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

——————— Sun, 07 Jan 2024 02:24:37 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 26 hubs —— 1—13—40—30—24—57—12—43—49—47—17—26—6—28—14—33—29—35—41—2—54—55—22—8—18—59
total time           3608.65 (TL 3600)    gap                  0.132                
blossom time         0                    nb blossom           0.0                  
LB <= UB             141487.62<=162931.8  subtour              415.0                
connectivity cuts    990.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:58                 
2-opt strategy       0                                                              
explored_nodes       1584                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—13—40—30—24—57—12—43—49—47—17—26—6—28—14—33—29—35—41—2—54—55—22—8—18—59

RING
1  --- 13 | cost [3248.0]
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]
12 --- 43 | cost [1953.0]
12 --- 57 | cost [1736.0]
13 --- 40 | cost [945.0]
14 --- 28 | cost [1568.0]
14 --- 33 | cost [1232.0]
17 --- 26 | cost [903.0]
17 --- 47 | cost [2744.0]
18 --- 59 | cost [2310.0]
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]
30 --- 40 | cost [1799.0]
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  --> 13 | cost [5874.0]
5  --> 43 | cost [1302.0]
7  --> 54 | cost [12897.0]
9  --> 13 | cost [441.0]
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 --> 40 | cost [2400.0]
21 --> 29 | cost [1560.0]
23 --> 57 | cost [1296.0]
25 --> 40 | cost [375.0]
27 --> 43 | cost [552.0]
31 --> 55 | cost [10242.0]
32 --> 40 | cost [891.0]
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]
42 --> 41 | cost [9882.0]
44 --> 18 | cost [342.0]
45 --> 33 | cost [639.0]
46 --> 33 | cost [1305.0]
48 --> 41 | cost [576.0]
50 --> 40 | cost [4746.0]
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  --- 40 | cost [35.84]
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]
8  --- 59 | cost [122.01]
12 --- 24 | cost [70.14]
12 --- 49 | cost [43.26]
13 --- 30 | cost [14.77]
14 --- 29 | cost [67.76]
17 --- 49 | cost [35.77]
18 --- 22 | cost [113.33]
22 --- 54 | cost [32.13]
24 --- 40 | cost [79.87]
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  --> 18 | cost [59.730000000000004]
5  --> 54 | cost [14.82]
7  --> 22 | cost [122.22]
9  --> 40 | cost [5.5200000000000005]
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]
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 --> 13 | cost [43.53]
51 --> 49 | cost [2.91]
52 --> 47 | cost [5.1000000000000005]
53 --> 40 | cost [34.38]
56 --> 14 | cost [23.13]
58 --> 18 | cost [19.080000000000002]

B = 138.6
i★ = 2
j★ = 54
k★ = 55

       
——————— Sun, 07 Jan 2024 03:25:16 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 29 hubs —— 1-44-24-57-12-43-49-47-17-26-6-28-14-33-29-35-41-54-55-22-8-53-50-20-32-9-13-30-59-1
total time           3603.5 (TL 3600)     gap                  0.171                
blossom time         0                    nb blossom           0.0                  
LB <= UB             137294.36<=165533.25 Master/SP costs      137031/28502.25      
Master time          3568.44              SP time              35.06                
subtour              12547.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            2619.0               SP method            poly                 
tildeV               2:58                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       88634                
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—44—24—57—12—43—49—47—17—26—6—28—14—33—29—35—41—54—55—22—8—53—50—20—32—9—13—30—59

RING
1  --- 44 | cost [2569.0]
1  --- 59 | cost [0.0]
6  --- 26 | cost [868.0]
6  --- 28 | cost [1323.0]
8  --- 22 | cost [1463.0]
8  --- 53 | cost [12523.0]
9  --- 13 | cost [1029.0]
9  --- 32 | cost [1596.0]
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]
20 --- 32 | cost [3759.0]
20 --- 50 | cost [7490.0]
22 --- 55 | cost [2513.0]
24 --- 44 | cost [3164.0]
24 --- 57 | cost [5278.0]
29 --- 33 | cost [3346.0]
29 --- 35 | cost [2478.0]
30 --- 59 | cost [2149.0]
35 --- 41 | cost [1036.0]
41 --- 54 | cost [1288.0]
43 --- 49 | cost [2373.0]
47 --- 49 | cost [602.0]
50 --- 53 | cost [3122.0]
54 --- 55 | cost [784.0]

STAR
2  --> 41 | cost [294.0]
3  --> 35 | cost [474.0]
4  --> 50 | cost [2418.0]
5  --> 43 | cost [1302.0]
7  --> 54 | cost [12897.0]
10 --> 35 | cost [225.0]
11 --> 29 | cost [2019.0]
15 --> 14 | cost [1995.0]
16 --> 22 | cost [2796.0]
18 --> 44 | cost [342.0]
19 -->  6 | cost [414.0]
21 --> 29 | cost [1560.0]
23 --> 57 | cost [1296.0]
25 -->  9 | cost [390.0]
27 --> 43 | cost [552.0]
31 --> 55 | cost [10242.0]
34 --> 14 | cost [1182.0]
36 --> 17 | cost [342.0]
37 --> 14 | cost [411.0]
38 --> 41 | cost [8283.0]
39 --> 35 | cost [987.0]
40 --> 13 | cost [405.0]
42 --> 22 | cost [8766.0]
45 --> 33 | cost [639.0]
46 --> 33 | cost [1305.0]
48 --> 41 | cost [576.0]
51 --> 47 | cost [216.0]
52 --> 35 | cost [321.0]
56 --> 33 | cost [1239.0]
58 --> 24 | cost [777.0]

BACKUP RING
1  --- 24 | cost [46.83]
6  --- 14 | cost [24.29]
6  --- 17 | cost [17.5]
8  --- 50 | cost [155.75]
8  --- 55 | cost [30.52]
9  --- 20 | cost [47.67]
9  --- 30 | cost [24.01]
12 --- 24 | cost [70.14]
12 --- 49 | cost [43.26]
13 --- 32 | cost [25.62]
13 --- 59 | cost [32.480000000000004]
14 --- 29 | cost [67.76]
17 --- 49 | cost [35.77]
20 --- 53 | cost [44.38]
22 --- 53 | cost [139.02]
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]
32 --- 50 | cost [112.49000000000001]
33 --- 35 | cost [72.87]
35 --- 54 | cost [22.05]
41 --- 55 | cost [19.740000000000002]
43 --- 47 | cost [38.78]
43 --- 57 | cost [36.89]
44 --- 57 | cost [85.82000000000001]

BACKUP STAR
2  --> 54 | cost [4.11]
3  --> 41 | cost [8.28]
4  --> 53 | cost [28.41]
5  --> 54 | cost [14.82]
7  --> 22 | cost [122.22]
10 --> 49 | cost [5.07]
11 --> 41 | cost [26.82]
15 --> 33 | cost [24.54]
16 --> 55 | cost [31.86]
18 -->  1 | cost [9.9]
19 --> 26 | cost [5.34]
21 --> 17 | cost [19.14]
23 --> 12 | cost [13.68]
25 --> 32 | cost [5.7]
27 --> 12 | cost [7.71]
31 --> 22 | cost [98.67]
34 --> 33 | cost [16.41]
36 --> 26 | cost [7.29]
37 --> 33 | cost [8.700000000000001]
38 --> 22 | cost [71.64]
39 --> 29 | cost [10.98]
40 -->  9 | cost [5.5200000000000005]
42 --> 55 | cost [91.41]
45 --> 14 | cost [14.370000000000001]
46 --> 14 | cost [18.87]
48 --> 54 | cost [7.17]
51 --> 49 | cost [2.91]
52 --> 47 | cost [5.1000000000000005]
56 --> 14 | cost [23.13]
58 --> 44 | cost [15.66]

B = 155.75
i★ = 8
j★ = 53
k★ = 50

       
——————— Sun, 07 Jan 2024 23:01:24 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
ILP ——— 31 hubs —— 1—44—24—57—12—43—49—47—17—26—6—28—14—33—29—39—35—41—2—54—55—22—8—4—53—20—32—25—40—30—59
total time           3610.99 (TL 3600)    gap                  0.137                
blossom time         2.64                 nb blossom           493.0                
LB <= UB             142185.7<=164707.53  subtour              515.0                
connectivity cuts    1554.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               2:58                 
2-opt strategy       0                                                              
explored_nodes       2173                 n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—44—24—57—12—43—49—47—17—26—6—28—14—33—29—39—35—41—2—54—55—22—8—4—53—20—32—25—40—30—59

RING
1  --- 44 | cost [2569.0]
1  --- 59 | cost [0.0]
2  --- 41 | cost [686.0]
2  --- 54 | cost [959.0]
4  ---  8 | cost [14840.0]
4  --- 53 | cost [6629.0]
6  --- 26 | cost [868.0]
6  --- 28 | cost [1323.0]
8  --- 22 | cost [1463.0]
12 --- 43 | cost [1953.0]
12 --- 57 | cost [1736.0]
14 --- 28 | cost [1568.0]
14 --- 33 | cost [1232.0]
17 --- 26 | cost [903.0]
17 --- 47 | cost [2744.0]
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]
29 --- 33 | cost [3346.0]
29 --- 39 | cost [2562.0]
30 --- 40 | cost [1799.0]
30 --- 59 | cost [2149.0]
35 --- 39 | cost [2303.0]
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]
5  --> 43 | cost [1302.0]
7  --> 54 | cost [12897.0]
9  --> 25 | cost [390.0]
10 --> 35 | cost [225.0]
11 --> 39 | cost [1365.0]
13 --> 40 | cost [405.0]
15 --> 14 | cost [1995.0]
16 --> 22 | cost [2796.0]
18 --> 44 | cost [342.0]
19 -->  6 | cost [414.0]
21 --> 29 | cost [1560.0]
23 --> 57 | cost [1296.0]
27 --> 43 | cost [552.0]
31 --> 55 | cost [10242.0]
34 --> 14 | cost [1182.0]
36 --> 17 | cost [342.0]
37 --> 14 | cost [411.0]
38 --> 22 | cost [7164.0]
42 --> 39 | cost [9372.0]
45 --> 33 | cost [639.0]
46 --> 33 | cost [1305.0]
48 --> 41 | cost [576.0]
50 --> 53 | cost [1338.0]
51 --> 47 | cost [216.0]
52 --> 35 | cost [321.0]
56 --> 33 | cost [1239.0]
58 --> 24 | cost [777.0]

BACKUP RING
1  --- 24 | cost [46.83]
2  --- 35 | cost [25.13]
2  --- 55 | cost [16.38]
4  --- 20 | cost [109.97]
4  --- 22 | cost [140.91]
6  --- 14 | cost [24.29]
6  --- 17 | cost [17.5]
8  --- 53 | cost [125.23]
8  --- 55 | cost [30.52]
12 --- 24 | cost [70.14]
12 --- 49 | cost [43.26]
14 --- 29 | cost [67.76]
17 --- 49 | cost [35.77]
20 --- 25 | cost [48.51]
22 --- 54 | cost [32.13]
25 --- 30 | cost [26.04]
26 --- 28 | cost [30.240000000000002]
26 --- 47 | cost [36.96]
28 --- 33 | cost [19.81]
29 --- 35 | cost [24.78]
32 --- 40 | cost [20.79]
32 --- 53 | cost [81.97]
33 --- 39 | cost [80.64]
39 --- 41 | cost [30.240000000000002]
40 --- 59 | cost [35.84]
41 --- 54 | cost [12.88]
43 --- 47 | cost [38.78]
43 --- 57 | cost [36.89]
44 --- 57 | cost [85.82000000000001]

BACKUP STAR
3  --> 41 | cost [8.28]
5  --> 54 | cost [14.82]
7  --> 22 | cost [122.22]
9  --> 40 | cost [5.5200000000000005]
10 --> 49 | cost [5.07]
11 --> 29 | cost [20.19]
13 --> 25 | cost [6.0]
15 --> 33 | cost [24.54]
16 --> 55 | cost [31.86]
18 -->  1 | cost [9.9]
19 --> 26 | cost [5.34]
21 --> 39 | cost [18.21]
23 --> 12 | cost [13.68]
27 --> 12 | cost [7.71]
31 --> 22 | cost [98.67]
34 --> 33 | cost [16.41]
36 --> 26 | cost [7.29]
37 --> 33 | cost [8.700000000000001]
38 --> 55 | cost [75.39]
42 --> 22 | cost [87.66]
45 --> 14 | cost [14.370000000000001]
46 --> 14 | cost [18.87]
48 -->  2 | cost [5.82]
50 -->  4 | cost [24.18]
51 --> 49 | cost [2.91]
52 --> 47 | cost [5.1000000000000005]
56 --> 14 | cost [23.13]
58 --> 44 | cost [15.66]

B = 140.91
i★ = 4
j★ = 8
k★ = 22

       
——————— Mon, 08 Jan 2024 00:02:00 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = true
BD  —— 33 hubs —— 1-44-24-57-12-43-49-47-17-26-6-28-14-37-34-45-33-29-3-35-41-54-55-22-8-53-50-20-32-25-40-30-59-1
total time           3604.79 (TL 3600)    gap                  0.177                
blossom time         353.67               nb blossom           91060.0              
LB <= UB             137830.2<=167507.08  Master/SP costs      138454/29053.08      
Master time          3576.66              SP time              28.13                
subtour              16108.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            2752.0               SP method            poly                 
tildeV               2:58                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       99171                
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—44—24—57—12—43—49—47—17—26—6—28—14—37—34—45—33—29—3—35—41—54—55—22—8—53—50—20—32—25—40—30—59

RING
1  --- 44 | cost [2569.0]
1  --- 59 | cost [0.0]
3  --- 29 | cost [2009.0]
3  --- 35 | cost [1106.0]
6  --- 26 | cost [868.0]
6  --- 28 | cost [1323.0]
8  --- 22 | cost [1463.0]
8  --- 53 | cost [12523.0]
12 --- 43 | cost [1953.0]
12 --- 57 | cost [1736.0]
14 --- 28 | cost [1568.0]
14 --- 37 | cost [959.0]
17 --- 26 | cost [903.0]
17 --- 47 | cost [2744.0]
20 --- 32 | cost [3759.0]
20 --- 50 | cost [7490.0]
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]
29 --- 33 | cost [3346.0]
30 --- 40 | cost [1799.0]
30 --- 59 | cost [2149.0]
33 --- 45 | cost [1491.0]
34 --- 37 | cost [1799.0]
34 --- 45 | cost [2478.0]
35 --- 41 | cost [1036.0]
41 --- 54 | cost [1288.0]
43 --- 49 | cost [2373.0]
47 --- 49 | cost [602.0]
50 --- 53 | cost [3122.0]
54 --- 55 | cost [784.0]

STAR
2  --> 41 | cost [294.0]
4  --> 50 | cost [2418.0]
5  --> 43 | cost [1302.0]
7  --> 22 | cost [12222.0]
9  --> 25 | cost [390.0]
10 --> 35 | cost [225.0]
11 --> 29 | cost [2019.0]
13 --> 40 | cost [405.0]
15 --> 34 | cost [786.0]
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]
27 --> 43 | cost [552.0]
31 --> 55 | cost [10242.0]
36 --> 17 | cost [342.0]
38 --> 54 | cost [7839.0]
39 -->  3 | cost [861.0]
42 --> 41 | cost [9882.0]
46 --> 34 | cost [687.0]
48 --> 41 | cost [576.0]
51 --> 47 | cost [216.0]
52 --> 35 | cost [321.0]
56 --> 34 | cost [900.0]
58 --> 24 | cost [777.0]

BACKUP RING
1  --- 24 | cost [46.83]
3  --- 33 | cost [77.14]
3  --- 41 | cost [19.32]
6  --- 14 | cost [24.29]
6  --- 17 | cost [17.5]
8  --- 50 | cost [155.75]
8  --- 55 | cost [30.52]
12 --- 24 | cost [70.14]
12 --- 49 | cost [43.26]
14 --- 34 | cost [27.580000000000002]
17 --- 49 | cost [35.77]
20 --- 25 | cost [48.51]
20 --- 53 | cost [44.38]
22 --- 53 | cost [139.02]
22 --- 54 | cost [32.13]
25 --- 30 | cost [26.04]
26 --- 28 | cost [30.240000000000002]
26 --- 47 | cost [36.96]
28 --- 37 | cost [25.13]
29 --- 35 | cost [24.78]
29 --- 45 | cost [49.56]
32 --- 40 | cost [20.79]
32 --- 50 | cost [112.49000000000001]
33 --- 34 | cost [38.29]
35 --- 54 | cost [22.05]
37 --- 45 | cost [23.94]
40 --- 59 | cost [35.84]
41 --- 55 | cost [19.740000000000002]
43 --- 47 | cost [38.78]
43 --- 57 | cost [36.89]
44 --- 57 | cost [85.82000000000001]

BACKUP STAR
2  --> 54 | cost [4.11]
4  --> 53 | cost [28.41]
5  --> 54 | cost [14.82]
7  --> 55 | cost [125.97]
9  --> 40 | cost [5.5200000000000005]
10 --> 49 | cost [5.07]
11 -->  3 | cost [22.8]
13 --> 25 | cost [6.0]
15 --> 37 | cost [15.84]
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]
27 --> 12 | cost [7.71]
31 --> 22 | cost [98.67]
36 --> 26 | cost [7.29]
38 --> 22 | cost [71.64]
39 --> 35 | cost [9.870000000000001]
42 --> 22 | cost [87.66]
46 --> 45 | cost [8.19]
48 --> 54 | cost [7.17]
51 --> 49 | cost [2.91]
52 --> 47 | cost [5.1000000000000005]
56 --> 45 | cost [9.36]
58 --> 44 | cost [15.66]

B = 158.76
i★ = 22
j★ = 55
k★ = 54