------------------------------------------------------------
                           α=7.0 —— eil51 —— 51 nodes       
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——————— Fri, 12 Jan 2024 19:36:37 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—32—52
total time           12.92                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2080<=2080           subtour              724.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1399                 n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—32—52

RING
1  --- 32 | cost [42.0]
3  --- 22 | cost [84.0]
3  --- 28 | cost [63.0]
4  --- 17 | cost [56.0]
4  --- 19 | cost [105.0]
6  --- 23 | cost [77.0]
6  --- 48 | cost [63.0]
9  --- 49 | cost [42.0]
9  --- 50 | cost [42.0]
11 --- 16 | cost [70.0]
11 --- 38 | cost [49.0]
16 --- 50 | cost [42.0]
17 --- 44 | cost [63.0]
19 --- 42 | cost [63.0]
22 --- 28 | cost [70.0]
23 --- 48 | cost [63.0]
32 --- 52 | cost [42.0]
38 --- 49 | cost [56.0]
42 --- 44 | cost [70.0]

STAR
2  --> 16 | cost [27.0]
5  --> 38 | cost [21.0]
7  --> 23 | cost [18.0]
8  --> 48 | cost [27.0]
10 --> 49 | cost [24.0]
12 --> 17 | cost [30.0]
13 --> 19 | cost [42.0]
14 -->  6 | cost [30.0]
15 --> 44 | cost [18.0]
18 -->  4 | cost [24.0]
20 -->  3 | cost [24.0]
21 --> 50 | cost [24.0]
24 --> 23 | cost [27.0]
25 -->  6 | cost [51.0]
26 --> 48 | cost [39.0]
27 -->  1 | cost [24.0]
29 --> 16 | cost [27.0]
30 -->  9 | cost [24.0]
31 --> 28 | cost [18.0]
33 --> 44 | cost [51.0]
34 --> 50 | cost [18.0]
35 -->  3 | cost [30.0]
36 -->  3 | cost [36.0]
37 --> 17 | cost [15.0]
39 --> 49 | cost [51.0]
40 --> 19 | cost [33.0]
41 --> 19 | cost [15.0]
43 --> 23 | cost [39.0]
45 --> 44 | cost [30.0]
46 --> 32 | cost [27.0]
47 -->  4 | cost [24.0]
51 --> 32 | cost [30.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Fri, 12 Jan 2024 19:37:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 18 hubs —— 1-22-20-29-50-9-49-5-37-17-4-18-14-24-23-48-27-52-1
total time           34.19                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             2113<=2113           Master/SP costs      2113/0               
Master time          34.19                SP time              0.0                  
subtour              6811.0               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       4384                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—22—20—29—50—9—49—5—37—17—4—18—14—24—23—48—27—52

RING
1  --- 22 | cost [49.0]
4  --- 17 | cost [56.0]
4  --- 18 | cost [56.0]
5  --- 37 | cost [77.0]
5  --- 49 | cost [56.0]
9  --- 49 | cost [42.0]
9  --- 50 | cost [42.0]
14 --- 18 | cost [70.0]
14 --- 24 | cost [77.0]
17 --- 37 | cost [35.0]
20 --- 22 | cost [105.0]
20 --- 29 | cost [70.0]
23 --- 24 | cost [63.0]
23 --- 48 | cost [63.0]
27 --- 48 | cost [63.0]
27 --- 52 | cost [56.0]
29 --- 50 | cost [77.0]

STAR
2  --> 29 | cost [27.0]
3  --> 20 | cost [24.0]
6  --> 48 | cost [27.0]
7  --> 23 | cost [18.0]
8  --> 48 | cost [27.0]
10 --> 49 | cost [24.0]
11 -->  5 | cost [33.0]
12 -->  5 | cost [27.0]
13 --> 18 | cost [42.0]
15 --> 37 | cost [21.0]
16 --> 50 | cost [18.0]
19 -->  4 | cost [45.0]
21 --> 29 | cost [21.0]
25 --> 14 | cost [18.0]
26 --> 48 | cost [39.0]
28 --> 22 | cost [30.0]
30 -->  9 | cost [24.0]
31 --> 22 | cost [39.0]
32 -->  1 | cost [18.0]
33 --> 37 | cost [54.0]
34 --> 50 | cost [18.0]
35 --> 20 | cost [21.0]
36 --> 20 | cost [39.0]
38 -->  9 | cost [21.0]
39 --> 49 | cost [51.0]
40 -->  4 | cost [75.0]
41 -->  4 | cost [39.0]
42 --> 17 | cost [42.0]
43 --> 24 | cost [36.0]
44 --> 37 | cost [21.0]
45 --> 37 | cost [42.0]
46 --> 27 | cost [27.0]
47 -->  4 | cost [24.0]
51 --> 27 | cost [24.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1