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

——————— Thu, 25 Jan 2024 21:04:48 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 42 hubs —— 1—18—44—24—57—12—27—5—54—2—41—35—10—51—47—17—26—6—28—14—37—34—46—45—33—29—39—11—31—38—16—22—4—50—53—20—32—25—40—13—30—59
total time           138.28               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             116802.25<=116802.25 subtour              113.0                
connectivity cuts    53.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:58                 
2-opt strategy       0                                                              
explored_nodes       9                    n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—18—44—24—57—12—27—5—54—2—41—35—10—51—47—17—26—6—28—14—37—34—46—45—33—29—39—11—31—38—16—22—4—50—53—20—32—25—40—13—30—59

RING
1  --- 18 | cost [1650.0]
2  --- 41 | cost [490.0]
2  --- 54 | cost [685.0]
4  --- 22 | cost [10065.0]
4  --- 50 | cost [4030.0]
5  --- 27 | cost [1300.0]
5  --- 54 | cost [2470.0]
6  --- 26 | cost [620.0]
6  --- 28 | cost [945.0]
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]
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]
30 --- 59 | cost [1535.0]
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]
50 --- 53 | cost [2230.0]

STAR
3  --> 35 | cost [790.0]
7  --> 31 | cost [3925.0]
8  --> 22 | cost [1045.0]
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]
52 --> 10 | cost [400.0]
55 --> 54 | cost [560.0]
56 --> 46 | cost [1270.0]
58 --> 24 | cost [1295.0]

BACKUP RING
1  --- 44 | cost [18.35]
2  ---  5 | cost [33.3]
2  --- 35 | cost [17.95]
4  --- 16 | cost [147.05]
4  --- 53 | cost [47.35]
5  --- 12 | cost [34.7]
6  --- 14 | cost [17.35]
6  --- 17 | cost [12.5]
10 --- 41 | cost [11.35]
10 --- 47 | cost [8.5]
11 --- 29 | cost [33.65]
11 --- 38 | cost [107.45]
12 --- 24 | cost [50.1]
13 --- 25 | cost [10.0]
13 --- 59 | cost [23.2]
14 --- 34 | cost [19.7]
16 --- 31 | cost [117.85000000000001]
17 --- 51 | cost [20.400000000000002]
18 --- 24 | cost [28.2]
20 --- 25 | cost [34.65]
20 --- 50 | cost [53.5]
22 --- 38 | cost [119.4]
22 --- 50 | cost [121.10000000000001]
26 --- 28 | cost [21.6]
26 --- 47 | cost [26.400000000000002]
27 --- 54 | cost [37.7]
27 --- 57 | cost [24.900000000000002]
28 --- 37 | cost [17.95]
29 --- 45 | cost [35.4]
30 --- 40 | cost [12.85]
31 --- 39 | cost [174.55]
32 --- 40 | cost [14.85]
32 --- 53 | cost [58.550000000000004]
33 --- 39 | cost [57.6]
33 --- 46 | cost [21.75]
34 --- 45 | cost [17.7]
35 --- 51 | cost [8.55]
37 --- 46 | cost [24.6]
41 --- 54 | cost [9.200000000000001]
44 --- 57 | cost [61.300000000000004]

BACKUP STAR
3  --> 10 | cost [10.85]
7  --> 38 | cost [84.3]
8  --> 54 | cost [26.85]
9  --> 13 | cost [7.3500000000000005]
15 --> 37 | cost [26.400000000000002]
19 --> 26 | cost [8.9]
21 --> 39 | cost [30.35]
23 --> 57 | cost [21.6]
36 --> 26 | cost [12.15]
42 --> 31 | cost [72.25]
43 --> 12 | cost [13.950000000000001]
48 -->  2 | cost [9.700000000000001]
49 --> 51 | cost [4.8500000000000005]
52 --> 51 | cost [5.1000000000000005]
55 -->  2 | cost [11.700000000000001]
56 --> 34 | cost [15.0]
58 --> 44 | cost [26.1]

B = 191.75
i★ = 11
j★ = 31
k★ = 38

       
——————— Thu, 25 Jan 2024 21:09:10 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 42 hubs —— 1-18-44-24-57-12-27-5-54-2-41-35-10-51-47-17-26-6-28-14-37-34-46-45-33-29-39-11-31-38-16-22-4-50-53-20-32-25-40-13-30-59-1
total time           226.96               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             116802.25<=116802.25 Master/SP costs      115460/1342.25       
Master time          226.37               SP time              0.59                 
subtour              6029.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            21.0                 SP method            poly                 
tildeV               2:58                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       2510                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—18—44—24—57—12—27—5—54—2—41—35—10—51—47—17—26—6—28—14—37—34—46—45—33—29—39—11—31—38—16—22—4—50—53—20—32—25—40—13—30—59

RING
1  --- 18 | cost [1650.0]
1  --- 59 | cost [0.0]
2  --- 41 | cost [490.0]
2  --- 54 | cost [685.0]
4  --- 22 | cost [10065.0]
4  --- 50 | cost [4030.0]
5  --- 27 | cost [1300.0]
5  --- 54 | cost [2470.0]
6  --- 26 | cost [620.0]
6  --- 28 | cost [945.0]
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]
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]
30 --- 59 | cost [1535.0]
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]
50 --- 53 | cost [2230.0]

STAR
3  --> 35 | cost [790.0]
7  --> 31 | cost [3925.0]
8  --> 22 | cost [1045.0]
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]
52 --> 10 | cost [400.0]
55 --> 54 | cost [560.0]
56 --> 46 | cost [1270.0]
58 --> 24 | cost [1295.0]

BACKUP RING
1  --- 44 | cost [18.35]
2  ---  5 | cost [33.3]
2  --- 35 | cost [17.95]
4  --- 16 | cost [147.05]
4  --- 53 | cost [47.35]
5  --- 12 | cost [34.7]
6  --- 14 | cost [17.35]
6  --- 17 | cost [12.5]
10 --- 41 | cost [11.35]
10 --- 47 | cost [8.5]
11 --- 29 | cost [33.65]
11 --- 38 | cost [107.45]
12 --- 24 | cost [50.1]
13 --- 25 | cost [10.0]
13 --- 59 | cost [23.2]
14 --- 34 | cost [19.7]
16 --- 31 | cost [117.85000000000001]
17 --- 51 | cost [20.400000000000002]
18 --- 24 | cost [28.2]
20 --- 25 | cost [34.65]
20 --- 50 | cost [53.5]
22 --- 38 | cost [119.4]
22 --- 50 | cost [121.10000000000001]
26 --- 28 | cost [21.6]
26 --- 47 | cost [26.400000000000002]
27 --- 54 | cost [37.7]
27 --- 57 | cost [24.900000000000002]
28 --- 37 | cost [17.95]
29 --- 45 | cost [35.4]
30 --- 40 | cost [12.85]
31 --- 39 | cost [174.55]
32 --- 40 | cost [14.85]
32 --- 53 | cost [58.550000000000004]
33 --- 39 | cost [57.6]
33 --- 46 | cost [21.75]
34 --- 45 | cost [17.7]
35 --- 51 | cost [8.55]
37 --- 46 | cost [24.6]
41 --- 54 | cost [9.200000000000001]
44 --- 57 | cost [61.300000000000004]

BACKUP STAR
3  --> 10 | cost [10.85]
7  --> 38 | cost [84.3]
8  --> 54 | cost [26.85]
9  --> 13 | cost [7.3500000000000005]
15 --> 37 | cost [26.400000000000002]
19 --> 26 | cost [8.9]
21 --> 39 | cost [30.35]
23 --> 57 | cost [21.6]
36 --> 26 | cost [12.15]
42 --> 31 | cost [72.25]
43 --> 12 | cost [13.950000000000001]
48 -->  2 | cost [9.700000000000001]
49 --> 51 | cost [4.8500000000000005]
52 --> 51 | cost [5.1000000000000005]
55 -->  2 | cost [11.700000000000001]
56 --> 34 | cost [15.0]
58 --> 44 | cost [26.1]

B = 191.75
i★ = 11
j★ = 31
k★ = 38