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

——————— Thu, 18 Jan 2024 15:33:09 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 80 hubs —— 1—63—6—49—92—8—42—89—31—80—56—97—4—65—66—70—22—16—88—53—79—18—24—38—36—84—10—21—74—59—17—15—11—32—45—91—98—23—62—86—27—12—20—57—7—55—83—34—29—46—43—3—41—71—100—48—52—78—96—39—5—37—33—13—82—40—2—50—68—85—44—73—64—81—25—61—58—28—93—101
total time           3639.02 (TL 3600)    gap                  0.118                
blossom time         0                    nb blossom           0.0                  
LB <= UB             99627.37<=112949.1   subtour              3093.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       641                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—63—6—49—92—8—42—89—31—80—56—97—4—65—66—70—22—16—88—53—79—18—24—38—36—84—10—21—74—59—17—15—11—32—45—91—98—23—62—86—27—12—20—57—7—55—83—34—29—46—43—3—41—71—100—48—52—78—96—39—5—37—33—13—82—40—2—50—68—85—44—73—64—81—25—61—58—28—93—101

RING
1  --- 63 | cost [1440.0]
2  --- 40 | cost [1685.0]
2  --- 50 | cost [2080.0]
3  --- 41 | cost [2255.0]
3  --- 43 | cost [855.0]
4  --- 65 | cost [735.0]
4  --- 97 | cost [1620.0]
5  --- 37 | cost [345.0]
5  --- 39 | cost [2185.0]
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 --- 21 | cost [2100.0]
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 --- 82 | cost [2000.0]
15 --- 17 | cost [65.0]
16 --- 22 | cost [350.0]
16 --- 88 | cost [290.0]
17 --- 59 | cost [1790.0]
18 --- 24 | cost [905.0]
18 --- 79 | cost [1150.0]
20 --- 57 | cost [1020.0]
21 --- 74 | cost [330.0]
22 --- 70 | cost [930.0]
23 --- 62 | cost [2465.0]
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]
31 --- 80 | cost [435.0]
31 --- 89 | cost [940.0]
32 --- 45 | cost [1110.0]
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 --- 82 | cost [4395.0]
41 --- 71 | cost [415.0]
42 --- 89 | cost [900.0]
43 --- 46 | cost [990.0]
44 --- 73 | cost [1165.0]
44 --- 85 | cost [2880.0]
45 --- 91 | cost [895.0]
48 --- 52 | cost [1980.0]
48 --- 100 | cost [1260.0]
49 --- 92 | cost [1760.0]
50 --- 68 | cost [1600.0]
52 --- 78 | cost [200.0]
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]
59 --- 74 | cost [445.0]
62 --- 86 | cost [1540.0]
64 --- 73 | cost [1880.0]
64 --- 81 | cost [2995.0]
65 --- 66 | cost [575.0]
66 --- 70 | cost [2000.0]
68 --- 85 | cost [765.0]
71 --- 100 | cost [605.0]
78 --- 96 | cost [340.0]
91 --- 98 | cost [495.0]
93 --- 101 | cost [2065.0]

STAR
9  -->  7 | cost [250.0]
14 -->  3 | cost [1105.0]
19 --> 53 | cost [1400.0]
26 --> 65 | cost [1415.0]
30 --> 39 | cost [1305.0]
35 --> 86 | cost [705.0]
47 --> 32 | cost [1805.0]
51 --> 61 | cost [930.0]
54 --> 40 | cost [520.0]
60 --> 62 | cost [755.0]
67 --> 28 | cost [1505.0]
69 --> 73 | cost [1465.0]
72 --> 21 | cost [760.0]
75 --> 97 | cost [1185.0]
76 --> 33 | cost [460.0]
77 --> 62 | cost [1105.0]
87 --> 57 | cost [990.0]
90 --> 49 | cost [1040.0]
94 --> 22 | cost [670.0]
95 --> 13 | cost [1080.0]
99 --> 36 | cost [1500.0]

BACKUP RING
1  ---  6 | cost [19.85]
2  --- 68 | cost [35.550000000000004]
2  --- 82 | cost [28.5]
3  --- 46 | cost [6.95]
3  --- 71 | cost [20.05]
4  --- 56 | cost [25.0]
4  --- 66 | cost [10.8]
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 --- 36 | cost [22.05]
10 --- 74 | cost [24.05]
11 --- 17 | cost [5.75]
11 --- 45 | cost [18.5]
12 --- 57 | cost [12.05]
12 --- 86 | cost [9.3]
13 --- 37 | cost [21.650000000000002]
13 --- 40 | cost [63.75]
15 --- 32 | cost [14.0]
15 --- 59 | cost [18.5]
16 --- 53 | cost [12.8]
16 --- 70 | cost [10.75]
17 --- 74 | cost [17.7]
18 --- 38 | cost [13.85]
18 --- 53 | cost [21.650000000000002]
20 --- 27 | cost [9.05]
21 --- 59 | cost [7.55]
21 --- 84 | cost [22.400000000000002]
22 --- 66 | cost [27.45]
22 --- 88 | cost [5.95]
23 --- 86 | cost [39.95]
23 --- 91 | cost [9.6]
24 --- 36 | cost [15.65]
24 --- 79 | cost [19.3]
25 --- 58 | cost [23.900000000000002]
25 --- 64 | cost [32.2]
27 --- 62 | cost [19.400000000000002]
28 --- 61 | cost [31.400000000000002]
28 --- 101 | cost [20.8]
29 --- 43 | cost [16.9]
29 --- 83 | cost [21.8]
31 --- 42 | cost [11.450000000000001]
31 --- 56 | cost [18.35]
32 --- 91 | cost [10.75]
33 --- 82 | cost [24.95]
34 --- 46 | cost [15.55]
34 --- 55 | cost [8.45]
37 --- 39 | cost [22.7]
38 --- 84 | cost [16.95]
39 --- 78 | cost [17.6]
40 --- 50 | cost [26.8]
41 --- 43 | cost [25.75]
41 --- 100 | cost [9.25]
42 --- 92 | cost [22.35]
44 --- 64 | cost [17.5]
44 --- 68 | cost [22.900000000000002]
45 --- 98 | cost [10.700000000000001]
48 --- 71 | cost [17.85]
48 --- 78 | cost [21.1]
49 --- 63 | cost [10.1]
50 --- 85 | cost [21.05]
52 --- 96 | cost [5.3]
52 --- 100 | cost [32.1]
55 --- 57 | cost [17.400000000000002]
58 --- 93 | cost [15.55]
61 --- 81 | cost [10.35]
62 --- 98 | cost [29.5]
65 --- 70 | cost [25.6]
65 --- 97 | cost [23.35]
73 --- 81 | cost [21.650000000000002]
73 --- 85 | cost [20.6]
79 --- 88 | cost [12.950000000000001]
80 --- 89 | cost [12.65]
80 --- 97 | cost [24.85]

BACKUP STAR
9  --> 57 | cost [5.0]
14 --> 71 | cost [13.4]
19 --> 97 | cost [16.3]
26 --> 66 | cost [16.15]
30 --> 96 | cost [15.35]
35 --> 27 | cost [8.9]
47 --> 91 | cost [18.3]
51 --> 25 | cost [12.700000000000001]
54 --> 64 | cost [9.05]
60 --> 23 | cost [17.25]
67 --> 58 | cost [17.25]
69 --> 64 | cost [14.85]
72 --> 74 | cost [10.75]
75 --> 49 | cost [17.45]
76 --> 13 | cost [5.15]
77 --> 23 | cost [19.1]
87 -->  7 | cost [11.9]
90 -->  6 | cost [12.450000000000001]
94 --> 16 | cost [8.05]
95 --> 82 | cost [12.25]
99 --> 38 | cost [15.65]

B = 76.30000000000001
i★ = 23
j★ = 62
k★ = 86

       
——————— Thu, 18 Jan 2024 16:34:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 83 hubs —— 1-63-6-49-92-8-42-89-31-80-56-97-4-65-66-70-22-16-88-53-79-18-24-38-36-84-10-72-59-74-17-15-11-32-45-91-98-23-60-77-62-20-86-27-12-57-7-55-83-34-3-46-29-14-71-41-100-48-30-39-96-5-78-52-37-33-13-82-44-2-40-54-69-73-68-81-25-61-58-93-28-67-101-1
total time           3608.93 (TL 3600)    gap                  0.09                 
blossom time         0                    nb blossom           0.0                  
LB <= UB             98935<=108723.25     Master/SP costs      108410/313.25        
Master time          3595.9               SP time              13.04                
subtour              55023.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            45.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       19683                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—63—6—49—92—8—42—89—31—80—56—97—4—65—66—70—22—16—88—53—79—18—24—38—36—84—10—72—59—74—17—15—11—32—45—91—98—23—60—77—62—20—86—27—12—57—7—55—83—34—3—46—29—14—71—41—100—48—30—39—96—5—78—52—37—33—13—82—44—2—40—54—69—73—68—81—25—61—58—93—28—67—101

RING
1  --- 63 | cost [1440.0]
2  --- 40 | cost [1685.0]
2  --- 44 | cost [1285.0]
3  --- 34 | cost [2240.0]
3  --- 46 | cost [695.0]
4  --- 65 | cost [735.0]
4  --- 97 | cost [1620.0]
5  --- 78 | cost [1210.0]
5  --- 96 | cost [1265.0]
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 --- 27 | cost [680.0]
12 --- 57 | cost [1205.0]
13 --- 33 | cost [505.0]
13 --- 82 | cost [2000.0]
14 --- 29 | cost [1505.0]
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]
20 --- 62 | cost [1580.0]
20 --- 86 | cost [775.0]
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 --- 67 | cost [1505.0]
28 --- 93 | cost [240.0]
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 --- 45 | cost [1110.0]
33 --- 37 | cost [2040.0]
34 --- 83 | cost [730.0]
36 --- 38 | cost [1140.0]
36 --- 84 | cost [1610.0]
37 --- 52 | cost [1630.0]
39 --- 96 | cost [1420.0]
40 --- 54 | cost [520.0]
41 --- 71 | cost [415.0]
41 --- 100 | cost [925.0]
42 --- 89 | cost [900.0]
44 --- 82 | cost [2590.0]
45 --- 91 | cost [895.0]
48 --- 100 | cost [1260.0]
49 --- 92 | cost [1760.0]
52 --- 78 | cost [200.0]
53 --- 79 | cost [1115.0]
53 --- 88 | cost [1150.0]
54 --- 69 | cost [2335.0]
55 --- 83 | cost [115.0]
56 --- 80 | cost [1405.0]
56 --- 97 | cost [1080.0]
58 --- 61 | cost [1625.0]
58 --- 93 | cost [1555.0]
59 --- 72 | cost [1440.0]
59 --- 74 | cost [445.0]
60 --- 77 | cost [955.0]
62 --- 77 | cost [1105.0]
65 --- 66 | cost [575.0]
66 --- 70 | cost [2000.0]
67 --- 101 | cost [2965.0]
68 --- 73 | cost [1335.0]
68 --- 81 | cost [2035.0]
69 --- 73 | cost [1465.0]
91 --- 98 | cost [495.0]

STAR
9  -->  7 | cost [250.0]
19 --> 53 | cost [1400.0]
21 --> 74 | cost [330.0]
26 --> 65 | cost [1415.0]
35 --> 86 | cost [705.0]
43 -->  3 | cost [855.0]
47 --> 91 | cost [1830.0]
50 --> 44 | cost [810.0]
51 --> 61 | cost [930.0]
64 --> 40 | cost [400.0]
75 --> 97 | cost [1185.0]
76 --> 33 | cost [460.0]
85 --> 68 | cost [765.0]
87 --> 57 | cost [990.0]
90 --> 49 | cost [1040.0]
94 --> 22 | cost [670.0]
95 --> 13 | cost [1080.0]
99 --> 36 | cost [1500.0]

BACKUP RING
1  ---  6 | cost [19.85]
2  --- 54 | cost [16.55]
2  --- 82 | cost [28.5]
3  --- 29 | cost [10.700000000000001]
3  --- 83 | cost [27.650000000000002]
4  --- 56 | cost [25.0]
4  --- 66 | cost [10.8]
5  --- 39 | cost [21.85]
5  --- 52 | cost [12.950000000000001]
6  --- 92 | cost [16.45]
7  --- 12 | cost [10.8]
7  --- 83 | cost [13.5]
8  --- 49 | cost [27.650000000000002]
8  --- 89 | cost [20.8]
10 --- 36 | cost [22.05]
10 --- 59 | cost [27.150000000000002]
11 --- 17 | cost [5.75]
11 --- 45 | cost [18.5]
12 --- 86 | cost [9.3]
13 --- 37 | cost [21.650000000000002]
13 --- 44 | cost [44.75]
14 --- 41 | cost [17.2]
14 --- 46 | cost [16.5]
15 --- 32 | cost [14.0]
15 --- 74 | cost [18.25]
16 --- 53 | cost [12.8]
16 --- 70 | cost [10.75]
17 --- 59 | cost [17.900000000000002]
18 --- 38 | cost [13.85]
18 --- 53 | cost [21.650000000000002]
20 --- 27 | cost [9.05]
20 --- 77 | cost [20.1]
22 --- 66 | cost [27.45]
22 --- 88 | cost [5.95]
23 --- 77 | cost [19.1]
23 --- 91 | cost [9.6]
24 --- 36 | cost [15.65]
24 --- 79 | cost [19.3]
25 --- 58 | cost [23.900000000000002]
25 --- 68 | cost [22.25]
27 --- 57 | cost [17.5]
28 --- 58 | cost [15.15]
28 --- 101 | cost [20.8]
29 --- 71 | cost [27.75]
30 --- 96 | cost [15.35]
30 --- 100 | cost [32.2]
31 --- 42 | cost [11.450000000000001]
31 --- 56 | cost [18.35]
32 --- 91 | cost [10.75]
33 --- 52 | cost [36.65]
33 --- 82 | cost [24.95]
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]
40 --- 44 | cost [20.35]
40 --- 69 | cost [18.2]
41 --- 48 | cost [21.650000000000002]
42 --- 92 | cost [22.35]
45 --- 98 | cost [10.700000000000001]
49 --- 63 | cost [10.1]
54 --- 73 | cost [27.25]
55 --- 57 | cost [17.400000000000002]
60 --- 62 | cost [7.55]
60 --- 98 | cost [22.3]
61 --- 81 | cost [10.35]
61 --- 93 | cost [31.7]
62 --- 86 | cost [15.4]
65 --- 70 | cost [25.6]
65 --- 97 | cost [23.35]
67 --- 93 | cost [17.35]
68 --- 69 | cost [23.0]
71 --- 100 | cost [6.05]
72 --- 74 | cost [10.75]
72 --- 84 | cost [15.700000000000001]
73 --- 81 | cost [21.650000000000002]
78 --- 96 | cost [3.4]
79 --- 88 | cost [12.950000000000001]
80 --- 89 | cost [12.65]
80 --- 97 | cost [24.85]

BACKUP STAR
9  --> 57 | cost [5.0]
19 --> 97 | cost [16.3]
21 --> 59 | cost [7.55]
26 --> 66 | cost [16.15]
35 --> 27 | cost [8.9]
43 --> 46 | cost [9.9]
47 --> 32 | cost [18.05]
50 --> 73 | cost [9.0]
51 --> 25 | cost [12.700000000000001]
64 --> 54 | cost [9.05]
75 --> 49 | cost [17.45]
76 --> 13 | cost [5.15]
85 --> 39 | cost [18.6]
87 -->  7 | cost [11.9]
90 -->  6 | cost [12.450000000000001]
94 --> 16 | cost [8.05]
95 --> 82 | cost [12.25]
99 --> 38 | cost [15.65]

B = 44.75
i★ = 13
j★ = 82
k★ = 44