------------------------------------------------------------
                          α=5.0 —— rd100 —— 100 nodes       
------------------------------------------------------------

——————— Sat, 13 Jan 2024 19:22:59 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—60—101
total time           3621.73 (TL 3600)    gap                  0.035                
blossom time         0                    nb blossom           0.0                  
LB <= UB             35240<=36525         subtour              78517.0              
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       10687                n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—60—101

RING
1  --- 60 | cost [110.0]
2  --- 23 | cost [435.0]
2  --- 89 | cost [540.0]
4  --- 32 | cost [210.0]
4  --- 75 | cost [390.0]
5  --- 61 | cost [250.0]
5  --- 81 | cost [640.0]
6  --- 53 | cost [295.0]
6  --- 79 | cost [230.0]
7  --- 40 | cost [355.0]
7  --- 41 | cost [530.0]
9  --- 26 | cost [210.0]
9  --- 32 | cost [600.0]
10 --- 33 | cost [205.0]
10 --- 79 | cost [590.0]
12 --- 14 | cost [240.0]
12 --- 85 | cost [205.0]
13 --- 49 | cost [440.0]
13 --- 64 | cost [995.0]
14 --- 85 | cost [205.0]
18 --- 62 | cost [335.0]
18 --- 87 | cost [720.0]
20 --- 74 | cost [95.0]
20 --- 78 | cost [195.0]
21 --- 49 | cost [175.0]
21 --- 75 | cost [125.0]
23 --- 89 | cost [805.0]
24 --- 42 | cost [340.0]
24 --- 43 | cost [225.0]
26 --- 74 | cost [195.0]
28 --- 77 | cost [370.0]
28 --- 95 | cost [575.0]
29 --- 96 | cost [800.0]
29 --- 100 | cost [470.0]
31 --- 84 | cost [270.0]
31 --- 88 | cost [295.0]
33 --- 78 | cost [575.0]
34 --- 41 | cost [485.0]
34 --- 61 | cost [540.0]
38 --- 70 | cost [435.0]
38 --- 72 | cost [335.0]
39 --- 55 | cost [560.0]
39 --- 96 | cost [200.0]
40 --- 55 | cost [595.0]
42 --- 43 | cost [330.0]
44 --- 52 | cost [865.0]
44 --- 100 | cost [365.0]
46 --- 73 | cost [145.0]
46 --- 92 | cost [430.0]
47 --- 57 | cost [500.0]
47 --- 99 | cost [460.0]
50 --- 73 | cost [135.0]
50 --- 92 | cost [410.0]
51 --- 83 | cost [170.0]
51 --- 90 | cost [210.0]
52 --- 57 | cost [815.0]
53 --- 99 | cost [240.0]
59 --- 77 | cost [240.0]
59 --- 95 | cost [95.0]
60 --- 101 | cost [110.0]
62 --- 87 | cost [420.0]
63 --- 86 | cost [75.0]
63 --- 97 | cost [40.0]
64 --- 91 | cost [695.0]
65 --- 80 | cost [300.0]
65 --- 91 | cost [600.0]
66 --- 76 | cost [340.0]
66 --- 98 | cost [360.0]
70 --- 72 | cost [285.0]
76 --- 98 | cost [590.0]
80 --- 81 | cost [335.0]
83 --- 90 | cost [360.0]
84 --- 88 | cost [95.0]
86 --- 97 | cost [65.0]

STAR
3  --> 33 | cost [575.0]
8  --> 60 | cost [170.0]
11 --> 61 | cost [405.0]
15 --> 63 | cost [150.0]
16 --> 98 | cost [590.0]
17 --> 72 | cost [270.0]
19 --> 46 | cost [420.0]
22 --> 41 | cost [250.0]
25 --> 43 | cost [210.0]
27 --> 92 | cost [185.0]
30 --> 80 | cost [420.0]
35 --> 29 | cost [290.0]
36 --> 57 | cost [500.0]
37 --> 28 | cost [180.0]
45 --> 44 | cost [695.0]
48 --> 80 | cost [385.0]
54 --> 38 | cost [355.0]
56 --> 46 | cost [125.0]
58 --> 76 | cost [480.0]
67 --> 97 | cost [160.0]
68 --> 83 | cost [405.0]
69 --> 60 | cost [415.0]
71 --> 60 | cost [640.0]
82 --> 75 | cost [180.0]
93 --> 77 | cost [220.0]
94 --> 98 | cost [380.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 13 Jan 2024 20:23:42 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 80 hubs —— 1-60-8-68-83-51-90-91-65-80-48-30-22-5-61-34-7-42-43-40-55-96-39-29-100-44-23-2-89-84-88-31-66-98-16-45-52-57-47-99-53-6-95-59-93-77-28-37-19-54-38-72-17-73-50-46-56-27-10-33-3-78-20-74-26-32-4-85-82-75-21-49-67-97-63-86-87-62-18-101-1
total time           3608.01 (TL 3600)    gap                  0.094                
blossom time         0                    nb blossom           0.0                  
LB <= UB             35445<=39120         Master/SP costs      39120/0              
Master time          3608.01              SP time              0.01                 
subtour              29662.0              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       20190                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—60—8—68—83—51—90—91—65—80—48—30—22—5—61—34—7—42—43—40—55—96—39—29—100—44—23—2—89—84—88—31—66—98—16—45—52—57—47—99—53—6—95—59—93—77—28—37—19—54—38—72—17—73—50—46—56—27—10—33—3—78—20—74—26—32—4—85—82—75—21—49—67—97—63—86—87—62—18—101

RING
1  --- 60 | cost [110.0]
2  --- 23 | cost [435.0]
2  --- 89 | cost [540.0]
3  --- 33 | cost [575.0]
3  --- 78 | cost [810.0]
4  --- 32 | cost [210.0]
4  --- 85 | cost [520.0]
5  --- 22 | cost [465.0]
5  --- 61 | cost [250.0]
6  --- 53 | cost [295.0]
6  --- 95 | cost [845.0]
7  --- 34 | cost [285.0]
7  --- 42 | cost [365.0]
8  --- 60 | cost [170.0]
8  --- 68 | cost [850.0]
10 --- 27 | cost [595.0]
10 --- 33 | cost [205.0]
16 --- 45 | cost [510.0]
16 --- 98 | cost [590.0]
17 --- 72 | cost [270.0]
17 --- 73 | cost [690.0]
18 --- 62 | cost [335.0]
18 --- 101 | cost [440.0]
19 --- 37 | cost [470.0]
19 --- 54 | cost [485.0]
20 --- 74 | cost [95.0]
20 --- 78 | cost [195.0]
21 --- 49 | cost [175.0]
21 --- 75 | cost [125.0]
22 --- 30 | cost [735.0]
23 --- 44 | cost [1300.0]
26 --- 32 | cost [615.0]
26 --- 74 | cost [195.0]
27 --- 56 | cost [455.0]
28 --- 37 | cost [180.0]
28 --- 77 | cost [370.0]
29 --- 39 | cost [850.0]
29 --- 100 | cost [470.0]
30 --- 48 | cost [395.0]
31 --- 66 | cost [475.0]
31 --- 88 | cost [295.0]
34 --- 61 | cost [540.0]
38 --- 54 | cost [355.0]
38 --- 72 | cost [335.0]
39 --- 96 | cost [200.0]
40 --- 43 | cost [605.0]
40 --- 55 | cost [595.0]
42 --- 43 | cost [330.0]
44 --- 100 | cost [365.0]
45 --- 52 | cost [630.0]
46 --- 50 | cost [25.0]
46 --- 56 | cost [125.0]
47 --- 57 | cost [500.0]
47 --- 99 | cost [460.0]
48 --- 80 | cost [385.0]
49 --- 67 | cost [435.0]
50 --- 73 | cost [135.0]
51 --- 83 | cost [170.0]
51 --- 90 | cost [210.0]
52 --- 57 | cost [815.0]
53 --- 99 | cost [240.0]
55 --- 96 | cost [580.0]
59 --- 93 | cost [385.0]
59 --- 95 | cost [95.0]
62 --- 87 | cost [420.0]
63 --- 86 | cost [75.0]
63 --- 97 | cost [40.0]
65 --- 80 | cost [300.0]
65 --- 91 | cost [600.0]
66 --- 98 | cost [360.0]
67 --- 97 | cost [160.0]
68 --- 83 | cost [405.0]
75 --- 82 | cost [180.0]
77 --- 93 | cost [220.0]
82 --- 85 | cost [205.0]
84 --- 88 | cost [95.0]
84 --- 89 | cost [1105.0]
86 --- 87 | cost [635.0]
90 --- 91 | cost [660.0]

STAR
9  --> 26 | cost [210.0]
11 --> 61 | cost [405.0]
12 --> 85 | cost [205.0]
13 --> 67 | cost [295.0]
14 --> 85 | cost [205.0]
15 --> 63 | cost [150.0]
24 --> 43 | cost [225.0]
25 --> 43 | cost [210.0]
35 --> 29 | cost [290.0]
36 --> 57 | cost [500.0]
41 --> 22 | cost [250.0]
58 --> 88 | cost [575.0]
64 --> 91 | cost [695.0]
69 -->  8 | cost [305.0]
70 --> 72 | cost [285.0]
71 -->  8 | cost [630.0]
76 --> 66 | cost [340.0]
79 -->  6 | cost [230.0]
81 --> 80 | cost [335.0]
92 --> 27 | cost [185.0]
94 --> 98 | cost [380.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1