------------------------------------------------------------
                        α=7.0 —— brazil58 —— 58 nodes       
------------------------------------------------------------

——————— Mon, 29 Jan 2024 08:38:34 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 26 hubs —— 1—18—8—22—55—54—2—41—35—29—33—14—28—6—26—17—47—49—43—12—57—24—30—13—9—59
total time           3609.66 (TL 3600)    gap                  0.137                
blossom time         0                    nb blossom           0.0                  
LB <= UB             140861.38<=163316.91 subtour              394.0                
connectivity cuts    1206.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               2:58                 
2-opt strategy       0                                                              
explored_nodes       3427                 n lazycuts edges     1.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—18—8—22—55—54—2—41—35—29—33—14—28—6—26—17—47—49—43—12—57—24—30—13—9—59

RING
1  --- 18 | cost [2310.0]
1  --- 59 | cost [0.0]
2  --- 41 | cost [686.0]
2  --- 54 | cost [959.0]
6  --- 26 | cost [868.0]
6  --- 28 | cost [1323.0]
8  --- 18 | cost [9954.0]
8  --- 22 | cost [1463.0]
9  --- 13 | cost [1029.0]
9  --- 59 | cost [4158.0]
12 --- 43 | cost [1953.0]
12 --- 57 | cost [1736.0]
13 --- 30 | cost [1477.0]
14 --- 28 | cost [1568.0]
14 --- 33 | cost [1232.0]
17 --- 26 | cost [903.0]
17 --- 47 | cost [2744.0]
22 --- 55 | cost [2513.0]
24 --- 30 | cost [6552.0]
24 --- 57 | cost [5278.0]
29 --- 33 | cost [3346.0]
29 --- 35 | cost [2478.0]
35 --- 41 | cost [1036.0]
43 --- 49 | cost [2373.0]
47 --- 49 | cost [602.0]
54 --- 55 | cost [784.0]

STAR
3  --> 35 | cost [474.0]
4  -->  9 | cost [6120.0]
5  --> 43 | cost [1302.0]
7  -->  2 | cost [13935.0]
10 --> 35 | cost [225.0]
11 --> 29 | cost [2019.0]
15 --> 14 | cost [1995.0]
16 --> 22 | cost [2796.0]
19 -->  6 | cost [414.0]
20 -->  9 | cost [2043.0]
21 --> 29 | cost [1560.0]
23 --> 57 | cost [1296.0]
25 -->  9 | cost [390.0]
27 --> 43 | cost [552.0]
31 --> 54 | cost [10542.0]
32 -->  9 | cost [684.0]
34 --> 14 | cost [1182.0]
36 --> 17 | cost [342.0]
37 --> 14 | cost [411.0]
38 --> 22 | cost [7164.0]
39 --> 35 | cost [987.0]
40 --> 13 | cost [405.0]
42 --> 55 | cost [9141.0]
44 --> 18 | cost [342.0]
45 --> 33 | cost [639.0]
46 --> 33 | cost [1305.0]
48 --> 41 | cost [576.0]
50 --> 13 | cost [4353.0]
51 --> 47 | cost [216.0]
52 --> 35 | cost [321.0]
53 --> 13 | cost [3033.0]
56 --> 33 | cost [1239.0]
58 --> 24 | cost [777.0]

BACKUP RING
1  ---  8 | cost [122.01]
2  --- 35 | cost [25.13]
2  --- 55 | cost [16.38]
6  --- 14 | cost [24.29]
6  --- 17 | cost [17.5]
8  --- 55 | cost [30.52]
9  --- 30 | cost [24.01]
12 --- 24 | cost [70.14]
12 --- 49 | cost [43.26]
13 --- 24 | cost [88.69]
13 --- 59 | cost [32.480000000000004]
14 --- 29 | cost [67.76]
17 --- 49 | cost [35.77]
18 --- 22 | cost [113.33]
22 --- 54 | cost [32.13]
26 --- 28 | cost [30.240000000000002]
26 --- 47 | cost [36.96]
28 --- 33 | cost [19.81]
29 --- 41 | cost [31.29]
30 --- 57 | cost [117.88]
33 --- 35 | cost [72.87]
41 --- 54 | cost [12.88]
43 --- 47 | cost [38.78]
43 --- 57 | cost [36.89]

BACKUP STAR
3  --> 41 | cost [8.28]
4  --> 13 | cost [58.74]
5  --> 54 | cost [14.82]
7  --> 22 | cost [122.22]
10 --> 49 | cost [5.07]
11 -->  2 | cost [23.16]
15 --> 33 | cost [24.54]
16 --> 55 | cost [31.86]
19 --> 26 | cost [5.34]
20 --> 13 | cost [24.51]
21 --> 17 | cost [19.14]
23 --> 12 | cost [13.68]
25 --> 13 | cost [6.0]
27 --> 12 | cost [7.71]
31 --> 22 | cost [98.67]
32 --> 13 | cost [10.98]
34 --> 33 | cost [16.41]
36 --> 26 | cost [7.29]
37 --> 33 | cost [8.700000000000001]
38 --> 55 | cost [75.39]
39 --> 29 | cost [10.98]
40 -->  9 | cost [5.5200000000000005]
42 --> 22 | cost [87.66]
44 -->  1 | cost [11.01]
45 --> 14 | cost [14.370000000000001]
46 --> 14 | cost [18.87]
48 -->  2 | cost [5.82]
50 -->  9 | cost [46.32]
51 --> 49 | cost [2.91]
52 --> 47 | cost [5.1000000000000005]
53 -->  9 | cost [33.09]
56 --> 14 | cost [23.13]
58 --> 18 | cost [19.080000000000002]

B = 137.76999999999998
i★ = 8
j★ = 22
k★ = 55

       
——————— Mon, 29 Jan 2024 09:39:14 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 27 hubs —— 1-30-40-25-32-20-53-8-22-55-54-2-3-29-33-14-28-6-26-17-51-27-12-57-24-44-59-1
total time           3604.92 (TL 3600)    gap                  0.24                 
blossom time         0                    nb blossom           0.0                  
LB <= UB             132073.42<=173862.42 Master/SP costs      134199/39663.42      
Master time          3597.86              SP time              7.06                 
subtour              47403.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            387.0                SP method            poly                 
tildeV               2:58                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       29921                
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—30—40—25—32—20—53—8—22—55—54—2—3—29—33—14—28—6—26—17—51—27—12—57—24—44—59

RING
1  --- 30 | cost [2149.0]
2  ---  3 | cost [2198.0]
2  --- 54 | cost [959.0]
3  --- 29 | cost [2009.0]
6  --- 26 | cost [868.0]
6  --- 28 | cost [1323.0]
8  --- 22 | cost [1463.0]
8  --- 53 | cost [12523.0]
12 --- 27 | cost [1799.0]
12 --- 57 | cost [1736.0]
14 --- 28 | cost [1568.0]
14 --- 33 | cost [1232.0]
17 --- 26 | cost [903.0]
17 --- 51 | cost [2856.0]
20 --- 32 | cost [3759.0]
20 --- 53 | cost [4438.0]
22 --- 55 | cost [2513.0]
24 --- 44 | cost [3164.0]
24 --- 57 | cost [5278.0]
25 --- 32 | cost [1330.0]
25 --- 40 | cost [875.0]
27 --- 51 | cost [3486.0]
29 --- 33 | cost [3346.0]
30 --- 40 | cost [1799.0]
44 --- 59 | cost [2569.0]
54 --- 55 | cost [784.0]

STAR
4  --> 53 | cost [2841.0]
5  --> 27 | cost [780.0]
7  --> 54 | cost [12897.0]
9  --> 25 | cost [390.0]
10 --> 51 | cost [294.0]
11 --> 29 | cost [2019.0]
13 --> 40 | cost [405.0]
15 --> 14 | cost [1995.0]
16 --> 55 | cost [3186.0]
18 --> 44 | cost [342.0]
19 -->  6 | cost [414.0]
21 --> 29 | cost [1560.0]
23 --> 57 | cost [1296.0]
31 --> 22 | cost [9867.0]
34 --> 14 | cost [1182.0]
35 -->  3 | cost [474.0]
36 --> 17 | cost [342.0]
37 --> 14 | cost [411.0]
38 --> 22 | cost [7164.0]
39 -->  3 | cost [861.0]
41 -->  2 | cost [294.0]
42 --> 55 | cost [9141.0]
43 --> 27 | cost [552.0]
45 --> 33 | cost [639.0]
46 --> 33 | cost [1305.0]
47 --> 51 | cost [216.0]
48 -->  2 | cost [582.0]
49 --> 51 | cost [291.0]
50 --> 20 | cost [3210.0]
52 --> 51 | cost [306.0]
56 --> 33 | cost [1239.0]
58 --> 24 | cost [777.0]

BACKUP RING
1  --- 40 | cost [35.84]
2  --- 29 | cost [41.93]
2  --- 55 | cost [16.38]
3  --- 33 | cost [77.14]
3  --- 54 | cost [31.57]
6  --- 14 | cost [24.29]
6  --- 17 | cost [17.5]
8  --- 20 | cost [169.61]
8  --- 55 | cost [30.52]
12 --- 24 | cost [70.14]
12 --- 51 | cost [49.0]
14 --- 29 | cost [67.76]
17 --- 27 | cost [64.05]
20 --- 25 | cost [48.51]
22 --- 53 | cost [139.02]
22 --- 54 | cost [32.13]
24 --- 59 | cost [46.83]
25 --- 30 | cost [26.04]
26 --- 28 | cost [30.240000000000002]
26 --- 51 | cost [37.52]
27 --- 57 | cost [34.86]
28 --- 33 | cost [19.81]
32 --- 40 | cost [20.79]
32 --- 53 | cost [81.97]
44 --- 57 | cost [85.82000000000001]

BACKUP STAR
4  --> 20 | cost [47.13]
5  --> 54 | cost [14.82]
7  --> 22 | cost [122.22]
9  --> 40 | cost [5.5200000000000005]
10 -->  3 | cost [6.51]
11 -->  3 | cost [22.8]
13 --> 25 | cost [6.0]
15 --> 33 | cost [24.54]
16 --> 22 | cost [27.96]
18 -->  1 | cost [9.9]
19 --> 26 | cost [5.34]
21 -->  3 | cost [17.34]
23 --> 12 | cost [13.68]
31 --> 55 | cost [102.42]
34 --> 33 | cost [16.41]
35 --> 51 | cost [5.13]
36 --> 26 | cost [7.29]
37 --> 33 | cost [8.700000000000001]
38 --> 55 | cost [75.39]
39 --> 29 | cost [10.98]
41 --> 54 | cost [5.5200000000000005]
42 --> 22 | cost [87.66]
43 --> 12 | cost [8.370000000000001]
45 --> 14 | cost [14.370000000000001]
46 --> 14 | cost [18.87]
47 --> 17 | cost [11.76]
48 --> 54 | cost [7.17]
49 -->  3 | cost [10.02]
50 --> 53 | cost [13.38]
52 -->  3 | cost [7.05]
56 --> 14 | cost [23.13]
58 --> 44 | cost [15.66]

B = 216.74
i★ = 8
j★ = 53
k★ = 20