------------------------------------------------------------
                            α=5.0 —— pr76 —— 76 nodes       
------------------------------------------------------------

——————— Mon, 15 Jan 2024 04:07:52 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—75—77
total time           3616.03 (TL 3600)    gap                  0.002                
blossom time         0                    nb blossom           0.0                  
LB <= UB             499089.25<=499844.25 subtour              57188.0              
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:76                 
2-opt strategy       0                                                              
explored_nodes       9065                 n lazycuts edges     2.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—75—77

RING
1  --- 75 | cost [18030.0]
3  ---  4 | cost [3500.0]
3  ---  7 | cost [8140.0]
4  ---  5 | cost [6845.0]
5  --- 20 | cost [5265.0]
6  ---  7 | cost [4530.0]
6  ---  9 | cost [6820.0]
9  --- 10 | cost [3500.0]
10 --- 11 | cost [8085.0]
11 --- 12 | cost [5590.0]
12 --- 13 | cost [5820.0]
13 --- 14 | cost [2610.0]
14 --- 15 | cost [8730.0]
15 --- 16 | cost [3500.0]
16 --- 17 | cost [7560.0]
17 --- 18 | cost [3335.0]
18 --- 37 | cost [2750.0]
19 --- 20 | cost [3580.0]
19 --- 31 | cost [2750.0]
21 --- 22 | cost [5965.0]
21 --- 25 | cost [2750.0]
22 --- 24 | cost [8500.0]
24 --- 46 | cost [9655.0]
25 --- 26 | cost [14630.0]
26 --- 27 | cost [3500.0]
27 --- 43 | cost [8665.0]
28 --- 33 | cost [6815.0]
28 --- 43 | cost [5265.0]
29 --- 30 | cost [4530.0]
29 --- 32 | cost [6820.0]
30 --- 31 | cost [2915.0]
32 --- 33 | cost [3500.0]
36 --- 37 | cost [2610.0]
36 --- 38 | cost [6950.0]
38 --- 39 | cost [3500.0]
39 --- 40 | cost [7560.0]
40 --- 41 | cost [3335.0]
41 --- 60 | cost [2750.0]
44 --- 45 | cost [5965.0]
44 --- 48 | cost [2750.0]
45 --- 46 | cost [7165.0]
47 --- 48 | cost [5590.0]
47 --- 69 | cost [9655.0]
49 --- 50 | cost [3500.0]
49 --- 52 | cost [6840.0]
50 --- 67 | cost [15500.0]
51 --- 56 | cost [6815.0]
51 --- 66 | cost [5265.0]
52 --- 53 | cost [4530.0]
53 --- 54 | cost [2915.0]
54 --- 55 | cost [10000.0]
55 --- 56 | cost [3500.0]
57 --- 58 | cost [5590.0]
57 --- 63 | cost [6400.0]
58 --- 61 | cost [8055.0]
59 --- 60 | cost [2610.0]
59 --- 61 | cost [6950.0]
63 --- 64 | cost [3335.0]
64 --- 73 | cost [16250.0]
65 --- 66 | cost [3580.0]
65 --- 71 | cost [20350.0]
67 --- 68 | cost [5965.0]
68 --- 69 | cost [7165.0]
71 --- 72 | cost [9500.0]
72 --- 73 | cost [1500.0]
75 --- 77 | cost [18030.0]

STAR
2  -->  1 | cost [5590.0]
8  -->  7 | cost [2915.0]
23 --> 22 | cost [7165.0]
34 --> 40 | cost [6400.0]
35 --> 36 | cost [5820.0]
42 --> 54 | cost [2750.0]
62 --> 61 | cost [3500.0]
70 --> 68 | cost [19730.0]
74 --> 14 | cost [15790.0]
76 --> 75 | cost [1500.0]

BACKUP RING
1  --- 77 | cost [0.0]
3  ---  5 | cost [81.45]
3  ---  6 | cost [68.4]
4  ---  7 | cost [108.15]
4  --- 20 | cost [86.65]
5  --- 19 | cost [84.9]
6  --- 10 | cost [81.25]
7  ---  9 | cost [93.0]
9  --- 11 | cost [92.15]
10 --- 12 | cost [92.05]
11 --- 13 | cost [107.2]
12 --- 14 | cost [82.85000000000001]
13 --- 15 | cost [69.5]
14 --- 16 | cost [120.2]
15 --- 17 | cost [106.35000000000001]
16 --- 18 | cost [101.25]
17 --- 37 | cost [60.45]
18 --- 36 | cost [53.050000000000004]
19 --- 30 | cost [54.6]
20 --- 31 | cost [61.85]
21 --- 24 | cost [72.5]
21 --- 26 | cost [163.0]
22 --- 25 | cost [78.10000000000001]
22 --- 46 | cost [178.45000000000002]
24 --- 45 | cost [152.5]
25 --- 27 | cost [168.0]
26 --- 43 | cost [114.5]
27 --- 28 | cost [68.45]
28 --- 32 | cost [81.2]
29 --- 31 | cost [70.05]
29 --- 33 | cost [81.25]
30 --- 32 | cost [93.0]
33 --- 43 | cost [97.65]
36 --- 39 | cost [99.55]
37 --- 38 | cost [87.3]
38 --- 40 | cost [106.35000000000001]
39 --- 41 | cost [101.25]
40 --- 60 | cost [60.45]
41 --- 59 | cost [53.050000000000004]
44 --- 46 | cost [127.5]
44 --- 47 | cost [72.5]
45 --- 48 | cost [78.10000000000001]
47 --- 68 | cost [152.5]
48 --- 69 | cost [143.0]
49 --- 53 | cost [81.4]
49 --- 67 | cost [178.6]
50 --- 52 | cost [81.4]
50 --- 68 | cost [183.45000000000002]
51 --- 55 | cost [81.2]
51 --- 65 | cost [84.9]
52 --- 54 | cost [70.05]
53 --- 55 | cost [93.0]
54 --- 56 | cost [129.7]
56 --- 66 | cost [97.65]
57 --- 61 | cost [91.9]
57 --- 64 | cost [95.65]
58 --- 59 | cost [58.2]
58 --- 63 | cost [114.2]
60 --- 61 | cost [87.3]
63 --- 73 | cost [195.45000000000002]
64 --- 72 | cost [157.35]
65 --- 72 | cost [276.7]
66 --- 71 | cost [237.85]
67 --- 69 | cost [127.5]
71 --- 73 | cost [110.0]

BACKUP STAR
8  -->  6 | cost [70.05]
23 -->  1 | cost [96.55]
34 --> 39 | cost [80.55]
35 --> 38 | cost [80.55]
42 --> 43 | cost [35.800000000000004]
62 --> 63 | cost [75.60000000000001]
70 --> 67 | cost [195.25]
74 --> 13 | cost [183.85]
76 -->  1 | cost [185.8]

B = 322.75
i★ = 67
j★ = 68
k★ = 69

       
——————— Mon, 15 Jan 2024 05:08:47 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 67 hubs —— 1-75-76-2-23-22-21-25-24-46-45-44-48-47-69-68-67-50-51-66-65-71-72-64-63-62-61-59-58-57-56-55-52-53-54-42-43-27-26-20-19-31-30-29-28-33-34-40-39-38-36-37-18-17-16-15-14-13-12-9-8-7-6-5-4-3-77-1
total time           3605.62 (TL 3600)    gap                  0.068                
blossom time         0                    nb blossom           0.0                  
LB <= UB             483985<=519484.25    Master/SP costs      517225/2259.25       
Master time          3603.65              SP time              1.97                 
subtour              79191.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            19.0                 SP method            poly                 
tildeV               2:76                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       18773                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—75—76—2—23—22—21—25—24—46—45—44—48—47—69—68—67—50—51—66—65—71—72—64—63—62—61—59—58—57—56—55—52—53—54—42—43—27—26—20—19—31—30—29—28—33—34—40—39—38—36—37—18—17—16—15—14—13—12—9—8—7—6—5—4—3—77

RING
1  --- 75 | cost [18030.0]
2  --- 23 | cost [14300.0]
2  --- 76 | cost [19145.0]
3  ---  4 | cost [3500.0]
3  --- 77 | cost [18105.0]
4  ---  5 | cost [6845.0]
5  ---  6 | cost [5575.0]
6  ---  7 | cost [4530.0]
7  ---  8 | cost [2915.0]
8  ---  9 | cost [10000.0]
9  --- 12 | cost [8075.0]
12 --- 13 | cost [5820.0]
13 --- 14 | cost [2610.0]
14 --- 15 | cost [8730.0]
15 --- 16 | cost [3500.0]
16 --- 17 | cost [7560.0]
17 --- 18 | cost [3335.0]
18 --- 37 | cost [2750.0]
19 --- 20 | cost [3580.0]
19 --- 31 | cost [2750.0]
20 --- 26 | cost [15230.0]
21 --- 22 | cost [5965.0]
21 --- 25 | cost [2750.0]
22 --- 23 | cost [7165.0]
24 --- 25 | cost [5590.0]
24 --- 46 | cost [9655.0]
26 --- 27 | cost [3500.0]
27 --- 43 | cost [8665.0]
28 --- 29 | cost [5575.0]
28 --- 33 | cost [6815.0]
29 --- 30 | cost [4530.0]
30 --- 31 | cost [2915.0]
33 --- 34 | cost [8085.0]
34 --- 40 | cost [6400.0]
36 --- 37 | cost [2610.0]
36 --- 38 | cost [6950.0]
38 --- 39 | cost [3500.0]
39 --- 40 | cost [7560.0]
42 --- 43 | cost [3580.0]
42 --- 54 | cost [2750.0]
44 --- 45 | cost [5965.0]
44 --- 48 | cost [2750.0]
45 --- 46 | cost [7165.0]
47 --- 48 | cost [5590.0]
47 --- 69 | cost [9655.0]
50 --- 51 | cost [6845.0]
50 --- 67 | cost [15500.0]
51 --- 66 | cost [5265.0]
52 --- 53 | cost [4530.0]
52 --- 55 | cost [6820.0]
53 --- 54 | cost [2915.0]
55 --- 56 | cost [3500.0]
56 --- 57 | cost [8085.0]
57 --- 58 | cost [5590.0]
58 --- 59 | cost [5820.0]
59 --- 61 | cost [6950.0]
61 --- 62 | cost [3500.0]
62 --- 63 | cost [7560.0]
63 --- 64 | cost [3335.0]
64 --- 72 | cost [15735.0]
65 --- 66 | cost [3580.0]
65 --- 71 | cost [20350.0]
67 --- 68 | cost [5965.0]
68 --- 69 | cost [7165.0]
71 --- 72 | cost [9500.0]
75 --- 76 | cost [1500.0]

STAR
10 -->  9 | cost [3500.0]
11 --> 12 | cost [5590.0]
32 --> 33 | cost [3500.0]
35 --> 34 | cost [5590.0]
41 --> 40 | cost [3335.0]
49 --> 50 | cost [3500.0]
60 --> 59 | cost [2610.0]
70 --> 68 | cost [19730.0]
73 --> 72 | cost [1500.0]
74 --> 14 | cost [15790.0]

BACKUP RING
1  --- 76 | cost [185.8]
2  --- 22 | cost [184.4]
2  --- 75 | cost [182.0]
3  ---  5 | cost [81.45]
4  ---  6 | cost [81.4]
4  --- 77 | cost [194.55]
5  ---  7 | cost [100.7]
6  ---  8 | cost [70.05]
7  ---  9 | cost [93.0]
8  --- 12 | cost [156.45000000000002]
9  --- 13 | cost [129.75]
12 --- 14 | cost [82.85000000000001]
13 --- 15 | cost [69.5]
14 --- 16 | cost [120.2]
15 --- 17 | cost [106.35000000000001]
16 --- 18 | cost [101.25]
17 --- 37 | cost [60.45]
18 --- 36 | cost [53.050000000000004]
19 --- 26 | cost [131.1]
19 --- 30 | cost [54.6]
20 --- 27 | cost [185.0]
20 --- 31 | cost [61.85]
21 --- 23 | cost [127.5]
21 --- 24 | cost [72.5]
22 --- 25 | cost [78.10000000000001]
23 --- 76 | cost [263.05]
24 --- 45 | cost [152.5]
25 --- 46 | cost [143.0]
26 --- 43 | cost [114.5]
27 --- 42 | cost [121.05]
28 --- 30 | cost [100.7]
28 --- 34 | cost [147.5]
29 --- 31 | cost [70.05]
29 --- 33 | cost [81.25]
33 --- 40 | cost [133.1]
34 --- 39 | cost [80.55]
36 --- 39 | cost [99.55]
37 --- 38 | cost [87.3]
38 --- 40 | cost [106.35000000000001]
42 --- 53 | cost [54.6]
43 --- 54 | cost [61.85]
44 --- 46 | cost [127.5]
44 --- 47 | cost [72.5]
45 --- 48 | cost [78.10000000000001]
47 --- 68 | cost [152.5]
48 --- 69 | cost [143.0]
50 --- 66 | cost [86.65]
50 --- 68 | cost [183.45000000000002]
51 --- 65 | cost [84.9]
51 --- 67 | cost [208.1]
52 --- 54 | cost [70.05]
52 --- 56 | cost [81.25]
53 --- 55 | cost [93.0]
55 --- 57 | cost [92.15]
56 --- 58 | cost [92.05]
57 --- 59 | cost [107.2]
58 --- 61 | cost [80.55]
59 --- 62 | cost [99.55]
61 --- 63 | cost [106.35000000000001]
62 --- 64 | cost [101.25]
63 --- 72 | cost [190.6]
64 --- 71 | cost [157.35]
65 --- 72 | cost [276.7]
66 --- 71 | cost [237.85]
67 --- 69 | cost [127.5]

BACKUP STAR
10 -->  5 | cost [68.15]
11 --> 17 | cost [64.0]
32 --> 29 | cost [68.2]
35 --> 36 | cost [58.2]
41 --> 59 | cost [53.050000000000004]
49 --> 52 | cost [68.4]
60 --> 40 | cost [60.45]
70 --> 67 | cost [195.25]
73 --> 71 | cost [110.0]
74 --> 13 | cost [183.85]

B = 322.75
i★ = 67
j★ = 68
k★ = 69