------------------------------------------------------------
                        α=3.0 —— kroB100 —— 100 nodes       
------------------------------------------------------------

——————— Mon, 08 Jan 2024 08:41:19 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 101 hubs —— 1—95—98—32—59—76—29—8—99—97—91—28—3—11—93—85—73—53—70—39—40—67—5—62—69—26—100—56—81—79—47—65—37—72—38—20—80—75—30—49—86—68—10—21—90—46—25—9—34—7—84—58—52—54—88—23—22—55—77—24—18—45—36—96—92—19—44—41—17—78—13—63—31—48—51—82—33—15—6—4—83—64—14—42—2—16—50—43—89—87—66—74—60—57—94—35—61—27—71—12—101
total time           26.56                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             66423<=66423         subtour              1037.0               
connectivity cuts    374.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       739                  n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—95—98—32—59—76—29—8—99—97—91—28—3—11—93—85—73—53—70—39—40—67—5—62—69—26—100—56—81—79—47—65—37—72—38—20—80—75—30—49—86—68—10—21—90—46—25—9—34—7—84—58—52—54—88—23—22—55—77—24—18—45—36—96—92—19—44—41—17—78—13—63—31—48—51—82—33—15—6—4—83—64—14—42—2—16—50—43—89—87—66—74—60—57—94—35—61—27—71—12—101

RING
1  --- 95 | cost [288.0]
1  --- 101 | cost [0.0]
2  --- 16 | cost [708.0]
2  --- 42 | cost [651.0]
3  --- 11 | cost [570.0]
3  --- 28 | cost [1032.0]
4  ---  6 | cost [672.0]
4  --- 83 | cost [663.0]
5  --- 62 | cost [918.0]
5  --- 67 | cost [687.0]
6  --- 15 | cost [774.0]
7  --- 34 | cost [882.0]
7  --- 84 | cost [93.0]
8  --- 29 | cost [300.0]
8  --- 99 | cost [126.0]
9  --- 25 | cost [90.0]
9  --- 34 | cost [990.0]
10 --- 21 | cost [1167.0]
10 --- 68 | cost [387.0]
11 --- 93 | cost [162.0]
12 --- 71 | cost [591.0]
12 --- 101 | cost [789.0]
13 --- 63 | cost [795.0]
13 --- 78 | cost [510.0]
14 --- 42 | cost [696.0]
14 --- 64 | cost [363.0]
15 --- 33 | cost [558.0]
16 --- 50 | cost [1392.0]
17 --- 41 | cost [486.0]
17 --- 78 | cost [768.0]
18 --- 24 | cost [459.0]
18 --- 45 | cost [816.0]
19 --- 44 | cost [1032.0]
19 --- 92 | cost [222.0]
20 --- 38 | cost [255.0]
20 --- 80 | cost [126.0]
21 --- 90 | cost [459.0]
22 --- 23 | cost [141.0]
22 --- 55 | cost [1098.0]
23 --- 88 | cost [384.0]
24 --- 77 | cost [576.0]
25 --- 46 | cost [186.0]
26 --- 69 | cost [465.0]
26 --- 100 | cost [264.0]
27 --- 61 | cost [723.0]
27 --- 71 | cost [780.0]
28 --- 91 | cost [192.0]
29 --- 76 | cost [579.0]
30 --- 49 | cost [756.0]
30 --- 75 | cost [177.0]
31 --- 48 | cost [375.0]
31 --- 63 | cost [498.0]
32 --- 59 | cost [468.0]
32 --- 98 | cost [714.0]
33 --- 82 | cost [849.0]
35 --- 61 | cost [318.0]
35 --- 94 | cost [1077.0]
36 --- 45 | cost [231.0]
36 --- 96 | cost [546.0]
37 --- 65 | cost [1029.0]
37 --- 72 | cost [324.0]
38 --- 72 | cost [1503.0]
39 --- 40 | cost [480.0]
39 --- 70 | cost [327.0]
40 --- 67 | cost [984.0]
41 --- 44 | cost [1341.0]
43 --- 50 | cost [1047.0]
43 --- 89 | cost [630.0]
46 --- 90 | cost [1092.0]
47 --- 65 | cost [780.0]
47 --- 79 | cost [753.0]
48 --- 51 | cost [1383.0]
49 --- 86 | cost [78.0]
51 --- 82 | cost [1911.0]
52 --- 54 | cost [567.0]
52 --- 58 | cost [738.0]
53 --- 70 | cost [690.0]
53 --- 73 | cost [1041.0]
54 --- 88 | cost [1590.0]
55 --- 77 | cost [1260.0]
56 --- 81 | cost [1191.0]
56 --- 100 | cost [192.0]
57 --- 60 | cost [1224.0]
57 --- 94 | cost [474.0]
58 --- 84 | cost [162.0]
59 --- 76 | cost [420.0]
60 --- 74 | cost [336.0]
62 --- 69 | cost [753.0]
64 --- 83 | cost [1086.0]
66 --- 74 | cost [1047.0]
66 --- 87 | cost [1068.0]
68 --- 86 | cost [861.0]
73 --- 85 | cost [264.0]
75 --- 80 | cost [636.0]
79 --- 81 | cost [528.0]
85 --- 93 | cost [840.0]
87 --- 89 | cost [924.0]
91 --- 97 | cost [600.0]
92 --- 96 | cost [414.0]
95 --- 98 | cost [615.0]
97 --- 99 | cost [366.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:44:12 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-95-98-32-59-76-29-8-99-97-91-28-3-11-93-85-73-53-70-39-40-67-5-62-69-26-100-56-81-79-47-65-37-72-38-20-80-75-30-49-86-68-10-21-90-46-25-9-34-7-84-58-52-54-88-23-22-55-77-24-18-45-36-96-92-19-44-41-17-78-13-63-31-48-51-82-33-15-6-4-83-64-14-42-2-16-50-43-89-87-66-74-60-57-94-35-61-27-71-12-101-1
total time           146.49               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             66423<=66423         Master/SP costs      66423/0              
Master time          146.49               SP time              0.0                  
subtour              3827.0               connectivity cuts    1511.0               
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       1508                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—95—98—32—59—76—29—8—99—97—91—28—3—11—93—85—73—53—70—39—40—67—5—62—69—26—100—56—81—79—47—65—37—72—38—20—80—75—30—49—86—68—10—21—90—46—25—9—34—7—84—58—52—54—88—23—22—55—77—24—18—45—36—96—92—19—44—41—17—78—13—63—31—48—51—82—33—15—6—4—83—64—14—42—2—16—50—43—89—87—66—74—60—57—94—35—61—27—71—12—101

RING
1  --- 95 | cost [288.0]
2  --- 16 | cost [708.0]
2  --- 42 | cost [651.0]
3  --- 11 | cost [570.0]
3  --- 28 | cost [1032.0]
4  ---  6 | cost [672.0]
4  --- 83 | cost [663.0]
5  --- 62 | cost [918.0]
5  --- 67 | cost [687.0]
6  --- 15 | cost [774.0]
7  --- 34 | cost [882.0]
7  --- 84 | cost [93.0]
8  --- 29 | cost [300.0]
8  --- 99 | cost [126.0]
9  --- 25 | cost [90.0]
9  --- 34 | cost [990.0]
10 --- 21 | cost [1167.0]
10 --- 68 | cost [387.0]
11 --- 93 | cost [162.0]
12 --- 71 | cost [591.0]
12 --- 101 | cost [789.0]
13 --- 63 | cost [795.0]
13 --- 78 | cost [510.0]
14 --- 42 | cost [696.0]
14 --- 64 | cost [363.0]
15 --- 33 | cost [558.0]
16 --- 50 | cost [1392.0]
17 --- 41 | cost [486.0]
17 --- 78 | cost [768.0]
18 --- 24 | cost [459.0]
18 --- 45 | cost [816.0]
19 --- 44 | cost [1032.0]
19 --- 92 | cost [222.0]
20 --- 38 | cost [255.0]
20 --- 80 | cost [126.0]
21 --- 90 | cost [459.0]
22 --- 23 | cost [141.0]
22 --- 55 | cost [1098.0]
23 --- 88 | cost [384.0]
24 --- 77 | cost [576.0]
25 --- 46 | cost [186.0]
26 --- 69 | cost [465.0]
26 --- 100 | cost [264.0]
27 --- 61 | cost [723.0]
27 --- 71 | cost [780.0]
28 --- 91 | cost [192.0]
29 --- 76 | cost [579.0]
30 --- 49 | cost [756.0]
30 --- 75 | cost [177.0]
31 --- 48 | cost [375.0]
31 --- 63 | cost [498.0]
32 --- 59 | cost [468.0]
32 --- 98 | cost [714.0]
33 --- 82 | cost [849.0]
35 --- 61 | cost [318.0]
35 --- 94 | cost [1077.0]
36 --- 45 | cost [231.0]
36 --- 96 | cost [546.0]
37 --- 65 | cost [1029.0]
37 --- 72 | cost [324.0]
38 --- 72 | cost [1503.0]
39 --- 40 | cost [480.0]
39 --- 70 | cost [327.0]
40 --- 67 | cost [984.0]
41 --- 44 | cost [1341.0]
43 --- 50 | cost [1047.0]
43 --- 89 | cost [630.0]
46 --- 90 | cost [1092.0]
47 --- 65 | cost [780.0]
47 --- 79 | cost [753.0]
48 --- 51 | cost [1383.0]
49 --- 86 | cost [78.0]
51 --- 82 | cost [1911.0]
52 --- 54 | cost [567.0]
52 --- 58 | cost [738.0]
53 --- 70 | cost [690.0]
53 --- 73 | cost [1041.0]
54 --- 88 | cost [1590.0]
55 --- 77 | cost [1260.0]
56 --- 81 | cost [1191.0]
56 --- 100 | cost [192.0]
57 --- 60 | cost [1224.0]
57 --- 94 | cost [474.0]
58 --- 84 | cost [162.0]
59 --- 76 | cost [420.0]
60 --- 74 | cost [336.0]
62 --- 69 | cost [753.0]
64 --- 83 | cost [1086.0]
66 --- 74 | cost [1047.0]
66 --- 87 | cost [1068.0]
68 --- 86 | cost [861.0]
73 --- 85 | cost [264.0]
75 --- 80 | cost [636.0]
79 --- 81 | cost [528.0]
85 --- 93 | cost [840.0]
87 --- 89 | cost [924.0]
91 --- 97 | cost [600.0]
92 --- 96 | cost [414.0]
95 --- 98 | cost [615.0]
97 --- 99 | cost [366.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 10 Jan 2024 00:54:29 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 5 hubs —— 1—90—21—95—101
total time           308.38               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             64932<=64932         subtour              5334.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1227                 n lazycuts edges     3.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—90—21—95—101

RING
1  --- 90 | cost [447.0]
2  --- 16 | cost [708.0]
2  --- 42 | cost [651.0]
3  --- 11 | cost [570.0]
3  --- 28 | cost [1032.0]
4  --- 66 | cost [1560.0]
4  --- 83 | cost [663.0]
5  --- 62 | cost [918.0]
5  --- 67 | cost [687.0]
6  --- 15 | cost [774.0]
6  --- 33 | cost [834.0]
7  --- 34 | cost [882.0]
7  --- 84 | cost [93.0]
8  --- 29 | cost [300.0]
8  --- 99 | cost [126.0]
9  --- 25 | cost [90.0]
9  --- 46 | cost [222.0]
10 --- 68 | cost [387.0]
10 --- 86 | cost [1128.0]
11 --- 93 | cost [162.0]
12 --- 71 | cost [591.0]
12 --- 98 | cost [561.0]
13 --- 63 | cost [795.0]
13 --- 78 | cost [510.0]
14 --- 42 | cost [696.0]
14 --- 64 | cost [363.0]
15 --- 33 | cost [558.0]
16 --- 77 | cost [780.0]
17 --- 41 | cost [486.0]
17 --- 78 | cost [768.0]
18 --- 24 | cost [459.0]
18 --- 45 | cost [816.0]
19 --- 44 | cost [1032.0]
19 --- 92 | cost [222.0]
20 --- 38 | cost [255.0]
20 --- 80 | cost [126.0]
21 --- 90 | cost [459.0]
21 --- 95 | cost [969.0]
22 --- 23 | cost [141.0]
22 --- 55 | cost [1098.0]
23 --- 88 | cost [384.0]
24 --- 77 | cost [576.0]
25 --- 46 | cost [186.0]
26 --- 69 | cost [465.0]
26 --- 100 | cost [264.0]
27 --- 61 | cost [723.0]
27 --- 71 | cost [780.0]
28 --- 91 | cost [192.0]
29 --- 99 | cost [387.0]
30 --- 69 | cost [855.0]
30 --- 75 | cost [177.0]
31 --- 48 | cost [375.0]
31 --- 63 | cost [498.0]
32 --- 59 | cost [468.0]
32 --- 98 | cost [714.0]
34 --- 72 | cost [1587.0]
35 --- 61 | cost [318.0]
35 --- 94 | cost [1077.0]
36 --- 45 | cost [231.0]
36 --- 96 | cost [546.0]
37 --- 65 | cost [1029.0]
37 --- 72 | cost [324.0]
38 --- 80 | cost [378.0]
39 --- 40 | cost [480.0]
39 --- 70 | cost [327.0]
40 --- 67 | cost [984.0]
41 --- 44 | cost [1341.0]
43 --- 50 | cost [1047.0]
43 --- 89 | cost [630.0]
47 --- 65 | cost [780.0]
47 --- 81 | cost [837.0]
48 --- 51 | cost [1383.0]
49 --- 68 | cost [867.0]
49 --- 86 | cost [78.0]
50 --- 55 | cost [1101.0]
51 --- 82 | cost [1911.0]
52 --- 54 | cost [567.0]
52 --- 58 | cost [738.0]
53 --- 70 | cost [690.0]
53 --- 73 | cost [1041.0]
54 --- 88 | cost [1590.0]
56 --- 62 | cost [834.0]
56 --- 100 | cost [192.0]
57 --- 74 | cost [1119.0]
57 --- 94 | cost [474.0]
58 --- 84 | cost [162.0]
59 --- 76 | cost [420.0]
60 --- 74 | cost [336.0]
60 --- 87 | cost [699.0]
64 --- 82 | cost [675.0]
66 --- 87 | cost [1068.0]
73 --- 85 | cost [264.0]
75 --- 79 | cost [1284.0]
76 --- 97 | cost [483.0]
79 --- 81 | cost [528.0]
83 --- 89 | cost [1407.0]
85 --- 93 | cost [840.0]
91 --- 97 | cost [600.0]
92 --- 96 | cost [414.0]
95 --- 101 | cost [288.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 10 Jan 2024 01:00:23 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-95-98-32-59-76-29-8-99-97-91-28-3-11-93-85-73-53-70-39-40-67-5-62-69-26-100-56-81-79-47-65-37-72-38-20-80-75-30-49-86-68-10-21-90-46-25-9-34-7-84-58-52-54-88-23-22-55-77-24-18-45-36-96-92-19-44-41-17-78-13-63-31-48-51-82-33-15-6-4-83-64-14-42-2-16-50-43-89-87-66-74-60-57-94-35-61-27-71-12-101-1
total time           323.64               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             66419<=66423         Master/SP costs      66423/0              
Master time          323.63               SP time              0.0                  
subtour              9582.0               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       5813                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—95—98—32—59—76—29—8—99—97—91—28—3—11—93—85—73—53—70—39—40—67—5—62—69—26—100—56—81—79—47—65—37—72—38—20—80—75—30—49—86—68—10—21—90—46—25—9—34—7—84—58—52—54—88—23—22—55—77—24—18—45—36—96—92—19—44—41—17—78—13—63—31—48—51—82—33—15—6—4—83—64—14—42—2—16—50—43—89—87—66—74—60—57—94—35—61—27—71—12—101

RING
1  --- 95 | cost [288.0]
2  --- 16 | cost [708.0]
2  --- 42 | cost [651.0]
3  --- 11 | cost [570.0]
3  --- 28 | cost [1032.0]
4  ---  6 | cost [672.0]
4  --- 83 | cost [663.0]
5  --- 62 | cost [918.0]
5  --- 67 | cost [687.0]
6  --- 15 | cost [774.0]
7  --- 34 | cost [882.0]
7  --- 84 | cost [93.0]
8  --- 29 | cost [300.0]
8  --- 99 | cost [126.0]
9  --- 25 | cost [90.0]
9  --- 34 | cost [990.0]
10 --- 21 | cost [1167.0]
10 --- 68 | cost [387.0]
11 --- 93 | cost [162.0]
12 --- 71 | cost [591.0]
12 --- 101 | cost [789.0]
13 --- 63 | cost [795.0]
13 --- 78 | cost [510.0]
14 --- 42 | cost [696.0]
14 --- 64 | cost [363.0]
15 --- 33 | cost [558.0]
16 --- 50 | cost [1392.0]
17 --- 41 | cost [486.0]
17 --- 78 | cost [768.0]
18 --- 24 | cost [459.0]
18 --- 45 | cost [816.0]
19 --- 44 | cost [1032.0]
19 --- 92 | cost [222.0]
20 --- 38 | cost [255.0]
20 --- 80 | cost [126.0]
21 --- 90 | cost [459.0]
22 --- 23 | cost [141.0]
22 --- 55 | cost [1098.0]
23 --- 88 | cost [384.0]
24 --- 77 | cost [576.0]
25 --- 46 | cost [186.0]
26 --- 69 | cost [465.0]
26 --- 100 | cost [264.0]
27 --- 61 | cost [723.0]
27 --- 71 | cost [780.0]
28 --- 91 | cost [192.0]
29 --- 76 | cost [579.0]
30 --- 49 | cost [756.0]
30 --- 75 | cost [177.0]
31 --- 48 | cost [375.0]
31 --- 63 | cost [498.0]
32 --- 59 | cost [468.0]
32 --- 98 | cost [714.0]
33 --- 82 | cost [849.0]
35 --- 61 | cost [318.0]
35 --- 94 | cost [1077.0]
36 --- 45 | cost [231.0]
36 --- 96 | cost [546.0]
37 --- 65 | cost [1029.0]
37 --- 72 | cost [324.0]
38 --- 72 | cost [1503.0]
39 --- 40 | cost [480.0]
39 --- 70 | cost [327.0]
40 --- 67 | cost [984.0]
41 --- 44 | cost [1341.0]
43 --- 50 | cost [1047.0]
43 --- 89 | cost [630.0]
46 --- 90 | cost [1092.0]
47 --- 65 | cost [780.0]
47 --- 79 | cost [753.0]
48 --- 51 | cost [1383.0]
49 --- 86 | cost [78.0]
51 --- 82 | cost [1911.0]
52 --- 54 | cost [567.0]
52 --- 58 | cost [738.0]
53 --- 70 | cost [690.0]
53 --- 73 | cost [1041.0]
54 --- 88 | cost [1590.0]
55 --- 77 | cost [1260.0]
56 --- 81 | cost [1191.0]
56 --- 100 | cost [192.0]
57 --- 60 | cost [1224.0]
57 --- 94 | cost [474.0]
58 --- 84 | cost [162.0]
59 --- 76 | cost [420.0]
60 --- 74 | cost [336.0]
62 --- 69 | cost [753.0]
64 --- 83 | cost [1086.0]
66 --- 74 | cost [1047.0]
66 --- 87 | cost [1068.0]
68 --- 86 | cost [861.0]
73 --- 85 | cost [264.0]
75 --- 80 | cost [636.0]
79 --- 81 | cost [528.0]
85 --- 93 | cost [840.0]
87 --- 89 | cost [924.0]
91 --- 97 | cost [600.0]
92 --- 96 | cost [414.0]
95 --- 98 | cost [615.0]
97 --- 99 | cost [366.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1