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

——————— Fri, 26 Jan 2024 08:47:23 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 83 hubs —— 1—13—79—88—24—41—84—15—73—39—71—4—44—60—53—62—37—51—100—2—48—92—55—26—95—56—28—12—47—21—10—9—20—25—18—6—83—40—59—64—77—54—63—16—96—86—65—14—68—33—45—99—31—57—72—76—61—74—7—75—67—36—29—58—22—70—49—98—97—32—94—17—90—89—42—23—8—52—66—38—34—50—101
total time           1442.17              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             101968.86<=101973.3  subtour              233.0                
connectivity cuts    68.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—13—79—88—24—41—84—15—73—39—71—4—44—60—53—62—37—51—100—2—48—92—55—26—95—56—28—12—47—21—10—9—20—25—18—6—83—40—59—64—77—54—63—16—96—86—65—14—68—33—45—99—31—57—72—76—61—74—7—75—67—36—29—58—22—70—49—98—97—32—94—17—90—89—42—23—8—52—66—38—34—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]
7  --- 74 | cost [1325.0]
7  --- 75 | cost [1690.0]
8  --- 23 | cost [1820.0]
8  --- 52 | cost [430.0]
9  --- 10 | cost [1015.0]
9  --- 20 | cost [1375.0]
10 --- 21 | cost [1620.0]
12 --- 28 | cost [905.0]
12 --- 47 | cost [1150.0]
13 --- 79 | cost [375.0]
14 --- 65 | cost [1025.0]
14 --- 68 | cost [105.0]
15 --- 73 | cost [1615.0]
15 --- 84 | cost [1585.0]
16 --- 63 | cost [735.0]
16 --- 96 | cost [1575.0]
17 --- 90 | cost [275.0]
17 --- 94 | cost [925.0]
18 --- 25 | cost [1570.0]
20 --- 25 | cost [175.0]
21 --- 47 | cost [1090.0]
22 --- 58 | cost [2090.0]
22 --- 70 | cost [2610.0]
23 --- 42 | cost [1065.0]
24 --- 41 | cost [1265.0]
24 --- 88 | cost [505.0]
26 --- 55 | cost [915.0]
26 --- 95 | cost [2455.0]
28 --- 56 | cost [1995.0]
29 --- 36 | cost [2075.0]
29 --- 58 | cost [1220.0]
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]
34 --- 50 | cost [1515.0]
36 --- 67 | cost [625.0]
37 --- 51 | cost [500.0]
37 --- 62 | cost [880.0]
38 --- 66 | cost [485.0]
39 --- 71 | cost [1525.0]
39 --- 73 | cost [750.0]
40 --- 59 | cost [790.0]
40 --- 83 | cost [155.0]
41 --- 84 | cost [680.0]
42 --- 89 | cost [2135.0]
44 --- 60 | cost [965.0]
45 --- 99 | cost [1065.0]
48 --- 92 | cost [1605.0]
49 --- 70 | cost [855.0]
49 --- 98 | cost [410.0]
50 --- 101 | cost [465.0]
51 --- 100 | cost [570.0]
52 --- 66 | cost [655.0]
53 --- 60 | cost [995.0]
53 --- 62 | cost [1840.0]
54 --- 63 | cost [665.0]
54 --- 77 | cost [815.0]
55 --- 92 | cost [1975.0]
56 --- 95 | cost [590.0]
57 --- 72 | cost [815.0]
59 --- 64 | cost [1205.0]
61 --- 74 | cost [865.0]
61 --- 76 | cost [2405.0]
64 --- 77 | cost [1305.0]
65 --- 86 | cost [1460.0]
67 --- 75 | cost [240.0]
72 --- 76 | cost [1880.0]
79 --- 88 | cost [635.0]
86 --- 96 | cost [300.0]
89 --- 90 | cost [950.0]
97 --- 98 | cost [1770.0]

STAR
3  --> 83 | cost [475.0]
5  --> 53 | cost [1090.0]
11 --> 90 | cost [960.0]
19 --> 37 | cost [590.0]
27 --> 24 | cost [310.0]
30 --> 100 | cost [650.0]
35 --> 51 | cost [1180.0]
43 --> 77 | cost [730.0]
46 --> 52 | cost [1210.0]
69 --> 15 | cost [1675.0]
78 --> 31 | cost [495.0]
80 --> 76 | cost [675.0]
81 --> 34 | cost [250.0]
82 --> 18 | cost [1830.0]
85 --> 59 | cost [740.0]
87 --> 26 | cost [60.0]
91 --> 54 | cost [70.0]
93 --> 44 | cost [775.0]

BACKUP RING
1  --- 79 | cost [21.900000000000002]
2  --- 51 | cost [9.4]
2  --- 92 | cost [19.400000000000002]
4  --- 39 | cost [24.2]
4  --- 60 | cost [16.85]
6  --- 25 | cost [17.7]
6  --- 40 | cost [2.05]
7  --- 61 | cost [14.05]
7  --- 67 | cost [17.3]
8  --- 42 | cost [28.85]
8  --- 66 | cost [4.4]
9  --- 21 | cost [26.150000000000002]
9  --- 25 | cost [15.5]
10 --- 20 | cost [15.75]
10 --- 47 | cost [23.0]
12 --- 21 | cost [20.5]
12 --- 56 | cost [27.5]
13 --- 88 | cost [6.8]
14 --- 33 | cost [4.8500000000000005]
14 --- 86 | cost [21.8]
15 --- 39 | cost [16.85]
15 --- 41 | cost [20.75]
16 --- 54 | cost [11.950000000000001]
16 --- 86 | cost [18.400000000000002]
17 --- 32 | cost [17.0]
17 --- 89 | cost [12.200000000000001]
18 --- 20 | cost [17.1]
18 --- 83 | cost [13.9]
22 --- 29 | cost [32.9]
22 --- 49 | cost [33.85]
23 --- 52 | cost [22.5]
23 --- 89 | cost [23.400000000000002]
24 --- 79 | cost [11.450000000000001]
24 --- 84 | cost [15.75]
26 --- 56 | cost [28.400000000000002]
26 --- 92 | cost [22.5]
28 --- 47 | cost [12.5]
28 --- 95 | cost [25.85]
29 --- 67 | cost [27.0]
31 --- 45 | cost [13.6]
31 --- 72 | cost [17.1]
32 --- 98 | cost [26.35]
33 --- 99 | cost [17.5]
34 --- 66 | cost [12.450000000000001]
34 --- 101 | cost [18.0]
36 --- 58 | cost [25.8]
36 --- 75 | cost [7.95]
37 --- 53 | cost [26.55]
37 --- 100 | cost [10.450000000000001]
38 --- 50 | cost [22.6]
38 --- 52 | cost [10.55]
40 --- 64 | cost [19.3]
41 --- 88 | cost [14.1]
42 --- 90 | cost [30.05]
44 --- 53 | cost [15.0]
44 --- 71 | cost [16.95]
45 --- 68 | cost [11.15]
48 --- 55 | cost [35.550000000000004]
48 --- 100 | cost [15.200000000000001]
49 --- 97 | cost [21.05]
51 --- 62 | cost [13.25]
54 --- 64 | cost [20.45]
55 --- 95 | cost [31.95]
57 --- 76 | cost [21.650000000000002]
57 --- 99 | cost [12.65]
58 --- 70 | cost [46.2]
59 --- 77 | cost [25.0]
59 --- 83 | cost [9.200000000000001]
60 --- 62 | cost [19.25]
61 --- 72 | cost [31.55]
63 --- 77 | cost [12.05]
63 --- 96 | cost [22.35]
65 --- 68 | cost [10.65]
65 --- 96 | cost [17.6]
70 --- 98 | cost [12.5]
71 --- 73 | cost [21.1]
73 --- 84 | cost [19.75]
74 --- 75 | cost [23.6]
74 --- 76 | cost [32.6]
90 --- 94 | cost [11.700000000000001]
94 --- 97 | cost [15.05]

BACKUP STAR
3  --> 40 | cost [6.05]
5  --> 83 | cost [17.35]
11 --> 89 | cost [10.0]
19 --> 51 | cost [7.1000000000000005]
27 --> 88 | cost [6.5]
30 --> 51 | cost [10.200000000000001]
35 --> 37 | cost [12.85]
43 --> 71 | cost [11.35]
46 -->  8 | cost [14.3]
69 --> 63 | cost [22.05]
78 --> 99 | cost [6.05]
80 --> 31 | cost [15.35]
81 --> 38 | cost [9.450000000000001]
82 --> 25 | cost [19.0]
85 --> 18 | cost [9.4]
87 --> 55 | cost [9.200000000000001]
91 --> 63 | cost [7.3]
93 -->  4 | cost [8.9]

B = 46.9
i★ = 61
j★ = 76
k★ = 72

       
——————— Fri, 26 Jan 2024 08:54:00 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 83 hubs —— 1-13-79-88-24-41-84-15-73-39-71-4-44-60-53-62-37-51-100-2-48-92-55-26-95-56-28-12-47-21-10-9-20-25-18-6-83-40-59-64-77-54-63-16-96-86-65-14-68-33-45-99-31-57-72-76-61-74-7-75-67-36-29-58-22-70-49-98-97-32-94-17-90-89-42-23-8-52-66-38-34-50-101-1
total time           330.15               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             101972.13<=101973.3  Master/SP costs      101645/328.3         
Master time          325.72               SP time              4.43                 
subtour              9544.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            22.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       6928                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—13—79—88—24—41—84—15—73—39—71—4—44—60—53—62—37—51—100—2—48—92—55—26—95—56—28—12—47—21—10—9—20—25—18—6—83—40—59—64—77—54—63—16—96—86—65—14—68—33—45—99—31—57—72—76—61—74—7—75—67—36—29—58—22—70—49—98—97—32—94—17—90—89—42—23—8—52—66—38—34—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]
7  --- 74 | cost [1325.0]
7  --- 75 | cost [1690.0]
8  --- 23 | cost [1820.0]
8  --- 52 | cost [430.0]
9  --- 10 | cost [1015.0]
9  --- 20 | cost [1375.0]
10 --- 21 | cost [1620.0]
12 --- 28 | cost [905.0]
12 --- 47 | cost [1150.0]
13 --- 79 | cost [375.0]
14 --- 65 | cost [1025.0]
14 --- 68 | cost [105.0]
15 --- 73 | cost [1615.0]
15 --- 84 | cost [1585.0]
16 --- 63 | cost [735.0]
16 --- 96 | cost [1575.0]
17 --- 90 | cost [275.0]
17 --- 94 | cost [925.0]
18 --- 25 | cost [1570.0]
20 --- 25 | cost [175.0]
21 --- 47 | cost [1090.0]
22 --- 58 | cost [2090.0]
22 --- 70 | cost [2610.0]
23 --- 42 | cost [1065.0]
24 --- 41 | cost [1265.0]
24 --- 88 | cost [505.0]
26 --- 55 | cost [915.0]
26 --- 95 | cost [2455.0]
28 --- 56 | cost [1995.0]
29 --- 36 | cost [2075.0]
29 --- 58 | cost [1220.0]
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]
34 --- 50 | cost [1515.0]
36 --- 67 | cost [625.0]
37 --- 51 | cost [500.0]
37 --- 62 | cost [880.0]
38 --- 66 | cost [485.0]
39 --- 71 | cost [1525.0]
39 --- 73 | cost [750.0]
40 --- 59 | cost [790.0]
40 --- 83 | cost [155.0]
41 --- 84 | cost [680.0]
42 --- 89 | cost [2135.0]
44 --- 60 | cost [965.0]
45 --- 99 | cost [1065.0]
48 --- 92 | cost [1605.0]
49 --- 70 | cost [855.0]
49 --- 98 | cost [410.0]
50 --- 101 | cost [465.0]
51 --- 100 | cost [570.0]
52 --- 66 | cost [655.0]
53 --- 60 | cost [995.0]
53 --- 62 | cost [1840.0]
54 --- 63 | cost [665.0]
54 --- 77 | cost [815.0]
55 --- 92 | cost [1975.0]
56 --- 95 | cost [590.0]
57 --- 72 | cost [815.0]
59 --- 64 | cost [1205.0]
61 --- 74 | cost [865.0]
61 --- 76 | cost [2405.0]
64 --- 77 | cost [1305.0]
65 --- 86 | cost [1460.0]
67 --- 75 | cost [240.0]
72 --- 76 | cost [1880.0]
79 --- 88 | cost [635.0]
86 --- 96 | cost [300.0]
89 --- 90 | cost [950.0]
97 --- 98 | cost [1770.0]

STAR
3  --> 83 | cost [475.0]
5  --> 53 | cost [1090.0]
11 --> 90 | cost [960.0]
19 --> 37 | cost [590.0]
27 --> 24 | cost [310.0]
30 --> 100 | cost [650.0]
35 --> 51 | cost [1180.0]
43 --> 77 | cost [730.0]
46 --> 52 | cost [1210.0]
69 --> 15 | cost [1675.0]
78 --> 31 | cost [495.0]
80 --> 76 | cost [675.0]
81 --> 34 | cost [250.0]
82 --> 18 | cost [1830.0]
85 --> 59 | cost [740.0]
87 --> 26 | cost [60.0]
91 --> 54 | cost [70.0]
93 --> 44 | cost [775.0]

BACKUP RING
1  --- 79 | cost [21.900000000000002]
2  --- 51 | cost [9.4]
2  --- 92 | cost [19.400000000000002]
4  --- 39 | cost [24.2]
4  --- 60 | cost [16.85]
6  --- 25 | cost [17.7]
6  --- 40 | cost [2.05]
7  --- 61 | cost [14.05]
7  --- 67 | cost [17.3]
8  --- 42 | cost [28.85]
8  --- 66 | cost [4.4]
9  --- 21 | cost [26.150000000000002]
9  --- 25 | cost [15.5]
10 --- 20 | cost [15.75]
10 --- 47 | cost [23.0]
12 --- 21 | cost [20.5]
12 --- 56 | cost [27.5]
13 --- 88 | cost [6.8]
14 --- 33 | cost [4.8500000000000005]
14 --- 86 | cost [21.8]
15 --- 39 | cost [16.85]
15 --- 41 | cost [20.75]
16 --- 54 | cost [11.950000000000001]
16 --- 86 | cost [18.400000000000002]
17 --- 32 | cost [17.0]
17 --- 89 | cost [12.200000000000001]
18 --- 20 | cost [17.1]
18 --- 83 | cost [13.9]
22 --- 29 | cost [32.9]
22 --- 49 | cost [33.85]
23 --- 52 | cost [22.5]
23 --- 89 | cost [23.400000000000002]
24 --- 79 | cost [11.450000000000001]
24 --- 84 | cost [15.75]
26 --- 56 | cost [28.400000000000002]
26 --- 92 | cost [22.5]
28 --- 47 | cost [12.5]
28 --- 95 | cost [25.85]
29 --- 67 | cost [27.0]
31 --- 45 | cost [13.6]
31 --- 72 | cost [17.1]
32 --- 98 | cost [26.35]
33 --- 99 | cost [17.5]
34 --- 66 | cost [12.450000000000001]
34 --- 101 | cost [18.0]
36 --- 58 | cost [25.8]
36 --- 75 | cost [7.95]
37 --- 53 | cost [26.55]
37 --- 100 | cost [10.450000000000001]
38 --- 50 | cost [22.6]
38 --- 52 | cost [10.55]
40 --- 64 | cost [19.3]
41 --- 88 | cost [14.1]
42 --- 90 | cost [30.05]
44 --- 53 | cost [15.0]
44 --- 71 | cost [16.95]
45 --- 68 | cost [11.15]
48 --- 55 | cost [35.550000000000004]
48 --- 100 | cost [15.200000000000001]
49 --- 97 | cost [21.05]
51 --- 62 | cost [13.25]
54 --- 64 | cost [20.45]
55 --- 95 | cost [31.95]
57 --- 76 | cost [21.650000000000002]
57 --- 99 | cost [12.65]
58 --- 70 | cost [46.2]
59 --- 77 | cost [25.0]
59 --- 83 | cost [9.200000000000001]
60 --- 62 | cost [19.25]
61 --- 72 | cost [31.55]
63 --- 77 | cost [12.05]
63 --- 96 | cost [22.35]
65 --- 68 | cost [10.65]
65 --- 96 | cost [17.6]
70 --- 98 | cost [12.5]
71 --- 73 | cost [21.1]
73 --- 84 | cost [19.75]
74 --- 75 | cost [23.6]
74 --- 76 | cost [32.6]
90 --- 94 | cost [11.700000000000001]
94 --- 97 | cost [15.05]

BACKUP STAR
3  --> 40 | cost [6.05]
5  --> 83 | cost [17.35]
11 --> 89 | cost [10.0]
19 --> 51 | cost [7.1000000000000005]
27 --> 88 | cost [6.5]
30 --> 51 | cost [10.200000000000001]
35 --> 37 | cost [12.85]
43 --> 71 | cost [11.35]
46 -->  8 | cost [14.3]
69 --> 63 | cost [22.05]
78 --> 99 | cost [6.05]
80 --> 31 | cost [15.35]
81 --> 38 | cost [9.450000000000001]
82 --> 25 | cost [19.0]
85 --> 18 | cost [9.4]
87 --> 55 | cost [9.200000000000001]
91 --> 63 | cost [7.3]
93 -->  4 | cost [8.9]

B = 46.9
i★ = 61
j★ = 76
k★ = 72