------------------------------------------------------------
                        α=5.0 —— kroB100 —— 100 nodes       
------------------------------------------------------------

——————— Mon, 08 Jan 2024 08:45:44 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 78 hubs —— 1—90—21—10—68—86—49—30—80—20—38—46—25—9—27—61—94—57—7—84—58—52—43—89—60—87—4—6—15—33—64—82—48—31—63—13—78—17—45—36—92—96—18—24—77—50—55—22—88—37—65—79—81—56—100—26—62—5—67—40—39—70—53—73—85—93—11—3—28—91—97—99—76—59—32—98—12—101
total time           67.03                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             104540.08<=104550    subtour              1600.0               
connectivity cuts    1564.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1550                 n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—90—21—10—68—86—49—30—80—20—38—46—25—9—27—61—94—57—7—84—58—52—43—89—60—87—4—6—15—33—64—82—48—31—63—13—78—17—45—36—92—96—18—24—77—50—55—22—88—37—65—79—81—56—100—26—62—5—67—40—39—70—53—73—85—93—11—3—28—91—97—99—76—59—32—98—12—101

RING
1  --- 90 | cost [745.0]
3  --- 11 | cost [950.0]
3  --- 28 | cost [1720.0]
4  ---  6 | cost [1120.0]
4  --- 87 | cost [2100.0]
5  --- 62 | cost [1530.0]
5  --- 67 | cost [1145.0]
6  --- 15 | cost [1290.0]
7  --- 57 | cost [1330.0]
7  --- 84 | cost [155.0]
9  --- 25 | cost [150.0]
9  --- 27 | cost [1470.0]
10 --- 21 | cost [1945.0]
10 --- 68 | cost [645.0]
11 --- 93 | cost [270.0]
12 --- 98 | cost [935.0]
12 --- 101 | cost [1315.0]
13 --- 63 | cost [1325.0]
13 --- 78 | cost [850.0]
15 --- 33 | cost [930.0]
17 --- 45 | cost [720.0]
17 --- 78 | cost [1280.0]
18 --- 24 | cost [765.0]
18 --- 96 | cost [1625.0]
20 --- 38 | cost [425.0]
20 --- 80 | cost [210.0]
21 --- 90 | cost [765.0]
22 --- 55 | cost [1830.0]
22 --- 88 | cost [565.0]
24 --- 77 | cost [960.0]
25 --- 46 | cost [310.0]
26 --- 62 | cost [905.0]
26 --- 100 | cost [440.0]
27 --- 61 | cost [1205.0]
28 --- 91 | cost [320.0]
30 --- 49 | cost [1260.0]
30 --- 80 | cost [880.0]
31 --- 48 | cost [625.0]
31 --- 63 | cost [830.0]
32 --- 59 | cost [780.0]
32 --- 98 | cost [1190.0]
33 --- 64 | cost [1420.0]
36 --- 45 | cost [385.0]
36 --- 92 | cost [1140.0]
37 --- 65 | cost [1715.0]
37 --- 88 | cost [3815.0]
38 --- 46 | cost [2325.0]
39 --- 40 | cost [800.0]
39 --- 70 | cost [545.0]
40 --- 67 | cost [1640.0]
43 --- 52 | cost [1595.0]
43 --- 89 | cost [1050.0]
48 --- 82 | cost [2025.0]
49 --- 86 | cost [130.0]
50 --- 55 | cost [1835.0]
50 --- 77 | cost [1890.0]
52 --- 58 | cost [1230.0]
53 --- 70 | cost [1150.0]
53 --- 73 | cost [1735.0]
56 --- 81 | cost [1985.0]
56 --- 100 | cost [320.0]
57 --- 94 | cost [790.0]
58 --- 84 | cost [270.0]
59 --- 76 | cost [700.0]
60 --- 87 | cost [1165.0]
60 --- 89 | cost [1765.0]
61 --- 94 | cost [1370.0]
64 --- 82 | cost [1125.0]
65 --- 79 | cost [960.0]
68 --- 86 | cost [1435.0]
73 --- 85 | cost [440.0]
76 --- 99 | cost [615.0]
79 --- 81 | cost [880.0]
85 --- 93 | cost [1400.0]
91 --- 97 | cost [1000.0]
92 --- 96 | cost [690.0]
97 --- 99 | cost [610.0]

STAR
2  --> 13 | cost [920.0]
8  --> 99 | cost [210.0]
14 --> 64 | cost [605.0]
16 --> 77 | cost [1300.0]
19 --> 92 | cost [370.0]
23 --> 22 | cost [235.0]
29 --> 99 | cost [645.0]
34 --> 57 | cost [1210.0]
35 --> 61 | cost [530.0]
41 --> 17 | cost [810.0]
42 --> 64 | cost [1270.0]
44 --> 92 | cost [1665.0]
47 --> 79 | cost [1255.0]
51 --> 48 | cost [2305.0]
54 --> 52 | cost [945.0]
66 --> 87 | cost [1780.0]
69 --> 26 | cost [775.0]
71 --> 12 | cost [985.0]
72 --> 37 | cost [540.0]
74 --> 60 | cost [560.0]
75 --> 30 | cost [295.0]
83 -->  4 | cost [1105.0]
95 -->  1 | cost [480.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:48:33 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 78 hubs —— 1-90-21-10-68-86-49-30-80-20-38-46-25-9-27-61-94-57-7-84-58-52-43-89-60-87-4-6-15-33-64-82-48-31-63-13-78-17-45-36-92-96-18-24-77-50-55-22-88-37-65-79-81-56-100-26-62-5-67-40-39-70-53-73-85-93-11-3-28-91-97-99-76-59-32-98-12-101-1
total time           142.6                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             104550<=104550       Master/SP costs      104550/0             
Master time          142.6                SP time              0.0                  
subtour              3038.0               connectivity cuts    1227.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1229                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—90—21—10—68—86—49—30—80—20—38—46—25—9—27—61—94—57—7—84—58—52—43—89—60—87—4—6—15—33—64—82—48—31—63—13—78—17—45—36—92—96—18—24—77—50—55—22—88—37—65—79—81—56—100—26—62—5—67—40—39—70—53—73—85—93—11—3—28—91—97—99—76—59—32—98—12—101

RING
1  --- 90 | cost [745.0]
1  --- 101 | cost [0.0]
3  --- 11 | cost [950.0]
3  --- 28 | cost [1720.0]
4  ---  6 | cost [1120.0]
4  --- 87 | cost [2100.0]
5  --- 62 | cost [1530.0]
5  --- 67 | cost [1145.0]
6  --- 15 | cost [1290.0]
7  --- 57 | cost [1330.0]
7  --- 84 | cost [155.0]
9  --- 25 | cost [150.0]
9  --- 27 | cost [1470.0]
10 --- 21 | cost [1945.0]
10 --- 68 | cost [645.0]
11 --- 93 | cost [270.0]
12 --- 98 | cost [935.0]
12 --- 101 | cost [1315.0]
13 --- 63 | cost [1325.0]
13 --- 78 | cost [850.0]
15 --- 33 | cost [930.0]
17 --- 45 | cost [720.0]
17 --- 78 | cost [1280.0]
18 --- 24 | cost [765.0]
18 --- 96 | cost [1625.0]
20 --- 38 | cost [425.0]
20 --- 80 | cost [210.0]
21 --- 90 | cost [765.0]
22 --- 55 | cost [1830.0]
22 --- 88 | cost [565.0]
24 --- 77 | cost [960.0]
25 --- 46 | cost [310.0]
26 --- 62 | cost [905.0]
26 --- 100 | cost [440.0]
27 --- 61 | cost [1205.0]
28 --- 91 | cost [320.0]
30 --- 49 | cost [1260.0]
30 --- 80 | cost [880.0]
31 --- 48 | cost [625.0]
31 --- 63 | cost [830.0]
32 --- 59 | cost [780.0]
32 --- 98 | cost [1190.0]
33 --- 64 | cost [1420.0]
36 --- 45 | cost [385.0]
36 --- 92 | cost [1140.0]
37 --- 65 | cost [1715.0]
37 --- 88 | cost [3815.0]
38 --- 46 | cost [2325.0]
39 --- 40 | cost [800.0]
39 --- 70 | cost [545.0]
40 --- 67 | cost [1640.0]
43 --- 52 | cost [1595.0]
43 --- 89 | cost [1050.0]
48 --- 82 | cost [2025.0]
49 --- 86 | cost [130.0]
50 --- 55 | cost [1835.0]
50 --- 77 | cost [1890.0]
52 --- 58 | cost [1230.0]
53 --- 70 | cost [1150.0]
53 --- 73 | cost [1735.0]
56 --- 81 | cost [1985.0]
56 --- 100 | cost [320.0]
57 --- 94 | cost [790.0]
58 --- 84 | cost [270.0]
59 --- 76 | cost [700.0]
60 --- 87 | cost [1165.0]
60 --- 89 | cost [1765.0]
61 --- 94 | cost [1370.0]
64 --- 82 | cost [1125.0]
65 --- 79 | cost [960.0]
68 --- 86 | cost [1435.0]
73 --- 85 | cost [440.0]
76 --- 99 | cost [615.0]
79 --- 81 | cost [880.0]
85 --- 93 | cost [1400.0]
91 --- 97 | cost [1000.0]
92 --- 96 | cost [690.0]
97 --- 99 | cost [610.0]

STAR
2  --> 13 | cost [920.0]
8  --> 99 | cost [210.0]
14 --> 64 | cost [605.0]
16 --> 77 | cost [1300.0]
19 --> 92 | cost [370.0]
23 --> 22 | cost [235.0]
29 --> 99 | cost [645.0]
34 --> 57 | cost [1210.0]
35 --> 61 | cost [530.0]
41 --> 17 | cost [810.0]
42 --> 64 | cost [1270.0]
44 --> 92 | cost [1665.0]
47 --> 79 | cost [1255.0]
51 --> 48 | cost [2305.0]
54 --> 52 | cost [945.0]
66 --> 87 | cost [1780.0]
69 --> 26 | cost [775.0]
71 --> 12 | cost [985.0]
72 --> 37 | cost [540.0]
74 --> 60 | cost [560.0]
75 --> 30 | cost [295.0]
83 -->  4 | cost [1105.0]
95 -->  1 | cost [480.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 10 Jan 2024 01:04:29 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—90—101
total time           217.31               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             100565<=100570       subtour              8439.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       997                  n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—90—101

RING
1  --- 90 | cost [745.0]
2  --- 13 | cost [920.0]
2  --- 42 | cost [1085.0]
3  --- 11 | cost [950.0]
3  --- 28 | cost [1720.0]
4  ---  6 | cost [1120.0]
4  --- 87 | cost [2100.0]
5  --- 62 | cost [1530.0]
5  --- 67 | cost [1145.0]
6  --- 15 | cost [1290.0]
7  --- 58 | cost [410.0]
7  --- 84 | cost [155.0]
8  --- 29 | cost [500.0]
8  --- 99 | cost [210.0]
9  --- 25 | cost [150.0]
9  --- 71 | cost [1645.0]
10 --- 68 | cost [645.0]
10 --- 86 | cost [1880.0]
11 --- 93 | cost [270.0]
12 --- 71 | cost [985.0]
12 --- 98 | cost [935.0]
13 --- 78 | cost [850.0]
14 --- 42 | cost [1160.0]
14 --- 64 | cost [605.0]
15 --- 33 | cost [930.0]
17 --- 45 | cost [720.0]
17 --- 78 | cost [1280.0]
18 --- 24 | cost [765.0]
18 --- 96 | cost [1625.0]
20 --- 38 | cost [425.0]
20 --- 80 | cost [210.0]
22 --- 23 | cost [235.0]
22 --- 55 | cost [1830.0]
23 --- 88 | cost [640.0]
24 --- 77 | cost [960.0]
25 --- 27 | cost [1595.0]
26 --- 62 | cost [905.0]
26 --- 100 | cost [440.0]
27 --- 61 | cost [1205.0]
28 --- 91 | cost [320.0]
29 --- 32 | cost [865.0]
30 --- 38 | cost [1280.0]
30 --- 75 | cost [295.0]
31 --- 48 | cost [625.0]
31 --- 63 | cost [830.0]
32 --- 98 | cost [1190.0]
33 --- 82 | cost [1415.0]
36 --- 45 | cost [385.0]
36 --- 92 | cost [1140.0]
37 --- 65 | cost [1715.0]
37 --- 72 | cost [540.0]
39 --- 40 | cost [800.0]
39 --- 70 | cost [545.0]
40 --- 67 | cost [1640.0]
43 --- 50 | cost [1745.0]
43 --- 52 | cost [1595.0]
48 --- 63 | cost [905.0]
50 --- 77 | cost [1890.0]
52 --- 54 | cost [945.0]
53 --- 70 | cost [1150.0]
53 --- 73 | cost [1735.0]
54 --- 72 | cost [2530.0]
55 --- 88 | cost [1970.0]
56 --- 81 | cost [1985.0]
56 --- 100 | cost [320.0]
57 --- 74 | cost [1865.0]
57 --- 94 | cost [790.0]
58 --- 84 | cost [270.0]
60 --- 74 | cost [560.0]
60 --- 87 | cost [1165.0]
61 --- 94 | cost [1370.0]
64 --- 82 | cost [1125.0]
65 --- 79 | cost [960.0]
68 --- 86 | cost [1435.0]
73 --- 85 | cost [440.0]
75 --- 80 | cost [1060.0]
79 --- 81 | cost [880.0]
85 --- 93 | cost [1400.0]
90 --- 101 | cost [745.0]
91 --- 97 | cost [1000.0]
92 --- 96 | cost [690.0]
97 --- 99 | cost [610.0]

STAR
16 -->  2 | cost [1180.0]
19 --> 92 | cost [370.0]
21 --> 90 | cost [765.0]
34 --> 57 | cost [1210.0]
35 --> 61 | cost [530.0]
41 --> 17 | cost [810.0]
44 --> 92 | cost [1665.0]
46 --> 25 | cost [310.0]
47 --> 79 | cost [1255.0]
49 --> 86 | cost [130.0]
51 --> 48 | cost [2305.0]
59 --> 32 | cost [780.0]
66 --> 74 | cost [1745.0]
69 --> 26 | cost [775.0]
76 --> 99 | cost [615.0]
83 -->  4 | cost [1105.0]
89 --> 43 | cost [1050.0]
95 -->  1 | cost [480.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 10 Jan 2024 02:05:11 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 84 hubs —— 1-90-21-10-68-86-49-30-80-20-72-37-65-79-81-56-100-26-62-5-67-40-39-70-53-73-85-93-11-3-28-91-97-99-76-59-32-98-12-71-35-57-94-58-7-84-52-43-50-55-22-23-77-24-18-96-19-92-36-45-17-41-78-13-63-31-48-42-14-64-82-33-15-83-6-4-87-60-61-27-9-25-46-101-1
total time           3611.65 (TL 3600)    gap                  0.122                
blossom time         0                    nb blossom           0.0                  
LB <= UB             100400<=114355       Master/SP costs      114355/0             
Master time          3611.65              SP time              0.0                  
subtour              47406.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       20068                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—90—21—10—68—86—49—30—80—20—72—37—65—79—81—56—100—26—62—5—67—40—39—70—53—73—85—93—11—3—28—91—97—99—76—59—32—98—12—71—35—57—94—58—7—84—52—43—50—55—22—23—77—24—18—96—19—92—36—45—17—41—78—13—63—31—48—42—14—64—82—33—15—83—6—4—87—60—61—27—9—25—46—101

RING
1  --- 90 | cost [745.0]
3  --- 11 | cost [950.0]
3  --- 28 | cost [1720.0]
4  ---  6 | cost [1120.0]
4  --- 87 | cost [2100.0]
5  --- 62 | cost [1530.0]
5  --- 67 | cost [1145.0]
6  --- 83 | cost [1375.0]
7  --- 58 | cost [410.0]
7  --- 84 | cost [155.0]
9  --- 25 | cost [150.0]
9  --- 27 | cost [1470.0]
10 --- 21 | cost [1945.0]
10 --- 68 | cost [645.0]
11 --- 93 | cost [270.0]
12 --- 71 | cost [985.0]
12 --- 98 | cost [935.0]
13 --- 63 | cost [1325.0]
13 --- 78 | cost [850.0]
14 --- 42 | cost [1160.0]
14 --- 64 | cost [605.0]
15 --- 33 | cost [930.0]
15 --- 83 | cost [2355.0]
17 --- 41 | cost [810.0]
17 --- 45 | cost [720.0]
18 --- 24 | cost [765.0]
18 --- 96 | cost [1625.0]
19 --- 92 | cost [370.0]
19 --- 96 | cost [760.0]
20 --- 72 | cost [2365.0]
20 --- 80 | cost [210.0]
21 --- 90 | cost [765.0]
22 --- 23 | cost [235.0]
22 --- 55 | cost [1830.0]
23 --- 77 | cost [4010.0]
24 --- 77 | cost [960.0]
25 --- 46 | cost [310.0]
26 --- 62 | cost [905.0]
26 --- 100 | cost [440.0]
27 --- 61 | cost [1205.0]
28 --- 91 | cost [320.0]
30 --- 49 | cost [1260.0]
30 --- 80 | cost [880.0]
31 --- 48 | cost [625.0]
31 --- 63 | cost [830.0]
32 --- 59 | cost [780.0]
32 --- 98 | cost [1190.0]
33 --- 82 | cost [1415.0]
35 --- 57 | cost [2560.0]
35 --- 71 | cost [2070.0]
36 --- 45 | cost [385.0]
36 --- 92 | cost [1140.0]
37 --- 65 | cost [1715.0]
37 --- 72 | cost [540.0]
39 --- 40 | cost [800.0]
39 --- 70 | cost [545.0]
40 --- 67 | cost [1640.0]
41 --- 78 | cost [2030.0]
42 --- 48 | cost [2340.0]
43 --- 50 | cost [1745.0]
43 --- 52 | cost [1595.0]
46 --- 101 | cost [2385.0]
49 --- 86 | cost [130.0]
50 --- 55 | cost [1835.0]
52 --- 84 | cost [1410.0]
53 --- 70 | cost [1150.0]
53 --- 73 | cost [1735.0]
56 --- 81 | cost [1985.0]
56 --- 100 | cost [320.0]
57 --- 94 | cost [790.0]
58 --- 94 | cost [2530.0]
59 --- 76 | cost [700.0]
60 --- 61 | cost [3615.0]
60 --- 87 | cost [1165.0]
64 --- 82 | cost [1125.0]
65 --- 79 | cost [960.0]
68 --- 86 | cost [1435.0]
73 --- 85 | cost [440.0]
76 --- 99 | cost [615.0]
79 --- 81 | cost [880.0]
85 --- 93 | cost [1400.0]
91 --- 97 | cost [1000.0]
97 --- 99 | cost [610.0]

STAR
2  --> 13 | cost [920.0]
8  --> 99 | cost [210.0]
16 --> 77 | cost [1300.0]
29 --> 99 | cost [645.0]
34 --> 57 | cost [1210.0]
38 --> 20 | cost [425.0]
44 --> 92 | cost [1665.0]
47 --> 79 | cost [1255.0]
51 --> 31 | cost [2495.0]
54 --> 52 | cost [945.0]
66 --> 87 | cost [1780.0]
69 --> 26 | cost [775.0]
74 --> 60 | cost [560.0]
75 --> 30 | cost [295.0]
88 --> 22 | cost [565.0]
89 --> 43 | cost [1050.0]
95 -->  1 | cost [480.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1