------------------------------------------------------------
                        α=5.0 —— kroC100 —— 100 nodes       
------------------------------------------------------------

——————— Sun, 21 Jan 2024 20:15:32 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 41 hubs —— 1—79—67—31—54—75—22—8—6—2—68—23—70—94—38—34—58—39—77—73—89—59—3—96—11—52—84—48—44—37—26—32—9—51—63—78—61—46—49—40—101
total time           3638.28 (TL 3600)    gap                  0.702                
blossom time         0                    nb blossom           0.0                  
LB <= UB             97404.47<=327282.6   subtour              4012.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1064                 n lazycuts edges     1.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—79—67—31—54—75—22—8—6—2—68—23—70—94—38—34—58—39—77—73—89—59—3—96—11—52—84—48—44—37—26—32—9—51—63—78—61—46—49—40—101

RING
1  --- 79 | cost [3705.0]
2  ---  6 | cost [2760.0]
2  --- 68 | cost [1045.0]
3  --- 59 | cost [650.0]
3  --- 96 | cost [7825.0]
6  ---  8 | cost [2565.0]
8  --- 22 | cost [640.0]
9  --- 32 | cost [2325.0]
9  --- 51 | cost [2435.0]
11 --- 52 | cost [135.0]
11 --- 96 | cost [1485.0]
22 --- 75 | cost [835.0]
23 --- 68 | cost [1675.0]
23 --- 70 | cost [1685.0]
26 --- 32 | cost [1280.0]
26 --- 37 | cost [2045.0]
31 --- 54 | cost [2115.0]
31 --- 67 | cost [650.0]
34 --- 38 | cost [4175.0]
34 --- 58 | cost [1660.0]
37 --- 44 | cost [2560.0]
38 --- 94 | cost [4190.0]
39 --- 58 | cost [2900.0]
39 --- 77 | cost [7350.0]
40 --- 49 | cost [3070.0]
40 --- 101 | cost [1895.0]
44 --- 48 | cost [1575.0]
46 --- 49 | cost [1675.0]
46 --- 61 | cost [2235.0]
48 --- 84 | cost [755.0]
51 --- 63 | cost [610.0]
52 --- 84 | cost [590.0]
54 --- 75 | cost [1180.0]
59 --- 89 | cost [1825.0]
61 --- 78 | cost [1595.0]
63 --- 78 | cost [3040.0]
67 --- 79 | cost [1510.0]
70 --- 94 | cost [1535.0]
73 --- 77 | cost [4870.0]
73 --- 89 | cost [2430.0]

STAR
4  -->  1 | cost [4710.0]
5  --> 38 | cost [1755.0]
7  --> 78 | cost [1800.0]
10 -->  1 | cost [6895.0]
12 -->  1 | cost [2715.0]
13 -->  1 | cost [3720.0]
14 -->  1 | cost [6445.0]
15 -->  1 | cost [2555.0]
16 -->  1 | cost [6855.0]
17 -->  8 | cost [1540.0]
18 --> 49 | cost [535.0]
19 -->  1 | cost [6335.0]
20 -->  1 | cost [4780.0]
21 --> 23 | cost [1770.0]
24 --> 32 | cost [760.0]
25 -->  8 | cost [2015.0]
27 -->  1 | cost [2310.0]
28 --> 38 | cost [545.0]
29 -->  1 | cost [4225.0]
30 --> 89 | cost [1880.0]
33 -->  1 | cost [8245.0]
35 --> 89 | cost [3010.0]
36 --> 89 | cost [6160.0]
41 --> 89 | cost [1065.0]
42 -->  1 | cost [5975.0]
43 -->  8 | cost [6660.0]
45 --> 89 | cost [7050.0]
47 --> 31 | cost [435.0]
50 -->  8 | cost [4445.0]
53 -->  1 | cost [160.0]
55 -->  8 | cost [3230.0]
56 --> 38 | cost [885.0]
57 -->  1 | cost [7565.0]
60 --> 89 | cost [4430.0]
62 -->  8 | cost [3050.0]
64 -->  1 | cost [4805.0]
65 -->  1 | cost [5120.0]
66 --> 44 | cost [950.0]
69 -->  1 | cost [7995.0]
71 --> 38 | cost [430.0]
72 --> 38 | cost [1575.0]
74 -->  1 | cost [7810.0]
76 --> 38 | cost [5460.0]
80 --> 89 | cost [4200.0]
81 -->  1 | cost [8620.0]
82 --> 78 | cost [580.0]
83 -->  8 | cost [2975.0]
85 -->  1 | cost [1080.0]
86 -->  8 | cost [5495.0]
87 --> 96 | cost [1410.0]
88 --> 38 | cost [1555.0]
90 -->  8 | cost [2305.0]
91 --> 38 | cost [4445.0]
92 -->  1 | cost [6810.0]
93 -->  1 | cost [4625.0]
95 --> 38 | cost [3590.0]
97 -->  1 | cost [9165.0]
98 --> 38 | cost [2305.0]
99 -->  1 | cost [6360.0]
100 --> 89 | cost [6305.0]

BACKUP RING
1  --- 67 | cost [52.0]
2  ---  8 | cost [48.6]
2  --- 23 | cost [17.45]
3  --- 11 | cost [88.5]
3  --- 89 | cost [24.150000000000002]
6  --- 22 | cost [21.7]
6  --- 68 | cost [36.0]
8  --- 75 | cost [13.15]
9  --- 26 | cost [11.05]
9  --- 63 | cost [26.900000000000002]
11 --- 84 | cost [4.75]
22 --- 54 | cost [19.900000000000002]
23 --- 94 | cost [23.95]
26 --- 44 | cost [41.15]
31 --- 75 | cost [25.3]
31 --- 79 | cost [20.6]
32 --- 37 | cost [24.650000000000002]
32 --- 51 | cost [44.65]
34 --- 39 | cost [36.85]
34 --- 94 | cost [78.4]
37 --- 48 | cost [39.5]
38 --- 58 | cost [32.35]
38 --- 70 | cost [56.2]
39 --- 73 | cost [107.45]
40 --- 46 | cost [23.1]
44 --- 84 | cost [19.05]
46 --- 78 | cost [38.25]
48 --- 52 | cost [13.1]
49 --- 61 | cost [26.5]
49 --- 101 | cost [43.1]
51 --- 78 | cost [27.35]
52 --- 96 | cost [15.35]
54 --- 67 | cost [27.3]
58 --- 77 | cost [91.45]
59 --- 73 | cost [6.95]
59 --- 96 | cost [82.75]
61 --- 63 | cost [32.95]
68 --- 70 | cost [33.1]
77 --- 89 | cost [34.4]

BACKUP STAR
5  --> 39 | cost [23.05]
7  --> 26 | cost [18.55]
17 --> 34 | cost [13.65]
18 --> 37 | cost [13.0]
21 --> 89 | cost [18.45]
24 --> 61 | cost [16.1]
25 --> 34 | cost [8.85]
28 --> 39 | cost [4.75]
30 --> 68 | cost [6.95]
35 -->  2 | cost [3.8000000000000003]
36 --> 48 | cost [38.45]
41 --> 59 | cost [14.25]
43 --> 38 | cost [25.05]
45 --> 96 | cost [30.650000000000002]
47 --> 67 | cost [8.35]
50 --> 94 | cost [21.1]
55 --> 67 | cost [10.8]
56 --> 39 | cost [14.55]
60 --> 77 | cost [32.2]
62 --> 54 | cost [22.900000000000002]
66 --> 63 | cost [13.450000000000001]
71 --> 39 | cost [7.8]
72 --> 39 | cost [14.1]
76 --> 70 | cost [5.8]
80 --> 77 | cost [9.700000000000001]
82 -->  9 | cost [8.950000000000001]
83 --> 39 | cost [21.55]
86 --> 38 | cost [21.45]
87 --> 52 | cost [22.400000000000002]
88 --> 39 | cost [13.25]
90 --> 34 | cost [4.5]
91 --> 94 | cost [6.45]
95 --> 94 | cost [6.15]
98 --> 58 | cost [10.3]
100 --> 96 | cost [37.6]

B = 184.60000000000002
i★ = 34
j★ = 38
k★ = 94

       
——————— Sun, 21 Jan 2024 21:16:48 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 81 hubs —— 1-85-40-66-93-14-36-57-4-74-73-59-89-21-91-94-5-56-71-38-39-28-88-98-58-34-90-25-17-8-54-80-13-79-15-64-20-55-67-31-47-6-75-22-62-83-72-50-86-95-70-23-2-35-68-30-3-97-81-33-45-61-32-26-78-82-9-44-92-99-10-11-52-84-63-18-29-46-12-53-101-1
total time           3609.46 (TL 3600)    gap                  0.393                
blossom time         0                    nb blossom           0.0                  
LB <= UB             91815<=151313.1      Master/SP costs      148675/2638.1        
Master time          3604.75              SP time              4.71                 
subtour              45091.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            14.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       22212                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—85—40—66—93—14—36—57—4—74—73—59—89—21—91—94—5—56—71—38—39—28—88—98—58—34—90—25—17—8—54—80—13—79—15—64—20—55—67—31—47—6—75—22—62—83—72—50—86—95—70—23—2—35—68—30—3—97—81—33—45—61—32—26—78—82—9—44—92—99—10—11—52—84—63—18—29—46—12—53—101

RING
1  --- 85 | cost [1080.0]
2  --- 23 | cost [1745.0]
2  --- 35 | cost [380.0]
3  --- 30 | cost [3965.0]
3  --- 97 | cost [5280.0]
4  --- 57 | cost [3015.0]
4  --- 74 | cost [3210.0]
5  --- 56 | cost [1095.0]
5  --- 94 | cost [3340.0]
6  --- 47 | cost [1400.0]
6  --- 75 | cost [1340.0]
8  --- 17 | cost [1540.0]
8  --- 54 | cost [2490.0]
9  --- 44 | cost [3225.0]
9  --- 82 | cost [895.0]
10 --- 11 | cost [4055.0]
10 --- 99 | cost [540.0]
11 --- 52 | cost [135.0]
12 --- 46 | cost [1625.0]
12 --- 53 | cost [2610.0]
13 --- 79 | cost [650.0]
13 --- 80 | cost [2810.0]
14 --- 36 | cost [1050.0]
14 --- 93 | cost [2020.0]
15 --- 64 | cost [2585.0]
15 --- 79 | cost [1225.0]
17 --- 25 | cost [510.0]
18 --- 29 | cost [535.0]
18 --- 63 | cost [3065.0]
20 --- 55 | cost [960.0]
20 --- 64 | cost [125.0]
21 --- 89 | cost [1845.0]
21 --- 91 | cost [2950.0]
22 --- 62 | cost [2435.0]
22 --- 75 | cost [835.0]
23 --- 70 | cost [1685.0]
25 --- 90 | cost [480.0]
26 --- 32 | cost [1280.0]
26 --- 78 | cost [1060.0]
28 --- 39 | cost [475.0]
28 --- 88 | cost [1015.0]
29 --- 46 | cost [1340.0]
30 --- 68 | cost [695.0]
31 --- 47 | cost [435.0]
31 --- 67 | cost [650.0]
32 --- 61 | cost [1195.0]
33 --- 45 | cost [535.0]
33 --- 81 | cost [585.0]
34 --- 58 | cost [1660.0]
34 --- 90 | cost [450.0]
35 --- 68 | cost [765.0]
36 --- 57 | cost [210.0]
38 --- 39 | cost [575.0]
38 --- 71 | cost [430.0]
40 --- 66 | cost [5960.0]
40 --- 85 | cost [1530.0]
44 --- 92 | cost [3030.0]
45 --- 61 | cost [6525.0]
50 --- 72 | cost [1285.0]
50 --- 86 | cost [1555.0]
52 --- 84 | cost [590.0]
53 --- 101 | cost [160.0]
54 --- 80 | cost [2485.0]
55 --- 67 | cost [1080.0]
56 --- 71 | cost [985.0]
58 --- 98 | cost [1030.0]
59 --- 73 | cost [695.0]
59 --- 89 | cost [1825.0]
62 --- 83 | cost [220.0]
63 --- 84 | cost [2385.0]
66 --- 93 | cost [3330.0]
70 --- 95 | cost [2065.0]
72 --- 83 | cost [950.0]
73 --- 74 | cost [3870.0]
78 --- 82 | cost [580.0]
81 --- 97 | cost [600.0]
86 --- 95 | cost [1625.0]
88 --- 98 | cost [910.0]
91 --- 94 | cost [645.0]
92 --- 99 | cost [530.0]

STAR
7  --> 82 | cost [1705.0]
16 --> 63 | cost [605.0]
19 --> 99 | cost [500.0]
24 --> 32 | cost [760.0]
27 --> 15 | cost [1250.0]
37 --> 29 | cost [1080.0]
41 --> 89 | cost [1065.0]
42 --> 55 | cost [545.0]
43 -->  5 | cost [850.0]
48 --> 84 | cost [755.0]
49 --> 18 | cost [535.0]
51 --> 63 | cost [610.0]
60 -->  4 | cost [1290.0]
65 --> 80 | cost [1285.0]
69 --> 74 | cost [1790.0]
76 --> 70 | cost [580.0]
77 --> 80 | cost [970.0]
87 --> 52 | cost [2240.0]
96 --> 11 | cost [1485.0]
100 --> 33 | cost [245.0]

BACKUP RING
1  --- 40 | cost [18.95]
2  --- 68 | cost [10.450000000000001]
2  --- 70 | cost [33.95]
3  --- 68 | cost [45.550000000000004]
3  --- 81 | cost [49.15]
4  --- 36 | cost [29.650000000000002]
4  --- 73 | cost [49.65]
5  --- 71 | cost [15.8]
5  --- 91 | cost [38.050000000000004]
6  --- 22 | cost [21.7]
6  --- 31 | cost [15.700000000000001]
8  --- 25 | cost [20.150000000000002]
8  --- 80 | cost [47.85]
9  --- 78 | cost [4.15]
9  --- 92 | cost [52.75]
10 --- 52 | cost [41.9]
10 --- 92 | cost [3.4]
11 --- 84 | cost [4.75]
11 --- 99 | cost [43.550000000000004]
12 --- 29 | cost [24.5]
12 --- 101 | cost [27.150000000000002]
13 --- 15 | cost [11.700000000000001]
13 --- 54 | cost [40.1]
14 --- 57 | cost [11.25]
14 --- 66 | cost [36.25]
15 --- 20 | cost [26.05]
17 --- 54 | cost [40.2]
17 --- 90 | cost [9.25]
18 --- 46 | cost [15.65]
18 --- 84 | cost [49.2]
20 --- 67 | cost [15.25]
21 --- 59 | cost [35.4]
21 --- 94 | cost [34.95]
22 --- 83 | cost [23.8]
23 --- 35 | cost [14.4]
23 --- 95 | cost [25.8]
25 --- 34 | cost [8.85]
26 --- 61 | cost [8.55]
26 --- 82 | cost [15.8]
28 --- 38 | cost [5.45]
28 --- 98 | cost [17.7]
29 --- 63 | cost [31.400000000000002]
30 --- 35 | cost [14.4]
30 --- 97 | cost [85.10000000000001]
31 --- 55 | cost [15.1]
32 --- 45 | cost [74.8]
32 --- 78 | cost [23.400000000000002]
33 --- 61 | cost [68.4]
33 --- 97 | cost [11.6]
34 --- 98 | cost [19.8]
36 --- 93 | cost [29.25]
38 --- 56 | cost [8.85]
39 --- 71 | cost [7.8]
39 --- 88 | cost [13.25]
40 --- 93 | cost [29.45]
44 --- 82 | cost [37.25]
44 --- 99 | cost [33.5]
45 --- 81 | cost [3.95]
46 --- 53 | cost [27.3]
47 --- 67 | cost [8.35]
47 --- 75 | cost [21.75]
50 --- 83 | cost [14.65]
50 --- 95 | cost [15.450000000000001]
52 --- 63 | cost [28.900000000000002]
55 --- 64 | cost [8.700000000000001]
56 --- 94 | cost [41.4]
57 --- 74 | cost [3.1]
58 --- 88 | cost [17.0]
58 --- 90 | cost [19.7]
59 --- 74 | cost [41.45]
62 --- 72 | cost [11.15]
62 --- 75 | cost [23.150000000000002]
64 --- 79 | cost [14.6]
66 --- 85 | cost [74.15]
70 --- 86 | cost [36.85]
72 --- 86 | cost [19.55]
73 --- 89 | cost [24.3]
79 --- 80 | cost [33.2]
89 --- 91 | cost [45.550000000000004]

BACKUP STAR
7  --> 78 | cost [18.0]
16 --> 44 | cost [11.05]
19 --> 92 | cost [5.3]
24 --> 61 | cost [16.1]
27 --> 85 | cost [12.85]
37 --> 18 | cost [13.0]
41 --> 59 | cost [14.25]
42 --> 64 | cost [11.75]
43 --> 56 | cost [16.95]
48 --> 11 | cost [11.8]
49 --> 29 | cost [10.3]
51 --> 44 | cost [10.65]
60 --> 14 | cost [24.900000000000002]
65 --> 31 | cost [12.950000000000001]
69 --> 57 | cost [19.900000000000002]
76 --> 91 | cost [11.8]
77 --> 30 | cost [19.2]
87 --> 11 | cost [22.8]
96 --> 52 | cost [15.35]
100 --> 74 | cost [6.0]

B = 85.10000000000001
i★ = 30
j★ = 3
k★ = 97