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

——————— Mon, 29 Jan 2024 03:31:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 27 hubs —— 1—35—36—39—40—38—24—5—6—4—25—12—28—27—26—46—16—50—20—23—21—31—18—19—45—32—53
total time           3607.86 (TL 3600)    gap                  0.097                
blossom time         0                    nb blossom           0.0                  
LB <= UB             41812.37<=46327.09   subtour              191.0                
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               2:52                 
2-opt strategy       0                                                              
explored_nodes       7888                 n lazycuts edges     4.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—35—36—39—40—38—24—5—6—4—25—12—28—27—26—46—16—50—20—23—21—31—18—19—45—32—53

RING
1  --- 35 | cost [854.0]
1  --- 53 | cost [0.0]
4  ---  6 | cost [490.0]
4  --- 25 | cost [763.0]
5  ---  6 | cost [245.0]
5  --- 24 | cost [224.0]
12 --- 25 | cost [1715.0]
12 --- 28 | cost [1274.0]
16 --- 46 | cost [1092.0]
16 --- 50 | cost [910.0]
18 --- 19 | cost [1806.0]
18 --- 31 | cost [560.0]
19 --- 45 | cost [525.0]
20 --- 23 | cost [658.0]
20 --- 50 | cost [245.0]
21 --- 23 | cost [1309.0]
21 --- 31 | cost [1050.0]
24 --- 38 | cost [315.0]
26 --- 27 | cost [882.0]
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]
36 --- 39 | cost [301.0]
38 --- 40 | cost [245.0]
39 --- 40 | cost [301.0]

STAR
2  --> 23 | cost [1530.0]
3  --> 18 | cost [405.0]
7  --> 21 | cost [1086.0]
8  --> 19 | cost [378.0]
9  --> 19 | cost [924.0]
10 --> 45 | cost [987.0]
11 --> 12 | cost [1161.0]
13 --> 27 | cost [555.0]
14 --> 27 | cost [1122.0]
15 -->  5 | cost [75.0]
17 --> 18 | cost [816.0]
22 -->  1 | cost [138.0]
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 --> 19 | cost [276.0]
42 --> 21 | cost [870.0]
43 -->  4 | cost [735.0]
44 --> 35 | cost [288.0]
47 --> 27 | cost [876.0]
48 --> 24 | cost [48.0]
49 --> 32 | cost [150.0]
51 --> 28 | cost [1011.0]
52 --> 28 | cost [1542.0]

BACKUP RING
1  --- 36 | cost [8.75]
4  ---  5 | cost [7.28]
4  --- 12 | cost [20.580000000000002]
5  --- 38 | cost [3.5700000000000003]
6  --- 24 | cost [3.99]
6  --- 25 | cost [8.68]
12 --- 27 | cost [19.81]
16 --- 20 | cost [11.55]
16 --- 26 | cost [35.42]
18 --- 21 | cost [14.35]
18 --- 45 | cost [15.96]
19 --- 31 | cost [23.240000000000002]
19 --- 32 | cost [15.4]
20 --- 21 | cost [19.53]
23 --- 31 | cost [10.64]
23 --- 50 | cost [8.89]
24 --- 40 | cost [5.53]
25 --- 28 | cost [23.03]
26 --- 28 | cost [11.13]
27 --- 46 | cost [36.33]
35 --- 39 | cost [3.71]
36 --- 40 | cost [5.95]
38 --- 39 | cost [5.32]
45 --- 53 | cost [16.8]
46 --- 50 | cost [18.62]

BACKUP STAR
2  --> 21 | cost [11.76]
3  --> 19 | cost [6.21]
7  --> 23 | cost [14.73]
8  --> 45 | cost [5.61]
9  --> 45 | cost [10.83]
10 --> 19 | cost [8.73]
11 --> 27 | cost [12.51]
13 --> 26 | cost [7.62]
14 --> 26 | cost [11.88]
15 -->  6 | cost [1.2]
17 --> 21 | cost [7.59]
29 --> 16 | cost [6.03]
30 --> 20 | cost [5.67]
33 -->  6 | cost [17.04]
34 --> 36 | cost [1.02]
37 --> 38 | cost [1.29]
41 --> 45 | cost [4.98]
42 --> 23 | cost [12.450000000000001]
43 -->  6 | cost [7.8]
44 --> 36 | cost [3.33]
47 --> 26 | cost [5.58]
48 -->  5 | cost [1.41]
49 -->  1 | cost [1.92]
51 --> 12 | cost [5.64]
52 --> 27 | cost [12.780000000000001]

B = 38.230000000000004
i★ = 12
j★ = 28
k★ = 27

       
——————— Mon, 29 Jan 2024 04:32:24 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 26 hubs —— 1-35-36-39-40-38-24-5-6-4-25-12-28-27-26-16-50-20-23-21-31-18-19-45-32-53-1
total time           3603.89 (TL 3600)    gap                  0.161                
blossom time         0                    nb blossom           0.0                  
LB <= UB             39296.64<=46815.11   Master/SP costs      38732/8083.11        
Master time          3542.91              SP time              60.98                
subtour              9148.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            4442.0               SP method            poly                 
tildeV               2:52                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       125345               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—35—36—39—40—38—24—5—6—4—25—12—28—27—26—16—50—20—23—21—31—18—19—45—32—53

RING
1  --- 35 | cost [854.0]
1  --- 53 | cost [0.0]
4  ---  6 | cost [490.0]
4  --- 25 | cost [763.0]
5  ---  6 | cost [245.0]
5  --- 24 | cost [224.0]
12 --- 25 | cost [1715.0]
12 --- 28 | cost [1274.0]
16 --- 26 | cost [3542.0]
16 --- 50 | cost [910.0]
18 --- 19 | cost [1806.0]
18 --- 31 | cost [560.0]
19 --- 45 | cost [525.0]
20 --- 23 | cost [658.0]
20 --- 50 | cost [245.0]
21 --- 23 | cost [1309.0]
21 --- 31 | cost [1050.0]
24 --- 38 | cost [315.0]
26 --- 27 | cost [882.0]
27 --- 28 | cost [770.0]
32 --- 45 | cost [1057.0]
32 --- 53 | cost [637.0]
35 --- 36 | cost [105.0]
36 --- 39 | cost [301.0]
38 --- 40 | cost [245.0]
39 --- 40 | cost [301.0]

STAR
2  --> 23 | cost [1530.0]
3  --> 18 | cost [405.0]
7  --> 21 | cost [1086.0]
8  --> 19 | cost [378.0]
9  --> 19 | cost [924.0]
10 --> 45 | cost [987.0]
11 --> 28 | cost [1254.0]
13 --> 28 | cost [882.0]
14 --> 27 | cost [1122.0]
15 -->  5 | cost [75.0]
17 --> 18 | cost [816.0]
22 -->  1 | cost [138.0]
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 --> 19 | cost [276.0]
42 --> 21 | cost [870.0]
43 -->  4 | cost [735.0]
44 --> 35 | cost [288.0]
46 --> 24 | cost [420.0]
47 --> 27 | cost [876.0]
48 --> 24 | cost [48.0]
49 --> 32 | cost [150.0]
51 --> 12 | cost [564.0]
52 --> 27 | cost [1278.0]

BACKUP RING
1  --- 36 | cost [8.75]
4  ---  5 | cost [7.28]
4  --- 12 | cost [20.580000000000002]
5  --- 38 | cost [3.5700000000000003]
6  --- 24 | cost [3.99]
6  --- 25 | cost [8.68]
12 --- 27 | cost [19.81]
16 --- 20 | cost [11.55]
16 --- 27 | cost [41.86]
18 --- 21 | cost [14.35]
18 --- 45 | cost [15.96]
19 --- 31 | cost [23.240000000000002]
19 --- 32 | cost [15.4]
20 --- 21 | cost [19.53]
23 --- 31 | cost [10.64]
23 --- 50 | cost [8.89]
24 --- 40 | cost [5.53]
25 --- 28 | cost [23.03]
26 --- 28 | cost [11.13]
26 --- 50 | cost [44.17]
35 --- 39 | cost [3.71]
36 --- 40 | cost [5.95]
38 --- 39 | cost [5.32]
45 --- 53 | cost [16.8]

BACKUP STAR
2  --> 21 | cost [11.76]
3  --> 19 | cost [6.21]
7  --> 23 | cost [14.73]
8  --> 45 | cost [5.61]
9  --> 45 | cost [10.83]
10 --> 19 | cost [8.73]
11 --> 12 | cost [11.61]
13 --> 27 | cost [5.55]
14 --> 26 | cost [11.88]
15 -->  6 | cost [1.2]
17 --> 21 | cost [7.59]
29 --> 16 | cost [6.03]
30 --> 20 | cost [5.67]
33 -->  6 | cost [17.04]
34 --> 36 | cost [1.02]
37 --> 38 | cost [1.29]
41 --> 45 | cost [4.98]
42 --> 23 | cost [12.450000000000001]
43 -->  6 | cost [7.8]
44 --> 36 | cost [3.33]
46 --> 16 | cost [4.68]
47 --> 26 | cost [5.58]
48 -->  5 | cost [1.41]
49 -->  1 | cost [1.92]
51 --> 28 | cost [10.11]
52 --> 28 | cost [15.42]

B = 44.17
i★ = 26
j★ = 16
k★ = 50