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

——————— Sat, 06 Jan 2024 10:55:43 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 25 hubs —— 1—35—36—39—40—38—24—5—6—4—12—28—27—26—16—50—20—23—21—31—18—19—45—32—53
total time           11.26                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             37376<=37376         subtour              179.0                
connectivity cuts    64.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—35—36—39—40—38—24—5—6—4—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  --- 12 | cost [2058.0]
5  ---  6 | cost [245.0]
5  --- 24 | cost [224.0]
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  --> 21 | cost [1176.0]
3  --> 18 | cost [405.0]
7  --> 21 | cost [1086.0]
8  --> 19 | cost [378.0]
9  --> 19 | cost [924.0]
10 --> 19 | cost [873.0]
11 --> 12 | cost [1161.0]
13 --> 27 | cost [555.0]
14 --> 27 | cost [1122.0]
15 -->  5 | cost [75.0]
17 --> 21 | cost [759.0]
22 -->  1 | cost [138.0]
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 --> 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 --> 26 | cost [558.0]
48 --> 24 | cost [48.0]
49 --> 32 | cost [150.0]
51 --> 12 | cost [564.0]
52 --> 27 | cost [1278.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 06 Jan 2024 10:56:20 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 25 hubs —— 1-35-36-39-40-38-24-5-6-4-12-28-27-26-16-50-20-23-21-31-18-19-45-32-53-1
total time           9.15                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             37376<=37376         Master/SP costs      37376/0              
Master time          9.15                 SP time              0.0                  
subtour              181.0                connectivity cuts    70.0                 
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       1                    
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—35—36—39—40—38—24—5—6—4—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  --- 12 | cost [2058.0]
5  ---  6 | cost [245.0]
5  --- 24 | cost [224.0]
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  --> 21 | cost [1176.0]
3  --> 18 | cost [405.0]
7  --> 21 | cost [1086.0]
8  --> 19 | cost [378.0]
9  --> 19 | cost [924.0]
10 --> 19 | cost [873.0]
11 --> 12 | cost [1161.0]
13 --> 27 | cost [555.0]
14 --> 27 | cost [1122.0]
15 -->  5 | cost [75.0]
17 --> 21 | cost [759.0]
22 -->  1 | cost [138.0]
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 --> 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 --> 26 | cost [558.0]
48 --> 24 | cost [48.0]
49 --> 32 | cost [150.0]
51 --> 12 | cost [564.0]
52 --> 27 | cost [1278.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 07:54:01 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 25 hubs —— 1—35—36—39—40—38—24—5—6—4—12—28—27—26—16—50—20—23—21—31—18—19—45—32—53
total time           11.68                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             37376<=37376         subtour              179.0                
connectivity cuts    64.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—35—36—39—40—38—24—5—6—4—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  --- 12 | cost [2058.0]
5  ---  6 | cost [245.0]
5  --- 24 | cost [224.0]
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  --> 21 | cost [1176.0]
3  --> 18 | cost [405.0]
7  --> 21 | cost [1086.0]
8  --> 19 | cost [378.0]
9  --> 19 | cost [924.0]
10 --> 19 | cost [873.0]
11 --> 12 | cost [1161.0]
13 --> 27 | cost [555.0]
14 --> 27 | cost [1122.0]
15 -->  5 | cost [75.0]
17 --> 21 | cost [759.0]
22 -->  1 | cost [138.0]
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 --> 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 --> 26 | cost [558.0]
48 --> 24 | cost [48.0]
49 --> 32 | cost [150.0]
51 --> 12 | cost [564.0]
52 --> 27 | cost [1278.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 07:54:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 25 hubs —— 1-35-36-39-40-38-24-5-6-4-12-28-27-26-16-50-20-23-21-31-18-19-45-32-53-1
total time           9.84                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             37376<=37376         Master/SP costs      37376/0              
Master time          9.84                 SP time              0.0                  
subtour              181.0                connectivity cuts    70.0                 
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       1                    
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—35—36—39—40—38—24—5—6—4—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  --- 12 | cost [2058.0]
5  ---  6 | cost [245.0]
5  --- 24 | cost [224.0]
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  --> 21 | cost [1176.0]
3  --> 18 | cost [405.0]
7  --> 21 | cost [1086.0]
8  --> 19 | cost [378.0]
9  --> 19 | cost [924.0]
10 --> 19 | cost [873.0]
11 --> 12 | cost [1161.0]
13 --> 27 | cost [555.0]
14 --> 27 | cost [1122.0]
15 -->  5 | cost [75.0]
17 --> 21 | cost [759.0]
22 -->  1 | cost [138.0]
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 --> 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 --> 26 | cost [558.0]
48 --> 24 | cost [48.0]
49 --> 32 | cost [150.0]
51 --> 12 | cost [564.0]
52 --> 27 | cost [1278.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1