7.5600000000000005]
22 --> 23 | cost [18.3]
27 --> 88 | cost [3.9]
28 --> 20 | cost [22.95]
29 --> 36 | cost [12.450000000000001]
30 --> 35 | cost [8.49]
32 --> 17 | cost [10.200000000000001]
33 --> 14 | cost [2.91]
37 --> 19 | cost [3.54]
40 --> 18 | cost [7.5]
42 --> 11 | cost [14.46]
43 --> 91 | cost [7.68]
44 --> 77 | cost [15.42]
46 --> 61 | cost [12.66]
47 --> 20 | cost [15.63]
48 --> 51 | cost [11.31]
49 --> 17 | cost [10.35]
52 --> 38 | cost [6.33]
55 --> 87 | cost [5.5200000000000005]
56 --> 26 | cost [17.04]
57 --> 99 | cost [7.59]
59 -->  6 | cost [5.19]
60 --> 62 | cost [11.55]
63 --> 91 | cost [4.38]
64 --> 85 | cost [7.95]
65 --> 68 | cost [6.390000000000001]
69 --> 91 | cost [16.59]
70 --> 17 | cost [10.74]
71 --> 77 | cost [10.74]
72 --> 76 | cost [11.28]
74 -->  7 | cost [7.95]
79 --> 24 | cost [6.87]
81 --> 38 | cost [5.67]
83 --> 18 | cost [8.34]
84 --> 24 | cost [9.450000000000001]
86 --> 68 | cost [13.59]
89 --> 11 | cost [6.0]
92 --> 87 | cost [13.200000000000001]
93 --> 77 | cost [17.01]
95 --> 26 | cost [14.73]
96 --> 14 | cost [14.64]
97 --> 17 | cost [10.41]
98 --> 90 | cost [10.53]
100 --> 19 | cost [5.8500000000000005]

B = 130.67
i★ = 20
j★ = 21
k★ = 26