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

——————— Mon, 08 Jan 2024 08:04:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 57 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—35—34—33—32—29—26—27—28—43—42—54—53—52—49—50—66—65—67—70—68—69—47—48—44—45—46—24—25—21—22—23—77
total time           32.77                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             322635<=322635       subtour              1670.0               
connectivity cuts    994.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1089                 n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
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—35—34—33—32—29—26—27—28—43—42—54—53—52—49—50—66—65—67—70—68—69—47—48—44—45—46—24—25—21—22—23—77

RING
1  --- 76 | cost [11148.0]
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 --- 30 | cost [5100.0]
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]
26 --- 29 | cost [4104.0]
27 --- 28 | cost [4107.0]
28 --- 43 | cost [3159.0]
29 --- 32 | cost [4092.0]
30 --- 31 | cost [1749.0]
32 --- 33 | cost [2100.0]
33 --- 34 | cost [4851.0]
34 --- 35 | cost [3354.0]
35 --- 39 | cost [5514.0]
36 --- 37 | cost [1566.0]
36 --- 38 | cost [4170.0]
38 --- 39 | cost [2100.0]
40 --- 41 | cost [2001.0]
40 --- 60 | cost [3627.0]
41 --- 60 | cost [1650.0]
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 --- 52 | cost [4104.0]
50 --- 66 | cost [5199.0]
51 --- 55 | cost [4872.0]
51 --- 56 | cost [4089.0]
52 --- 53 | cost [2718.0]
53 --- 54 | cost [1749.0]
55 --- 56 | cost [2100.0]
57 --- 58 | cost [3354.0]
57 --- 63 | cost [3840.0]
58 --- 59 | cost [3492.0]
59 --- 61 | cost [4170.0]
61 --- 62 | cost [2100.0]
62 --- 63 | cost [4536.0]
64 --- 71 | cost [9441.0]
64 --- 73 | cost [9750.0]
65 --- 66 | cost [2148.0]
65 --- 67 | cost [11850.0]
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

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:06:33 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 77 hubs —— 1-23-22-21-25-24-46-45-44-48-47-69-68-70-67-50-49-51-66-65-71-72-73-64-63-62-61-41-60-59-58-57-56-55-52-53-54-42-43-28-27-26-20-19-31-30-29-32-33-35-34-40-39-38-36-37-18-17-16-15-74-14-13-12-11-10-9-8-7-6-5-4-3-2-75-76-77-1
total time           73.92                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             324477<=324477       Master/SP costs      324477/0             
Master time          73.92                SP time              0.0                  
subtour              2570.0               connectivity cuts    1439.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       2166                 
F                    0.0                  
                                          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

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 15:08:44 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 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
total time           42.5                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             324477<=324477       subtour              3188.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       2349                 n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
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

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 15:10:02 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 77 hubs —— 1-23-22-21-25-24-46-45-44-48-47-69-68-70-67-50-49-51-66-65-71-72-73-64-63-62-61-41-60-59-58-57-56-55-52-53-54-42-43-28-27-26-20-19-31-30-29-32-33-35-34-40-39-38-36-37-18-17-16-15-74-14-13-12-11-10-9-8-7-6-5-4-3-2-75-76-77-1
total time           49.92                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             324477<=324477       Master/SP costs      324477/0             
Master time          49.92                SP time              0.0                  
subtour              2044.0               connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       4284                 
F                    0.0                  
                                          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]
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

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1