------------------------------------------------------------
                        α=7.0 —— kroC100 —— 100 nodes       
------------------------------------------------------------

——————— Sun, 21 Jan 2024 22:17:54 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 64 hubs —— 1—53—94—91—68—30—95—92—45—33—69—100—6—83—8—39—5—98—88—58—72—71—38—90—25—17—23—55—42—67—54—4—2—21—89—3—36—74—14—41—18—32—82—78—10—99—81—9—79—93—26—61—37—51—44—11—87—84—49—29—13—47—31—101
total time           3635.6 (TL 3600)     gap                  0.699                
blossom time         0                    nb blossom           0.0                  
LB <= UB             103036.25<=342354.6  subtour              919.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       61                   n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—53—94—91—68—30—95—92—45—33—69—100—6—83—8—39—5—98—88—58—72—71—38—90—25—17—23—55—42—67—54—4—2—21—89—3—36—74—14—41—18—32—82—78—10—99—81—9—79—93—26—61—37—51—44—11—87—84—49—29—13—47—31—101

RING
1  --- 53 | cost [224.0]
2  ---  4 | cost [9471.0]
2  --- 21 | cost [4319.0]
3  --- 36 | cost [5943.0]
3  --- 89 | cost [3381.0]
4  --- 54 | cost [10507.0]
5  --- 39 | cost [3227.0]
5  --- 98 | cost [5593.0]
6  --- 83 | cost [4130.0]
6  --- 100 | cost [14147.0]
8  --- 39 | cost [5138.0]
8  --- 83 | cost [4165.0]
9  --- 79 | cost [13363.0]
9  --- 81 | cost [9891.0]
10 --- 78 | cost [8421.0]
10 --- 99 | cost [756.0]
11 --- 44 | cost [3297.0]
11 --- 87 | cost [3192.0]
13 --- 29 | cost [9639.0]
13 --- 47 | cost [3276.0]
14 --- 41 | cost [6846.0]
14 --- 74 | cost [1918.0]
17 --- 23 | cost [10507.0]
17 --- 25 | cost [714.0]
18 --- 32 | cost [3990.0]
18 --- 41 | cost [11011.0]
21 --- 89 | cost [2583.0]
23 --- 55 | cost [9765.0]
25 --- 90 | cost [672.0]
26 --- 61 | cost [1197.0]
26 --- 93 | cost [6818.0]
29 --- 49 | cost [1442.0]
30 --- 68 | cost [973.0]
30 --- 95 | cost [6636.0]
31 --- 47 | cost [609.0]
31 --- 101 | cost [7959.0]
32 --- 82 | cost [3997.0]
33 --- 45 | cost [749.0]
33 --- 69 | cost [3479.0]
36 --- 74 | cost [721.0]
37 --- 51 | cost [3360.0]
37 --- 61 | cost [1897.0]
38 --- 71 | cost [602.0]
38 --- 90 | cost [5803.0]
42 --- 55 | cost [763.0]
42 --- 67 | cost [2240.0]
44 --- 51 | cost [1491.0]
45 --- 92 | cost [2247.0]
49 --- 84 | cost [7014.0]
53 --- 94 | cost [17129.0]
54 --- 67 | cost [3822.0]
58 --- 72 | cost [5768.0]
58 --- 88 | cost [2380.0]
68 --- 91 | cost [4711.0]
69 --- 100 | cost [3150.0]
71 --- 72 | cost [1764.0]
78 --- 82 | cost [812.0]
79 --- 93 | cost [8911.0]
81 --- 99 | cost [3241.0]
84 --- 87 | cost [3745.0]
88 --- 98 | cost [1274.0]
91 --- 94 | cost [903.0]
92 --- 95 | cost [17654.0]

STAR
7  --> 78 | cost [1080.0]
12 --> 49 | cost [1179.0]
15 --> 13 | cost [702.0]
16 --> 44 | cost [663.0]
19 --> 99 | cost [300.0]
20 -->  1 | cost [2868.0]
22 -->  8 | cost [384.0]
24 --> 61 | cost [966.0]
27 --> 13 | cost [1185.0]
28 --> 39 | cost [285.0]
34 --> 90 | cost [270.0]
35 --> 68 | cost [459.0]
40 --> 53 | cost [1107.0]
43 --> 71 | cost [1434.0]
46 --> 29 | cost [804.0]
48 --> 84 | cost [453.0]
50 --> 72 | cost [771.0]
52 --> 11 | cost [81.0]
56 --> 38 | cost [531.0]
57 --> 33 | cost [486.0]
59 --> 41 | cost [855.0]
60 --> 14 | cost [1494.0]
62 --> 72 | cost [669.0]
63 --> 44 | cost [327.0]
64 -->  1 | cost [2883.0]
65 --> 31 | cost [777.0]
66 --> 44 | cost [570.0]
70 --> 91 | cost [708.0]
73 -->  3 | cost [54.0]
75 -->  8 | cost [789.0]
76 --> 91 | cost [708.0]
77 --> 30 | cost [1152.0]
80 --> 31 | cost [1293.0]
85 -->  1 | cost [648.0]
86 --> 95 | cost [975.0]
96 --> 11 | cost [891.0]
97 --> 81 | cost [360.0]

BACKUP RING
1  --- 94 | cost [170.17000000000002]
2  --- 54 | cost [34.93]
2  --- 89 | cost [46.69]
3  --- 21 | cost [56.42]
3  --- 74 | cost [53.410000000000004]
4  --- 21 | cost [104.09]
4  --- 67 | cost [88.2]
5  ---  8 | cost [81.62]
5  --- 88 | cost [44.03]
6  ---  8 | cost [35.910000000000004]
6  --- 69 | cost [115.57000000000001]
9  --- 93 | cost [68.60000000000001]
9  --- 99 | cost [74.2]
10 --- 81 | cost [25.060000000000002]
10 --- 82 | cost [89.53]
11 --- 51 | cost [42.35]
11 --- 84 | cost [6.65]
13 --- 31 | cost [27.650000000000002]
13 --- 49 | cost [90.02]
14 --- 18 | cost [51.52]
14 --- 36 | cost [14.700000000000001]
17 --- 55 | cost [59.22]
17 --- 90 | cost [12.950000000000001]
18 --- 82 | cost [55.160000000000004]
23 --- 25 | cost [109.9]
23 --- 42 | cost [101.43]
25 --- 38 | cost [62.02]
26 --- 37 | cost [28.63]
26 --- 79 | cost [123.13000000000001]
29 --- 47 | cost [128.1]
29 --- 84 | cost [72.45]
30 --- 91 | cost [55.79]
30 --- 92 | cost [110.60000000000001]
32 --- 41 | cost [143.78]
32 --- 78 | cost [32.76]
33 --- 92 | cost [26.46]
33 --- 100 | cost [3.43]
36 --- 89 | cost [86.24]
37 --- 44 | cost [35.84]
38 --- 72 | cost [22.05]
39 --- 83 | cost [30.17]
39 --- 98 | cost [26.740000000000002]
41 --- 74 | cost [69.44]
42 --- 54 | cost [46.27]
44 --- 87 | cost [63.84]
45 --- 69 | cost [42.0]
45 --- 95 | cost [174.23]
47 --- 101 | cost [84.21000000000001]
49 --- 87 | cost [101.99000000000001]
51 --- 61 | cost [45.99]
53 --- 91 | cost [163.17000000000002]
55 --- 67 | cost [15.120000000000001]
58 --- 71 | cost [50.68]
58 --- 98 | cost [14.42]
61 --- 93 | cost [56.21]
68 --- 94 | cost [56.07]
68 --- 95 | cost [57.050000000000004]
71 --- 90 | cost [61.53]
72 --- 88 | cost [37.800000000000004]
78 --- 99 | cost [80.01]
79 --- 81 | cost [136.92000000000002]
83 --- 100 | cost [166.95000000000002]

BACKUP STAR
7  --> 82 | cost [10.23]
12 --> 93 | cost [11.49]
15 --> 79 | cost [7.3500000000000005]
16 --> 51 | cost [4.71]
19 --> 92 | cost [3.18]
22 --> 54 | cost [11.94]
24 --> 32 | cost [4.5600000000000005]
27 -->  1 | cost [13.86]
28 --> 38 | cost [3.27]
34 --> 25 | cost [5.3100000000000005]
35 -->  2 | cost [2.2800000000000002]
40 -->  1 | cost [11.370000000000001]
43 -->  5 | cost [5.1000000000000005]
46 --> 18 | cost [9.39]
48 --> 11 | cost [7.08]
50 --> 83 | cost [8.790000000000001]
52 --> 84 | cost [3.54]
56 --> 71 | cost [5.91]
57 --> 36 | cost [1.26]
59 -->  3 | cost [3.9]
60 -->  4 | cost [7.74]
62 --> 83 | cost [1.32]
63 --> 51 | cost [3.66]
65 --> 67 | cost [9.15]
66 --> 51 | cost [11.700000000000001]
70 --> 94 | cost [9.21]
73 --> 41 | cost [12.72]
75 --> 54 | cost [7.08]
76 --> 94 | cost [7.62]
77 --> 68 | cost [13.59]
80 -->  6 | cost [13.38]
86 -->  5 | cost [7.5600000000000005]
96 --> 87 | cost [8.46]
97 --> 45 | cost [5.64]

B = 181.54000000000002
i★ = 1
j★ = 53
k★ = 94

       
——————— Sun, 21 Jan 2024 23:19:10 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 56 hubs —— 1-40-46-61-26-9-78-16-63-44-84-11-52-48-92-99-14-36-57-100-33-74-69-3-73-59-41-30-68-35-23-91-95-86-72-71-38-28-88-98-90-25-17-8-22-75-54-6-47-55-64-79-15-27-85-101-1
total time           3606.93 (TL 3600)    gap                  0.147                
blossom time         0                    nb blossom           0.0                  
LB <= UB             104449.43<=122455.85 Master/SP costs      119624/2831.85       
Master time          3593.38              SP time              13.56                
subtour              36009.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            46.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       26639                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—40—46—61—26—9—78—16—63—44—84—11—52—48—92—99—14—36—57—100—33—74—69—3—73—59—41—30—68—35—23—91—95—86—72—71—38—28—88—98—90—25—17—8—22—75—54—6—47—55—64—79—15—27—85—101

RING
1  --- 40 | cost [2653.0]
3  --- 69 | cost [2905.0]
3  --- 73 | cost [126.0]
6  --- 47 | cost [1960.0]
6  --- 54 | cost [763.0]
8  --- 17 | cost [2156.0]
8  --- 22 | cost [896.0]
9  --- 26 | cost [1547.0]
9  --- 78 | cost [581.0]
11 --- 52 | cost [189.0]
11 --- 84 | cost [665.0]
14 --- 36 | cost [1470.0]
14 --- 99 | cost [1715.0]
15 --- 27 | cost [1750.0]
15 --- 79 | cost [1715.0]
16 --- 63 | cost [847.0]
16 --- 78 | cost [3507.0]
17 --- 25 | cost [714.0]
22 --- 75 | cost [1169.0]
23 --- 35 | cost [2016.0]
23 --- 91 | cost [2450.0]
25 --- 90 | cost [672.0]
26 --- 61 | cost [1197.0]
27 --- 85 | cost [1799.0]
28 --- 38 | cost [763.0]
28 --- 88 | cost [1421.0]
30 --- 41 | cost [2688.0]
30 --- 68 | cost [973.0]
33 --- 74 | cost [1085.0]
33 --- 100 | cost [343.0]
35 --- 68 | cost [1071.0]
36 --- 57 | cost [294.0]
38 --- 71 | cost [602.0]
40 --- 46 | cost [3234.0]
41 --- 59 | cost [1995.0]
44 --- 63 | cost [763.0]
44 --- 84 | cost [2667.0]
46 --- 61 | cost [3129.0]
47 --- 55 | cost [1890.0]
48 --- 52 | cost [1834.0]
48 --- 92 | cost [3822.0]
54 --- 75 | cost [1652.0]
55 --- 64 | cost [1218.0]
57 --- 100 | cost [1008.0]
59 --- 73 | cost [973.0]
64 --- 79 | cost [2044.0]
69 --- 74 | cost [2506.0]
71 --- 72 | cost [1764.0]
72 --- 86 | cost [2737.0]
85 --- 101 | cost [1512.0]
86 --- 95 | cost [2275.0]
88 --- 98 | cost [1274.0]
90 --- 98 | cost [2919.0]
91 --- 95 | cost [1344.0]
92 --- 99 | cost [742.0]

STAR
2  --> 35 | cost [228.0]
4  --> 14 | cost [1152.0]
5  --> 86 | cost [756.0]
7  --> 78 | cost [1080.0]
10 --> 99 | cost [324.0]
12 --> 40 | cost [672.0]
13 --> 79 | cost [390.0]
18 --> 46 | cost [939.0]
19 --> 92 | cost [318.0]
20 --> 64 | cost [75.0]
21 --> 23 | cost [1062.0]
24 --> 61 | cost [966.0]
29 --> 61 | cost [975.0]
31 --> 47 | cost [261.0]
32 --> 61 | cost [717.0]
34 --> 90 | cost [270.0]
37 --> 61 | cost [813.0]
39 --> 28 | cost [285.0]
42 --> 55 | cost [327.0]
43 --> 86 | cost [1131.0]
45 --> 33 | cost [321.0]
49 --> 46 | cost [1005.0]
50 --> 72 | cost [771.0]
51 --> 63 | cost [366.0]
53 --> 85 | cost [705.0]
56 --> 38 | cost [531.0]
58 --> 98 | cost [618.0]
60 --> 14 | cost [1494.0]
62 --> 72 | cost [669.0]
65 --> 47 | cost [1032.0]
66 --> 44 | cost [570.0]
67 --> 47 | cost [501.0]
70 --> 91 | cost [708.0]
76 --> 91 | cost [708.0]
77 --> 30 | cost [1152.0]
80 --> 47 | cost [1476.0]
81 --> 33 | cost [351.0]
82 --> 78 | cost [348.0]
83 --> 72 | cost [570.0]
87 --> 52 | cost [1344.0]
89 --> 41 | cost [639.0]
93 --> 99 | cost [1044.0]
94 --> 95 | cost [369.0]
96 --> 11 | cost [891.0]
97 --> 33 | cost [696.0]

BACKUP RING
1  --- 46 | cost [40.39]
3  --- 59 | cost [9.1]
3  --- 74 | cost [53.410000000000004]
6  --- 55 | cost [37.24]
6  --- 75 | cost [18.76]
8  --- 25 | cost [28.21]
8  --- 75 | cost [18.41]
9  --- 16 | cost [29.89]
9  --- 61 | cost [19.6]
11 --- 44 | cost [32.97]
11 --- 48 | cost [16.52]
14 --- 57 | cost [15.75]
14 --- 92 | cost [22.19]
15 --- 64 | cost [36.19]
15 --- 85 | cost [21.63]
16 --- 44 | cost [15.47]
17 --- 22 | cost [28.98]
17 --- 90 | cost [12.950000000000001]
22 --- 54 | cost [27.86]
23 --- 68 | cost [23.45]
23 --- 95 | cost [36.12]
25 --- 98 | cost [34.86]
26 --- 46 | cost [42.0]
26 --- 78 | cost [14.84]
27 --- 79 | cost [32.62]
27 --- 101 | cost [32.34]
28 --- 71 | cost [13.23]
28 --- 98 | cost [24.78]
30 --- 35 | cost [20.16]
30 --- 59 | cost [46.410000000000004]
33 --- 57 | cost [11.34]
33 --- 69 | cost [34.79]
35 --- 91 | cost [40.81]
36 --- 99 | cost [21.28]
36 --- 100 | cost [11.13]
38 --- 72 | cost [22.05]
38 --- 88 | cost [21.77]
40 --- 61 | cost [63.63]
41 --- 68 | cost [35.7]
41 --- 73 | cost [29.68]
47 --- 54 | cost [27.09]
47 --- 64 | cost [28.21]
48 --- 99 | cost [45.01]
52 --- 84 | cost [8.26]
52 --- 92 | cost [55.79]
55 --- 79 | cost [27.72]
63 --- 78 | cost [42.56]
63 --- 84 | cost [33.39]
69 --- 73 | cost [29.96]
71 --- 86 | cost [24.64]
72 --- 95 | cost [38.22]
74 --- 100 | cost [8.4]
86 --- 91 | cost [36.050000000000004]
88 --- 90 | cost [41.72]

BACKUP STAR
2  --> 68 | cost [6.2700000000000005]
4  --> 99 | cost [14.91]
5  --> 71 | cost [9.48]
7  --> 26 | cost [11.13]
10 --> 92 | cost [2.04]
12 --> 46 | cost [9.75]
13 --> 15 | cost [7.0200000000000005]
18 --> 61 | cost [12.81]
19 --> 99 | cost [3.0]
20 --> 55 | cost [5.76]
21 --> 68 | cost [14.25]
24 --> 46 | cost [9.78]
29 --> 46 | cost [8.040000000000001]
31 --> 55 | cost [9.06]
32 --> 26 | cost [7.68]
34 --> 25 | cost [5.3100000000000005]
37 --> 16 | cost [9.93]
39 --> 38 | cost [3.45]
42 --> 64 | cost [7.05]
43 --> 71 | cost [14.34]
45 --> 100 | cost [4.68]
49 --> 99 | cost [14.91]
50 --> 95 | cost [9.27]
51 --> 16 | cost [4.71]
53 -->  1 | cost [0.96]
56 --> 71 | cost [5.91]
58 --> 88 | cost [10.200000000000001]
60 --> 69 | cost [17.16]
62 --> 54 | cost [13.74]
65 --> 79 | cost [12.24]
66 --> 63 | cost [8.07]
67 --> 55 | cost [6.48]
70 --> 23 | cost [10.11]
76 --> 95 | cost [11.25]
77 --> 68 | cost [13.59]
80 -->  6 | cost [13.38]
81 --> 100 | cost [4.74]
82 -->  9 | cost [5.37]
83 --> 71 | cost [13.14]
87 --> 11 | cost [13.68]
89 --> 59 | cost [10.950000000000001]
93 --> 14 | cost [12.120000000000001]
94 --> 91 | cost [3.87]
96 --> 52 | cost [9.21]
97 --> 100 | cost [7.98]

B = 91.35
i★ = 40
j★ = 46
k★ = 61