------------------------------------------------------------
                        α=3.0 —— berlin52 —— 52 nodes       
------------------------------------------------------------

——————— Mon, 15 Jan 2024 16:41:06 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 53 hubs —— 1—22—31—18—3—17—21—42—7—2—30—23—20—50—29—16—46—44—34—35—36—39—40—37—38—48—24—5—15—6—4—25—12—28—27—26—47—13—14—52—11—51—33—43—10—9—8—41—19—45—32—49—53
total time           7.13                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             22626<=22626         subtour              163.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—22—31—18—3—17—21—42—7—2—30—23—20—50—29—16—46—44—34—35—36—39—40—37—38—48—24—5—15—6—4—25—12—28—27—26—47—13—14—52—11—51—33—43—10—9—8—41—19—45—32—49—53

RING
1  --- 22 | cost [138.0]
2  ---  7 | cost [135.0]
2  --- 30 | cost [1170.0]
3  --- 17 | cost [651.0]
3  --- 18 | cost [405.0]
4  ---  6 | cost [210.0]
4  --- 25 | cost [327.0]
5  --- 15 | cost [75.0]
5  --- 24 | cost [96.0]
6  --- 15 | cost [120.0]
7  --- 42 | cost [228.0]
8  ---  9 | cost [549.0]
8  --- 41 | cost [192.0]
9  --- 10 | cost [249.0]
10 --- 43 | cost [924.0]
11 --- 51 | cost [855.0]
11 --- 52 | cost [1197.0]
12 --- 25 | cost [735.0]
12 --- 28 | cost [546.0]
13 --- 14 | cost [618.0]
13 --- 47 | cost [972.0]
14 --- 52 | cost [957.0]
16 --- 29 | cost [603.0]
16 --- 46 | cost [468.0]
17 --- 21 | cost [759.0]
18 --- 31 | cost [240.0]
19 --- 41 | cost [276.0]
19 --- 45 | cost [225.0]
20 --- 23 | cost [282.0]
20 --- 50 | cost [105.0]
21 --- 42 | cost [870.0]
22 --- 31 | cost [312.0]
23 --- 30 | cost [537.0]
24 --- 48 | cost [48.0]
26 --- 27 | cost [378.0]
26 --- 47 | cost [558.0]
27 --- 28 | cost [330.0]
29 --- 50 | cost [573.0]
32 --- 45 | cost [453.0]
32 --- 49 | cost [150.0]
33 --- 43 | cost [1095.0]
33 --- 51 | cost [1425.0]
34 --- 35 | cost [63.0]
34 --- 44 | cost [240.0]
35 --- 36 | cost [45.0]
36 --- 39 | cost [129.0]
37 --- 38 | cost [129.0]
37 --- 40 | cost [123.0]
38 --- 48 | cost [147.0]
39 --- 40 | cost [129.0]
44 --- 46 | cost [393.0]
49 --- 53 | cost [192.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 15 Jan 2024 16:41:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 53 hubs —— 1-22-31-18-3-17-21-42-7-2-30-23-20-50-29-16-46-44-34-35-36-39-40-37-38-48-24-5-15-6-4-25-12-28-27-26-47-13-14-52-11-51-33-43-10-9-8-41-19-45-32-49-53-1
total time           7.41                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             22626<=22626         Master/SP costs      22626/0              
Master time          7.41                 SP time              0.0                  
subtour              244.0                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       1                    
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—22—31—18—3—17—21—42—7—2—30—23—20—50—29—16—46—44—34—35—36—39—40—37—38—48—24—5—15—6—4—25—12—28—27—26—47—13—14—52—11—51—33—43—10—9—8—41—19—45—32—49—53

RING
1  --- 22 | cost [138.0]
2  ---  7 | cost [135.0]
2  --- 30 | cost [1170.0]
3  --- 17 | cost [651.0]
3  --- 18 | cost [405.0]
4  ---  6 | cost [210.0]
4  --- 25 | cost [327.0]
5  --- 15 | cost [75.0]
5  --- 24 | cost [96.0]
6  --- 15 | cost [120.0]
7  --- 42 | cost [228.0]
8  ---  9 | cost [549.0]
8  --- 41 | cost [192.0]
9  --- 10 | cost [249.0]
10 --- 43 | cost [924.0]
11 --- 51 | cost [855.0]
11 --- 52 | cost [1197.0]
12 --- 25 | cost [735.0]
12 --- 28 | cost [546.0]
13 --- 14 | cost [618.0]
13 --- 47 | cost [972.0]
14 --- 52 | cost [957.0]
16 --- 29 | cost [603.0]
16 --- 46 | cost [468.0]
17 --- 21 | cost [759.0]
18 --- 31 | cost [240.0]
19 --- 41 | cost [276.0]
19 --- 45 | cost [225.0]
20 --- 23 | cost [282.0]
20 --- 50 | cost [105.0]
21 --- 42 | cost [870.0]
22 --- 31 | cost [312.0]
23 --- 30 | cost [537.0]
24 --- 48 | cost [48.0]
26 --- 27 | cost [378.0]
26 --- 47 | cost [558.0]
27 --- 28 | cost [330.0]
29 --- 50 | cost [573.0]
32 --- 45 | cost [453.0]
32 --- 49 | cost [150.0]
33 --- 43 | cost [1095.0]
33 --- 51 | cost [1425.0]
34 --- 35 | cost [63.0]
34 --- 44 | cost [240.0]
35 --- 36 | cost [45.0]
36 --- 39 | cost [129.0]
37 --- 38 | cost [129.0]
37 --- 40 | cost [123.0]
38 --- 48 | cost [147.0]
39 --- 40 | cost [129.0]
44 --- 46 | cost [393.0]
49 --- 53 | cost [192.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1