------------------------------------------------------------
                        α=5.0 —— brazil58 —— 58 nodes       
------------------------------------------------------------

——————— Sat, 06 Jan 2024 10:58:16 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 22 hubs —— 1—30—13—40—25—32—20—53—50—4—54—55—22—8—5—27—12—57—24—44—18—59
total time           8.05                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             107605<=107605       subtour              252.0                
connectivity cuts    43.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—30—13—40—25—32—20—53—50—4—54—55—22—8—5—27—12—57—24—44—18—59

RING
1  --- 30 | cost [1535.0]
2  --- 41 | cost [490.0]
2  --- 48 | cost [970.0]
3  --- 35 | cost [790.0]
3  --- 39 | cost [1435.0]
4  --- 50 | cost [4030.0]
4  --- 54 | cost [12320.0]
5  ---  8 | cost [3580.0]
5  --- 27 | cost [1300.0]
6  --- 19 | cost [690.0]
6  --- 26 | cost [620.0]
8  --- 22 | cost [1045.0]
12 --- 27 | cost [1285.0]
12 --- 57 | cost [1240.0]
13 --- 30 | cost [1055.0]
13 --- 40 | cost [675.0]
14 --- 33 | cost [880.0]
14 --- 37 | cost [685.0]
17 --- 26 | cost [645.0]
17 --- 36 | cost [570.0]
18 --- 44 | cost [570.0]
18 --- 59 | cost [1650.0]
19 --- 21 | cost [4725.0]
20 --- 32 | cost [2685.0]
20 --- 53 | cost [3170.0]
21 --- 29 | cost [2600.0]
22 --- 55 | cost [1795.0]
24 --- 44 | cost [2260.0]
24 --- 57 | cost [3770.0]
25 --- 32 | cost [950.0]
25 --- 40 | cost [625.0]
29 --- 36 | cost [1370.0]
31 --- 38 | cost [4505.0]
31 --- 42 | cost [7225.0]
33 --- 45 | cost [1065.0]
34 --- 37 | cost [1285.0]
34 --- 46 | cost [1145.0]
35 --- 41 | cost [740.0]
38 --- 42 | cost [2720.0]
39 --- 48 | cost [1725.0]
45 --- 46 | cost [1365.0]
47 --- 49 | cost [430.0]
47 --- 51 | cost [360.0]
49 --- 51 | cost [485.0]
50 --- 53 | cost [2230.0]
54 --- 55 | cost [560.0]

STAR
7  --> 31 | cost [3925.0]
9  --> 25 | cost [650.0]
10 --> 35 | cost [375.0]
11 --> 39 | cost [2275.0]
15 --> 34 | cost [1310.0]
16 --> 22 | cost [4660.0]
23 -->  5 | cost [1620.0]
28 -->  6 | cost [945.0]
43 --> 27 | cost [920.0]
52 --> 51 | cost [510.0]
56 --> 46 | cost [1270.0]
58 --> 24 | cost [1295.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 06 Jan 2024 11:00:33 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 41 hubs —— 1-30-13-40-25-32-20-53-8-22-16-38-31-11-39-29-33-45-46-34-37-14-28-6-26-17-47-51-10-35-41-2-54-5-27-12-57-24-44-18-59-1
total time           110.37               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             115045<=115045       Master/SP costs      115045/0             
Master time          110.37               SP time              0.0                  
subtour              14300.0              connectivity cuts    1769.0               
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       2592                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—30—13—40—25—32—20—53—8—22—16—38—31—11—39—29—33—45—46—34—37—14—28—6—26—17—47—51—10—35—41—2—54—5—27—12—57—24—44—18—59

RING
1  --- 30 | cost [1535.0]
2  --- 41 | cost [490.0]
2  --- 54 | cost [685.0]
5  --- 27 | cost [1300.0]
5  --- 54 | cost [2470.0]
6  --- 26 | cost [620.0]
6  --- 28 | cost [945.0]
8  --- 22 | cost [1045.0]
8  --- 53 | cost [8945.0]
10 --- 35 | cost [375.0]
10 --- 51 | cost [490.0]
11 --- 31 | cost [15225.0]
11 --- 39 | cost [2275.0]
12 --- 27 | cost [1285.0]
12 --- 57 | cost [1240.0]
13 --- 30 | cost [1055.0]
13 --- 40 | cost [675.0]
14 --- 28 | cost [1120.0]
14 --- 37 | cost [685.0]
16 --- 22 | cost [4660.0]
16 --- 38 | cost [7280.0]
17 --- 26 | cost [645.0]
17 --- 47 | cost [1960.0]
18 --- 44 | cost [570.0]
18 --- 59 | cost [1650.0]
20 --- 32 | cost [2685.0]
20 --- 53 | cost [3170.0]
24 --- 44 | cost [2260.0]
24 --- 57 | cost [3770.0]
25 --- 32 | cost [950.0]
25 --- 40 | cost [625.0]
29 --- 33 | cost [2390.0]
29 --- 39 | cost [1830.0]
31 --- 38 | cost [4505.0]
33 --- 45 | cost [1065.0]
34 --- 37 | cost [1285.0]
34 --- 46 | cost [1145.0]
35 --- 41 | cost [740.0]
45 --- 46 | cost [1365.0]
47 --- 51 | cost [360.0]

STAR
3  --> 35 | cost [790.0]
4  --> 53 | cost [4735.0]
7  --> 31 | cost [3925.0]
9  --> 25 | cost [650.0]
15 --> 34 | cost [1310.0]
19 -->  6 | cost [690.0]
21 --> 29 | cost [2600.0]
23 -->  5 | cost [1620.0]
36 --> 17 | cost [570.0]
42 --> 38 | cost [2720.0]
43 --> 27 | cost [920.0]
48 --> 41 | cost [960.0]
49 --> 47 | cost [430.0]
50 --> 53 | cost [2230.0]
52 --> 10 | cost [400.0]
55 --> 54 | cost [560.0]
56 --> 46 | cost [1270.0]
58 --> 24 | cost [1295.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 07:56:53 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 22 hubs —— 1—30—13—40—25—32—20—53—50—4—54—55—22—8—5—27—12—57—24—44—18—59
total time           8.87                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             107605<=107605       subtour              252.0                
connectivity cuts    43.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—30—13—40—25—32—20—53—50—4—54—55—22—8—5—27—12—57—24—44—18—59

RING
1  --- 30 | cost [1535.0]
2  --- 41 | cost [490.0]
2  --- 48 | cost [970.0]
3  --- 35 | cost [790.0]
3  --- 39 | cost [1435.0]
4  --- 50 | cost [4030.0]
4  --- 54 | cost [12320.0]
5  ---  8 | cost [3580.0]
5  --- 27 | cost [1300.0]
6  --- 19 | cost [690.0]
6  --- 26 | cost [620.0]
8  --- 22 | cost [1045.0]
12 --- 27 | cost [1285.0]
12 --- 57 | cost [1240.0]
13 --- 30 | cost [1055.0]
13 --- 40 | cost [675.0]
14 --- 33 | cost [880.0]
14 --- 37 | cost [685.0]
17 --- 26 | cost [645.0]
17 --- 36 | cost [570.0]
18 --- 44 | cost [570.0]
18 --- 59 | cost [1650.0]
19 --- 21 | cost [4725.0]
20 --- 32 | cost [2685.0]
20 --- 53 | cost [3170.0]
21 --- 29 | cost [2600.0]
22 --- 55 | cost [1795.0]
24 --- 44 | cost [2260.0]
24 --- 57 | cost [3770.0]
25 --- 32 | cost [950.0]
25 --- 40 | cost [625.0]
29 --- 36 | cost [1370.0]
31 --- 38 | cost [4505.0]
31 --- 42 | cost [7225.0]
33 --- 45 | cost [1065.0]
34 --- 37 | cost [1285.0]
34 --- 46 | cost [1145.0]
35 --- 41 | cost [740.0]
38 --- 42 | cost [2720.0]
39 --- 48 | cost [1725.0]
45 --- 46 | cost [1365.0]
47 --- 49 | cost [430.0]
47 --- 51 | cost [360.0]
49 --- 51 | cost [485.0]
50 --- 53 | cost [2230.0]
54 --- 55 | cost [560.0]

STAR
7  --> 31 | cost [3925.0]
9  --> 25 | cost [650.0]
10 --> 35 | cost [375.0]
11 --> 39 | cost [2275.0]
15 --> 34 | cost [1310.0]
16 --> 22 | cost [4660.0]
23 -->  5 | cost [1620.0]
28 -->  6 | cost [945.0]
43 --> 27 | cost [920.0]
52 --> 51 | cost [510.0]
56 --> 46 | cost [1270.0]
58 --> 24 | cost [1295.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 07 Jan 2024 07:59:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 41 hubs —— 1-30-13-40-25-32-20-53-8-22-16-38-31-11-39-29-33-45-46-34-37-14-28-6-26-17-47-51-10-35-41-2-54-5-27-12-57-24-44-18-59-1
total time           137.04               gap                  0.0                  
blossom time         0.93                 nb blossom           1.0                  
LB <= UB             115045<=115045       Master/SP costs      115045/0             
Master time          137.04               SP time              0.0                  
subtour              14300.0              connectivity cuts    1769.0               
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       2592                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—30—13—40—25—32—20—53—8—22—16—38—31—11—39—29—33—45—46—34—37—14—28—6—26—17—47—51—10—35—41—2—54—5—27—12—57—24—44—18—59

RING
1  --- 30 | cost [1535.0]
2  --- 41 | cost [490.0]
2  --- 54 | cost [685.0]
5  --- 27 | cost [1300.0]
5  --- 54 | cost [2470.0]
6  --- 26 | cost [620.0]
6  --- 28 | cost [945.0]
8  --- 22 | cost [1045.0]
8  --- 53 | cost [8945.0]
10 --- 35 | cost [375.0]
10 --- 51 | cost [490.0]
11 --- 31 | cost [15225.0]
11 --- 39 | cost [2275.0]
12 --- 27 | cost [1285.0]
12 --- 57 | cost [1240.0]
13 --- 30 | cost [1055.0]
13 --- 40 | cost [675.0]
14 --- 28 | cost [1120.0]
14 --- 37 | cost [685.0]
16 --- 22 | cost [4660.0]
16 --- 38 | cost [7280.0]
17 --- 26 | cost [645.0]
17 --- 47 | cost [1960.0]
18 --- 44 | cost [570.0]
18 --- 59 | cost [1650.0]
20 --- 32 | cost [2685.0]
20 --- 53 | cost [3170.0]
24 --- 44 | cost [2260.0]
24 --- 57 | cost [3770.0]
25 --- 32 | cost [950.0]
25 --- 40 | cost [625.0]
29 --- 33 | cost [2390.0]
29 --- 39 | cost [1830.0]
31 --- 38 | cost [4505.0]
33 --- 45 | cost [1065.0]
34 --- 37 | cost [1285.0]
34 --- 46 | cost [1145.0]
35 --- 41 | cost [740.0]
45 --- 46 | cost [1365.0]
47 --- 51 | cost [360.0]

STAR
3  --> 35 | cost [790.0]
4  --> 53 | cost [4735.0]
7  --> 31 | cost [3925.0]
9  --> 25 | cost [650.0]
15 --> 34 | cost [1310.0]
19 -->  6 | cost [690.0]
21 --> 29 | cost [2600.0]
23 -->  5 | cost [1620.0]
36 --> 17 | cost [570.0]
42 --> 38 | cost [2720.0]
43 --> 27 | cost [920.0]
48 --> 41 | cost [960.0]
49 --> 47 | cost [430.0]
50 --> 53 | cost [2230.0]
52 --> 10 | cost [400.0]
55 --> 54 | cost [560.0]
56 --> 46 | cost [1270.0]
58 --> 24 | cost [1295.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1