------------------------------------------------------------
                        α=7.0 —— berlin52 —— 52 nodes       
------------------------------------------------------------

——————— Thu, 04 Jan 2024 00:49:37 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 16 hubs —— 1—18—19—38—48—24—15—4—51—28—52—13—16—50—23—53
total time           3604.98 (TL 3600)    gap                  0.313                
blossom time         0                    nb blossom           0.0                  
LB <= UB             31401<=45698         subtour              56768.0              
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       15590                n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—18—19—38—48—24—15—4—51—28—52—13—16—50—23—53

RING
1  --- 18 | cost [1134.0]
4  --- 15 | cost [700.0]
4  --- 51 | cost [2779.0]
13 --- 16 | cost [5313.0]
13 --- 52 | cost [1953.0]
15 --- 24 | cost [392.0]
16 --- 50 | cost [910.0]
18 --- 19 | cost [1806.0]
19 --- 38 | cost [2562.0]
23 --- 50 | cost [889.0]
23 --- 53 | cost [1267.0]
24 --- 48 | cost [112.0]
28 --- 51 | cost [2359.0]
28 --- 52 | cost [3598.0]
38 --- 48 | cost [343.0]

STAR
2  --> 23 | cost [1530.0]
3  --> 18 | cost [405.0]
5  --> 15 | cost [75.0]
6  --> 15 | cost [120.0]
7  --> 23 | cost [1473.0]
8  --> 19 | cost [378.0]
9  --> 19 | cost [924.0]
10 --> 19 | cost [873.0]
11 --> 51 | cost [855.0]
12 --> 28 | cost [546.0]
14 --> 13 | cost [618.0]
17 --> 18 | cost [816.0]
20 --> 50 | cost [105.0]
21 --> 23 | cost [561.0]
22 -->  1 | cost [138.0]
25 -->  4 | cost [327.0]
26 --> 28 | cost [477.0]
27 --> 28 | cost [330.0]
29 --> 50 | cost [573.0]
30 --> 23 | cost [537.0]
31 --> 18 | cost [240.0]
32 -->  1 | cost [273.0]
33 --> 51 | cost [1425.0]
34 --> 38 | cost [345.0]
35 --> 38 | cost [363.0]
36 --> 38 | cost [345.0]
37 --> 38 | cost [129.0]
39 --> 38 | cost [228.0]
40 --> 38 | cost [105.0]
41 --> 19 | cost [276.0]
42 --> 23 | cost [1245.0]
43 --> 15 | cost [726.0]
44 --> 16 | cost [396.0]
45 --> 19 | cost [225.0]
46 --> 48 | cost [375.0]
47 --> 28 | cost [1032.0]
49 -->  1 | cost [192.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Thu, 04 Jan 2024 01:50:15 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 25 hubs —— 1-22-31-21-23-20-50-16-46-26-13-27-28-12-4-6-5-38-40-39-35-36-45-32-53-1
total time           3604.93 (TL 3600)    gap                  0.146                
blossom time         0                    nb blossom           0.0                  
LB <= UB             33056<=38685         Master/SP costs      38685/0              
Master time          3604.93              SP time              0.0                  
subtour              60736.0              connectivity cuts    2000.0               
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       24061                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—22—31—21—23—20—50—16—46—26—13—27—28—12—4—6—5—38—40—39—35—36—45—32—53

RING
1  --- 22 | cost [322.0]
4  ---  6 | cost [490.0]
4  --- 12 | cost [2058.0]
5  ---  6 | cost [245.0]
5  --- 38 | cost [357.0]
12 --- 28 | cost [1274.0]
13 --- 26 | cost [1778.0]
13 --- 27 | cost [1295.0]
16 --- 46 | cost [1092.0]
16 --- 50 | cost [910.0]
20 --- 23 | cost [658.0]
20 --- 50 | cost [245.0]
21 --- 23 | cost [1309.0]
21 --- 31 | cost [1050.0]
22 --- 31 | cost [728.0]
26 --- 46 | cost [3178.0]
27 --- 28 | cost [770.0]
32 --- 45 | cost [1057.0]
32 --- 53 | cost [637.0]
35 --- 36 | cost [105.0]
35 --- 39 | cost [371.0]
36 --- 45 | cost [1701.0]
38 --- 40 | cost [245.0]
39 --- 40 | cost [301.0]

STAR
2  --> 21 | cost [1176.0]
3  --> 31 | cost [627.0]
7  --> 21 | cost [1086.0]
8  --> 45 | cost [561.0]
9  --> 45 | cost [1083.0]
10 --> 45 | cost [987.0]
11 --> 12 | cost [1161.0]
14 --> 13 | cost [618.0]
15 -->  5 | cost [75.0]
17 --> 21 | cost [759.0]
18 --> 31 | cost [240.0]
19 --> 45 | cost [225.0]
24 -->  5 | cost [96.0]
25 -->  4 | cost [327.0]
29 --> 50 | cost [573.0]
30 --> 23 | cost [537.0]
33 -->  4 | cost [1551.0]
34 --> 35 | cost [63.0]
37 --> 40 | cost [123.0]
41 --> 45 | cost [498.0]
42 --> 21 | cost [870.0]
43 -->  4 | cost [735.0]
44 --> 35 | cost [288.0]
47 --> 26 | cost [558.0]
48 -->  5 | cost [141.0]
49 --> 32 | cost [150.0]
51 --> 12 | cost [564.0]
52 --> 13 | cost [837.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1