------------------------------------------------------------
                        α=3.0 —— brazil58 —— 58 nodes       
------------------------------------------------------------

——————— Sat, 06 Jan 2024 22:17:07 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 59 hubs —— 1—18—44—24—58—5—23—57—12—27—43—49—47—51—52—10—35—41—2—54—55—48—3—29—33—45—56—46—34—15—37—14—28—6—19—26—17—36—21—39—11—16—31—7—38—42—22—8—4—50—53—20—32—9—25—40—13—30—59
total time           2111.11              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             93449.58<=93449.58   subtour              202.0                
connectivity cuts    1595.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               2:58                 
2-opt strategy       0                                                              
explored_nodes       5603                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—18—44—24—58—5—23—57—12—27—43—49—47—51—52—10—35—41—2—54—55—48—3—29—33—45—56—46—34—15—37—14—28—6—19—26—17—36—21—39—11—16—31—7—38—42—22—8—4—50—53—20—32—9—25—40—13—30—59

RING
1  --- 18 | cost [990.0]
1  --- 59 | cost [0.0]
2  --- 41 | cost [294.0]
2  --- 54 | cost [411.0]
3  --- 29 | cost [861.0]
3  --- 48 | cost [837.0]
4  ---  8 | cost [6360.0]
4  --- 50 | cost [2418.0]
5  --- 23 | cost [972.0]
5  --- 58 | cost [2553.0]
6  --- 19 | cost [414.0]
6  --- 28 | cost [567.0]
7  --- 31 | cost [2355.0]
7  --- 38 | cost [5058.0]
8  --- 22 | cost [627.0]
9  --- 25 | cost [390.0]
9  --- 32 | cost [684.0]
10 --- 35 | cost [225.0]
10 --- 52 | cost [240.0]
11 --- 16 | cost [2079.0]
11 --- 39 | cost [1365.0]
12 --- 27 | cost [771.0]
12 --- 57 | cost [744.0]
13 --- 30 | cost [633.0]
13 --- 40 | cost [405.0]
14 --- 28 | cost [672.0]
14 --- 37 | cost [411.0]
15 --- 34 | cost [786.0]
15 --- 37 | cost [1584.0]
16 --- 31 | cost [7071.0]
17 --- 26 | cost [387.0]
17 --- 36 | cost [342.0]
18 --- 44 | cost [342.0]
19 --- 26 | cost [534.0]
20 --- 32 | cost [1611.0]
20 --- 53 | cost [1902.0]
21 --- 36 | cost [1572.0]
21 --- 39 | cost [1821.0]
22 --- 42 | cost [8766.0]
23 --- 57 | cost [1296.0]
24 --- 44 | cost [1356.0]
24 --- 58 | cost [777.0]
25 --- 40 | cost [375.0]
27 --- 43 | cost [552.0]
29 --- 33 | cost [1434.0]
30 --- 59 | cost [921.0]
33 --- 45 | cost [639.0]
34 --- 46 | cost [687.0]
35 --- 41 | cost [444.0]
38 --- 42 | cost [1632.0]
43 --- 49 | cost [1017.0]
45 --- 56 | cost [936.0]
46 --- 56 | cost [762.0]
47 --- 49 | cost [258.0]
47 --- 51 | cost [216.0]
48 --- 55 | cost [864.0]
50 --- 53 | cost [1338.0]
51 --- 52 | cost [306.0]
54 --- 55 | cost [336.0]

STAR

BACKUP RING
1  --- 44 | cost [11.01]
2  --- 35 | cost [10.77]
2  --- 55 | cost [7.0200000000000005]
3  --- 33 | cost [33.06]
3  --- 55 | cost [16.38]
4  --- 22 | cost [60.39]
4  --- 53 | cost [28.41]
5  --- 24 | cost [33.480000000000004]
5  --- 57 | cost [15.72]
6  --- 14 | cost [10.41]
6  --- 26 | cost [3.72]
7  --- 16 | cost [94.26]
7  --- 42 | cost [66.9]
8  --- 42 | cost [93.75]
8  --- 50 | cost [66.75]
9  --- 20 | cost [20.43]
9  --- 40 | cost [5.5200000000000005]
10 --- 41 | cost [6.8100000000000005]
10 --- 51 | cost [2.94]
11 --- 21 | cost [26.61]
11 --- 31 | cost [91.35000000000001]
12 --- 23 | cost [13.68]
12 --- 43 | cost [8.370000000000001]
13 --- 25 | cost [6.0]
13 --- 59 | cost [13.92]
14 --- 15 | cost [19.95]
15 --- 46 | cost [18.21]
16 --- 39 | cost [34.32]
17 --- 19 | cost [9.0]
17 --- 21 | cost [19.14]
18 --- 24 | cost [16.92]
19 --- 28 | cost [7.62]
20 --- 50 | cost [32.1]
22 --- 38 | cost [71.64]
23 --- 58 | cost [41.82]
25 --- 32 | cost [5.7]
26 --- 36 | cost [7.29]
27 --- 49 | cost [15.69]
27 --- 57 | cost [14.94]
28 --- 37 | cost [10.77]
29 --- 45 | cost [21.240000000000002]
29 --- 48 | cost [11.01]
30 --- 40 | cost [7.71]
31 --- 38 | cost [27.03]
32 --- 53 | cost [35.13]
33 --- 56 | cost [12.39]
34 --- 37 | cost [7.71]
34 --- 56 | cost [9.0]
35 --- 52 | cost [3.21]
36 --- 39 | cost [21.150000000000002]
41 --- 54 | cost [5.5200000000000005]
43 --- 47 | cost [16.62]
44 --- 58 | cost [15.66]
45 --- 46 | cost [8.19]
47 --- 52 | cost [5.1000000000000005]
48 --- 54 | cost [7.17]
49 --- 51 | cost [2.91]

BACKUP STAR

B = 94.26
i★ = 7
j★ = 31
k★ = 16

       
——————— Sat, 06 Jan 2024 23:22:41 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 59 hubs —— 1-18-44-58-24-57-12-23-5-27-43-49-47-51-52-10-35-41-2-54-55-48-3-29-33-45-56-46-34-15-37-14-28-6-19-26-17-36-21-39-11-16-31-7-38-42-22-8-4-50-53-20-32-9-25-40-13-30-59-1
total time           3903.07 (TL 3600)    gap                  0.132                
blossom time         0                    nb blossom           0.0                  
LB <= UB             81085<=93449.58      Master/SP costs      76200/17249.58       
Master time          3880.48              SP time              22.59                
subtour              14149.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            2064.0               SP method            poly                 
tildeV               2:58                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       107958               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—18—44—58—24—57—12—23—5—27—43—49—47—51—52—10—35—41—2—54—55—48—3—29—33—45—56—46—34—15—37—14—28—6—19—26—17—36—21—39—11—16—31—7—38—42—22—8—4—50—53—20—32—9—25—40—13—30—59

RING
1  --- 18 | cost [990.0]
1  --- 59 | cost [0.0]
2  --- 41 | cost [294.0]
2  --- 54 | cost [411.0]
3  --- 29 | cost [861.0]
3  --- 48 | cost [837.0]
4  ---  8 | cost [6360.0]
4  --- 50 | cost [2418.0]
5  --- 23 | cost [972.0]
5  --- 27 | cost [780.0]
6  --- 19 | cost [414.0]
6  --- 28 | cost [567.0]
7  --- 31 | cost [2355.0]
7  --- 38 | cost [5058.0]
8  --- 22 | cost [627.0]
9  --- 25 | cost [390.0]
9  --- 32 | cost [684.0]
10 --- 35 | cost [225.0]
10 --- 52 | cost [240.0]
11 --- 16 | cost [2079.0]
11 --- 39 | cost [1365.0]
12 --- 23 | cost [1368.0]
12 --- 57 | cost [744.0]
13 --- 30 | cost [633.0]
13 --- 40 | cost [405.0]
14 --- 28 | cost [672.0]
14 --- 37 | cost [411.0]
15 --- 34 | cost [786.0]
15 --- 37 | cost [1584.0]
16 --- 31 | cost [7071.0]
17 --- 26 | cost [387.0]
17 --- 36 | cost [342.0]
18 --- 44 | cost [342.0]
19 --- 26 | cost [534.0]
20 --- 32 | cost [1611.0]
20 --- 53 | cost [1902.0]
21 --- 36 | cost [1572.0]
21 --- 39 | cost [1821.0]
22 --- 42 | cost [8766.0]
24 --- 57 | cost [2262.0]
24 --- 58 | cost [777.0]
25 --- 40 | cost [375.0]
27 --- 43 | cost [552.0]
29 --- 33 | cost [1434.0]
30 --- 59 | cost [921.0]
33 --- 45 | cost [639.0]
34 --- 46 | cost [687.0]
35 --- 41 | cost [444.0]
38 --- 42 | cost [1632.0]
43 --- 49 | cost [1017.0]
44 --- 58 | cost [1566.0]
45 --- 56 | cost [936.0]
46 --- 56 | cost [762.0]
47 --- 49 | cost [258.0]
47 --- 51 | cost [216.0]
48 --- 55 | cost [864.0]
50 --- 53 | cost [1338.0]
51 --- 52 | cost [306.0]
54 --- 55 | cost [336.0]

STAR

BACKUP RING
1  --- 44 | cost [11.01]
2  --- 35 | cost [10.77]
2  --- 55 | cost [7.0200000000000005]
3  --- 33 | cost [33.06]
3  --- 55 | cost [16.38]
4  --- 22 | cost [60.39]
4  --- 53 | cost [28.41]
5  --- 12 | cost [20.82]
5  --- 43 | cost [13.02]
6  --- 14 | cost [10.41]
6  --- 26 | cost [3.72]
7  --- 16 | cost [94.26]
7  --- 42 | cost [66.9]
8  --- 42 | cost [93.75]
8  --- 50 | cost [66.75]
9  --- 20 | cost [20.43]
9  --- 40 | cost [5.5200000000000005]
10 --- 41 | cost [6.8100000000000005]
10 --- 51 | cost [2.94]
11 --- 21 | cost [26.61]
11 --- 31 | cost [91.35000000000001]
12 --- 24 | cost [30.060000000000002]
13 --- 25 | cost [6.0]
13 --- 59 | cost [13.92]
14 --- 15 | cost [19.95]
15 --- 46 | cost [18.21]
16 --- 39 | cost [34.32]
17 --- 19 | cost [9.0]
17 --- 21 | cost [19.14]
18 --- 58 | cost [19.080000000000002]
19 --- 28 | cost [7.62]
20 --- 50 | cost [32.1]
22 --- 38 | cost [71.64]
23 --- 27 | cost [16.62]
23 --- 57 | cost [12.96]
24 --- 44 | cost [13.56]
25 --- 32 | cost [5.7]
26 --- 36 | cost [7.29]
27 --- 49 | cost [15.69]
28 --- 37 | cost [10.77]
29 --- 45 | cost [21.240000000000002]
29 --- 48 | cost [11.01]
30 --- 40 | cost [7.71]
31 --- 38 | cost [27.03]
32 --- 53 | cost [35.13]
33 --- 56 | cost [12.39]
34 --- 37 | cost [7.71]
34 --- 56 | cost [9.0]
35 --- 52 | cost [3.21]
36 --- 39 | cost [21.150000000000002]
41 --- 54 | cost [5.5200000000000005]
43 --- 47 | cost [16.62]
45 --- 46 | cost [8.19]
47 --- 52 | cost [5.1000000000000005]
48 --- 54 | cost [7.17]
49 --- 51 | cost [2.91]
57 --- 58 | cost [28.86]

BACKUP STAR

B = 94.26
i★ = 7
j★ = 31
k★ = 16

       
——————— Sun, 07 Jan 2024 18:58:58 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 59 hubs —— 1—18—44—58—24—57—12—23—5—27—43—49—47—51—52—10—35—41—2—54—55—48—3—29—33—45—56—46—34—15—37—14—28—6—19—26—17—36—21—39—11—16—31—7—38—42—22—8—4—50—53—20—32—9—25—40—13—30—59
total time           1002.43              gap                  0.0                  
blossom time         5.33                 nb blossom           1276.0               
LB <= UB             93449.58<=93449.58   subtour              124.0                
connectivity cuts    589.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:58                 
2-opt strategy       0                                                              
explored_nodes       2162                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—18—44—58—24—57—12—23—5—27—43—49—47—51—52—10—35—41—2—54—55—48—3—29—33—45—56—46—34—15—37—14—28—6—19—26—17—36—21—39—11—16—31—7—38—42—22—8—4—50—53—20—32—9—25—40—13—30—59

RING
1  --- 18 | cost [990.0]
1  --- 59 | cost [0.0]
2  --- 41 | cost [294.0]
2  --- 54 | cost [411.0]
3  --- 29 | cost [861.0]
3  --- 48 | cost [837.0]
4  ---  8 | cost [6360.0]
4  --- 50 | cost [2418.0]
5  --- 23 | cost [972.0]
5  --- 27 | cost [780.0]
6  --- 19 | cost [414.0]
6  --- 28 | cost [567.0]
7  --- 31 | cost [2355.0]
7  --- 38 | cost [5058.0]
8  --- 22 | cost [627.0]
9  --- 25 | cost [390.0]
9  --- 32 | cost [684.0]
10 --- 35 | cost [225.0]
10 --- 52 | cost [240.0]
11 --- 16 | cost [2079.0]
11 --- 39 | cost [1365.0]
12 --- 23 | cost [1368.0]
12 --- 57 | cost [744.0]
13 --- 30 | cost [633.0]
13 --- 40 | cost [405.0]
14 --- 28 | cost [672.0]
14 --- 37 | cost [411.0]
15 --- 34 | cost [786.0]
15 --- 37 | cost [1584.0]
16 --- 31 | cost [7071.0]
17 --- 26 | cost [387.0]
17 --- 36 | cost [342.0]
18 --- 44 | cost [342.0]
19 --- 26 | cost [534.0]
20 --- 32 | cost [1611.0]
20 --- 53 | cost [1902.0]
21 --- 36 | cost [1572.0]
21 --- 39 | cost [1821.0]
22 --- 42 | cost [8766.0]
24 --- 57 | cost [2262.0]
24 --- 58 | cost [777.0]
25 --- 40 | cost [375.0]
27 --- 43 | cost [552.0]
29 --- 33 | cost [1434.0]
30 --- 59 | cost [921.0]
33 --- 45 | cost [639.0]
34 --- 46 | cost [687.0]
35 --- 41 | cost [444.0]
38 --- 42 | cost [1632.0]
43 --- 49 | cost [1017.0]
44 --- 58 | cost [1566.0]
45 --- 56 | cost [936.0]
46 --- 56 | cost [762.0]
47 --- 49 | cost [258.0]
47 --- 51 | cost [216.0]
48 --- 55 | cost [864.0]
50 --- 53 | cost [1338.0]
51 --- 52 | cost [306.0]
54 --- 55 | cost [336.0]

STAR

BACKUP RING
1  --- 44 | cost [11.01]
2  --- 35 | cost [10.77]
2  --- 55 | cost [7.0200000000000005]
3  --- 33 | cost [33.06]
3  --- 55 | cost [16.38]
4  --- 22 | cost [60.39]
4  --- 53 | cost [28.41]
5  --- 12 | cost [20.82]
5  --- 43 | cost [13.02]
6  --- 14 | cost [10.41]
6  --- 26 | cost [3.72]
7  --- 16 | cost [94.26]
7  --- 42 | cost [66.9]
8  --- 42 | cost [93.75]
8  --- 50 | cost [66.75]
9  --- 20 | cost [20.43]
9  --- 40 | cost [5.5200000000000005]
10 --- 41 | cost [6.8100000000000005]
10 --- 51 | cost [2.94]
11 --- 21 | cost [26.61]
11 --- 31 | cost [91.35000000000001]
12 --- 24 | cost [30.060000000000002]
13 --- 25 | cost [6.0]
13 --- 59 | cost [13.92]
14 --- 15 | cost [19.95]
15 --- 46 | cost [18.21]
16 --- 39 | cost [34.32]
17 --- 19 | cost [9.0]
17 --- 21 | cost [19.14]
18 --- 58 | cost [19.080000000000002]
19 --- 28 | cost [7.62]
20 --- 50 | cost [32.1]
22 --- 38 | cost [71.64]
23 --- 27 | cost [16.62]
23 --- 57 | cost [12.96]
24 --- 44 | cost [13.56]
25 --- 32 | cost [5.7]
26 --- 36 | cost [7.29]
27 --- 49 | cost [15.69]
28 --- 37 | cost [10.77]
29 --- 45 | cost [21.240000000000002]
29 --- 48 | cost [11.01]
30 --- 40 | cost [7.71]
31 --- 38 | cost [27.03]
32 --- 53 | cost [35.13]
33 --- 56 | cost [12.39]
34 --- 37 | cost [7.71]
34 --- 56 | cost [9.0]
35 --- 52 | cost [3.21]
36 --- 39 | cost [21.150000000000002]
41 --- 54 | cost [5.5200000000000005]
43 --- 47 | cost [16.62]
45 --- 46 | cost [8.19]
47 --- 52 | cost [5.1000000000000005]
48 --- 54 | cost [7.17]
49 --- 51 | cost [2.91]
57 --- 58 | cost [28.86]

BACKUP STAR

B = 94.26
i★ = 7
j★ = 31
k★ = 16

       
——————— Sun, 07 Jan 2024 19:59:33 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 59 hubs —— 1-18-44-58-24-57-12-23-5-27-43-49-47-51-52-10-35-41-2-54-55-48-3-29-33-45-56-46-34-15-37-14-28-6-19-26-17-36-21-39-11-38-31-7-42-16-22-8-4-50-53-20-32-9-25-40-13-30-59-1
total time           3603.94 (TL 3600)    gap                  0.087                
blossom time         475.99               nb blossom           108980.0             
LB <= UB             85362<=93449.58      Master/SP costs      76200/17249.58       
Master time          3573.56              SP time              30.38                
subtour              16404.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            2833.0               SP method            poly                 
tildeV               2:58                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       129225               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—18—44—58—24—57—12—23—5—27—43—49—47—51—52—10—35—41—2—54—55—48—3—29—33—45—56—46—34—15—37—14—28—6—19—26—17—36—21—39—11—38—31—7—42—16—22—8—4—50—53—20—32—9—25—40—13—30—59

RING
1  --- 18 | cost [990.0]
1  --- 59 | cost [0.0]
2  --- 41 | cost [294.0]
2  --- 54 | cost [411.0]
3  --- 29 | cost [861.0]
3  --- 48 | cost [837.0]
4  ---  8 | cost [6360.0]
4  --- 50 | cost [2418.0]
5  --- 23 | cost [972.0]
5  --- 27 | cost [780.0]
6  --- 19 | cost [414.0]
6  --- 28 | cost [567.0]
7  --- 31 | cost [2355.0]
7  --- 42 | cost [6690.0]
8  --- 22 | cost [627.0]
9  --- 25 | cost [390.0]
9  --- 32 | cost [684.0]
10 --- 35 | cost [225.0]
10 --- 52 | cost [240.0]
11 --- 38 | cost [6447.0]
11 --- 39 | cost [1365.0]
12 --- 23 | cost [1368.0]
12 --- 57 | cost [744.0]
13 --- 30 | cost [633.0]
13 --- 40 | cost [405.0]
14 --- 28 | cost [672.0]
14 --- 37 | cost [411.0]
15 --- 34 | cost [786.0]
15 --- 37 | cost [1584.0]
16 --- 22 | cost [2796.0]
16 --- 42 | cost [5970.0]
17 --- 26 | cost [387.0]
17 --- 36 | cost [342.0]
18 --- 44 | cost [342.0]
19 --- 26 | cost [534.0]
20 --- 32 | cost [1611.0]
20 --- 53 | cost [1902.0]
21 --- 36 | cost [1572.0]
21 --- 39 | cost [1821.0]
24 --- 57 | cost [2262.0]
24 --- 58 | cost [777.0]
25 --- 40 | cost [375.0]
27 --- 43 | cost [552.0]
29 --- 33 | cost [1434.0]
30 --- 59 | cost [921.0]
31 --- 38 | cost [2703.0]
33 --- 45 | cost [639.0]
34 --- 46 | cost [687.0]
35 --- 41 | cost [444.0]
43 --- 49 | cost [1017.0]
44 --- 58 | cost [1566.0]
45 --- 56 | cost [936.0]
46 --- 56 | cost [762.0]
47 --- 49 | cost [258.0]
47 --- 51 | cost [216.0]
48 --- 55 | cost [864.0]
50 --- 53 | cost [1338.0]
51 --- 52 | cost [306.0]
54 --- 55 | cost [336.0]

STAR

BACKUP RING
1  --- 44 | cost [11.01]
2  --- 35 | cost [10.77]
2  --- 55 | cost [7.0200000000000005]
3  --- 33 | cost [33.06]
3  --- 55 | cost [16.38]
4  --- 22 | cost [60.39]
4  --- 53 | cost [28.41]
5  --- 12 | cost [20.82]
5  --- 43 | cost [13.02]
6  --- 14 | cost [10.41]
6  --- 26 | cost [3.72]
7  --- 16 | cost [94.26]
7  --- 38 | cost [50.58]
8  --- 16 | cost [33.99]
8  --- 50 | cost [66.75]
9  --- 20 | cost [20.43]
9  --- 40 | cost [5.5200000000000005]
10 --- 41 | cost [6.8100000000000005]
10 --- 51 | cost [2.94]
11 --- 21 | cost [26.61]
11 --- 31 | cost [91.35000000000001]
12 --- 24 | cost [30.060000000000002]
13 --- 25 | cost [6.0]
13 --- 59 | cost [13.92]
14 --- 15 | cost [19.95]
15 --- 46 | cost [18.21]
17 --- 19 | cost [9.0]
17 --- 21 | cost [19.14]
18 --- 58 | cost [19.080000000000002]
19 --- 28 | cost [7.62]
20 --- 50 | cost [32.1]
22 --- 42 | cost [87.66]
23 --- 27 | cost [16.62]
23 --- 57 | cost [12.96]
24 --- 44 | cost [13.56]
25 --- 32 | cost [5.7]
26 --- 36 | cost [7.29]
27 --- 49 | cost [15.69]
28 --- 37 | cost [10.77]
29 --- 45 | cost [21.240000000000002]
29 --- 48 | cost [11.01]
30 --- 40 | cost [7.71]
31 --- 42 | cost [43.35]
32 --- 53 | cost [35.13]
33 --- 56 | cost [12.39]
34 --- 37 | cost [7.71]
34 --- 56 | cost [9.0]
35 --- 52 | cost [3.21]
36 --- 39 | cost [21.150000000000002]
38 --- 39 | cost [77.7]
41 --- 54 | cost [5.5200000000000005]
43 --- 47 | cost [16.62]
45 --- 46 | cost [8.19]
47 --- 52 | cost [5.1000000000000005]
48 --- 54 | cost [7.17]
49 --- 51 | cost [2.91]
57 --- 58 | cost [28.86]

BACKUP STAR

B = 94.26
i★ = 7
j★ = 42
k★ = 16