------------------------------------------------------------
                        α=5.0 —— kroA100 —— 100 nodes       
------------------------------------------------------------

——————— Tue, 23 Jan 2024 14:43:39 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 81 hubs —— 1—93—28—58—61—25—81—69—64—40—54—2—44—73—68—50—82—95—13—33—37—5—78—96—39—30—48—100—71—14—3—46—29—34—83—55—7—57—20—12—27—86—62—60—23—98—91—32—11—15—17—74—21—72—10—84—36—38—24—18—79—53—88—16—22—70—66—65—4—97—56—80—31—89—42—8—92—49—6—63—101
total time           220.99               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             100785<=100785       subtour              4365.0               
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       3138                 n lazycuts edges     6.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—93—28—58—61—25—81—69—64—40—54—2—44—73—68—50—82—95—13—33—37—5—78—96—39—30—48—100—71—14—3—46—29—34—83—55—7—57—20—12—27—86—62—60—23—98—91—32—11—15—17—74—21—72—10—84—36—38—24—18—79—53—88—16—22—70—66—65—4—97—56—80—31—89—42—8—92—49—6—63—101

RING
1  --- 93 | cost [2065.0]
1  --- 101 | cost [0.0]
2  --- 44 | cost [1285.0]
2  --- 54 | cost [1655.0]
3  --- 14 | cost [1105.0]
3  --- 46 | cost [695.0]
4  --- 65 | cost [735.0]
4  --- 97 | cost [1620.0]
5  --- 37 | cost [345.0]
5  --- 78 | cost [1210.0]
6  --- 49 | cost [235.0]
6  --- 63 | cost [785.0]
7  --- 55 | cost [1320.0]
7  --- 57 | cost [465.0]
8  --- 42 | cost [1240.0]
8  --- 92 | cost [1030.0]
10 --- 72 | cost [1350.0]
10 --- 84 | cost [700.0]
11 --- 15 | cost [565.0]
11 --- 32 | cost [1010.0]
12 --- 20 | cost [770.0]
12 --- 27 | cost [680.0]
13 --- 33 | cost [505.0]
13 --- 95 | cost [1080.0]
14 --- 71 | cost [1340.0]
15 --- 17 | cost [65.0]
16 --- 22 | cost [350.0]
16 --- 88 | cost [290.0]
17 --- 74 | cost [1770.0]
18 --- 24 | cost [905.0]
18 --- 79 | cost [1150.0]
20 --- 57 | cost [1020.0]
21 --- 72 | cost [760.0]
21 --- 74 | cost [330.0]
22 --- 70 | cost [930.0]
23 --- 60 | cost [1725.0]
23 --- 98 | cost [540.0]
24 --- 38 | cost [480.0]
25 --- 61 | cost [825.0]
25 --- 81 | cost [255.0]
27 --- 86 | cost [405.0]
28 --- 58 | cost [1515.0]
28 --- 93 | cost [240.0]
29 --- 34 | cost [1505.0]
29 --- 46 | cost [740.0]
30 --- 39 | cost [1305.0]
30 --- 48 | cost [2135.0]
31 --- 80 | cost [435.0]
31 --- 89 | cost [940.0]
32 --- 91 | cost [1075.0]
33 --- 37 | cost [2040.0]
34 --- 83 | cost [730.0]
36 --- 38 | cost [1140.0]
36 --- 84 | cost [1610.0]
39 --- 96 | cost [1420.0]
40 --- 54 | cost [520.0]
40 --- 64 | cost [400.0]
42 --- 89 | cost [900.0]
44 --- 73 | cost [1165.0]
48 --- 100 | cost [1260.0]
49 --- 92 | cost [1760.0]
50 --- 68 | cost [1600.0]
50 --- 82 | cost [2575.0]
53 --- 79 | cost [1115.0]
53 --- 88 | cost [1150.0]
55 --- 83 | cost [115.0]
56 --- 80 | cost [1405.0]
56 --- 97 | cost [1080.0]
58 --- 61 | cost [1625.0]
60 --- 62 | cost [755.0]
62 --- 86 | cost [1540.0]
63 --- 101 | cost [1440.0]
64 --- 69 | cost [1485.0]
65 --- 66 | cost [575.0]
66 --- 70 | cost [2000.0]
68 --- 73 | cost [1335.0]
69 --- 81 | cost [1515.0]
71 --- 100 | cost [605.0]
78 --- 96 | cost [340.0]
82 --- 95 | cost [1225.0]
91 --- 98 | cost [495.0]

STAR
9  -->  7 | cost [250.0]
19 --> 53 | cost [1400.0]
26 --> 65 | cost [1415.0]
35 --> 86 | cost [705.0]
41 --> 71 | cost [415.0]
43 -->  3 | cost [855.0]
45 --> 91 | cost [895.0]
47 --> 32 | cost [1805.0]
51 --> 61 | cost [930.0]
52 --> 78 | cost [200.0]
59 --> 74 | cost [445.0]
67 --> 28 | cost [1505.0]
75 --> 97 | cost [1185.0]
76 --> 33 | cost [460.0]
77 --> 60 | cost [955.0]
85 --> 68 | cost [765.0]
87 --> 57 | cost [990.0]
90 --> 49 | cost [1040.0]
94 --> 22 | cost [670.0]
99 --> 36 | cost [1500.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 23 Jan 2024 14:48:09 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 81 hubs —— 1-93-28-58-61-25-81-69-64-40-54-2-44-73-68-50-82-95-13-33-37-5-78-96-39-30-48-100-71-14-3-46-29-34-83-55-7-57-20-12-27-86-62-60-23-98-91-32-11-15-17-74-21-72-10-84-36-38-24-18-79-53-88-16-22-70-66-65-4-97-56-80-31-89-42-8-92-49-6-63-101-1
total time           239.65               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             100785<=100785       Master/SP costs      100785/0             
Master time          239.65               SP time              0.0                  
subtour              13920.0              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       4003                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—93—28—58—61—25—81—69—64—40—54—2—44—73—68—50—82—95—13—33—37—5—78—96—39—30—48—100—71—14—3—46—29—34—83—55—7—57—20—12—27—86—62—60—23—98—91—32—11—15—17—74—21—72—10—84—36—38—24—18—79—53—88—16—22—70—66—65—4—97—56—80—31—89—42—8—92—49—6—63—101

RING
1  --- 93 | cost [2065.0]
2  --- 44 | cost [1285.0]
2  --- 54 | cost [1655.0]
3  --- 14 | cost [1105.0]
3  --- 46 | cost [695.0]
4  --- 65 | cost [735.0]
4  --- 97 | cost [1620.0]
5  --- 37 | cost [345.0]
5  --- 78 | cost [1210.0]
6  --- 49 | cost [235.0]
6  --- 63 | cost [785.0]
7  --- 55 | cost [1320.0]
7  --- 57 | cost [465.0]
8  --- 42 | cost [1240.0]
8  --- 92 | cost [1030.0]
10 --- 72 | cost [1350.0]
10 --- 84 | cost [700.0]
11 --- 15 | cost [565.0]
11 --- 32 | cost [1010.0]
12 --- 20 | cost [770.0]
12 --- 27 | cost [680.0]
13 --- 33 | cost [505.0]
13 --- 95 | cost [1080.0]
14 --- 71 | cost [1340.0]
15 --- 17 | cost [65.0]
16 --- 22 | cost [350.0]
16 --- 88 | cost [290.0]
17 --- 74 | cost [1770.0]
18 --- 24 | cost [905.0]
18 --- 79 | cost [1150.0]
20 --- 57 | cost [1020.0]
21 --- 72 | cost [760.0]
21 --- 74 | cost [330.0]
22 --- 70 | cost [930.0]
23 --- 60 | cost [1725.0]
23 --- 98 | cost [540.0]
24 --- 38 | cost [480.0]
25 --- 61 | cost [825.0]
25 --- 81 | cost [255.0]
27 --- 86 | cost [405.0]
28 --- 58 | cost [1515.0]
28 --- 93 | cost [240.0]
29 --- 34 | cost [1505.0]
29 --- 46 | cost [740.0]
30 --- 39 | cost [1305.0]
30 --- 48 | cost [2135.0]
31 --- 80 | cost [435.0]
31 --- 89 | cost [940.0]
32 --- 91 | cost [1075.0]
33 --- 37 | cost [2040.0]
34 --- 83 | cost [730.0]
36 --- 38 | cost [1140.0]
36 --- 84 | cost [1610.0]
39 --- 96 | cost [1420.0]
40 --- 54 | cost [520.0]
40 --- 64 | cost [400.0]
42 --- 89 | cost [900.0]
44 --- 73 | cost [1165.0]
48 --- 100 | cost [1260.0]
49 --- 92 | cost [1760.0]
50 --- 68 | cost [1600.0]
50 --- 82 | cost [2575.0]
53 --- 79 | cost [1115.0]
53 --- 88 | cost [1150.0]
55 --- 83 | cost [115.0]
56 --- 80 | cost [1405.0]
56 --- 97 | cost [1080.0]
58 --- 61 | cost [1625.0]
60 --- 62 | cost [755.0]
62 --- 86 | cost [1540.0]
63 --- 101 | cost [1440.0]
64 --- 69 | cost [1485.0]
65 --- 66 | cost [575.0]
66 --- 70 | cost [2000.0]
68 --- 73 | cost [1335.0]
69 --- 81 | cost [1515.0]
71 --- 100 | cost [605.0]
78 --- 96 | cost [340.0]
82 --- 95 | cost [1225.0]
91 --- 98 | cost [495.0]

STAR
9  -->  7 | cost [250.0]
19 --> 53 | cost [1400.0]
26 --> 65 | cost [1415.0]
35 --> 86 | cost [705.0]
41 --> 71 | cost [415.0]
43 -->  3 | cost [855.0]
45 --> 91 | cost [895.0]
47 --> 32 | cost [1805.0]
51 --> 61 | cost [930.0]
52 --> 78 | cost [200.0]
59 --> 74 | cost [445.0]
67 --> 28 | cost [1505.0]
75 --> 97 | cost [1185.0]
76 --> 33 | cost [460.0]
77 --> 60 | cost [955.0]
85 --> 68 | cost [765.0]
87 --> 57 | cost [990.0]
90 --> 49 | cost [1040.0]
94 --> 22 | cost [670.0]
99 --> 36 | cost [1500.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1