------------------------------------------------------------
                        α=5.0 —— kroD100 —— 100 nodes       
------------------------------------------------------------

——————— Fri, 19 Jan 2024 02:18:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 70 hubs —— 1—13—79—88—84—41—73—39—15—63—54—91—77—43—71—4—44—60—53—62—37—51—100—2—48—92—26—55—9—10—95—56—21—47—25—18—6—83—40—59—64—96—14—68—33—45—78—99—31—57—80—76—72—67—61—46—52—8—34—38—23—89—90—49—98—97—32—94—50—101
total time           3643.43 (TL 3600)    gap                  0.157                
blossom time         0                    nb blossom           0.0                  
LB <= UB             98205.77<=116461.8   subtour              3736.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       953                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—13—79—88—84—41—73—39—15—63—54—91—77—43—71—4—44—60—53—62—37—51—100—2—48—92—26—55—9—10—95—56—21—47—25—18—6—83—40—59—64—96—14—68—33—45—78—99—31—57—80—76—72—67—61—46—52—8—34—38—23—89—90—49—98—97—32—94—50—101

RING
1  --- 13 | cost [1825.0]
2  --- 48 | cost [1010.0]
2  --- 100 | cost [510.0]
4  --- 44 | cost [725.0]
4  --- 71 | cost [1010.0]
6  --- 18 | cost [1095.0]
6  --- 83 | cost [300.0]
8  --- 34 | cost [1625.0]
8  --- 52 | cost [430.0]
9  --- 10 | cost [1015.0]
9  --- 55 | cost [1045.0]
10 --- 95 | cost [2240.0]
13 --- 79 | cost [375.0]
14 --- 68 | cost [105.0]
14 --- 96 | cost [2440.0]
15 --- 39 | cost [1685.0]
15 --- 63 | cost [1380.0]
18 --- 25 | cost [1570.0]
21 --- 47 | cost [1090.0]
21 --- 56 | cost [1185.0]
23 --- 38 | cost [1910.0]
23 --- 89 | cost [2340.0]
25 --- 47 | cost [2625.0]
26 --- 55 | cost [915.0]
26 --- 92 | cost [2250.0]
31 --- 57 | cost [1090.0]
31 --- 99 | cost [295.0]
32 --- 94 | cost [895.0]
32 --- 97 | cost [1150.0]
33 --- 45 | cost [825.0]
33 --- 68 | cost [380.0]
34 --- 38 | cost [855.0]
37 --- 51 | cost [500.0]
37 --- 62 | cost [880.0]
39 --- 73 | cost [750.0]
40 --- 59 | cost [790.0]
40 --- 83 | cost [155.0]
41 --- 73 | cost [1925.0]
41 --- 84 | cost [680.0]
43 --- 71 | cost [1135.0]
43 --- 77 | cost [730.0]
44 --- 60 | cost [965.0]
45 --- 78 | cost [1465.0]
46 --- 52 | cost [1210.0]
46 --- 61 | cost [2110.0]
48 --- 92 | cost [1605.0]
49 --- 90 | cost [1685.0]
49 --- 98 | cost [410.0]
50 --- 94 | cost [2210.0]
50 --- 101 | cost [465.0]
51 --- 100 | cost [570.0]
53 --- 60 | cost [995.0]
53 --- 62 | cost [1840.0]
54 --- 63 | cost [665.0]
54 --- 91 | cost [70.0]
56 --- 95 | cost [590.0]
57 --- 80 | cost [1995.0]
59 --- 64 | cost [1205.0]
61 --- 67 | cost [2860.0]
64 --- 96 | cost [2370.0]
67 --- 72 | cost [4375.0]
72 --- 76 | cost [1880.0]
76 --- 80 | cost [675.0]
77 --- 91 | cost [820.0]
78 --- 99 | cost [605.0]
79 --- 88 | cost [635.0]
84 --- 88 | cost [1885.0]
89 --- 90 | cost [950.0]
97 --- 98 | cost [1770.0]

STAR
3  --> 83 | cost [475.0]
5  --> 53 | cost [1090.0]
7  --> 61 | cost [1405.0]
11 --> 90 | cost [960.0]
12 --> 47 | cost [1150.0]
16 --> 63 | cost [735.0]
17 --> 90 | cost [275.0]
19 --> 37 | cost [590.0]
20 --> 25 | cost [175.0]
22 --> 89 | cost [2935.0]
24 --> 88 | cost [505.0]
27 --> 88 | cost [650.0]
28 --> 47 | cost [1250.0]
29 --> 67 | cost [2700.0]
30 --> 100 | cost [650.0]
35 --> 51 | cost [1180.0]
36 --> 67 | cost [625.0]
42 --> 23 | cost [1065.0]
58 --> 67 | cost [3135.0]
65 --> 14 | cost [1025.0]
66 -->  8 | cost [440.0]
69 --> 15 | cost [1675.0]
70 --> 49 | cost [855.0]
74 --> 61 | cost [865.0]
75 --> 67 | cost [240.0]
81 --> 34 | cost [250.0]
82 --> 18 | cost [1830.0]
85 --> 59 | cost [740.0]
86 --> 96 | cost [300.0]
87 --> 26 | cost [60.0]
93 --> 44 | cost [775.0]

BACKUP RING
1  --- 79 | cost [21.900000000000002]
2  --- 51 | cost [9.4]
2  --- 92 | cost [19.400000000000002]
4  --- 43 | cost [12.6]
4  --- 60 | cost [16.85]
6  --- 25 | cost [17.7]
6  --- 40 | cost [2.05]
8  --- 38 | cost [9.25]
8  --- 46 | cost [14.3]
9  --- 26 | cost [15.9]
9  --- 95 | cost [31.45]
10 --- 55 | cost [16.4]
10 --- 56 | cost [22.7]
13 --- 88 | cost [6.8]
14 --- 33 | cost [4.8500000000000005]
14 --- 64 | cost [44.7]
15 --- 54 | cost [15.05]
15 --- 73 | cost [16.15]
18 --- 47 | cost [39.300000000000004]
18 --- 83 | cost [13.9]
21 --- 25 | cost [26.650000000000002]
21 --- 95 | cost [15.85]
23 --- 34 | cost [27.2]
23 --- 90 | cost [29.900000000000002]
26 --- 48 | cost [36.6]
31 --- 78 | cost [4.95]
31 --- 80 | cost [15.35]
32 --- 50 | cost [25.900000000000002]
32 --- 98 | cost [26.35]
33 --- 78 | cost [19.5]
34 --- 52 | cost [15.5]
37 --- 53 | cost [26.55]
37 --- 100 | cost [10.450000000000001]
38 --- 89 | cost [29.400000000000002]
39 --- 41 | cost [26.150000000000002]
39 --- 63 | cost [17.900000000000002]
40 --- 64 | cost [19.3]
41 --- 88 | cost [14.1]
43 --- 91 | cost [12.8]
44 --- 53 | cost [15.0]
44 --- 71 | cost [16.95]
45 --- 68 | cost [11.15]
45 --- 99 | cost [10.65]
46 --- 67 | cost [47.6]
47 --- 56 | cost [21.25]
48 --- 100 | cost [15.200000000000001]
49 --- 89 | cost [16.65]
49 --- 97 | cost [21.05]
51 --- 62 | cost [13.25]
52 --- 61 | cost [29.8]
54 --- 77 | cost [8.15]
55 --- 92 | cost [19.75]
57 --- 76 | cost [21.650000000000002]
57 --- 99 | cost [12.65]
59 --- 83 | cost [9.200000000000001]
59 --- 96 | cost [28.3]
60 --- 62 | cost [19.25]
61 --- 72 | cost [31.55]
63 --- 91 | cost [7.3]
67 --- 76 | cost [47.7]
68 --- 96 | cost [25.3]
71 --- 77 | cost [17.900000000000002]
72 --- 80 | cost [19.85]
73 --- 84 | cost [19.75]
79 --- 84 | cost [23.6]
90 --- 98 | cost [17.55]
94 --- 97 | cost [15.05]
94 --- 101 | cost [25.45]

BACKUP STAR
3  --> 40 | cost [6.05]
5  --> 83 | cost [17.35]
7  --> 67 | cost [17.3]
11 --> 89 | cost [10.0]
12 --> 21 | cost [20.5]
16 --> 54 | cost [11.950000000000001]
17 --> 94 | cost [9.25]
19 --> 51 | cost [7.1000000000000005]
20 -->  9 | cost [13.75]
22 --> 23 | cost [30.5]
24 --> 13 | cost [11.450000000000001]
27 --> 13 | cost [11.6]
28 --> 21 | cost [16.4]
29 --> 23 | cost [46.550000000000004]
30 --> 51 | cost [10.200000000000001]
35 --> 37 | cost [12.85]
36 --> 61 | cost [33.25]
42 --> 89 | cost [21.35]
58 --> 23 | cost [37.050000000000004]
65 --> 68 | cost [10.65]
66 --> 38 | cost [4.8500000000000005]
69 --> 63 | cost [22.05]
70 --> 89 | cost [11.3]
74 --> 67 | cost [22.6]
75 --> 61 | cost [29.0]
81 --> 38 | cost [9.450000000000001]
82 --> 25 | cost [19.0]
85 --> 18 | cost [9.4]
86 --> 14 | cost [21.8]
87 --> 55 | cost [9.200000000000001]
93 -->  4 | cost [8.9]

B = 177.4
i★ = 61
j★ = 67
k★ = 72

       
——————— Fri, 19 Jan 2024 03:20:06 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 75 hubs —— 1-11-89-90-17-94-32-13-79-88-41-39-15-54-91-16-63-77-43-53-44-60-37-100-30-51-19-2-48-92-87-95-56-28-12-47-21-10-9-20-18-83-3-85-59-86-78-57-14-68-33-45-99-31-65-80-46-61-7-75-67-36-58-22-42-23-70-98-49-52-66-34-38-27-101-1
total time           3608.92 (TL 3600)    gap                  0.28                 
blossom time         0                    nb blossom           0.0                  
LB <= UB             95535<=132655.65     Master/SP costs      132145/510.65        
Master time          3605.41              SP time              3.51                 
subtour              36830.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            10.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       22234                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—11—89—90—17—94—32—13—79—88—41—39—15—54—91—16—63—77—43—53—44—60—37—100—30—51—19—2—48—92—87—95—56—28—12—47—21—10—9—20—18—83—3—85—59—86—78—57—14—68—33—45—99—31—65—80—46—61—7—75—67—36—58—22—42—23—70—98—49—52—66—34—38—27—101

RING
1  --- 11 | cost [2950.0]
2  --- 19 | cost [975.0]
2  --- 48 | cost [1010.0]
3  --- 83 | cost [475.0]
3  --- 85 | cost [1860.0]
7  --- 61 | cost [1405.0]
7  --- 75 | cost [1690.0]
9  --- 10 | cost [1015.0]
9  --- 20 | cost [1375.0]
10 --- 21 | cost [1620.0]
11 --- 89 | cost [1000.0]
12 --- 28 | cost [905.0]
12 --- 47 | cost [1150.0]
13 --- 32 | cost [4410.0]
13 --- 79 | cost [375.0]
14 --- 57 | cost [3215.0]
14 --- 68 | cost [105.0]
15 --- 39 | cost [1685.0]
15 --- 54 | cost [1505.0]
16 --- 63 | cost [735.0]
16 --- 91 | cost [1260.0]
17 --- 90 | cost [275.0]
17 --- 94 | cost [925.0]
18 --- 20 | cost [1710.0]
18 --- 83 | cost [1390.0]
19 --- 51 | cost [710.0]
21 --- 47 | cost [1090.0]
22 --- 42 | cost [1985.0]
22 --- 58 | cost [2090.0]
23 --- 42 | cost [1065.0]
23 --- 70 | cost [3205.0]
27 --- 38 | cost [2910.0]
27 --- 101 | cost [1750.0]
28 --- 56 | cost [1995.0]
30 --- 51 | cost [1020.0]
30 --- 100 | cost [650.0]
31 --- 65 | cost [1900.0]
31 --- 99 | cost [295.0]
32 --- 94 | cost [895.0]
33 --- 45 | cost [825.0]
33 --- 68 | cost [380.0]
34 --- 38 | cost [855.0]
34 --- 66 | cost [1245.0]
36 --- 58 | cost [2580.0]
36 --- 67 | cost [625.0]
37 --- 60 | cost [2805.0]
37 --- 100 | cost [1045.0]
39 --- 41 | cost [2615.0]
41 --- 88 | cost [1410.0]
43 --- 53 | cost [3010.0]
43 --- 77 | cost [730.0]
44 --- 53 | cost [1500.0]
44 --- 60 | cost [965.0]
45 --- 99 | cost [1065.0]
46 --- 61 | cost [2110.0]
46 --- 80 | cost [3525.0]
48 --- 92 | cost [1605.0]
49 --- 52 | cost [5510.0]
49 --- 98 | cost [410.0]
52 --- 66 | cost [655.0]
54 --- 91 | cost [70.0]
56 --- 95 | cost [590.0]
57 --- 78 | cost [1520.0]
59 --- 85 | cost [740.0]
59 --- 86 | cost [3065.0]
63 --- 77 | cost [1205.0]
65 --- 80 | cost [2265.0]
67 --- 75 | cost [240.0]
70 --- 98 | cost [1250.0]
78 --- 86 | cost [2755.0]
79 --- 88 | cost [635.0]
87 --- 92 | cost [2200.0]
87 --- 95 | cost [2495.0]
89 --- 90 | cost [950.0]

STAR
4  --> 44 | cost [725.0]
5  --> 53 | cost [1090.0]
6  --> 83 | cost [300.0]
8  --> 52 | cost [430.0]
24 --> 27 | cost [310.0]
25 --> 20 | cost [175.0]
26 --> 87 | cost [60.0]
29 --> 58 | cost [1220.0]
35 --> 51 | cost [1180.0]
40 --> 83 | cost [155.0]
50 -->  1 | cost [465.0]
55 --> 87 | cost [920.0]
62 --> 37 | cost [880.0]
64 --> 77 | cost [1305.0]
69 --> 15 | cost [1675.0]
71 --> 43 | cost [1135.0]
72 --> 57 | cost [815.0]
73 --> 39 | cost [750.0]
74 --> 61 | cost [865.0]
76 --> 80 | cost [675.0]
81 --> 34 | cost [250.0]
82 --> 18 | cost [1830.0]
84 --> 41 | cost [680.0]
93 --> 44 | cost [775.0]
96 --> 86 | cost [300.0]
97 --> 32 | cost [1150.0]

BACKUP RING
1  --- 89 | cost [39.0]
2  --- 51 | cost [9.4]
2  --- 92 | cost [19.400000000000002]
3  --- 18 | cost [18.55]
3  --- 59 | cost [11.6]
7  --- 46 | cost [35.050000000000004]
7  --- 67 | cost [17.3]
9  --- 18 | cost [27.95]
9  --- 21 | cost [26.150000000000002]
10 --- 20 | cost [15.75]
10 --- 47 | cost [23.0]
11 --- 90 | cost [9.6]
12 --- 21 | cost [20.5]
12 --- 56 | cost [27.5]
13 --- 88 | cost [6.8]
13 --- 94 | cost [43.2]
14 --- 33 | cost [4.8500000000000005]
14 --- 78 | cost [20.25]
15 --- 41 | cost [20.75]
15 --- 91 | cost [15.05]
16 --- 54 | cost [11.950000000000001]
16 --- 77 | cost [12.6]
17 --- 32 | cost [17.0]
17 --- 89 | cost [12.200000000000001]
19 --- 30 | cost [16.0]
19 --- 48 | cost [16.0]
20 --- 83 | cost [20.2]
22 --- 23 | cost [30.5]
22 --- 36 | cost [43.75]
23 --- 98 | cost [42.6]
27 --- 34 | cost [21.35]
28 --- 47 | cost [12.5]
28 --- 95 | cost [25.85]
30 --- 37 | cost [15.15]
31 --- 45 | cost [13.6]
31 --- 80 | cost [15.35]
32 --- 79 | cost [47.85]
33 --- 99 | cost [17.5]
34 --- 52 | cost [15.5]
36 --- 75 | cost [7.95]
37 --- 44 | cost [37.6]
38 --- 66 | cost [4.8500000000000005]
38 --- 101 | cost [26.05]
39 --- 54 | cost [12.200000000000001]
39 --- 88 | cost [39.6]
41 --- 79 | cost [17.75]
42 --- 58 | cost [28.7]
42 --- 70 | cost [26.6]
43 --- 44 | cost [19.0]
43 --- 63 | cost [18.6]
45 --- 68 | cost [11.15]
46 --- 65 | cost [54.15]
48 --- 87 | cost [36.050000000000004]
49 --- 66 | cost [48.5]
49 --- 70 | cost [8.55]
51 --- 100 | cost [5.7]
52 --- 98 | cost [57.1]
53 --- 60 | cost [9.950000000000001]
53 --- 77 | cost [35.0]
56 --- 87 | cost [28.8]
57 --- 68 | cost [31.400000000000002]
57 --- 86 | cost [42.75]
58 --- 67 | cost [31.35]
59 --- 78 | cost [57.2]
60 --- 100 | cost [37.9]
61 --- 75 | cost [29.0]
61 --- 80 | cost [30.85]
63 --- 91 | cost [7.3]
65 --- 99 | cost [17.75]
83 --- 85 | cost [15.25]
85 --- 86 | cost [24.0]
90 --- 94 | cost [11.700000000000001]
92 --- 95 | cost [46.4]

BACKUP STAR
4  --> 43 | cost [12.6]
5  -->  3 | cost [13.4]
6  -->  3 | cost [7.8]
8  --> 66 | cost [4.4]
24 --> 88 | cost [5.05]
25 -->  9 | cost [15.5]
26 -->  9 | cost [15.9]
29 --> 36 | cost [20.75]
35 --> 37 | cost [12.85]
40 -->  3 | cost [6.05]
55 -->  9 | cost [10.450000000000001]
62 --> 51 | cost [13.25]
64 --> 59 | cost [12.05]
69 --> 63 | cost [22.05]
71 --> 39 | cost [15.25]
72 --> 31 | cost [17.1]
73 --> 15 | cost [16.15]
74 -->  7 | cost [13.25]
76 --> 78 | cost [18.45]
81 --> 38 | cost [9.450000000000001]
82 --> 20 | cost [20.650000000000002]
84 --> 15 | cost [15.85]
93 --> 60 | cost [13.450000000000001]
96 --> 16 | cost [15.75]
97 --> 94 | cost [15.05]

B = 72.95
i★ = 59
j★ = 86
k★ = 78