------------------------------------------------------------
                        α=5.0 —— berlin52 —— 52 nodes       
------------------------------------------------------------

——————— Wed, 24 Jan 2024 18:15:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 42 hubs —— 1—49—32—45—19—41—8—10—43—33—51—11—52—13—27—26—28—12—25—4—6—5—24—48—38—40—39—36—35—34—44—16—50—20—23—30—42—21—31—18—22—53
total time           45.92                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             36115<=36115         subtour              7282.0               
connectivity cuts    560.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       730                  n lazycuts edges     4.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—49—32—45—19—41—8—10—43—33—51—11—52—13—27—26—28—12—25—4—6—5—24—48—38—40—39—36—35—34—44—16—50—20—23—30—42—21—31—18—22—53

RING
1  --- 49 | cost [320.0]
4  ---  6 | cost [350.0]
4  --- 25 | cost [545.0]
5  ---  6 | cost [175.0]
5  --- 24 | cost [160.0]
8  --- 10 | cost [900.0]
8  --- 41 | cost [320.0]
10 --- 43 | cost [1540.0]
11 --- 51 | cost [1425.0]
11 --- 52 | cost [1995.0]
12 --- 25 | cost [1225.0]
12 --- 28 | cost [910.0]
13 --- 27 | cost [925.0]
13 --- 52 | cost [1395.0]
16 --- 44 | cost [660.0]
16 --- 50 | cost [650.0]
18 --- 22 | cost [580.0]
18 --- 31 | cost [400.0]
19 --- 41 | cost [460.0]
19 --- 45 | cost [375.0]
20 --- 23 | cost [470.0]
20 --- 50 | cost [175.0]
21 --- 31 | cost [750.0]
21 --- 42 | cost [1450.0]
22 --- 53 | cost [230.0]
23 --- 30 | cost [895.0]
24 --- 48 | cost [80.0]
26 --- 27 | cost [630.0]
26 --- 28 | cost [795.0]
30 --- 42 | cost [1575.0]
32 --- 45 | cost [755.0]
32 --- 49 | cost [250.0]
33 --- 43 | cost [1825.0]
33 --- 51 | cost [2375.0]
34 --- 35 | cost [105.0]
34 --- 44 | cost [400.0]
35 --- 36 | cost [75.0]
36 --- 39 | cost [215.0]
38 --- 40 | cost [175.0]
38 --- 48 | cost [245.0]
39 --- 40 | cost [215.0]

STAR
2  --> 42 | cost [515.0]
3  --> 18 | cost [675.0]
7  --> 42 | cost [380.0]
9  --> 10 | cost [415.0]
14 --> 13 | cost [1030.0]
15 -->  5 | cost [125.0]
17 --> 21 | cost [1265.0]
29 --> 50 | cost [955.0]
37 --> 40 | cost [205.0]
46 --> 48 | cost [625.0]
47 --> 26 | cost [930.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 24 Jan 2024 18:17:16 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 42 hubs —— 1-49-32-45-19-41-8-10-43-33-51-11-52-13-27-26-28-12-25-4-6-5-24-48-38-40-39-36-35-34-44-16-50-20-23-30-42-21-31-18-22-53-1
total time           56.9                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             36115<=36115         Master/SP costs      36115/0              
Master time          56.9                 SP time              0.0                  
subtour              8095.0               connectivity cuts    728.0                
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       943                  
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—49—32—45—19—41—8—10—43—33—51—11—52—13—27—26—28—12—25—4—6—5—24—48—38—40—39—36—35—34—44—16—50—20—23—30—42—21—31—18—22—53

RING
1  --- 49 | cost [320.0]
4  ---  6 | cost [350.0]
4  --- 25 | cost [545.0]
5  ---  6 | cost [175.0]
5  --- 24 | cost [160.0]
8  --- 10 | cost [900.0]
8  --- 41 | cost [320.0]
10 --- 43 | cost [1540.0]
11 --- 51 | cost [1425.0]
11 --- 52 | cost [1995.0]
12 --- 25 | cost [1225.0]
12 --- 28 | cost [910.0]
13 --- 27 | cost [925.0]
13 --- 52 | cost [1395.0]
16 --- 44 | cost [660.0]
16 --- 50 | cost [650.0]
18 --- 22 | cost [580.0]
18 --- 31 | cost [400.0]
19 --- 41 | cost [460.0]
19 --- 45 | cost [375.0]
20 --- 23 | cost [470.0]
20 --- 50 | cost [175.0]
21 --- 31 | cost [750.0]
21 --- 42 | cost [1450.0]
22 --- 53 | cost [230.0]
23 --- 30 | cost [895.0]
24 --- 48 | cost [80.0]
26 --- 27 | cost [630.0]
26 --- 28 | cost [795.0]
30 --- 42 | cost [1575.0]
32 --- 45 | cost [755.0]
32 --- 49 | cost [250.0]
33 --- 43 | cost [1825.0]
33 --- 51 | cost [2375.0]
34 --- 35 | cost [105.0]
34 --- 44 | cost [400.0]
35 --- 36 | cost [75.0]
36 --- 39 | cost [215.0]
38 --- 40 | cost [175.0]
38 --- 48 | cost [245.0]
39 --- 40 | cost [215.0]

STAR
2  --> 42 | cost [515.0]
3  --> 18 | cost [675.0]
7  --> 42 | cost [380.0]
9  --> 10 | cost [415.0]
14 --> 13 | cost [1030.0]
15 -->  5 | cost [125.0]
17 --> 21 | cost [1265.0]
29 --> 50 | cost [955.0]
37 --> 40 | cost [205.0]
46 --> 48 | cost [625.0]
47 --> 26 | cost [930.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1