------------------------------------------------------------
                        α=5.0 —— kroA100 —— 100 nodes       
------------------------------------------------------------

——————— Sat, 27 Jan 2024 19:14:58 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 83 hubs —— 1—63—6—49—92—8—42—89—31—80—56—97—75—19—4—65—66—70—22—16—88—53—79—18—24—38—36—84—10—72—21—74—17—15—11—32—91—98—23—60—62—86—27—12—20—57—7—55—83—34—29—46—3—14—71—100—48—30—39—96—78—5—37—33—13—95—82—50—68—73—44—2—54—40—64—69—81—25—61—58—28—93—101
total time           1542.84              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             102005.55<=102005.55 subtour              132.0                
connectivity cuts    86.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     2.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—63—6—49—92—8—42—89—31—80—56—97—75—19—4—65—66—70—22—16—88—53—79—18—24—38—36—84—10—72—21—74—17—15—11—32—91—98—23—60—62—86—27—12—20—57—7—55—83—34—29—46—3—14—71—100—48—30—39—96—78—5—37—33—13—95—82—50—68—73—44—2—54—40—64—69—81—25—61—58—28—93—101

RING
1  --- 63 | cost [1440.0]
1  --- 101 | cost [0.0]
2  --- 44 | cost [1285.0]
2  --- 54 | cost [1655.0]
3  --- 14 | cost [1105.0]
3  --- 46 | cost [695.0]
4  --- 19 | cost [1860.0]
4  --- 65 | cost [735.0]
5  --- 37 | cost [345.0]
5  --- 78 | cost [1210.0]
6  --- 49 | cost [235.0]
6  --- 63 | cost [785.0]
7  --- 55 | cost [1320.0]
7  --- 57 | cost [465.0]
8  --- 42 | cost [1240.0]
8  --- 92 | cost [1030.0]
10 --- 72 | cost [1350.0]
10 --- 84 | cost [700.0]
11 --- 15 | cost [565.0]
11 --- 32 | cost [1010.0]
12 --- 20 | cost [770.0]
12 --- 27 | cost [680.0]
13 --- 33 | cost [505.0]
13 --- 95 | cost [1080.0]
14 --- 71 | cost [1340.0]
15 --- 17 | cost [65.0]
16 --- 22 | cost [350.0]
16 --- 88 | cost [290.0]
17 --- 74 | cost [1770.0]
18 --- 24 | cost [905.0]
18 --- 79 | cost [1150.0]
19 --- 75 | cost [1170.0]
20 --- 57 | cost [1020.0]
21 --- 72 | cost [760.0]
21 --- 74 | cost [330.0]
22 --- 70 | cost [930.0]
23 --- 60 | cost [1725.0]
23 --- 98 | cost [540.0]
24 --- 38 | cost [480.0]
25 --- 61 | cost [825.0]
25 --- 81 | cost [255.0]
27 --- 86 | cost [405.0]
28 --- 58 | cost [1515.0]
28 --- 93 | cost [240.0]
29 --- 34 | cost [1505.0]
29 --- 46 | cost [740.0]
30 --- 39 | cost [1305.0]
30 --- 48 | cost [2135.0]
31 --- 80 | cost [435.0]
31 --- 89 | cost [940.0]
32 --- 91 | cost [1075.0]
33 --- 37 | cost [2040.0]
34 --- 83 | cost [730.0]
36 --- 38 | cost [1140.0]
36 --- 84 | cost [1610.0]
39 --- 96 | cost [1420.0]
40 --- 54 | cost [520.0]
40 --- 64 | cost [400.0]
42 --- 89 | cost [900.0]
44 --- 73 | cost [1165.0]
48 --- 100 | cost [1260.0]
49 --- 92 | cost [1760.0]
50 --- 68 | cost [1600.0]
50 --- 82 | cost [2575.0]
53 --- 79 | cost [1115.0]
53 --- 88 | cost [1150.0]
55 --- 83 | cost [115.0]
56 --- 80 | cost [1405.0]
56 --- 97 | cost [1080.0]
58 --- 61 | cost [1625.0]
60 --- 62 | cost [755.0]
62 --- 86 | cost [1540.0]
64 --- 69 | cost [1485.0]
65 --- 66 | cost [575.0]
66 --- 70 | cost [2000.0]
68 --- 73 | cost [1335.0]
69 --- 81 | cost [1515.0]
71 --- 100 | cost [605.0]
75 --- 97 | cost [1185.0]
78 --- 96 | cost [340.0]
82 --- 95 | cost [1225.0]
91 --- 98 | cost [495.0]
93 --- 101 | cost [2065.0]

STAR
9  -->  7 | cost [250.0]
26 --> 65 | cost [1415.0]
35 --> 86 | cost [705.0]
41 --> 71 | cost [415.0]
43 -->  3 | cost [855.0]
45 --> 91 | cost [895.0]
47 --> 32 | cost [1805.0]
51 --> 61 | cost [930.0]
52 --> 78 | cost [200.0]
59 --> 74 | cost [445.0]
67 --> 28 | cost [1505.0]
76 --> 33 | cost [460.0]
77 --> 60 | cost [955.0]
85 --> 68 | cost [765.0]
87 --> 57 | cost [990.0]
90 --> 49 | cost [1040.0]
94 --> 22 | cost [670.0]
99 --> 36 | cost [1500.0]

BACKUP RING
1  ---  6 | cost [19.85]
2  --- 40 | cost [16.85]
2  --- 73 | cost [23.1]
3  --- 29 | cost [10.700000000000001]
3  --- 71 | cost [20.05]
4  --- 66 | cost [10.8]
4  --- 75 | cost [23.85]
5  --- 33 | cost [23.75]
5  --- 96 | cost [12.65]
6  --- 92 | cost [16.45]
7  --- 20 | cost [12.1]
7  --- 83 | cost [13.5]
8  --- 49 | cost [27.650000000000002]
8  --- 89 | cost [20.8]
10 --- 21 | cost [21.0]
10 --- 36 | cost [22.05]
11 --- 17 | cost [5.75]
11 --- 91 | cost [20.75]
12 --- 57 | cost [12.05]
12 --- 86 | cost [9.3]
13 --- 37 | cost [21.650000000000002]
13 --- 82 | cost [20.0]
14 --- 46 | cost [16.5]
14 --- 100 | cost [13.4]
15 --- 32 | cost [14.0]
15 --- 74 | cost [18.25]
16 --- 53 | cost [12.8]
16 --- 70 | cost [10.75]
17 --- 21 | cost [19.650000000000002]
18 --- 38 | cost [13.85]
18 --- 53 | cost [21.650000000000002]
19 --- 65 | cost [24.85]
19 --- 97 | cost [16.3]
20 --- 27 | cost [9.05]
22 --- 66 | cost [27.45]
22 --- 88 | cost [5.95]
23 --- 62 | cost [24.650000000000002]
23 --- 91 | cost [9.6]
24 --- 36 | cost [15.65]
24 --- 79 | cost [19.3]
25 --- 58 | cost [23.900000000000002]
25 --- 69 | cost [17.35]
27 --- 62 | cost [19.400000000000002]
28 --- 61 | cost [31.400000000000002]
28 --- 101 | cost [20.8]
29 --- 83 | cost [21.8]
30 --- 96 | cost [15.35]
30 --- 100 | cost [32.2]
31 --- 42 | cost [11.450000000000001]
31 --- 56 | cost [18.35]
32 --- 98 | cost [15.6]
33 --- 95 | cost [15.55]
34 --- 46 | cost [15.55]
34 --- 55 | cost [8.45]
37 --- 78 | cost [15.3]
38 --- 84 | cost [16.95]
39 --- 48 | cost [31.75]
39 --- 78 | cost [17.6]
40 --- 69 | cost [18.2]
42 --- 92 | cost [22.35]
44 --- 54 | cost [23.150000000000002]
44 --- 68 | cost [22.900000000000002]
48 --- 71 | cost [17.85]
49 --- 63 | cost [10.1]
50 --- 73 | cost [9.0]
50 --- 95 | cost [37.65]
54 --- 64 | cost [9.05]
55 --- 57 | cost [17.400000000000002]
56 --- 75 | cost [18.5]
58 --- 93 | cost [15.55]
60 --- 86 | cost [22.95]
60 --- 98 | cost [22.3]
61 --- 81 | cost [10.35]
64 --- 81 | cost [29.95]
65 --- 70 | cost [25.6]
68 --- 82 | cost [38.800000000000004]
72 --- 74 | cost [10.75]
72 --- 84 | cost [15.700000000000001]
79 --- 88 | cost [12.950000000000001]
80 --- 89 | cost [12.65]
80 --- 97 | cost [24.85]

BACKUP STAR
9  --> 57 | cost [5.0]
26 --> 66 | cost [16.15]
35 --> 27 | cost [8.9]
41 --> 100 | cost [9.25]
43 --> 46 | cost [9.9]
45 --> 98 | cost [10.700000000000001]
47 --> 91 | cost [18.3]
51 --> 25 | cost [12.700000000000001]
52 --> 96 | cost [5.3]
59 --> 21 | cost [7.55]
67 --> 58 | cost [17.25]
76 --> 13 | cost [5.15]
77 --> 62 | cost [11.05]
85 --> 39 | cost [18.6]
87 -->  7 | cost [11.9]
90 -->  6 | cost [12.450000000000001]
94 --> 16 | cost [8.05]
99 --> 38 | cost [15.65]

B = 39.05
i★ = 11
j★ = 32
k★ = 91

       
——————— Sat, 27 Jan 2024 19:19:16 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 83 hubs —— 1-63-6-49-92-8-42-89-31-80-56-97-75-19-4-65-66-70-22-16-88-53-79-18-24-38-36-84-10-72-21-74-17-15-11-32-91-98-23-60-62-86-27-12-20-57-7-55-83-34-29-46-3-14-71-100-48-30-39-96-78-5-37-33-13-95-82-50-68-73-44-2-54-40-64-69-81-25-61-58-28-93-101-1
total time           194.7                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             102005.55<=102005.55 Master/SP costs      100795/1210.55       
Master time          185.76               SP time              8.94                 
subtour              4646.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            53.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       5367                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—63—6—49—92—8—42—89—31—80—56—97—75—19—4—65—66—70—22—16—88—53—79—18—24—38—36—84—10—72—21—74—17—15—11—32—91—98—23—60—62—86—27—12—20—57—7—55—83—34—29—46—3—14—71—100—48—30—39—96—78—5—37—33—13—95—82—50—68—73—44—2—54—40—64—69—81—25—61—58—28—93—101

RING
1  --- 63 | cost [1440.0]
2  --- 44 | cost [1285.0]
2  --- 54 | cost [1655.0]
3  --- 14 | cost [1105.0]
3  --- 46 | cost [695.0]
4  --- 19 | cost [1860.0]
4  --- 65 | cost [735.0]
5  --- 37 | cost [345.0]
5  --- 78 | cost [1210.0]
6  --- 49 | cost [235.0]
6  --- 63 | cost [785.0]
7  --- 55 | cost [1320.0]
7  --- 57 | cost [465.0]
8  --- 42 | cost [1240.0]
8  --- 92 | cost [1030.0]
10 --- 72 | cost [1350.0]
10 --- 84 | cost [700.0]
11 --- 15 | cost [565.0]
11 --- 32 | cost [1010.0]
12 --- 20 | cost [770.0]
12 --- 27 | cost [680.0]
13 --- 33 | cost [505.0]
13 --- 95 | cost [1080.0]
14 --- 71 | cost [1340.0]
15 --- 17 | cost [65.0]
16 --- 22 | cost [350.0]
16 --- 88 | cost [290.0]
17 --- 74 | cost [1770.0]
18 --- 24 | cost [905.0]
18 --- 79 | cost [1150.0]
19 --- 75 | cost [1170.0]
20 --- 57 | cost [1020.0]
21 --- 72 | cost [760.0]
21 --- 74 | cost [330.0]
22 --- 70 | cost [930.0]
23 --- 60 | cost [1725.0]
23 --- 98 | cost [540.0]
24 --- 38 | cost [480.0]
25 --- 61 | cost [825.0]
25 --- 81 | cost [255.0]
27 --- 86 | cost [405.0]
28 --- 58 | cost [1515.0]
28 --- 93 | cost [240.0]
29 --- 34 | cost [1505.0]
29 --- 46 | cost [740.0]
30 --- 39 | cost [1305.0]
30 --- 48 | cost [2135.0]
31 --- 80 | cost [435.0]
31 --- 89 | cost [940.0]
32 --- 91 | cost [1075.0]
33 --- 37 | cost [2040.0]
34 --- 83 | cost [730.0]
36 --- 38 | cost [1140.0]
36 --- 84 | cost [1610.0]
39 --- 96 | cost [1420.0]
40 --- 54 | cost [520.0]
40 --- 64 | cost [400.0]
42 --- 89 | cost [900.0]
44 --- 73 | cost [1165.0]
48 --- 100 | cost [1260.0]
49 --- 92 | cost [1760.0]
50 --- 68 | cost [1600.0]
50 --- 82 | cost [2575.0]
53 --- 79 | cost [1115.0]
53 --- 88 | cost [1150.0]
55 --- 83 | cost [115.0]
56 --- 80 | cost [1405.0]
56 --- 97 | cost [1080.0]
58 --- 61 | cost [1625.0]
60 --- 62 | cost [755.0]
62 --- 86 | cost [1540.0]
64 --- 69 | cost [1485.0]
65 --- 66 | cost [575.0]
66 --- 70 | cost [2000.0]
68 --- 73 | cost [1335.0]
69 --- 81 | cost [1515.0]
71 --- 100 | cost [605.0]
75 --- 97 | cost [1185.0]
78 --- 96 | cost [340.0]
82 --- 95 | cost [1225.0]
91 --- 98 | cost [495.0]
93 --- 101 | cost [2065.0]

STAR
9  -->  7 | cost [250.0]
26 --> 65 | cost [1415.0]
35 --> 86 | cost [705.0]
41 --> 71 | cost [415.0]
43 -->  3 | cost [855.0]
45 --> 91 | cost [895.0]
47 --> 32 | cost [1805.0]
51 --> 61 | cost [930.0]
52 --> 78 | cost [200.0]
59 --> 74 | cost [445.0]
67 --> 28 | cost [1505.0]
76 --> 33 | cost [460.0]
77 --> 60 | cost [955.0]
85 --> 68 | cost [765.0]
87 --> 57 | cost [990.0]
90 --> 49 | cost [1040.0]
94 --> 22 | cost [670.0]
99 --> 36 | cost [1500.0]

BACKUP RING
1  ---  6 | cost [19.85]
2  --- 40 | cost [16.85]
2  --- 73 | cost [23.1]
3  --- 29 | cost [10.700000000000001]
3  --- 71 | cost [20.05]
4  --- 66 | cost [10.8]
4  --- 75 | cost [23.85]
5  --- 33 | cost [23.75]
5  --- 96 | cost [12.65]
6  --- 92 | cost [16.45]
7  --- 20 | cost [12.1]
7  --- 83 | cost [13.5]
8  --- 49 | cost [27.650000000000002]
8  --- 89 | cost [20.8]
10 --- 21 | cost [21.0]
10 --- 36 | cost [22.05]
11 --- 17 | cost [5.75]
11 --- 91 | cost [20.75]
12 --- 57 | cost [12.05]
12 --- 86 | cost [9.3]
13 --- 37 | cost [21.650000000000002]
13 --- 82 | cost [20.0]
14 --- 46 | cost [16.5]
14 --- 100 | cost [13.4]
15 --- 32 | cost [14.0]
15 --- 74 | cost [18.25]
16 --- 53 | cost [12.8]
16 --- 70 | cost [10.75]
17 --- 21 | cost [19.650000000000002]
18 --- 38 | cost [13.85]
18 --- 53 | cost [21.650000000000002]
19 --- 65 | cost [24.85]
19 --- 97 | cost [16.3]
20 --- 27 | cost [9.05]
22 --- 66 | cost [27.45]
22 --- 88 | cost [5.95]
23 --- 62 | cost [24.650000000000002]
23 --- 91 | cost [9.6]
24 --- 36 | cost [15.65]
24 --- 79 | cost [19.3]
25 --- 58 | cost [23.900000000000002]
25 --- 69 | cost [17.35]
27 --- 62 | cost [19.400000000000002]
28 --- 61 | cost [31.400000000000002]
28 --- 101 | cost [20.8]
29 --- 83 | cost [21.8]
30 --- 96 | cost [15.35]
30 --- 100 | cost [32.2]
31 --- 42 | cost [11.450000000000001]
31 --- 56 | cost [18.35]
32 --- 98 | cost [15.6]
33 --- 95 | cost [15.55]
34 --- 46 | cost [15.55]
34 --- 55 | cost [8.45]
37 --- 78 | cost [15.3]
38 --- 84 | cost [16.95]
39 --- 48 | cost [31.75]
39 --- 78 | cost [17.6]
40 --- 69 | cost [18.2]
42 --- 92 | cost [22.35]
44 --- 54 | cost [23.150000000000002]
44 --- 68 | cost [22.900000000000002]
48 --- 71 | cost [17.85]
49 --- 63 | cost [10.1]
50 --- 73 | cost [9.0]
50 --- 95 | cost [37.65]
54 --- 64 | cost [9.05]
55 --- 57 | cost [17.400000000000002]
56 --- 75 | cost [18.5]
58 --- 93 | cost [15.55]
60 --- 86 | cost [22.95]
60 --- 98 | cost [22.3]
61 --- 81 | cost [10.35]
64 --- 81 | cost [29.95]
65 --- 70 | cost [25.6]
68 --- 82 | cost [38.800000000000004]
72 --- 74 | cost [10.75]
72 --- 84 | cost [15.700000000000001]
79 --- 88 | cost [12.950000000000001]
80 --- 89 | cost [12.65]
80 --- 97 | cost [24.85]

BACKUP STAR
9  --> 57 | cost [5.0]
26 --> 66 | cost [16.15]
35 --> 27 | cost [8.9]
41 --> 100 | cost [9.25]
43 --> 46 | cost [9.9]
45 --> 98 | cost [10.700000000000001]
47 --> 91 | cost [18.3]
51 --> 25 | cost [12.700000000000001]
52 --> 96 | cost [5.3]
59 --> 21 | cost [7.55]
67 --> 58 | cost [17.25]
76 --> 13 | cost [5.15]
77 --> 62 | cost [11.05]
85 --> 39 | cost [18.6]
87 -->  7 | cost [11.9]
90 -->  6 | cost [12.450000000000001]
94 --> 16 | cost [8.05]
99 --> 38 | cost [15.65]

B = 39.05
i★ = 11
j★ = 32
k★ = 91