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

——————— Sat, 27 Jan 2024 23:15:29 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 52 hubs —— 1—40—12—49—18—29—61—9—16—63—44—84—11—48—92—10—33—100—74—69—3—73—59—41—30—68—35—23—91—95—50—72—71—38—28—88—98—90—25—17—8—22—75—6—31—67—55—64—79—15—85—101
total time           3633.96 (TL 3600)    gap                  0.027                
blossom time         0                    nb blossom           0.0                  
LB <= UB             113743.93<=116946.57 subtour              89.0                 
connectivity cuts    145.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—40—12—49—18—29—61—9—16—63—44—84—11—48—92—10—33—100—74—69—3—73—59—41—30—68—35—23—91—95—50—72—71—38—28—88—98—90—25—17—8—22—75—6—31—67—55—64—79—15—85—101

RING
1  --- 40 | cost [2653.0]
1  --- 101 | cost [0.0]
3  --- 69 | cost [2905.0]
3  --- 73 | cost [126.0]
6  --- 31 | cost [2198.0]
6  --- 75 | cost [1876.0]
8  --- 17 | cost [2156.0]
8  --- 22 | cost [896.0]
9  --- 16 | cost [2989.0]
9  --- 61 | cost [1960.0]
10 --- 33 | cost [2254.0]
10 --- 92 | cost [476.0]
11 --- 48 | cost [1652.0]
11 --- 84 | cost [665.0]
12 --- 40 | cost [1568.0]
12 --- 49 | cost [2751.0]
15 --- 79 | cost [1715.0]
15 --- 85 | cost [2163.0]
16 --- 63 | cost [847.0]
17 --- 25 | cost [714.0]
18 --- 29 | cost [749.0]
18 --- 49 | cost [749.0]
22 --- 75 | cost [1169.0]
23 --- 35 | cost [2016.0]
23 --- 91 | cost [2450.0]
25 --- 90 | cost [672.0]
28 --- 38 | cost [763.0]
28 --- 88 | cost [1421.0]
29 --- 61 | cost [2275.0]
30 --- 41 | cost [2688.0]
30 --- 68 | cost [973.0]
31 --- 67 | cost [910.0]
33 --- 100 | cost [343.0]
35 --- 68 | cost [1071.0]
38 --- 71 | cost [602.0]
41 --- 59 | cost [1995.0]
44 --- 63 | cost [763.0]
44 --- 84 | cost [2667.0]
48 --- 92 | cost [3822.0]
50 --- 72 | cost [1799.0]
50 --- 95 | cost [2163.0]
55 --- 64 | cost [1218.0]
55 --- 67 | cost [1512.0]
59 --- 73 | cost [973.0]
64 --- 79 | cost [2044.0]
69 --- 74 | cost [2506.0]
71 --- 72 | cost [1764.0]
74 --- 100 | cost [840.0]
85 --- 101 | cost [1512.0]
88 --- 98 | cost [1274.0]
90 --- 98 | cost [2919.0]
91 --- 95 | cost [1344.0]

STAR
2  --> 35 | cost [228.0]
4  --> 12 | cost [1335.0]
5  --> 71 | cost [948.0]
7  -->  9 | cost [1317.0]
13 --> 79 | cost [390.0]
14 --> 10 | cost [789.0]
19 --> 92 | cost [318.0]
20 --> 64 | cost [75.0]
21 --> 23 | cost [1062.0]
24 --> 61 | cost [966.0]
26 --> 61 | cost [513.0]
27 --> 15 | cost [750.0]
32 --> 61 | cost [717.0]
34 --> 90 | cost [270.0]
36 --> 74 | cost [309.0]
37 --> 29 | cost [648.0]
39 --> 28 | cost [285.0]
42 --> 55 | cost [327.0]
43 --> 71 | cost [1434.0]
45 --> 33 | cost [321.0]
46 --> 29 | cost [804.0]
47 --> 31 | cost [261.0]
51 --> 63 | cost [366.0]
52 --> 11 | cost [81.0]
53 -->  1 | cost [96.0]
54 -->  6 | cost [327.0]
56 --> 38 | cost [531.0]
57 --> 74 | cost [186.0]
58 --> 98 | cost [618.0]
60 --> 69 | cost [1716.0]
62 --> 72 | cost [669.0]
65 --> 31 | cost [777.0]
66 --> 44 | cost [570.0]
70 --> 91 | cost [708.0]
76 --> 91 | cost [708.0]
77 --> 30 | cost [1152.0]
78 -->  9 | cost [249.0]
80 --> 31 | cost [1293.0]
81 --> 33 | cost [351.0]
82 -->  9 | cost [537.0]
83 --> 72 | cost [570.0]
86 --> 50 | cost [933.0]
87 --> 84 | cost [1605.0]
89 --> 41 | cost [639.0]
93 --> 49 | cost [819.0]
94 --> 95 | cost [369.0]
96 --> 48 | cost [1095.0]
97 --> 33 | cost [696.0]
99 --> 92 | cost [318.0]

BACKUP RING
1  --- 12 | cost [38.01]
3  --- 59 | cost [9.1]
3  --- 74 | cost [53.410000000000004]
6  --- 22 | cost [30.38]
6  --- 67 | cost [30.59]
8  --- 25 | cost [28.21]
8  --- 75 | cost [18.41]
9  --- 29 | cost [37.24]
9  --- 63 | cost [37.660000000000004]
10 --- 48 | cost [41.58]
10 --- 100 | cost [24.5]
11 --- 44 | cost [32.97]
11 --- 92 | cost [53.9]
12 --- 18 | cost [32.06]
15 --- 64 | cost [36.19]
15 --- 101 | cost [35.77]
16 --- 44 | cost [15.47]
16 --- 61 | cost [37.59]
17 --- 22 | cost [28.98]
17 --- 90 | cost [12.950000000000001]
18 --- 61 | cost [29.89]
23 --- 68 | cost [23.45]
23 --- 95 | cost [36.12]
25 --- 98 | cost [34.86]
28 --- 71 | cost [13.23]
28 --- 98 | cost [24.78]
29 --- 49 | cost [14.42]
30 --- 35 | cost [20.16]
30 --- 59 | cost [46.410000000000004]
31 --- 55 | cost [21.14]
31 --- 75 | cost [35.42]
33 --- 74 | cost [10.85]
33 --- 92 | cost [26.46]
35 --- 91 | cost [40.81]
38 --- 72 | cost [22.05]
38 --- 88 | cost [21.77]
40 --- 49 | cost [42.980000000000004]
41 --- 68 | cost [35.7]
41 --- 73 | cost [29.68]
48 --- 84 | cost [10.57]
50 --- 71 | cost [29.96]
50 --- 91 | cost [29.400000000000002]
55 --- 79 | cost [27.72]
63 --- 84 | cost [33.39]
64 --- 67 | cost [19.6]
69 --- 73 | cost [29.96]
69 --- 100 | cost [31.5]
72 --- 95 | cost [38.22]
79 --- 85 | cost [38.5]
88 --- 90 | cost [41.72]

BACKUP STAR
2  --> 68 | cost [6.2700000000000005]
4  --> 49 | cost [16.44]
5  --> 38 | cost [10.53]
7  --> 61 | cost [16.26]
13 --> 15 | cost [7.0200000000000005]
14 --> 74 | cost [8.22]
19 --> 10 | cost [4.74]
20 --> 55 | cost [5.76]
21 --> 68 | cost [14.25]
24 --> 29 | cost [12.870000000000001]
26 -->  9 | cost [6.63]
27 --> 85 | cost [7.71]
32 --> 29 | cost [13.89]
34 --> 25 | cost [5.3100000000000005]
36 --> 100 | cost [4.7700000000000005]
37 --> 18 | cost [7.8]
39 --> 38 | cost [3.45]
42 --> 64 | cost [7.05]
43 --> 38 | cost [15.030000000000001]
45 --> 100 | cost [4.68]
46 --> 18 | cost [9.39]
47 --> 67 | cost [5.01]
51 --> 16 | cost [4.71]
52 --> 84 | cost [3.54]
54 --> 75 | cost [7.08]
56 --> 71 | cost [5.91]
57 --> 100 | cost [4.32]
58 --> 88 | cost [10.200000000000001]
60 --> 12 | cost [19.2]
62 --> 50 | cost [8.55]
65 --> 67 | cost [9.15]
66 --> 63 | cost [8.07]
70 --> 23 | cost [10.11]
76 --> 95 | cost [11.25]
77 --> 68 | cost [13.59]
78 --> 61 | cost [9.57]
80 -->  6 | cost [13.38]
81 --> 100 | cost [4.74]
82 --> 61 | cost [13.05]
83 --> 50 | cost [8.790000000000001]
86 --> 95 | cost [9.75]
87 --> 11 | cost [13.68]
89 --> 59 | cost [10.950000000000001]
93 --> 18 | cost [11.370000000000001]
94 --> 91 | cost [3.87]
96 --> 11 | cost [8.91]
97 --> 100 | cost [7.98]
99 --> 10 | cost [3.24]

B = 76.47000000000001
i★ = 16
j★ = 9
k★ = 61

       
——————— Sat, 27 Jan 2024 23:21:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 52 hubs —— 1-85-15-79-64-55-67-31-6-75-22-8-17-25-90-98-88-28-38-71-72-50-95-91-23-35-68-30-41-59-3-69-74-100-33-45-10-92-48-84-44-63-16-9-26-61-29-18-49-12-40-101-1
total time           295.65               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             115850.91<=115850.91 Master/SP costs      113600/2250.91       
Master time          271.39               SP time              24.25                
subtour              772.0                connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            138.0                SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       16371                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—85—15—79—64—55—67—31—6—75—22—8—17—25—90—98—88—28—38—71—72—50—95—91—23—35—68—30—41—59—3—69—74—100—33—45—10—92—48—84—44—63—16—9—26—61—29—18—49—12—40—101

RING
1  --- 85 | cost [1512.0]
1  --- 101 | cost [0.0]
3  --- 59 | cost [910.0]
3  --- 69 | cost [2905.0]
6  --- 31 | cost [2198.0]
6  --- 75 | cost [1876.0]
8  --- 17 | cost [2156.0]
8  --- 22 | cost [896.0]
9  --- 16 | cost [2989.0]
9  --- 26 | cost [1547.0]
10 --- 45 | cost [1953.0]
10 --- 92 | cost [476.0]
12 --- 40 | cost [1568.0]
12 --- 49 | cost [2751.0]
15 --- 79 | cost [1715.0]
15 --- 85 | cost [2163.0]
16 --- 63 | cost [847.0]
17 --- 25 | cost [714.0]
18 --- 29 | cost [749.0]
18 --- 49 | cost [749.0]
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]
28 --- 38 | cost [763.0]
28 --- 88 | cost [1421.0]
29 --- 61 | cost [2275.0]
30 --- 41 | cost [2688.0]
30 --- 68 | cost [973.0]
31 --- 67 | cost [910.0]
33 --- 45 | cost [749.0]
33 --- 100 | cost [343.0]
35 --- 68 | cost [1071.0]
38 --- 71 | cost [602.0]
40 --- 101 | cost [2653.0]
41 --- 59 | cost [1995.0]
44 --- 63 | cost [763.0]
44 --- 84 | cost [2667.0]
48 --- 84 | cost [1057.0]
48 --- 92 | cost [3822.0]
50 --- 72 | cost [1799.0]
50 --- 95 | cost [2163.0]
55 --- 64 | cost [1218.0]
55 --- 67 | cost [1512.0]
64 --- 79 | cost [2044.0]
69 --- 74 | cost [2506.0]
71 --- 72 | cost [1764.0]
74 --- 100 | cost [840.0]
88 --- 98 | cost [1274.0]
90 --- 98 | cost [2919.0]
91 --- 95 | cost [1344.0]

STAR
2  --> 35 | cost [228.0]
4  --> 12 | cost [1335.0]
5  --> 71 | cost [948.0]
7  --> 26 | cost [1113.0]
11 --> 84 | cost [285.0]
13 --> 79 | cost [390.0]
14 --> 10 | cost [789.0]
19 --> 92 | cost [318.0]
20 --> 64 | cost [75.0]
21 --> 23 | cost [1062.0]
24 --> 61 | cost [966.0]
27 --> 15 | cost [750.0]
32 --> 61 | cost [717.0]
34 --> 90 | cost [270.0]
36 --> 74 | cost [309.0]
37 --> 29 | cost [648.0]
39 --> 28 | cost [285.0]
42 --> 55 | cost [327.0]
43 --> 71 | cost [1434.0]
46 --> 29 | cost [804.0]
47 --> 31 | cost [261.0]
51 --> 63 | cost [366.0]
52 --> 84 | cost [354.0]
53 -->  1 | cost [96.0]
54 -->  6 | cost [327.0]
56 --> 38 | cost [531.0]
57 --> 74 | cost [186.0]
58 --> 98 | cost [618.0]
60 --> 69 | cost [1716.0]
62 --> 72 | cost [669.0]
65 --> 31 | cost [777.0]
66 --> 44 | cost [570.0]
70 --> 91 | cost [708.0]
73 -->  3 | cost [54.0]
76 --> 91 | cost [708.0]
77 --> 30 | cost [1152.0]
78 -->  9 | cost [249.0]
80 --> 31 | cost [1293.0]
81 --> 45 | cost [237.0]
82 -->  9 | cost [537.0]
83 --> 72 | cost [570.0]
86 --> 50 | cost [933.0]
87 --> 84 | cost [1605.0]
89 --> 41 | cost [639.0]
93 --> 49 | cost [819.0]
94 --> 95 | cost [369.0]
96 --> 84 | cost [1008.0]
97 --> 45 | cost [564.0]
99 --> 92 | cost [318.0]

BACKUP RING
1  --- 15 | cost [35.77]
3  --- 41 | cost [28.98]
3  --- 74 | cost [53.410000000000004]
6  --- 22 | cost [30.38]
6  --- 67 | cost [30.59]
8  --- 25 | cost [28.21]
8  --- 75 | cost [18.41]
9  --- 61 | cost [19.6]
9  --- 63 | cost [37.660000000000004]
10 --- 33 | cost [22.54]
10 --- 48 | cost [41.58]
12 --- 18 | cost [32.06]
12 --- 101 | cost [38.01]
15 --- 64 | cost [36.19]
16 --- 26 | cost [42.21]
16 --- 44 | cost [15.47]
17 --- 22 | cost [28.98]
17 --- 90 | cost [12.950000000000001]
18 --- 61 | cost [29.89]
23 --- 68 | cost [23.45]
23 --- 95 | cost [36.12]
25 --- 98 | cost [34.86]
26 --- 29 | cost [34.72]
28 --- 71 | cost [13.23]
28 --- 98 | cost [24.78]
29 --- 49 | cost [14.42]
30 --- 35 | cost [20.16]
30 --- 59 | cost [46.410000000000004]
31 --- 55 | cost [21.14]
31 --- 75 | cost [35.42]
33 --- 74 | cost [10.85]
35 --- 91 | cost [40.81]
38 --- 72 | cost [22.05]
38 --- 88 | cost [21.77]
40 --- 49 | cost [42.980000000000004]
41 --- 68 | cost [35.7]
44 --- 48 | cost [22.05]
45 --- 92 | cost [22.47]
45 --- 100 | cost [10.92]
50 --- 71 | cost [29.96]
50 --- 91 | cost [29.400000000000002]
55 --- 79 | cost [27.72]
59 --- 69 | cost [32.97]
63 --- 84 | cost [33.39]
64 --- 67 | cost [19.6]
69 --- 100 | cost [31.5]
72 --- 95 | cost [38.22]
79 --- 85 | cost [38.5]
84 --- 92 | cost [48.65]
88 --- 90 | cost [41.72]

BACKUP STAR
2  --> 68 | cost [6.2700000000000005]
4  --> 49 | cost [16.44]
5  --> 38 | cost [10.53]
7  -->  9 | cost [13.17]
11 --> 48 | cost [7.08]
13 --> 15 | cost [7.0200000000000005]
14 --> 74 | cost [8.22]
19 --> 10 | cost [4.74]
20 --> 55 | cost [5.76]
21 --> 68 | cost [14.25]
24 --> 26 | cost [11.82]
27 --> 85 | cost [7.71]
32 --> 26 | cost [7.68]
34 --> 25 | cost [5.3100000000000005]
36 --> 100 | cost [4.7700000000000005]
37 --> 18 | cost [7.8]
39 --> 38 | cost [3.45]
42 --> 64 | cost [7.05]
43 --> 38 | cost [15.030000000000001]
46 --> 18 | cost [9.39]
47 --> 67 | cost [5.01]
51 --> 16 | cost [4.71]
52 --> 48 | cost [7.86]
54 --> 75 | cost [7.08]
56 --> 71 | cost [5.91]
57 --> 100 | cost [4.32]
58 --> 88 | cost [10.200000000000001]
60 --> 12 | cost [19.2]
62 --> 50 | cost [8.55]
65 --> 67 | cost [9.15]
66 --> 63 | cost [8.07]
70 --> 23 | cost [10.11]
73 --> 59 | cost [4.17]
76 --> 95 | cost [11.25]
77 --> 68 | cost [13.59]
78 --> 26 | cost [6.36]
80 -->  6 | cost [13.38]
81 --> 33 | cost [3.5100000000000002]
82 --> 26 | cost [9.48]
83 --> 50 | cost [8.790000000000001]
86 --> 95 | cost [9.75]
87 --> 48 | cost [18.48]
89 --> 59 | cost [10.950000000000001]
93 --> 18 | cost [11.370000000000001]
94 --> 91 | cost [3.87]
96 --> 48 | cost [10.950000000000001]
97 --> 33 | cost [6.96]
99 --> 10 | cost [3.24]

B = 72.61
i★ = 3
j★ = 69
k★ = 74