------------------------------------------------------------
                            α=3.0 —— pr76 —— 76 nodes       
------------------------------------------------------------

——————— Thu, 25 Jan 2024 22:26:12 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 77 hubs —— 1—23—22—21—25—24—46—45—44—48—47—69—68—70—67—50—49—51—66—65—71—72—73—64—63—62—61—41—60—59—58—57—56—55—52—53—54—42—43—28—27—26—20—19—31—30—29—32—33—35—34—40—39—38—36—37—18—17—16—15—74—14—13—12—11—10—9—8—7—6—5—4—3—2—75—76—77
total time           886.78               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             325939.65<=325939.65 subtour              496.0                
connectivity cuts    88.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:76                 
2-opt strategy       0                                                              
explored_nodes       433                  n lazycuts edges     4.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—23—22—21—25—24—46—45—44—48—47—69—68—70—67—50—49—51—66—65—71—72—73—64—63—62—61—41—60—59—58—57—56—55—52—53—54—42—43—28—27—26—20—19—31—30—29—32—33—35—34—40—39—38—36—37—18—17—16—15—74—14—13—12—11—10—9—8—7—6—5—4—3—2—75—76—77

RING
1  --- 23 | cost [5793.0]
1  --- 77 | cost [0.0]
2  ---  3 | cost [8778.0]
2  --- 75 | cost [10920.0]
3  ---  4 | cost [2100.0]
4  ---  5 | cost [4107.0]
5  ---  6 | cost [3345.0]
6  ---  7 | cost [2718.0]
7  ---  8 | cost [1749.0]
8  ---  9 | cost [6000.0]
9  --- 10 | cost [2100.0]
10 --- 11 | cost [4851.0]
11 --- 12 | cost [3354.0]
12 --- 13 | cost [3492.0]
13 --- 14 | cost [1566.0]
14 --- 74 | cost [9474.0]
15 --- 16 | cost [2100.0]
15 --- 74 | cost [13599.0]
16 --- 17 | cost [4536.0]
17 --- 18 | cost [2001.0]
18 --- 37 | cost [1650.0]
19 --- 20 | cost [2148.0]
19 --- 31 | cost [1650.0]
20 --- 26 | cost [9138.0]
21 --- 22 | cost [3579.0]
21 --- 25 | cost [1650.0]
22 --- 23 | cost [4299.0]
24 --- 25 | cost [3354.0]
24 --- 46 | cost [5793.0]
26 --- 27 | cost [2100.0]
27 --- 28 | cost [4107.0]
28 --- 43 | cost [3159.0]
29 --- 30 | cost [2718.0]
29 --- 32 | cost [4092.0]
30 --- 31 | cost [1749.0]
32 --- 33 | cost [2100.0]
33 --- 35 | cost [5523.0]
34 --- 35 | cost [3354.0]
34 --- 40 | cost [3840.0]
36 --- 37 | cost [1566.0]
36 --- 38 | cost [4170.0]
38 --- 39 | cost [2100.0]
39 --- 40 | cost [4536.0]
41 --- 60 | cost [1650.0]
41 --- 61 | cost [6783.0]
42 --- 43 | cost [2148.0]
42 --- 54 | cost [1650.0]
44 --- 45 | cost [3579.0]
44 --- 48 | cost [1650.0]
45 --- 46 | cost [4299.0]
47 --- 48 | cost [3354.0]
47 --- 69 | cost [5793.0]
49 --- 50 | cost [2100.0]
49 --- 51 | cost [4887.0]
50 --- 67 | cost [9300.0]
51 --- 66 | cost [3159.0]
52 --- 53 | cost [2718.0]
52 --- 55 | cost [4092.0]
53 --- 54 | cost [1749.0]
55 --- 56 | cost [2100.0]
56 --- 57 | cost [4851.0]
57 --- 58 | cost [3354.0]
58 --- 59 | cost [3492.0]
59 --- 60 | cost [1566.0]
61 --- 62 | cost [2100.0]
62 --- 63 | cost [4536.0]
63 --- 64 | cost [2001.0]
64 --- 73 | cost [9750.0]
65 --- 66 | cost [2148.0]
65 --- 71 | cost [12210.0]
67 --- 70 | cost [11715.0]
68 --- 69 | cost [4299.0]
68 --- 70 | cost [11838.0]
71 --- 72 | cost [5700.0]
72 --- 73 | cost [900.0]
75 --- 76 | cost [900.0]
76 --- 77 | cost [11148.0]

STAR

BACKUP RING
1  --- 22 | cost [91.5]
2  ---  4 | cost [100.8]
2  --- 76 | cost [114.87]
3  ---  5 | cost [48.870000000000005]
3  --- 75 | cost [194.13]
4  ---  6 | cost [48.84]
5  ---  7 | cost [60.42]
6  ---  8 | cost [42.03]
7  ---  9 | cost [55.800000000000004]
8  --- 10 | cost [77.82000000000001]
9  --- 11 | cost [55.29]
10 --- 12 | cost [55.230000000000004]
11 --- 13 | cost [64.32000000000001]
12 --- 14 | cost [49.71]
13 --- 74 | cost [110.31]
14 --- 15 | cost [52.38]
15 --- 17 | cost [63.81]
16 --- 18 | cost [60.75]
16 --- 74 | cost [156.87]
17 --- 37 | cost [36.27]
18 --- 36 | cost [31.830000000000002]
19 --- 26 | cost [78.66]
19 --- 30 | cost [32.76]
20 --- 27 | cost [111.0]
20 --- 31 | cost [37.11]
21 --- 23 | cost [76.5]
21 --- 24 | cost [43.5]
22 --- 25 | cost [46.86]
24 --- 45 | cost [91.5]
25 --- 46 | cost [85.8]
26 --- 28 | cost [48.870000000000005]
27 --- 43 | cost [51.99]
28 --- 42 | cost [50.94]
29 --- 31 | cost [42.03]
29 --- 33 | cost [48.75]
30 --- 32 | cost [55.800000000000004]
32 --- 35 | cost [48.45]
33 --- 34 | cost [48.51]
34 --- 39 | cost [48.33]
35 --- 40 | cost [68.52]
36 --- 39 | cost [59.730000000000004]
37 --- 38 | cost [52.38]
38 --- 40 | cost [63.81]
41 --- 59 | cost [31.830000000000002]
41 --- 62 | cost [88.05]
42 --- 53 | cost [32.76]
43 --- 54 | cost [37.11]
44 --- 46 | cost [76.5]
44 --- 47 | cost [43.5]
45 --- 48 | cost [46.86]
47 --- 68 | cost [91.5]
48 --- 69 | cost [85.8]
49 --- 66 | cost [68.7]
49 --- 67 | cost [107.16]
50 --- 51 | cost [41.07]
50 --- 70 | cost [208.95000000000002]
51 --- 65 | cost [50.94]
52 --- 54 | cost [42.03]
52 --- 56 | cost [48.75]
53 --- 55 | cost [55.800000000000004]
55 --- 57 | cost [55.29]
56 --- 58 | cost [55.230000000000004]
57 --- 59 | cost [64.32000000000001]
58 --- 60 | cost [49.71]
60 --- 61 | cost [52.38]
61 --- 63 | cost [63.81]
62 --- 64 | cost [60.75]
63 --- 73 | cost [117.27]
64 --- 72 | cost [94.41]
65 --- 72 | cost [166.02]
66 --- 71 | cost [142.71]
67 --- 68 | cost [35.79]
69 --- 70 | cost [148.95000000000002]
71 --- 73 | cost [66.0]
75 --- 77 | cost [108.18]

BACKUP STAR

B = 208.95000000000002
i★ = 50
j★ = 67
k★ = 70

       
——————— Thu, 25 Jan 2024 22:28:42 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 77 hubs —— 1-76-75-2-3-4-5-6-7-8-9-10-11-12-13-14-74-15-16-17-18-37-36-38-39-40-34-35-33-32-29-30-31-19-20-26-27-28-43-42-54-53-52-55-56-57-58-59-60-41-61-62-63-64-73-72-71-65-66-51-49-50-67-70-68-69-47-48-44-45-46-24-25-21-22-23-77-1
total time           109.21               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             325939.65<=325939.65 Master/SP costs      324477/1462.65       
Master time          108.12               SP time              1.1                  
subtour              4252.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            10.0                 SP method            poly                 
tildeV               2:76                 inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       6941                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—76—75—2—3—4—5—6—7—8—9—10—11—12—13—14—74—15—16—17—18—37—36—38—39—40—34—35—33—32—29—30—31—19—20—26—27—28—43—42—54—53—52—55—56—57—58—59—60—41—61—62—63—64—73—72—71—65—66—51—49—50—67—70—68—69—47—48—44—45—46—24—25—21—22—23—77

RING
1  --- 76 | cost [11148.0]
2  ---  3 | cost [8778.0]
2  --- 75 | cost [10920.0]
3  ---  4 | cost [2100.0]
4  ---  5 | cost [4107.0]
5  ---  6 | cost [3345.0]
6  ---  7 | cost [2718.0]
7  ---  8 | cost [1749.0]
8  ---  9 | cost [6000.0]
9  --- 10 | cost [2100.0]
10 --- 11 | cost [4851.0]
11 --- 12 | cost [3354.0]
12 --- 13 | cost [3492.0]
13 --- 14 | cost [1566.0]
14 --- 74 | cost [9474.0]
15 --- 16 | cost [2100.0]
15 --- 74 | cost [13599.0]
16 --- 17 | cost [4536.0]
17 --- 18 | cost [2001.0]
18 --- 37 | cost [1650.0]
19 --- 20 | cost [2148.0]
19 --- 31 | cost [1650.0]
20 --- 26 | cost [9138.0]
21 --- 22 | cost [3579.0]
21 --- 25 | cost [1650.0]
22 --- 23 | cost [4299.0]
23 --- 77 | cost [5793.0]
24 --- 25 | cost [3354.0]
24 --- 46 | cost [5793.0]
26 --- 27 | cost [2100.0]
27 --- 28 | cost [4107.0]
28 --- 43 | cost [3159.0]
29 --- 30 | cost [2718.0]
29 --- 32 | cost [4092.0]
30 --- 31 | cost [1749.0]
32 --- 33 | cost [2100.0]
33 --- 35 | cost [5523.0]
34 --- 35 | cost [3354.0]
34 --- 40 | cost [3840.0]
36 --- 37 | cost [1566.0]
36 --- 38 | cost [4170.0]
38 --- 39 | cost [2100.0]
39 --- 40 | cost [4536.0]
41 --- 60 | cost [1650.0]
41 --- 61 | cost [6783.0]
42 --- 43 | cost [2148.0]
42 --- 54 | cost [1650.0]
44 --- 45 | cost [3579.0]
44 --- 48 | cost [1650.0]
45 --- 46 | cost [4299.0]
47 --- 48 | cost [3354.0]
47 --- 69 | cost [5793.0]
49 --- 50 | cost [2100.0]
49 --- 51 | cost [4887.0]
50 --- 67 | cost [9300.0]
51 --- 66 | cost [3159.0]
52 --- 53 | cost [2718.0]
52 --- 55 | cost [4092.0]
53 --- 54 | cost [1749.0]
55 --- 56 | cost [2100.0]
56 --- 57 | cost [4851.0]
57 --- 58 | cost [3354.0]
58 --- 59 | cost [3492.0]
59 --- 60 | cost [1566.0]
61 --- 62 | cost [2100.0]
62 --- 63 | cost [4536.0]
63 --- 64 | cost [2001.0]
64 --- 73 | cost [9750.0]
65 --- 66 | cost [2148.0]
65 --- 71 | cost [12210.0]
67 --- 70 | cost [11715.0]
68 --- 69 | cost [4299.0]
68 --- 70 | cost [11838.0]
71 --- 72 | cost [5700.0]
72 --- 73 | cost [900.0]
75 --- 76 | cost [900.0]

STAR

BACKUP RING
1  --- 75 | cost [108.18]
2  ---  4 | cost [100.8]
2  --- 76 | cost [114.87]
3  ---  5 | cost [48.870000000000005]
3  --- 75 | cost [194.13]
4  ---  6 | cost [48.84]
5  ---  7 | cost [60.42]
6  ---  8 | cost [42.03]
7  ---  9 | cost [55.800000000000004]
8  --- 10 | cost [77.82000000000001]
9  --- 11 | cost [55.29]
10 --- 12 | cost [55.230000000000004]
11 --- 13 | cost [64.32000000000001]
12 --- 14 | cost [49.71]
13 --- 74 | cost [110.31]
14 --- 15 | cost [52.38]
15 --- 17 | cost [63.81]
16 --- 18 | cost [60.75]
16 --- 74 | cost [156.87]
17 --- 37 | cost [36.27]
18 --- 36 | cost [31.830000000000002]
19 --- 26 | cost [78.66]
19 --- 30 | cost [32.76]
20 --- 27 | cost [111.0]
20 --- 31 | cost [37.11]
21 --- 23 | cost [76.5]
21 --- 24 | cost [43.5]
22 --- 25 | cost [46.86]
22 --- 77 | cost [91.5]
24 --- 45 | cost [91.5]
25 --- 46 | cost [85.8]
26 --- 28 | cost [48.870000000000005]
27 --- 43 | cost [51.99]
28 --- 42 | cost [50.94]
29 --- 31 | cost [42.03]
29 --- 33 | cost [48.75]
30 --- 32 | cost [55.800000000000004]
32 --- 35 | cost [48.45]
33 --- 34 | cost [48.51]
34 --- 39 | cost [48.33]
35 --- 40 | cost [68.52]
36 --- 39 | cost [59.730000000000004]
37 --- 38 | cost [52.38]
38 --- 40 | cost [63.81]
41 --- 59 | cost [31.830000000000002]
41 --- 62 | cost [88.05]
42 --- 53 | cost [32.76]
43 --- 54 | cost [37.11]
44 --- 46 | cost [76.5]
44 --- 47 | cost [43.5]
45 --- 48 | cost [46.86]
47 --- 68 | cost [91.5]
48 --- 69 | cost [85.8]
49 --- 66 | cost [68.7]
49 --- 67 | cost [107.16]
50 --- 51 | cost [41.07]
50 --- 70 | cost [208.95000000000002]
51 --- 65 | cost [50.94]
52 --- 54 | cost [42.03]
52 --- 56 | cost [48.75]
53 --- 55 | cost [55.800000000000004]
55 --- 57 | cost [55.29]
56 --- 58 | cost [55.230000000000004]
57 --- 59 | cost [64.32000000000001]
58 --- 60 | cost [49.71]
60 --- 61 | cost [52.38]
61 --- 63 | cost [63.81]
62 --- 64 | cost [60.75]
63 --- 73 | cost [117.27]
64 --- 72 | cost [94.41]
65 --- 72 | cost [166.02]
66 --- 71 | cost [142.71]
67 --- 68 | cost [35.79]
69 --- 70 | cost [148.95000000000002]
71 --- 73 | cost [66.0]

BACKUP STAR

B = 208.95000000000002
i★ = 50
j★ = 67
k★ = 70