------------------------------------------------------------
                        α=3.0 —— kroD100 —— 100 nodes       
------------------------------------------------------------

——————— Sat, 13 Jan 2024 14:37:28 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—50—101
total time           173.63               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             62301<=62301         subtour              4582.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       809                  n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—50—101

RING
1  --- 50 | cost [279.0]
2  --- 48 | cost [606.0]
2  --- 100 | cost [306.0]
3  --- 40 | cost [363.0]
3  --- 83 | cost [285.0]
4  --- 71 | cost [606.0]
4  --- 93 | cost [534.0]
5  --- 53 | cost [654.0]
5  --- 62 | cost [1212.0]
6  --- 40 | cost [123.0]
6  --- 83 | cost [180.0]
7  --- 74 | cost [795.0]
7  --- 75 | cost [1014.0]
8  --- 46 | cost [858.0]
8  --- 52 | cost [258.0]
9  --- 10 | cost [609.0]
9  --- 20 | cost [825.0]
10 --- 21 | cost [972.0]
11 --- 89 | cost [600.0]
11 --- 90 | cost [576.0]
12 --- 28 | cost [543.0]
12 --- 47 | cost [690.0]
13 --- 79 | cost [225.0]
13 --- 88 | cost [408.0]
14 --- 65 | cost [615.0]
14 --- 68 | cost [63.0]
15 --- 69 | cost [1005.0]
15 --- 73 | cost [969.0]
16 --- 63 | cost [441.0]
16 --- 96 | cost [945.0]
17 --- 90 | cost [165.0]
17 --- 94 | cost [555.0]
18 --- 82 | cost [1098.0]
18 --- 85 | cost [564.0]
19 --- 37 | cost [354.0]
19 --- 51 | cost [426.0]
20 --- 25 | cost [105.0]
21 --- 56 | cost [711.0]
22 --- 58 | cost [1254.0]
22 --- 70 | cost [1566.0]
23 --- 42 | cost [639.0]
23 --- 66 | cost [1071.0]
24 --- 27 | cost [186.0]
24 --- 41 | cost [759.0]
25 --- 82 | cost [1140.0]
26 --- 87 | cost [36.0]
26 --- 95 | cost [1473.0]
27 --- 81 | cost [1185.0]
28 --- 47 | cost [750.0]
29 --- 36 | cost [1245.0]
29 --- 58 | cost [732.0]
30 --- 35 | cost [849.0]
30 --- 100 | cost [390.0]
31 --- 57 | cost [654.0]
31 --- 78 | cost [297.0]
32 --- 94 | cost [537.0]
32 --- 97 | cost [690.0]
33 --- 45 | cost [495.0]
33 --- 68 | cost [228.0]
34 --- 38 | cost [513.0]
34 --- 81 | cost [150.0]
35 --- 62 | cost [849.0]
36 --- 67 | cost [375.0]
37 --- 51 | cost [300.0]
38 --- 66 | cost [291.0]
39 --- 71 | cost [915.0]
39 --- 73 | cost [450.0]
41 --- 84 | cost [408.0]
42 --- 89 | cost [1281.0]
43 --- 64 | cost [927.0]
43 --- 77 | cost [438.0]
44 --- 60 | cost [579.0]
44 --- 93 | cost [465.0]
45 --- 99 | cost [639.0]
46 --- 52 | cost [726.0]
48 --- 92 | cost [963.0]
49 --- 70 | cost [513.0]
49 --- 98 | cost [246.0]
50 --- 101 | cost [279.0]
53 --- 60 | cost [597.0]
54 --- 63 | cost [399.0]
54 --- 91 | cost [42.0]
55 --- 87 | cost [552.0]
55 --- 92 | cost [1185.0]
56 --- 95 | cost [354.0]
57 --- 72 | cost [489.0]
59 --- 64 | cost [723.0]
59 --- 85 | cost [444.0]
61 --- 74 | cost [519.0]
61 --- 76 | cost [1443.0]
65 --- 86 | cost [876.0]
67 --- 75 | cost [144.0]
69 --- 84 | cost [1440.0]
72 --- 80 | cost [1191.0]
76 --- 80 | cost [405.0]
77 --- 91 | cost [492.0]
78 --- 99 | cost [363.0]
79 --- 88 | cost [381.0]
86 --- 96 | cost [180.0]
97 --- 98 | cost [1062.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 13 Jan 2024 14:42:26 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-13-79-88-27-24-41-84-69-15-73-39-71-4-93-44-60-53-5-62-37-19-51-35-30-100-2-48-92-55-87-26-95-56-28-12-47-21-10-9-20-25-82-18-6-40-83-3-59-85-64-43-77-91-54-63-16-96-86-65-14-68-33-45-99-78-31-57-72-80-76-61-74-7-75-67-36-29-58-22-70-49-98-97-32-94-17-90-11-89-42-23-46-52-8-66-38-81-34-50-101-1
total time           267.58               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             63882<=63882         Master/SP costs      63882/0              
Master time          267.58               SP time              0.0                  
subtour              6706.0               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       2441                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—13—79—88—27—24—41—84—69—15—73—39—71—4—93—44—60—53—5—62—37—19—51—35—30—100—2—48—92—55—87—26—95—56—28—12—47—21—10—9—20—25—82—18—6—40—83—3—59—85—64—43—77—91—54—63—16—96—86—65—14—68—33—45—99—78—31—57—72—80—76—61—74—7—75—67—36—29—58—22—70—49—98—97—32—94—17—90—11—89—42—23—46—52—8—66—38—81—34—50—101

RING
1  --- 13 | cost [1095.0]
2  --- 48 | cost [606.0]
2  --- 100 | cost [306.0]
3  --- 59 | cost [696.0]
3  --- 83 | cost [285.0]
4  --- 71 | cost [606.0]
4  --- 93 | cost [534.0]
5  --- 53 | cost [654.0]
5  --- 62 | cost [1212.0]
6  --- 18 | cost [657.0]
6  --- 40 | cost [123.0]
7  --- 74 | cost [795.0]
7  --- 75 | cost [1014.0]
8  --- 52 | cost [258.0]
8  --- 66 | cost [264.0]
9  --- 10 | cost [609.0]
9  --- 20 | cost [825.0]
10 --- 21 | cost [972.0]
11 --- 89 | cost [600.0]
11 --- 90 | cost [576.0]
12 --- 28 | cost [543.0]
12 --- 47 | cost [690.0]
13 --- 79 | cost [225.0]
14 --- 65 | cost [615.0]
14 --- 68 | cost [63.0]
15 --- 69 | cost [1005.0]
15 --- 73 | cost [969.0]
16 --- 63 | cost [441.0]
16 --- 96 | cost [945.0]
17 --- 90 | cost [165.0]
17 --- 94 | cost [555.0]
18 --- 82 | cost [1098.0]
19 --- 37 | cost [354.0]
19 --- 51 | cost [426.0]
20 --- 25 | cost [105.0]
21 --- 47 | cost [654.0]
22 --- 58 | cost [1254.0]
22 --- 70 | cost [1566.0]
23 --- 42 | cost [639.0]
23 --- 46 | cost [1782.0]
24 --- 27 | cost [186.0]
24 --- 41 | cost [759.0]
25 --- 82 | cost [1140.0]
26 --- 87 | cost [36.0]
26 --- 95 | cost [1473.0]
27 --- 88 | cost [390.0]
28 --- 56 | cost [1197.0]
29 --- 36 | cost [1245.0]
29 --- 58 | cost [732.0]
30 --- 35 | cost [849.0]
30 --- 100 | cost [390.0]
31 --- 57 | cost [654.0]
31 --- 78 | cost [297.0]
32 --- 94 | cost [537.0]
32 --- 97 | cost [690.0]
33 --- 45 | cost [495.0]
33 --- 68 | cost [228.0]
34 --- 50 | cost [909.0]
34 --- 81 | cost [150.0]
35 --- 51 | cost [708.0]
36 --- 67 | cost [375.0]
37 --- 62 | cost [528.0]
38 --- 66 | cost [291.0]
38 --- 81 | cost [567.0]
39 --- 71 | cost [915.0]
39 --- 73 | cost [450.0]
40 --- 83 | cost [93.0]
41 --- 84 | cost [408.0]
42 --- 89 | cost [1281.0]
43 --- 64 | cost [927.0]
43 --- 77 | cost [438.0]
44 --- 60 | cost [579.0]
44 --- 93 | cost [465.0]
45 --- 99 | cost [639.0]
46 --- 52 | cost [726.0]
48 --- 92 | cost [963.0]
49 --- 70 | cost [513.0]
49 --- 98 | cost [246.0]
50 --- 101 | cost [279.0]
53 --- 60 | cost [597.0]
54 --- 63 | cost [399.0]
54 --- 91 | cost [42.0]
55 --- 87 | cost [552.0]
55 --- 92 | cost [1185.0]
56 --- 95 | cost [354.0]
57 --- 72 | cost [489.0]
59 --- 85 | cost [444.0]
61 --- 74 | cost [519.0]
61 --- 76 | cost [1443.0]
64 --- 85 | cost [795.0]
65 --- 86 | cost [876.0]
67 --- 75 | cost [144.0]
69 --- 84 | cost [1440.0]
72 --- 80 | cost [1191.0]
76 --- 80 | cost [405.0]
77 --- 91 | cost [492.0]
78 --- 99 | cost [363.0]
79 --- 88 | cost [381.0]
86 --- 96 | cost [180.0]
97 --- 98 | cost [1062.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1