------------------------------------------------------------
                          α=3.0 —— rd100 —— 100 nodes       
------------------------------------------------------------

——————— Wed, 24 Jan 2024 23:26:46 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 101 hubs —— 1—60—69—8—71—68—83—51—90—65—48—30—80—81—91—64—36—57—47—99—53—79—6—94—98—66—88—84—31—16—45—52—11—61—5—22—41—34—7—42—24—25—43—40—55—96—39—100—44—29—35—23—2—89—58—76—59—95—77—93—28—37—19—56—46—50—73—54—38—70—72—17—92—27—10—33—3—78—20—74—26—9—32—4—12—14—85—82—75—21—49—13—67—97—86—63—15—87—62—18—101
total time           17.35                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             23730<=23730         subtour              524.0                
connectivity cuts    290.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       461                  n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—60—69—8—71—68—83—51—90—65—48—30—80—81—91—64—36—57—47—99—53—79—6—94—98—66—88—84—31—16—45—52—11—61—5—22—41—34—7—42—24—25—43—40—55—96—39—100—44—29—35—23—2—89—58—76—59—95—77—93—28—37—19—56—46—50—73—54—38—70—72—17—92—27—10—33—3—78—20—74—26—9—32—4—12—14—85—82—75—21—49—13—67—97—86—63—15—87—62—18—101

RING
1  --- 60 | cost [66.0]
1  --- 101 | cost [0.0]
2  --- 23 | cost [261.0]
2  --- 89 | cost [324.0]
3  --- 33 | cost [345.0]
3  --- 78 | cost [486.0]
4  --- 12 | cost [360.0]
4  --- 32 | cost [126.0]
5  --- 22 | cost [279.0]
5  --- 61 | cost [150.0]
6  --- 79 | cost [138.0]
6  --- 94 | cost [363.0]
7  --- 34 | cost [171.0]
7  --- 42 | cost [219.0]
8  --- 69 | cost [183.0]
8  --- 71 | cost [378.0]
9  --- 26 | cost [126.0]
9  --- 32 | cost [360.0]
10 --- 27 | cost [357.0]
10 --- 33 | cost [123.0]
11 --- 52 | cost [534.0]
11 --- 61 | cost [243.0]
12 --- 14 | cost [144.0]
13 --- 49 | cost [264.0]
13 --- 67 | cost [177.0]
14 --- 85 | cost [123.0]
15 --- 63 | cost [90.0]
15 --- 87 | cost [360.0]
16 --- 31 | cost [375.0]
16 --- 45 | cost [306.0]
17 --- 72 | cost [162.0]
17 --- 92 | cost [450.0]
18 --- 62 | cost [201.0]
18 --- 101 | cost [264.0]
19 --- 37 | cost [282.0]
19 --- 56 | cost [264.0]
20 --- 74 | cost [57.0]
20 --- 78 | cost [117.0]
21 --- 49 | cost [105.0]
21 --- 75 | cost [75.0]
22 --- 41 | cost [150.0]
23 --- 35 | cost [750.0]
24 --- 25 | cost [198.0]
24 --- 42 | cost [204.0]
25 --- 43 | cost [126.0]
26 --- 74 | cost [117.0]
27 --- 92 | cost [111.0]
28 --- 37 | cost [108.0]
28 --- 93 | cost [267.0]
29 --- 35 | cost [174.0]
29 --- 44 | cost [258.0]
30 --- 48 | cost [237.0]
30 --- 80 | cost [252.0]
31 --- 84 | cost [162.0]
34 --- 41 | cost [291.0]
36 --- 57 | cost [300.0]
36 --- 64 | cost [408.0]
38 --- 54 | cost [213.0]
38 --- 70 | cost [261.0]
39 --- 96 | cost [120.0]
39 --- 100 | cost [486.0]
40 --- 43 | cost [363.0]
40 --- 55 | cost [357.0]
44 --- 100 | cost [219.0]
45 --- 52 | cost [378.0]
46 --- 50 | cost [15.0]
46 --- 56 | cost [75.0]
47 --- 57 | cost [300.0]
47 --- 99 | cost [276.0]
48 --- 65 | cost [309.0]
50 --- 73 | cost [81.0]
51 --- 83 | cost [102.0]
51 --- 90 | cost [126.0]
53 --- 79 | cost [195.0]
53 --- 99 | cost [144.0]
54 --- 73 | cost [240.0]
55 --- 96 | cost [348.0]
58 --- 76 | cost [288.0]
58 --- 89 | cost [729.0]
59 --- 76 | cost [390.0]
59 --- 95 | cost [57.0]
60 --- 69 | cost [249.0]
62 --- 87 | cost [252.0]
63 --- 86 | cost [45.0]
64 --- 91 | cost [417.0]
65 --- 90 | cost [288.0]
66 --- 88 | cost [306.0]
66 --- 98 | cost [216.0]
67 --- 97 | cost [96.0]
68 --- 71 | cost [423.0]
68 --- 83 | cost [243.0]
70 --- 72 | cost [171.0]
75 --- 82 | cost [108.0]
77 --- 93 | cost [132.0]
77 --- 95 | cost [156.0]
80 --- 81 | cost [201.0]
81 --- 91 | cost [387.0]
82 --- 85 | cost [123.0]
84 --- 88 | cost [57.0]
86 --- 97 | cost [39.0]
94 --- 98 | cost [228.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 24 Jan 2024 23:34:07 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-18-62-87-15-63-86-97-67-13-49-21-75-82-85-14-12-4-32-9-26-74-20-78-3-33-10-27-92-17-72-70-38-54-73-50-46-56-19-37-28-93-77-95-59-76-58-89-2-23-35-29-44-100-39-96-55-40-43-25-24-42-7-34-41-22-5-61-11-52-45-16-31-84-88-66-98-94-6-79-53-99-47-57-36-64-91-81-80-30-48-65-90-51-83-68-71-8-69-60-101-1
total time           411.74               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             23730<=23730         Master/SP costs      23730/0              
Master time          411.74               SP time              0.0                  
subtour              8230.0               connectivity cuts    2000.0               
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       3456                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—18—62—87—15—63—86—97—67—13—49—21—75—82—85—14—12—4—32—9—26—74—20—78—3—33—10—27—92—17—72—70—38—54—73—50—46—56—19—37—28—93—77—95—59—76—58—89—2—23—35—29—44—100—39—96—55—40—43—25—24—42—7—34—41—22—5—61—11—52—45—16—31—84—88—66—98—94—6—79—53—99—47—57—36—64—91—81—80—30—48—65—90—51—83—68—71—8—69—60—101

RING
1  --- 18 | cost [264.0]
2  --- 23 | cost [261.0]
2  --- 89 | cost [324.0]
3  --- 33 | cost [345.0]
3  --- 78 | cost [486.0]
4  --- 12 | cost [360.0]
4  --- 32 | cost [126.0]
5  --- 22 | cost [279.0]
5  --- 61 | cost [150.0]
6  --- 79 | cost [138.0]
6  --- 94 | cost [363.0]
7  --- 34 | cost [171.0]
7  --- 42 | cost [219.0]
8  --- 69 | cost [183.0]
8  --- 71 | cost [378.0]
9  --- 26 | cost [126.0]
9  --- 32 | cost [360.0]
10 --- 27 | cost [357.0]
10 --- 33 | cost [123.0]
11 --- 52 | cost [534.0]
11 --- 61 | cost [243.0]
12 --- 14 | cost [144.0]
13 --- 49 | cost [264.0]
13 --- 67 | cost [177.0]
14 --- 85 | cost [123.0]
15 --- 63 | cost [90.0]
15 --- 87 | cost [360.0]
16 --- 31 | cost [375.0]
16 --- 45 | cost [306.0]
17 --- 72 | cost [162.0]
17 --- 92 | cost [450.0]
18 --- 62 | cost [201.0]
19 --- 37 | cost [282.0]
19 --- 56 | cost [264.0]
20 --- 74 | cost [57.0]
20 --- 78 | cost [117.0]
21 --- 49 | cost [105.0]
21 --- 75 | cost [75.0]
22 --- 41 | cost [150.0]
23 --- 35 | cost [750.0]
24 --- 25 | cost [198.0]
24 --- 42 | cost [204.0]
25 --- 43 | cost [126.0]
26 --- 74 | cost [117.0]
27 --- 92 | cost [111.0]
28 --- 37 | cost [108.0]
28 --- 93 | cost [267.0]
29 --- 35 | cost [174.0]
29 --- 44 | cost [258.0]
30 --- 48 | cost [237.0]
30 --- 80 | cost [252.0]
31 --- 84 | cost [162.0]
34 --- 41 | cost [291.0]
36 --- 57 | cost [300.0]
36 --- 64 | cost [408.0]
38 --- 54 | cost [213.0]
38 --- 70 | cost [261.0]
39 --- 96 | cost [120.0]
39 --- 100 | cost [486.0]
40 --- 43 | cost [363.0]
40 --- 55 | cost [357.0]
44 --- 100 | cost [219.0]
45 --- 52 | cost [378.0]
46 --- 50 | cost [15.0]
46 --- 56 | cost [75.0]
47 --- 57 | cost [300.0]
47 --- 99 | cost [276.0]
48 --- 65 | cost [309.0]
50 --- 73 | cost [81.0]
51 --- 83 | cost [102.0]
51 --- 90 | cost [126.0]
53 --- 79 | cost [195.0]
53 --- 99 | cost [144.0]
54 --- 73 | cost [240.0]
55 --- 96 | cost [348.0]
58 --- 76 | cost [288.0]
58 --- 89 | cost [729.0]
59 --- 76 | cost [390.0]
59 --- 95 | cost [57.0]
60 --- 69 | cost [249.0]
60 --- 101 | cost [66.0]
62 --- 87 | cost [252.0]
63 --- 86 | cost [45.0]
64 --- 91 | cost [417.0]
65 --- 90 | cost [288.0]
66 --- 88 | cost [306.0]
66 --- 98 | cost [216.0]
67 --- 97 | cost [96.0]
68 --- 71 | cost [423.0]
68 --- 83 | cost [243.0]
70 --- 72 | cost [171.0]
75 --- 82 | cost [108.0]
77 --- 93 | cost [132.0]
77 --- 95 | cost [156.0]
80 --- 81 | cost [201.0]
81 --- 91 | cost [387.0]
82 --- 85 | cost [123.0]
84 --- 88 | cost [57.0]
86 --- 97 | cost [39.0]
94 --- 98 | cost [228.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1