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

——————— Sat, 20 Jan 2024 14:16:45 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 43 hubs —— 1—22—18—31—21—42—7—30—23—20—50—16—44—34—35—36—39—40—38—48—24—5—6—4—25—12—28—26—27—13—52—11—51—33—43—10—8—41—19—45—32—49—53
total time           295.8                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             37334.75<=37334.75   subtour              6469.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:52                 
2-opt strategy       0                                                              
explored_nodes       2334                 n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—22—18—31—21—42—7—30—23—20—50—16—44—34—35—36—39—40—38—48—24—5—6—4—25—12—28—26—27—13—52—11—51—33—43—10—8—41—19—45—32—49—53

RING
1  --- 22 | cost [230.0]
4  ---  6 | cost [350.0]
4  --- 25 | cost [545.0]
5  ---  6 | cost [175.0]
5  --- 24 | cost [160.0]
7  --- 30 | cost [1930.0]
7  --- 42 | cost [380.0]
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]
23 --- 30 | cost [895.0]
24 --- 48 | cost [80.0]
26 --- 27 | cost [630.0]
26 --- 28 | cost [795.0]
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]
49 --- 53 | cost [320.0]

STAR
2  -->  7 | cost [225.0]
3  --> 18 | cost [675.0]
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
1  --- 18 | cost [8.1]
4  ---  5 | cost [5.2]
4  --- 12 | cost [14.700000000000001]
5  --- 48 | cost [2.35]
6  --- 24 | cost [2.85]
6  --- 25 | cost [6.2]
7  --- 21 | cost [18.1]
7  --- 23 | cost [24.55]
8  --- 19 | cost [6.3]
8  --- 43 | cost [17.95]
10 --- 33 | cost [25.05]
10 --- 41 | cost [12.200000000000001]
11 --- 13 | cost [22.150000000000002]
11 --- 33 | cost [35.300000000000004]
12 --- 26 | cost [16.75]
13 --- 26 | cost [12.700000000000001]
16 --- 20 | cost [8.25]
16 --- 34 | cost [10.55]
18 --- 21 | cost [10.25]
19 --- 32 | cost [11.0]
20 --- 30 | cost [9.450000000000001]
22 --- 31 | cost [5.2]
23 --- 50 | cost [6.3500000000000005]
24 --- 38 | cost [2.25]
25 --- 28 | cost [16.45]
27 --- 28 | cost [5.5]
27 --- 52 | cost [21.3]
30 --- 42 | cost [15.75]
31 --- 42 | cost [21.95]
32 --- 53 | cost [4.55]
34 --- 36 | cost [1.7]
35 --- 39 | cost [2.65]
35 --- 44 | cost [4.8]
36 --- 40 | cost [4.25]
38 --- 39 | cost [3.8000000000000003]
40 --- 48 | cost [4.05]
41 --- 45 | cost [8.3]
43 --- 51 | cost [25.2]
44 --- 50 | cost [8.75]
45 --- 49 | cost [9.8]
51 --- 52 | cost [31.25]

BACKUP STAR
2  --> 42 | cost [5.15]
3  --> 19 | cost [10.35]
9  -->  8 | cost [9.15]
14 --> 52 | cost [15.950000000000001]
15 -->  6 | cost [2.0]
17 --> 18 | cost [13.6]
29 --> 16 | cost [10.05]
37 --> 38 | cost [2.15]
46 --> 44 | cost [6.55]
47 --> 27 | cost [14.6]

B = 37.25
i★ = 27
j★ = 13
k★ = 52

       
——————— Sat, 20 Jan 2024 14:20:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 43 hubs —— 1-49-32-45-19-41-8-10-43-33-51-11-52-13-27-26-28-12-25-4-6-5-24-48-38-40-39-36-35-34-44-16-50-20-23-30-7-42-21-31-18-22-53-1
total time           192.46               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             37334.75<=37334.75   Master/SP costs      36180/1154.75        
Master time          191.69               SP time              0.77                 
subtour              26168.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            43.0                 SP method            poly                 
tildeV               2:52                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       4370                 
F                    31.0                 
                                          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—7—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]
7  --- 30 | cost [1930.0]
7  --- 42 | cost [380.0]
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]
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  -->  7 | cost [225.0]
3  --> 18 | cost [675.0]
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
1  --- 32 | cost [4.55]
4  ---  5 | cost [5.2]
4  --- 12 | cost [14.700000000000001]
5  --- 48 | cost [2.35]
6  --- 24 | cost [2.85]
6  --- 25 | cost [6.2]
7  --- 21 | cost [18.1]
7  --- 23 | cost [24.55]
8  --- 19 | cost [6.3]
8  --- 43 | cost [17.95]
10 --- 33 | cost [25.05]
10 --- 41 | cost [12.200000000000001]
11 --- 13 | cost [22.150000000000002]
11 --- 33 | cost [35.300000000000004]
12 --- 26 | cost [16.75]
13 --- 26 | cost [12.700000000000001]
16 --- 20 | cost [8.25]
16 --- 34 | cost [10.55]
18 --- 21 | cost [10.25]
18 --- 53 | cost [8.1]
19 --- 32 | cost [11.0]
20 --- 30 | cost [9.450000000000001]
22 --- 31 | cost [5.2]
23 --- 50 | cost [6.3500000000000005]
24 --- 38 | cost [2.25]
25 --- 28 | cost [16.45]
27 --- 28 | cost [5.5]
27 --- 52 | cost [21.3]
30 --- 42 | cost [15.75]
31 --- 42 | cost [21.95]
34 --- 36 | cost [1.7]
35 --- 39 | cost [2.65]
35 --- 44 | cost [4.8]
36 --- 40 | cost [4.25]
38 --- 39 | cost [3.8000000000000003]
40 --- 48 | cost [4.05]
41 --- 45 | cost [8.3]
43 --- 51 | cost [25.2]
44 --- 50 | cost [8.75]
45 --- 49 | cost [9.8]
51 --- 52 | cost [31.25]

BACKUP STAR
2  --> 42 | cost [5.15]
3  --> 19 | cost [10.35]
9  -->  8 | cost [9.15]
14 --> 52 | cost [15.950000000000001]
15 -->  6 | cost [2.0]
17 --> 18 | cost [13.6]
29 --> 16 | cost [10.05]
37 --> 38 | cost [2.15]
46 --> 44 | cost [6.55]
47 --> 27 | cost [14.6]

B = 37.25
i★ = 27
j★ = 13
k★ = 52