------------------------------------------------------------
                        α=3.0 —— kroA100 —— 100 nodes       
------------------------------------------------------------

——————— Wed, 24 Jan 2024 21:21:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 101 hubs —— 1—63—6—49—90—19—75—92—8—42—89—31—80—56—97—4—65—26—66—70—22—94—16—88—53—79—18—24—38—99—36—84—10—72—21—74—59—17—15—11—32—45—91—98—23—77—60—62—35—86—27—12—20—57—9—7—55—83—34—29—46—43—3—14—71—41—100—48—30—39—96—78—52—5—37—33—76—13—95—82—85—68—73—50—44—2—54—40—64—69—81—25—87—51—61—58—67—28—93—47—101
total time           283.02               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             63846<=63846         subtour              3766.0               
connectivity cuts    1643.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       2429                 n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—63—6—49—90—19—75—92—8—42—89—31—80—56—97—4—65—26—66—70—22—94—16—88—53—79—18—24—38—99—36—84—10—72—21—74—59—17—15—11—32—45—91—98—23—77—60—62—35—86—27—12—20—57—9—7—55—83—34—29—46—43—3—14—71—41—100—48—30—39—96—78—52—5—37—33—76—13—95—82—85—68—73—50—44—2—54—40—64—69—81—25—87—51—61—58—67—28—93—47—101

RING
1  --- 63 | cost [864.0]
2  --- 44 | cost [771.0]
2  --- 54 | cost [993.0]
3  --- 14 | cost [663.0]
3  --- 43 | cost [513.0]
4  --- 65 | cost [441.0]
4  --- 97 | cost [972.0]
5  --- 37 | cost [207.0]
5  --- 52 | cost [777.0]
6  --- 49 | cost [141.0]
6  --- 63 | cost [471.0]
7  ---  9 | cost [150.0]
7  --- 55 | cost [792.0]
8  --- 42 | cost [744.0]
8  --- 92 | cost [618.0]
9  --- 57 | cost [300.0]
10 --- 72 | cost [810.0]
10 --- 84 | cost [420.0]
11 --- 15 | cost [339.0]
11 --- 32 | cost [606.0]
12 --- 20 | cost [462.0]
12 --- 27 | cost [408.0]
13 --- 76 | cost [309.0]
13 --- 95 | cost [648.0]
14 --- 71 | cost [804.0]
15 --- 17 | cost [39.0]
16 --- 88 | cost [174.0]
16 --- 94 | cost [483.0]
17 --- 59 | cost [1074.0]
18 --- 24 | cost [543.0]
18 --- 79 | cost [690.0]
19 --- 75 | cost [702.0]
19 --- 90 | cost [1128.0]
20 --- 57 | cost [612.0]
21 --- 72 | cost [456.0]
21 --- 74 | cost [198.0]
22 --- 70 | cost [558.0]
22 --- 94 | cost [402.0]
23 --- 77 | cost [1146.0]
23 --- 98 | cost [324.0]
24 --- 38 | cost [288.0]
25 --- 81 | cost [153.0]
25 --- 87 | cost [1020.0]
26 --- 65 | cost [849.0]
26 --- 66 | cost [969.0]
27 --- 86 | cost [243.0]
28 --- 67 | cost [903.0]
28 --- 93 | cost [144.0]
29 --- 34 | cost [903.0]
29 --- 46 | cost [444.0]
30 --- 39 | cost [783.0]
30 --- 48 | cost [1281.0]
31 --- 80 | cost [261.0]
31 --- 89 | cost [564.0]
32 --- 45 | cost [666.0]
33 --- 37 | cost [1224.0]
33 --- 76 | cost [276.0]
34 --- 83 | cost [438.0]
35 --- 62 | cost [975.0]
35 --- 86 | cost [423.0]
36 --- 84 | cost [966.0]
36 --- 99 | cost [900.0]
38 --- 99 | cost [939.0]
39 --- 96 | cost [852.0]
40 --- 54 | cost [312.0]
40 --- 64 | cost [240.0]
41 --- 71 | cost [249.0]
41 --- 100 | cost [555.0]
42 --- 89 | cost [540.0]
43 --- 46 | cost [594.0]
44 --- 50 | cost [486.0]
45 --- 91 | cost [537.0]
47 --- 93 | cost [1599.0]
47 --- 101 | cost [1287.0]
48 --- 100 | cost [756.0]
49 --- 90 | cost [624.0]
50 --- 73 | cost [540.0]
51 --- 61 | cost [558.0]
51 --- 87 | cost [438.0]
52 --- 78 | cost [120.0]
53 --- 79 | cost [669.0]
53 --- 88 | cost [690.0]
55 --- 83 | cost [69.0]
56 --- 80 | cost [843.0]
56 --- 97 | cost [648.0]
58 --- 61 | cost [975.0]
58 --- 67 | cost [1035.0]
59 --- 74 | cost [267.0]
60 --- 62 | cost [453.0]
60 --- 77 | cost [573.0]
64 --- 69 | cost [891.0]
66 --- 70 | cost [1200.0]
68 --- 73 | cost [801.0]
68 --- 85 | cost [459.0]
69 --- 81 | cost [909.0]
75 --- 92 | cost [1074.0]
78 --- 96 | cost [204.0]
82 --- 85 | cost [2403.0]
82 --- 95 | cost [735.0]
91 --- 98 | cost [297.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 24 Jan 2024 21:29:02 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-63-6-49-90-19-75-92-8-42-89-31-80-56-97-4-65-26-66-70-22-94-16-88-53-79-18-24-38-99-36-84-10-72-21-74-59-17-15-11-32-45-91-98-23-77-60-62-35-86-27-12-20-57-9-7-55-83-34-29-46-43-3-14-71-41-100-48-30-39-96-78-52-5-37-33-76-13-95-82-85-68-73-50-44-2-54-40-64-69-81-25-87-51-61-58-67-28-93-47-101-1
total time           401.57               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             63840<=63846         Master/SP costs      63846/0              
Master time          401.57               SP time              0.0                  
subtour              4450.0               connectivity cuts    1791.0               
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       1801                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—63—6—49—90—19—75—92—8—42—89—31—80—56—97—4—65—26—66—70—22—94—16—88—53—79—18—24—38—99—36—84—10—72—21—74—59—17—15—11—32—45—91—98—23—77—60—62—35—86—27—12—20—57—9—7—55—83—34—29—46—43—3—14—71—41—100—48—30—39—96—78—52—5—37—33—76—13—95—82—85—68—73—50—44—2—54—40—64—69—81—25—87—51—61—58—67—28—93—47—101

RING
1  --- 63 | cost [864.0]
1  --- 101 | cost [0.0]
2  --- 44 | cost [771.0]
2  --- 54 | cost [993.0]
3  --- 14 | cost [663.0]
3  --- 43 | cost [513.0]
4  --- 65 | cost [441.0]
4  --- 97 | cost [972.0]
5  --- 37 | cost [207.0]
5  --- 52 | cost [777.0]
6  --- 49 | cost [141.0]
6  --- 63 | cost [471.0]
7  ---  9 | cost [150.0]
7  --- 55 | cost [792.0]
8  --- 42 | cost [744.0]
8  --- 92 | cost [618.0]
9  --- 57 | cost [300.0]
10 --- 72 | cost [810.0]
10 --- 84 | cost [420.0]
11 --- 15 | cost [339.0]
11 --- 32 | cost [606.0]
12 --- 20 | cost [462.0]
12 --- 27 | cost [408.0]
13 --- 76 | cost [309.0]
13 --- 95 | cost [648.0]
14 --- 71 | cost [804.0]
15 --- 17 | cost [39.0]
16 --- 88 | cost [174.0]
16 --- 94 | cost [483.0]
17 --- 59 | cost [1074.0]
18 --- 24 | cost [543.0]
18 --- 79 | cost [690.0]
19 --- 75 | cost [702.0]
19 --- 90 | cost [1128.0]
20 --- 57 | cost [612.0]
21 --- 72 | cost [456.0]
21 --- 74 | cost [198.0]
22 --- 70 | cost [558.0]
22 --- 94 | cost [402.0]
23 --- 77 | cost [1146.0]
23 --- 98 | cost [324.0]
24 --- 38 | cost [288.0]
25 --- 81 | cost [153.0]
25 --- 87 | cost [1020.0]
26 --- 65 | cost [849.0]
26 --- 66 | cost [969.0]
27 --- 86 | cost [243.0]
28 --- 67 | cost [903.0]
28 --- 93 | cost [144.0]
29 --- 34 | cost [903.0]
29 --- 46 | cost [444.0]
30 --- 39 | cost [783.0]
30 --- 48 | cost [1281.0]
31 --- 80 | cost [261.0]
31 --- 89 | cost [564.0]
32 --- 45 | cost [666.0]
33 --- 37 | cost [1224.0]
33 --- 76 | cost [276.0]
34 --- 83 | cost [438.0]
35 --- 62 | cost [975.0]
35 --- 86 | cost [423.0]
36 --- 84 | cost [966.0]
36 --- 99 | cost [900.0]
38 --- 99 | cost [939.0]
39 --- 96 | cost [852.0]
40 --- 54 | cost [312.0]
40 --- 64 | cost [240.0]
41 --- 71 | cost [249.0]
41 --- 100 | cost [555.0]
42 --- 89 | cost [540.0]
43 --- 46 | cost [594.0]
44 --- 50 | cost [486.0]
45 --- 91 | cost [537.0]
47 --- 93 | cost [1599.0]
47 --- 101 | cost [1287.0]
48 --- 100 | cost [756.0]
49 --- 90 | cost [624.0]
50 --- 73 | cost [540.0]
51 --- 61 | cost [558.0]
51 --- 87 | cost [438.0]
52 --- 78 | cost [120.0]
53 --- 79 | cost [669.0]
53 --- 88 | cost [690.0]
55 --- 83 | cost [69.0]
56 --- 80 | cost [843.0]
56 --- 97 | cost [648.0]
58 --- 61 | cost [975.0]
58 --- 67 | cost [1035.0]
59 --- 74 | cost [267.0]
60 --- 62 | cost [453.0]
60 --- 77 | cost [573.0]
64 --- 69 | cost [891.0]
66 --- 70 | cost [1200.0]
68 --- 73 | cost [801.0]
68 --- 85 | cost [459.0]
69 --- 81 | cost [909.0]
75 --- 92 | cost [1074.0]
78 --- 96 | cost [204.0]
82 --- 85 | cost [2403.0]
82 --- 95 | cost [735.0]
91 --- 98 | cost [297.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1