------------------------------------------------------------
                           α=3.0 —— rat99 —— 99 nodes       
------------------------------------------------------------

——————— Tue, 23 Jan 2024 13:05:57 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 100 hubs —— 1—2—3—4—14—5—6—7—8—9—18—17—16—15—23—24—25—26—27—35—36—44—45—54—53—52—51—50—49—60—61—62—63—72—81—80—71—70—69—78—77—76—84—85—86—87—88—79—89—90—99—98—97—96—95—94—93—92—91—83—82—73—74—75—66—67—68—59—58—57—56—65—64—55—46—47—38—48—39—40—41—42—43—34—33—32—31—30—29—37—28—19—20—21—22—13—12—11—10—100
total time           10.94                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3633<=3633           subtour              523.0                
connectivity cuts    62.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       87                   n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—3—4—14—5—6—7—8—9—18—17—16—15—23—24—25—26—27—35—36—44—45—54—53—52—51—50—49—60—61—62—63—72—81—80—71—70—69—78—77—76—84—85—86—87—88—79—89—90—99—98—97—96—95—94—93—92—91—83—82—73—74—75—66—67—68—59—58—57—56—65—64—55—46—47—38—48—39—40—41—42—43—34—33—32—31—30—29—37—28—19—20—21—22—13—12—11—10—100

RING
1  ---  2 | cost [42.0]
2  ---  3 | cost [27.0]
3  ---  4 | cost [33.0]
4  --- 14 | cost [45.0]
5  ---  6 | cost [27.0]
5  --- 14 | cost [36.0]
6  ---  7 | cost [33.0]
7  ---  8 | cost [30.0]
8  ---  9 | cost [30.0]
9  --- 18 | cost [60.0]
10 --- 11 | cost [36.0]
10 --- 100 | cost [51.0]
11 --- 12 | cost [18.0]
12 --- 13 | cost [39.0]
13 --- 22 | cost [42.0]
15 --- 16 | cost [30.0]
15 --- 23 | cost [42.0]
16 --- 17 | cost [39.0]
17 --- 18 | cost [30.0]
19 --- 20 | cost [39.0]
19 --- 28 | cost [57.0]
20 --- 21 | cost [54.0]
21 --- 22 | cost [18.0]
23 --- 24 | cost [30.0]
24 --- 25 | cost [27.0]
25 --- 26 | cost [30.0]
26 --- 27 | cost [48.0]
27 --- 35 | cost [39.0]
28 --- 37 | cost [27.0]
29 --- 30 | cost [33.0]
29 --- 37 | cost [27.0]
30 --- 31 | cost [36.0]
31 --- 32 | cost [33.0]
32 --- 33 | cost [36.0]
33 --- 34 | cost [36.0]
34 --- 43 | cost [18.0]
35 --- 36 | cost [33.0]
36 --- 44 | cost [39.0]
38 --- 47 | cost [48.0]
38 --- 48 | cost [33.0]
39 --- 40 | cost [18.0]
39 --- 48 | cost [12.0]
40 --- 41 | cost [42.0]
41 --- 42 | cost [42.0]
42 --- 43 | cost [24.0]
44 --- 45 | cost [48.0]
45 --- 54 | cost [39.0]
46 --- 47 | cost [24.0]
46 --- 55 | cost [45.0]
49 --- 50 | cost [42.0]
49 --- 60 | cost [48.0]
50 --- 51 | cost [36.0]
51 --- 52 | cost [27.0]
52 --- 53 | cost [24.0]
53 --- 54 | cost [42.0]
55 --- 64 | cost [66.0]
56 --- 57 | cost [24.0]
56 --- 65 | cost [39.0]
57 --- 58 | cost [39.0]
58 --- 59 | cost [24.0]
59 --- 68 | cost [63.0]
60 --- 61 | cost [48.0]
61 --- 62 | cost [27.0]
62 --- 63 | cost [48.0]
63 --- 72 | cost [60.0]
64 --- 65 | cost [42.0]
66 --- 67 | cost [39.0]
66 --- 75 | cost [48.0]
67 --- 68 | cost [15.0]
69 --- 70 | cost [27.0]
69 --- 78 | cost [36.0]
70 --- 71 | cost [21.0]
71 --- 80 | cost [30.0]
72 --- 81 | cost [39.0]
73 --- 74 | cost [51.0]
73 --- 82 | cost [54.0]
74 --- 75 | cost [42.0]
76 --- 77 | cost [36.0]
76 --- 84 | cost [42.0]
77 --- 78 | cost [30.0]
79 --- 88 | cost [42.0]
79 --- 89 | cost [66.0]
80 --- 81 | cost [39.0]
82 --- 83 | cost [36.0]
83 --- 91 | cost [48.0]
84 --- 85 | cost [30.0]
85 --- 86 | cost [33.0]
86 --- 87 | cost [33.0]
87 --- 88 | cost [24.0]
89 --- 90 | cost [24.0]
90 --- 99 | cost [30.0]
91 --- 92 | cost [21.0]
92 --- 93 | cost [36.0]
93 --- 94 | cost [39.0]
94 --- 95 | cost [54.0]
95 --- 96 | cost [45.0]
96 --- 97 | cost [33.0]
97 --- 98 | cost [39.0]
98 --- 99 | cost [27.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 23 Jan 2024 13:06:39 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 100 hubs —— 1-10-11-12-13-22-21-20-19-28-37-29-30-31-32-33-34-43-42-41-40-39-48-38-47-46-55-64-65-56-57-58-59-68-67-66-75-74-73-82-83-91-92-93-94-95-96-97-98-99-90-89-79-88-87-86-85-84-76-77-78-69-70-71-80-81-72-63-62-61-60-49-50-51-52-53-54-45-44-36-35-27-26-25-24-23-15-16-17-18-9-8-7-6-5-14-4-3-2-100-1
total time           13.19                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             3633<=3633           Master/SP costs      3633/0               
Master time          13.19                SP time              0.0                  
subtour              337.0                connectivity cuts    151.0                
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       214                  
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—10—11—12—13—22—21—20—19—28—37—29—30—31—32—33—34—43—42—41—40—39—48—38—47—46—55—64—65—56—57—58—59—68—67—66—75—74—73—82—83—91—92—93—94—95—96—97—98—99—90—89—79—88—87—86—85—84—76—77—78—69—70—71—80—81—72—63—62—61—60—49—50—51—52—53—54—45—44—36—35—27—26—25—24—23—15—16—17—18—9—8—7—6—5—14—4—3—2—100

RING
1  --- 10 | cost [51.0]
2  ---  3 | cost [27.0]
2  --- 100 | cost [42.0]
3  ---  4 | cost [33.0]
4  --- 14 | cost [45.0]
5  ---  6 | cost [27.0]
5  --- 14 | cost [36.0]
6  ---  7 | cost [33.0]
7  ---  8 | cost [30.0]
8  ---  9 | cost [30.0]
9  --- 18 | cost [60.0]
10 --- 11 | cost [36.0]
11 --- 12 | cost [18.0]
12 --- 13 | cost [39.0]
13 --- 22 | cost [42.0]
15 --- 16 | cost [30.0]
15 --- 23 | cost [42.0]
16 --- 17 | cost [39.0]
17 --- 18 | cost [30.0]
19 --- 20 | cost [39.0]
19 --- 28 | cost [57.0]
20 --- 21 | cost [54.0]
21 --- 22 | cost [18.0]
23 --- 24 | cost [30.0]
24 --- 25 | cost [27.0]
25 --- 26 | cost [30.0]
26 --- 27 | cost [48.0]
27 --- 35 | cost [39.0]
28 --- 37 | cost [27.0]
29 --- 30 | cost [33.0]
29 --- 37 | cost [27.0]
30 --- 31 | cost [36.0]
31 --- 32 | cost [33.0]
32 --- 33 | cost [36.0]
33 --- 34 | cost [36.0]
34 --- 43 | cost [18.0]
35 --- 36 | cost [33.0]
36 --- 44 | cost [39.0]
38 --- 47 | cost [48.0]
38 --- 48 | cost [33.0]
39 --- 40 | cost [18.0]
39 --- 48 | cost [12.0]
40 --- 41 | cost [42.0]
41 --- 42 | cost [42.0]
42 --- 43 | cost [24.0]
44 --- 45 | cost [48.0]
45 --- 54 | cost [39.0]
46 --- 47 | cost [24.0]
46 --- 55 | cost [45.0]
49 --- 50 | cost [42.0]
49 --- 60 | cost [48.0]
50 --- 51 | cost [36.0]
51 --- 52 | cost [27.0]
52 --- 53 | cost [24.0]
53 --- 54 | cost [42.0]
55 --- 64 | cost [66.0]
56 --- 57 | cost [24.0]
56 --- 65 | cost [39.0]
57 --- 58 | cost [39.0]
58 --- 59 | cost [24.0]
59 --- 68 | cost [63.0]
60 --- 61 | cost [48.0]
61 --- 62 | cost [27.0]
62 --- 63 | cost [48.0]
63 --- 72 | cost [60.0]
64 --- 65 | cost [42.0]
66 --- 67 | cost [39.0]
66 --- 75 | cost [48.0]
67 --- 68 | cost [15.0]
69 --- 70 | cost [27.0]
69 --- 78 | cost [36.0]
70 --- 71 | cost [21.0]
71 --- 80 | cost [30.0]
72 --- 81 | cost [39.0]
73 --- 74 | cost [51.0]
73 --- 82 | cost [54.0]
74 --- 75 | cost [42.0]
76 --- 77 | cost [36.0]
76 --- 84 | cost [42.0]
77 --- 78 | cost [30.0]
79 --- 88 | cost [42.0]
79 --- 89 | cost [66.0]
80 --- 81 | cost [39.0]
82 --- 83 | cost [36.0]
83 --- 91 | cost [48.0]
84 --- 85 | cost [30.0]
85 --- 86 | cost [33.0]
86 --- 87 | cost [33.0]
87 --- 88 | cost [24.0]
89 --- 90 | cost [24.0]
90 --- 99 | cost [30.0]
91 --- 92 | cost [21.0]
92 --- 93 | cost [36.0]
93 --- 94 | cost [39.0]
94 --- 95 | cost [54.0]
95 --- 96 | cost [45.0]
96 --- 97 | cost [33.0]
97 --- 98 | cost [39.0]
98 --- 99 | cost [27.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1