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

——————— Sat, 27 Jan 2024 22:05:23 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 84 hubs —— 1—53—40—12—4—93—49—18—29—46—24—32—61—26—78—9—16—63—44—66—48—84—11—96—97—81—45—33—100—74—57—36—10—92—19—99—14—69—3—59—41—89—30—68—35—23—70—76—91—94—95—50—62—83—72—86—5—56—38—28—88—98—58—34—90—25—17—8—22—75—54—6—80—65—31—67—55—64—79—13—15—27—85—101
total time           1191.55              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             100911.05<=100911.05 subtour              122.0                
connectivity cuts    94.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       62                   n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—53—40—12—4—93—49—18—29—46—24—32—61—26—78—9—16—63—44—66—48—84—11—96—97—81—45—33—100—74—57—36—10—92—19—99—14—69—3—59—41—89—30—68—35—23—70—76—91—94—95—50—62—83—72—86—5—56—38—28—88—98—58—34—90—25—17—8—22—75—54—6—80—65—31—67—55—64—79—13—15—27—85—101

RING
1  --- 53 | cost [160.0]
1  --- 101 | cost [0.0]
3  --- 59 | cost [650.0]
3  --- 69 | cost [2075.0]
4  --- 12 | cost [2225.0]
4  --- 93 | cost [1450.0]
5  --- 56 | cost [1095.0]
5  --- 86 | cost [1260.0]
6  --- 54 | cost [545.0]
6  --- 80 | cost [2230.0]
8  --- 17 | cost [1540.0]
8  --- 22 | cost [640.0]
9  --- 16 | cost [2135.0]
9  --- 78 | cost [415.0]
10 --- 36 | cost [1195.0]
10 --- 92 | cost [340.0]
11 --- 84 | cost [475.0]
11 --- 96 | cost [1485.0]
12 --- 40 | cost [1120.0]
13 --- 15 | cost [1170.0]
13 --- 79 | cost [650.0]
14 --- 69 | cost [2295.0]
14 --- 99 | cost [1225.0]
15 --- 27 | cost [1250.0]
16 --- 63 | cost [605.0]
17 --- 25 | cost [510.0]
18 --- 29 | cost [535.0]
18 --- 49 | cost [535.0]
19 --- 92 | cost [530.0]
19 --- 99 | cost [500.0]
22 --- 75 | cost [835.0]
23 --- 35 | cost [1440.0]
23 --- 70 | cost [1685.0]
24 --- 32 | cost [760.0]
24 --- 46 | cost [1630.0]
25 --- 90 | cost [480.0]
26 --- 61 | cost [855.0]
26 --- 78 | cost [1060.0]
27 --- 85 | cost [1285.0]
28 --- 38 | cost [545.0]
28 --- 88 | cost [1015.0]
29 --- 46 | cost [1340.0]
30 --- 68 | cost [695.0]
30 --- 89 | cost [1880.0]
31 --- 65 | cost [1295.0]
31 --- 67 | cost [650.0]
32 --- 61 | cost [1195.0]
33 --- 45 | cost [535.0]
33 --- 100 | cost [245.0]
34 --- 58 | cost [1660.0]
34 --- 90 | cost [450.0]
35 --- 68 | cost [765.0]
36 --- 57 | cost [210.0]
38 --- 56 | cost [885.0]
40 --- 53 | cost [1845.0]
41 --- 59 | cost [1425.0]
41 --- 89 | cost [1065.0]
44 --- 63 | cost [545.0]
44 --- 66 | cost [950.0]
45 --- 81 | cost [395.0]
48 --- 66 | cost [1445.0]
48 --- 84 | cost [755.0]
49 --- 93 | cost [1365.0]
50 --- 62 | cost [1425.0]
50 --- 95 | cost [1545.0]
54 --- 75 | cost [1180.0]
55 --- 64 | cost [870.0]
55 --- 67 | cost [1080.0]
57 --- 74 | cost [310.0]
58 --- 98 | cost [1030.0]
62 --- 83 | cost [220.0]
64 --- 79 | cost [1460.0]
65 --- 80 | cost [1285.0]
70 --- 76 | cost [580.0]
72 --- 83 | cost [950.0]
72 --- 86 | cost [1955.0]
74 --- 100 | cost [600.0]
76 --- 91 | cost [1180.0]
81 --- 97 | cost [600.0]
85 --- 101 | cost [1080.0]
88 --- 98 | cost [910.0]
91 --- 94 | cost [645.0]
94 --- 95 | cost [615.0]
96 --- 97 | cost [2545.0]

STAR
2  --> 35 | cost [380.0]
7  --> 78 | cost [1800.0]
20 --> 64 | cost [125.0]
21 --> 23 | cost [1770.0]
37 --> 29 | cost [1080.0]
39 --> 28 | cost [475.0]
42 --> 55 | cost [545.0]
43 -->  5 | cost [850.0]
47 --> 31 | cost [435.0]
51 --> 63 | cost [610.0]
52 --> 11 | cost [135.0]
60 -->  4 | cost [1290.0]
71 --> 38 | cost [430.0]
73 -->  3 | cost [90.0]
77 --> 80 | cost [970.0]
82 --> 78 | cost [580.0]
87 --> 96 | cost [1410.0]

BACKUP RING
1  --- 40 | cost [18.95]
3  --- 14 | cost [43.15]
3  --- 41 | cost [20.7]
4  --- 40 | cost [28.25]
4  --- 49 | cost [27.400000000000002]
5  --- 38 | cost [17.55]
5  --- 72 | cost [24.95]
6  --- 65 | cost [22.75]
6  --- 75 | cost [13.4]
8  --- 25 | cost [20.150000000000002]
8  --- 75 | cost [13.15]
9  --- 26 | cost [11.05]
9  --- 63 | cost [26.900000000000002]
10 --- 19 | cost [7.9]
10 --- 57 | cost [14.05]
11 --- 48 | cost [11.8]
11 --- 97 | cost [36.75]
12 --- 53 | cost [26.1]
12 --- 93 | cost [19.150000000000002]
13 --- 27 | cost [19.75]
13 --- 64 | cost [20.05]
14 --- 19 | cost [17.25]
15 --- 79 | cost [12.25]
15 --- 85 | cost [15.450000000000001]
16 --- 44 | cost [11.05]
16 --- 78 | cost [25.05]
17 --- 22 | cost [20.7]
17 --- 90 | cost [9.25]
18 --- 46 | cost [15.65]
18 --- 93 | cost [18.95]
22 --- 54 | cost [19.900000000000002]
23 --- 68 | cost [16.75]
23 --- 76 | cost [22.05]
24 --- 29 | cost [21.45]
24 --- 61 | cost [16.1]
25 --- 34 | cost [8.85]
26 --- 32 | cost [12.8]
27 --- 101 | cost [23.1]
28 --- 56 | cost [12.450000000000001]
28 --- 98 | cost [17.7]
29 --- 49 | cost [10.3]
30 --- 35 | cost [14.4]
30 --- 41 | cost [19.2]
31 --- 55 | cost [15.1]
31 --- 80 | cost [21.55]
32 --- 46 | cost [22.1]
33 --- 74 | cost [7.75]
33 --- 81 | cost [5.8500000000000005]
34 --- 98 | cost [19.8]
35 --- 70 | cost [31.150000000000002]
36 --- 74 | cost [5.15]
36 --- 92 | cost [15.3]
38 --- 88 | cost [15.55]
44 --- 48 | cost [15.75]
45 --- 97 | cost [9.4]
45 --- 100 | cost [7.8]
50 --- 83 | cost [14.65]
50 --- 94 | cost [21.1]
54 --- 80 | cost [24.85]
55 --- 79 | cost [19.8]
56 --- 86 | cost [19.75]
57 --- 100 | cost [7.2]
58 --- 88 | cost [17.0]
58 --- 90 | cost [19.7]
59 --- 69 | cost [23.55]
59 --- 89 | cost [18.25]
61 --- 78 | cost [15.950000000000001]
62 --- 72 | cost [11.15]
62 --- 95 | cost [29.3]
63 --- 66 | cost [13.450000000000001]
64 --- 67 | cost [14.0]
65 --- 67 | cost [15.25]
66 --- 84 | cost [20.85]
68 --- 89 | cost [23.0]
69 --- 99 | cost [34.4]
70 --- 91 | cost [11.8]
76 --- 94 | cost [12.700000000000001]
81 --- 96 | cost [29.7]
83 --- 86 | cost [26.95]
84 --- 96 | cost [16.8]
91 --- 95 | cost [9.6]
92 --- 99 | cost [5.3]

BACKUP STAR
2  --> 68 | cost [10.450000000000001]
7  --> 26 | cost [18.55]
20 --> 55 | cost [9.6]
21 --> 89 | cost [18.45]
37 --> 18 | cost [13.0]
39 --> 38 | cost [5.75]
42 --> 64 | cost [11.75]
43 --> 56 | cost [16.95]
47 --> 67 | cost [8.35]
51 --> 16 | cost [7.8500000000000005]
52 --> 84 | cost [5.9]
60 --> 14 | cost [24.900000000000002]
71 --> 28 | cost [9.450000000000001]
73 --> 59 | cost [6.95]
77 --> 30 | cost [19.2]
82 -->  9 | cost [8.950000000000001]
87 --> 11 | cost [22.8]

B = 59.55
i★ = 11
j★ = 96
k★ = 97

       
——————— Sat, 27 Jan 2024 22:14:24 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 82 hubs —— 1-53-40-12-4-93-49-18-29-46-24-32-61-26-78-9-16-63-44-66-48-84-11-96-97-81-45-33-100-74-57-36-10-92-99-14-69-3-59-41-89-30-68-35-23-70-91-94-95-50-62-83-72-86-5-56-38-28-88-98-58-34-90-25-17-8-22-75-54-6-80-65-31-67-55-64-79-13-15-27-85-101-1
total time           475.64               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             100911.05<=100911.05 Master/SP costs      99065/1846.05        
Master time          468.45               SP time              7.19                 
subtour              20960.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            40.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       7125                 
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—53—40—12—4—93—49—18—29—46—24—32—61—26—78—9—16—63—44—66—48—84—11—96—97—81—45—33—100—74—57—36—10—92—99—14—69—3—59—41—89—30—68—35—23—70—91—94—95—50—62—83—72—86—5—56—38—28—88—98—58—34—90—25—17—8—22—75—54—6—80—65—31—67—55—64—79—13—15—27—85—101

RING
1  --- 53 | cost [160.0]
3  --- 59 | cost [650.0]
3  --- 69 | cost [2075.0]
4  --- 12 | cost [2225.0]
4  --- 93 | cost [1450.0]
5  --- 56 | cost [1095.0]
5  --- 86 | cost [1260.0]
6  --- 54 | cost [545.0]
6  --- 80 | cost [2230.0]
8  --- 17 | cost [1540.0]
8  --- 22 | cost [640.0]
9  --- 16 | cost [2135.0]
9  --- 78 | cost [415.0]
10 --- 36 | cost [1195.0]
10 --- 92 | cost [340.0]
11 --- 84 | cost [475.0]
11 --- 96 | cost [1485.0]
12 --- 40 | cost [1120.0]
13 --- 15 | cost [1170.0]
13 --- 79 | cost [650.0]
14 --- 69 | cost [2295.0]
14 --- 99 | cost [1225.0]
15 --- 27 | cost [1250.0]
16 --- 63 | cost [605.0]
17 --- 25 | cost [510.0]
18 --- 29 | cost [535.0]
18 --- 49 | cost [535.0]
22 --- 75 | cost [835.0]
23 --- 35 | cost [1440.0]
23 --- 70 | cost [1685.0]
24 --- 32 | cost [760.0]
24 --- 46 | cost [1630.0]
25 --- 90 | cost [480.0]
26 --- 61 | cost [855.0]
26 --- 78 | cost [1060.0]
27 --- 85 | cost [1285.0]
28 --- 38 | cost [545.0]
28 --- 88 | cost [1015.0]
29 --- 46 | cost [1340.0]
30 --- 68 | cost [695.0]
30 --- 89 | cost [1880.0]
31 --- 65 | cost [1295.0]
31 --- 67 | cost [650.0]
32 --- 61 | cost [1195.0]
33 --- 45 | cost [535.0]
33 --- 100 | cost [245.0]
34 --- 58 | cost [1660.0]
34 --- 90 | cost [450.0]
35 --- 68 | cost [765.0]
36 --- 57 | cost [210.0]
38 --- 56 | cost [885.0]
40 --- 53 | cost [1845.0]
41 --- 59 | cost [1425.0]
41 --- 89 | cost [1065.0]
44 --- 63 | cost [545.0]
44 --- 66 | cost [950.0]
45 --- 81 | cost [395.0]
48 --- 66 | cost [1445.0]
48 --- 84 | cost [755.0]
49 --- 93 | cost [1365.0]
50 --- 62 | cost [1425.0]
50 --- 95 | cost [1545.0]
54 --- 75 | cost [1180.0]
55 --- 64 | cost [870.0]
55 --- 67 | cost [1080.0]
57 --- 74 | cost [310.0]
58 --- 98 | cost [1030.0]
62 --- 83 | cost [220.0]
64 --- 79 | cost [1460.0]
65 --- 80 | cost [1285.0]
70 --- 91 | cost [1180.0]
72 --- 83 | cost [950.0]
72 --- 86 | cost [1955.0]
74 --- 100 | cost [600.0]
81 --- 97 | cost [600.0]
85 --- 101 | cost [1080.0]
88 --- 98 | cost [910.0]
91 --- 94 | cost [645.0]
92 --- 99 | cost [530.0]
94 --- 95 | cost [615.0]
96 --- 97 | cost [2545.0]

STAR
2  --> 35 | cost [380.0]
7  --> 78 | cost [1800.0]
19 --> 99 | cost [500.0]
20 --> 64 | cost [125.0]
21 --> 23 | cost [1770.0]
37 --> 29 | cost [1080.0]
39 --> 28 | cost [475.0]
42 --> 55 | cost [545.0]
43 -->  5 | cost [850.0]
47 --> 31 | cost [435.0]
51 --> 63 | cost [610.0]
52 --> 11 | cost [135.0]
60 -->  4 | cost [1290.0]
71 --> 38 | cost [430.0]
73 -->  3 | cost [90.0]
76 --> 70 | cost [580.0]
77 --> 80 | cost [970.0]
82 --> 78 | cost [580.0]
87 --> 96 | cost [1410.0]

BACKUP RING
1  --- 40 | cost [18.95]
3  --- 14 | cost [43.15]
3  --- 41 | cost [20.7]
4  --- 40 | cost [28.25]
4  --- 49 | cost [27.400000000000002]
5  --- 38 | cost [17.55]
5  --- 72 | cost [24.95]
6  --- 65 | cost [22.75]
6  --- 75 | cost [13.4]
8  --- 25 | cost [20.150000000000002]
8  --- 75 | cost [13.15]
9  --- 26 | cost [11.05]
9  --- 63 | cost [26.900000000000002]
10 --- 57 | cost [14.05]
10 --- 99 | cost [5.4]
11 --- 48 | cost [11.8]
11 --- 97 | cost [36.75]
12 --- 53 | cost [26.1]
12 --- 93 | cost [19.150000000000002]
13 --- 27 | cost [19.75]
13 --- 64 | cost [20.05]
14 --- 92 | cost [15.85]
15 --- 79 | cost [12.25]
15 --- 85 | cost [15.450000000000001]
16 --- 44 | cost [11.05]
16 --- 78 | cost [25.05]
17 --- 22 | cost [20.7]
17 --- 90 | cost [9.25]
18 --- 46 | cost [15.65]
18 --- 93 | cost [18.95]
22 --- 54 | cost [19.900000000000002]
23 --- 68 | cost [16.75]
23 --- 91 | cost [17.5]
24 --- 29 | cost [21.45]
24 --- 61 | cost [16.1]
25 --- 34 | cost [8.85]
26 --- 32 | cost [12.8]
27 --- 101 | cost [23.1]
28 --- 56 | cost [12.450000000000001]
28 --- 98 | cost [17.7]
29 --- 49 | cost [10.3]
30 --- 35 | cost [14.4]
30 --- 41 | cost [19.2]
31 --- 55 | cost [15.1]
31 --- 80 | cost [21.55]
32 --- 46 | cost [22.1]
33 --- 74 | cost [7.75]
33 --- 81 | cost [5.8500000000000005]
34 --- 98 | cost [19.8]
35 --- 70 | cost [31.150000000000002]
36 --- 74 | cost [5.15]
36 --- 92 | cost [15.3]
38 --- 88 | cost [15.55]
44 --- 48 | cost [15.75]
45 --- 97 | cost [9.4]
45 --- 100 | cost [7.8]
50 --- 83 | cost [14.65]
50 --- 94 | cost [21.1]
54 --- 80 | cost [24.85]
55 --- 79 | cost [19.8]
56 --- 86 | cost [19.75]
57 --- 100 | cost [7.2]
58 --- 88 | cost [17.0]
58 --- 90 | cost [19.7]
59 --- 69 | cost [23.55]
59 --- 89 | cost [18.25]
61 --- 78 | cost [15.950000000000001]
62 --- 72 | cost [11.15]
62 --- 95 | cost [29.3]
63 --- 66 | cost [13.450000000000001]
64 --- 67 | cost [14.0]
65 --- 67 | cost [15.25]
66 --- 84 | cost [20.85]
68 --- 89 | cost [23.0]
69 --- 99 | cost [34.4]
70 --- 94 | cost [15.35]
81 --- 96 | cost [29.7]
83 --- 86 | cost [26.95]
84 --- 96 | cost [16.8]
91 --- 95 | cost [9.6]

BACKUP STAR
2  --> 68 | cost [10.450000000000001]
7  --> 26 | cost [18.55]
19 --> 92 | cost [5.3]
20 --> 55 | cost [9.6]
21 --> 89 | cost [18.45]
37 --> 18 | cost [13.0]
39 --> 38 | cost [5.75]
42 --> 64 | cost [11.75]
43 --> 56 | cost [16.95]
47 --> 67 | cost [8.35]
51 --> 16 | cost [7.8500000000000005]
52 --> 84 | cost [5.9]
60 --> 14 | cost [24.900000000000002]
71 --> 28 | cost [9.450000000000001]
73 --> 59 | cost [6.95]
76 --> 91 | cost [11.8]
77 --> 30 | cost [19.2]
82 -->  9 | cost [8.950000000000001]
87 --> 11 | cost [22.8]

B = 59.55
i★ = 11
j★ = 96
k★ = 97