------------------------------------------------------------
                           α=5.0 —— rat99 —— 99 nodes       
------------------------------------------------------------

——————— Mon, 08 Jan 2024 08:26:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 90 hubs —— 1—10—11—12—13—22—21—20—19—28—37—29—30—31—32—33—34—43—42—41—40—39—48—47—46—55—56—57—58—59—67—66—65—74—73—82—83—91—92—93—94—96—97—98—99—90—89—88—87—86—85—76—77—78—69—70—71—80—81—72—63—62—61—60—51—52—53—54—45—44—36—35—26—25—24—23—15—16—17—18—9—8—7—6—5—14—4—3—2—100
total time           93.3                 gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             5885<=5885           subtour              2992.0               
connectivity cuts    1143.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1143                 n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—10—11—12—13—22—21—20—19—28—37—29—30—31—32—33—34—43—42—41—40—39—48—47—46—55—56—57—58—59—67—66—65—74—73—82—83—91—92—93—94—96—97—98—99—90—89—88—87—86—85—76—77—78—69—70—71—80—81—72—63—62—61—60—51—52—53—54—45—44—36—35—26—25—24—23—15—16—17—18—9—8—7—6—5—14—4—3—2—100

RING
1  --- 10 | cost [85.0]
1  --- 100 | cost [0.0]
2  ---  3 | cost [45.0]
2  --- 100 | cost [70.0]
3  ---  4 | cost [55.0]
4  --- 14 | cost [75.0]
5  ---  6 | cost [45.0]
5  --- 14 | cost [60.0]
6  ---  7 | cost [55.0]
7  ---  8 | cost [50.0]
8  ---  9 | cost [50.0]
9  --- 18 | cost [100.0]
10 --- 11 | cost [60.0]
11 --- 12 | cost [30.0]
12 --- 13 | cost [65.0]
13 --- 22 | cost [70.0]
15 --- 16 | cost [50.0]
15 --- 23 | cost [70.0]
16 --- 17 | cost [65.0]
17 --- 18 | cost [50.0]
19 --- 20 | cost [65.0]
19 --- 28 | cost [95.0]
20 --- 21 | cost [90.0]
21 --- 22 | cost [30.0]
23 --- 24 | cost [50.0]
24 --- 25 | cost [45.0]
25 --- 26 | cost [50.0]
26 --- 35 | cost [60.0]
28 --- 37 | cost [45.0]
29 --- 30 | cost [55.0]
29 --- 37 | cost [45.0]
30 --- 31 | cost [60.0]
31 --- 32 | cost [55.0]
32 --- 33 | cost [60.0]
33 --- 34 | cost [60.0]
34 --- 43 | cost [30.0]
35 --- 36 | cost [55.0]
36 --- 44 | cost [65.0]
39 --- 40 | cost [30.0]
39 --- 48 | cost [20.0]
40 --- 41 | cost [70.0]
41 --- 42 | cost [70.0]
42 --- 43 | cost [40.0]
44 --- 45 | cost [80.0]
45 --- 54 | cost [65.0]
46 --- 47 | cost [40.0]
46 --- 55 | cost [75.0]
47 --- 48 | cost [75.0]
51 --- 52 | cost [45.0]
51 --- 60 | cost [70.0]
52 --- 53 | cost [40.0]
53 --- 54 | cost [70.0]
55 --- 56 | cost [90.0]
56 --- 57 | cost [40.0]
57 --- 58 | cost [65.0]
58 --- 59 | cost [40.0]
59 --- 67 | cost [90.0]
60 --- 61 | cost [80.0]
61 --- 62 | cost [45.0]
62 --- 63 | cost [80.0]
63 --- 72 | cost [100.0]
65 --- 66 | cost [55.0]
65 --- 74 | cost [75.0]
66 --- 67 | cost [65.0]
69 --- 70 | cost [45.0]
69 --- 78 | cost [60.0]
70 --- 71 | cost [35.0]
71 --- 80 | cost [50.0]
72 --- 81 | cost [65.0]
73 --- 74 | cost [85.0]
73 --- 82 | cost [90.0]
76 --- 77 | cost [60.0]
76 --- 85 | cost [50.0]
77 --- 78 | cost [50.0]
80 --- 81 | cost [65.0]
82 --- 83 | cost [60.0]
83 --- 91 | cost [80.0]
85 --- 86 | cost [55.0]
86 --- 87 | cost [55.0]
87 --- 88 | cost [40.0]
88 --- 89 | cost [75.0]
89 --- 90 | cost [40.0]
90 --- 99 | cost [50.0]
91 --- 92 | cost [35.0]
92 --- 93 | cost [60.0]
93 --- 94 | cost [65.0]
94 --- 96 | cost [120.0]
96 --- 97 | cost [55.0]
97 --- 98 | cost [65.0]
98 --- 99 | cost [45.0]

STAR
27 --> 35 | cost [65.0]
38 --> 39 | cost [45.0]
49 --> 58 | cost [60.0]
50 --> 51 | cost [60.0]
64 --> 65 | cost [70.0]
68 --> 67 | cost [25.0]
75 --> 76 | cost [65.0]
79 --> 88 | cost [70.0]
84 --> 85 | cost [50.0]
95 --> 86 | cost [40.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:29:48 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 88 hubs —— 1-10-11-12-13-22-21-20-19-28-37-29-30-31-32-33-34-43-42-41-40-39-48-47-46-55-56-57-58-59-67-66-65-74-73-82-83-91-92-93-94-96-97-98-99-90-89-88-87-86-85-76-77-78-69-70-71-72-63-62-61-60-51-52-53-54-45-44-36-35-26-25-24-23-15-16-17-18-9-8-7-6-5-14-4-3-2-100-1
total time           172.69               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             5885<=5885           Master/SP costs      5885/0               
Master time          172.69               SP time              0.0                  
subtour              5064.0               connectivity cuts    1111.0               
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       1114                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—10—11—12—13—22—21—20—19—28—37—29—30—31—32—33—34—43—42—41—40—39—48—47—46—55—56—57—58—59—67—66—65—74—73—82—83—91—92—93—94—96—97—98—99—90—89—88—87—86—85—76—77—78—69—70—71—72—63—62—61—60—51—52—53—54—45—44—36—35—26—25—24—23—15—16—17—18—9—8—7—6—5—14—4—3—2—100

RING
1  --- 10 | cost [85.0]
2  ---  3 | cost [45.0]
2  --- 100 | cost [70.0]
3  ---  4 | cost [55.0]
4  --- 14 | cost [75.0]
5  ---  6 | cost [45.0]
5  --- 14 | cost [60.0]
6  ---  7 | cost [55.0]
7  ---  8 | cost [50.0]
8  ---  9 | cost [50.0]
9  --- 18 | cost [100.0]
10 --- 11 | cost [60.0]
11 --- 12 | cost [30.0]
12 --- 13 | cost [65.0]
13 --- 22 | cost [70.0]
15 --- 16 | cost [50.0]
15 --- 23 | cost [70.0]
16 --- 17 | cost [65.0]
17 --- 18 | cost [50.0]
19 --- 20 | cost [65.0]
19 --- 28 | cost [95.0]
20 --- 21 | cost [90.0]
21 --- 22 | cost [30.0]
23 --- 24 | cost [50.0]
24 --- 25 | cost [45.0]
25 --- 26 | cost [50.0]
26 --- 35 | cost [60.0]
28 --- 37 | cost [45.0]
29 --- 30 | cost [55.0]
29 --- 37 | cost [45.0]
30 --- 31 | cost [60.0]
31 --- 32 | cost [55.0]
32 --- 33 | cost [60.0]
33 --- 34 | cost [60.0]
34 --- 43 | cost [30.0]
35 --- 36 | cost [55.0]
36 --- 44 | cost [65.0]
39 --- 40 | cost [30.0]
39 --- 48 | cost [20.0]
40 --- 41 | cost [70.0]
41 --- 42 | cost [70.0]
42 --- 43 | cost [40.0]
44 --- 45 | cost [80.0]
45 --- 54 | cost [65.0]
46 --- 47 | cost [40.0]
46 --- 55 | cost [75.0]
47 --- 48 | cost [75.0]
51 --- 52 | cost [45.0]
51 --- 60 | cost [70.0]
52 --- 53 | cost [40.0]
53 --- 54 | cost [70.0]
55 --- 56 | cost [90.0]
56 --- 57 | cost [40.0]
57 --- 58 | cost [65.0]
58 --- 59 | cost [40.0]
59 --- 67 | cost [90.0]
60 --- 61 | cost [80.0]
61 --- 62 | cost [45.0]
62 --- 63 | cost [80.0]
63 --- 72 | cost [100.0]
65 --- 66 | cost [55.0]
65 --- 74 | cost [75.0]
66 --- 67 | cost [65.0]
69 --- 70 | cost [45.0]
69 --- 78 | cost [60.0]
70 --- 71 | cost [35.0]
71 --- 72 | cost [65.0]
73 --- 74 | cost [85.0]
73 --- 82 | cost [90.0]
76 --- 77 | cost [60.0]
76 --- 85 | cost [50.0]
77 --- 78 | cost [50.0]
82 --- 83 | cost [60.0]
83 --- 91 | cost [80.0]
85 --- 86 | cost [55.0]
86 --- 87 | cost [55.0]
87 --- 88 | cost [40.0]
88 --- 89 | cost [75.0]
89 --- 90 | cost [40.0]
90 --- 99 | cost [50.0]
91 --- 92 | cost [35.0]
92 --- 93 | cost [60.0]
93 --- 94 | cost [65.0]
94 --- 96 | cost [120.0]
96 --- 97 | cost [55.0]
97 --- 98 | cost [65.0]
98 --- 99 | cost [45.0]

STAR
27 --> 35 | cost [65.0]
38 --> 39 | cost [45.0]
49 --> 58 | cost [60.0]
50 --> 51 | cost [60.0]
64 --> 65 | cost [70.0]
68 --> 67 | cost [25.0]
75 --> 76 | cost [65.0]
79 --> 88 | cost [70.0]
80 --> 71 | cost [50.0]
81 --> 72 | cost [65.0]
84 --> 85 | cost [50.0]
95 --> 86 | cost [40.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 19:34:58 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 39 hubs —— 1—2—3—4—5—6—7—8—9—18—17—16—15—23—24—25—26—35—36—44—34—43—42—33—32—31—30—29—37—28—19—20—21—22—13—12—11—10—100
total time           3606.33 (TL 3600)    gap                  0.002                
blossom time         0                    nb blossom           0.0                  
LB <= UB             5865<=5875           subtour              149272.0             
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       21423                n lazycuts edges     4.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—3—4—5—6—7—8—9—18—17—16—15—23—24—25—26—35—36—44—34—43—42—33—32—31—30—29—37—28—19—20—21—22—13—12—11—10—100

RING
1  ---  2 | cost [70.0]
2  ---  3 | cost [45.0]
3  ---  4 | cost [55.0]
4  ---  5 | cost [75.0]
5  ---  6 | cost [45.0]
6  ---  7 | cost [55.0]
7  ---  8 | cost [50.0]
8  ---  9 | cost [50.0]
9  --- 18 | cost [100.0]
10 --- 11 | cost [60.0]
10 --- 100 | cost [85.0]
11 --- 12 | cost [30.0]
12 --- 13 | cost [65.0]
13 --- 22 | cost [70.0]
15 --- 16 | cost [50.0]
15 --- 23 | cost [70.0]
16 --- 17 | cost [65.0]
17 --- 18 | cost [50.0]
19 --- 20 | cost [65.0]
19 --- 28 | cost [95.0]
20 --- 21 | cost [90.0]
21 --- 22 | cost [30.0]
23 --- 24 | cost [50.0]
24 --- 25 | cost [45.0]
25 --- 26 | cost [50.0]
26 --- 35 | cost [60.0]
28 --- 37 | cost [45.0]
29 --- 30 | cost [55.0]
29 --- 37 | cost [45.0]
30 --- 31 | cost [60.0]
31 --- 32 | cost [55.0]
32 --- 33 | cost [60.0]
33 --- 42 | cost [60.0]
34 --- 43 | cost [30.0]
34 --- 44 | cost [65.0]
35 --- 36 | cost [55.0]
36 --- 44 | cost [65.0]
38 --- 39 | cost [45.0]
38 --- 47 | cost [80.0]
39 --- 48 | cost [20.0]
42 --- 43 | cost [40.0]
47 --- 48 | cost [75.0]
49 --- 50 | cost [70.0]
49 --- 58 | cost [60.0]
50 --- 51 | cost [60.0]
51 --- 52 | cost [45.0]
52 --- 53 | cost [40.0]
53 --- 54 | cost [70.0]
54 --- 63 | cost [95.0]
56 --- 57 | cost [40.0]
56 --- 64 | cost [95.0]
57 --- 58 | cost [65.0]
61 --- 62 | cost [45.0]
61 --- 70 | cost [80.0]
62 --- 63 | cost [80.0]
64 --- 65 | cost [70.0]
65 --- 66 | cost [55.0]
66 --- 67 | cost [65.0]
67 --- 68 | cost [25.0]
68 --- 77 | cost [75.0]
70 --- 71 | cost [35.0]
71 --- 80 | cost [50.0]
73 --- 74 | cost [85.0]
73 --- 82 | cost [90.0]
74 --- 75 | cost [70.0]
75 --- 76 | cost [65.0]
76 --- 85 | cost [50.0]
77 --- 78 | cost [50.0]
78 --- 79 | cost [70.0]
79 --- 80 | cost [75.0]
82 --- 91 | cost [85.0]
83 --- 84 | cost [80.0]
83 --- 93 | cost [80.0]
84 --- 85 | cost [50.0]
86 --- 87 | cost [55.0]
86 --- 95 | cost [40.0]
87 --- 88 | cost [40.0]
88 --- 89 | cost [75.0]
89 --- 90 | cost [40.0]
90 --- 99 | cost [50.0]
91 --- 92 | cost [35.0]
92 --- 93 | cost [60.0]
95 --- 96 | cost [75.0]
96 --- 97 | cost [55.0]
97 --- 98 | cost [65.0]
98 --- 99 | cost [45.0]

STAR
14 -->  5 | cost [60.0]
27 --> 35 | cost [65.0]
40 --> 39 | cost [30.0]
41 --> 32 | cost [45.0]
45 --> 54 | cost [65.0]
46 --> 47 | cost [40.0]
55 --> 47 | cost [85.0]
59 --> 58 | cost [40.0]
60 --> 51 | cost [70.0]
69 --> 70 | cost [45.0]
72 --> 71 | cost [65.0]
81 --> 80 | cost [65.0]
94 --> 93 | cost [65.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 09 Jan 2024 20:35:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 76 hubs —— 1-10-30-29-46-47-55-48-39-43-52-51-53-45-36-44-54-60-61-62-71-70-79-88-87-99-90-98-97-89-92-94-86-84-76-85-95-69-66-67-59-58-57-65-74-93-83-73-82-31-32-34-42-41-35-26-25-24-23-22-21-20-13-3-15-17-18-9-8-7-6-5-14-12-11-100-1
total time           3610.38 (TL 3600)    gap                  0.369                
blossom time         0                    nb blossom           0.0                  
LB <= UB             5800<=9190           Master/SP costs      9190/0               
Master time          3610.38              SP time              0.0                  
subtour              53117.0              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       8839                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—10—30—29—46—47—55—48—39—43—52—51—53—45—36—44—54—60—61—62—71—70—79—88—87—99—90—98—97—89—92—94—86—84—76—85—95—69—66—67—59—58—57—65—74—93—83—73—82—31—32—34—42—41—35—26—25—24—23—22—21—20—13—3—15—17—18—9—8—7—6—5—14—12—11—100

RING
1  --- 10 | cost [85.0]
3  --- 13 | cost [95.0]
3  --- 15 | cost [175.0]
5  ---  6 | cost [45.0]
5  --- 14 | cost [60.0]
6  ---  7 | cost [55.0]
7  ---  8 | cost [50.0]
8  ---  9 | cost [50.0]
9  --- 18 | cost [100.0]
10 --- 30 | cost [260.0]
11 --- 12 | cost [30.0]
11 --- 100 | cost [125.0]
12 --- 14 | cost [100.0]
13 --- 20 | cost [110.0]
15 --- 17 | cost [115.0]
17 --- 18 | cost [50.0]
20 --- 21 | cost [90.0]
21 --- 22 | cost [30.0]
22 --- 23 | cost [70.0]
23 --- 24 | cost [50.0]
24 --- 25 | cost [45.0]
25 --- 26 | cost [50.0]
26 --- 35 | cost [60.0]
29 --- 30 | cost [55.0]
29 --- 46 | cost [165.0]
31 --- 32 | cost [55.0]
31 --- 82 | cost [640.0]
32 --- 34 | cost [120.0]
34 --- 42 | cost [65.0]
35 --- 41 | cost [205.0]
36 --- 44 | cost [65.0]
36 --- 45 | cost [125.0]
39 --- 43 | cost [200.0]
39 --- 48 | cost [20.0]
41 --- 42 | cost [70.0]
43 --- 52 | cost [125.0]
44 --- 54 | cost [145.0]
45 --- 53 | cost [85.0]
46 --- 47 | cost [40.0]
47 --- 55 | cost [85.0]
48 --- 55 | cost [160.0]
51 --- 52 | cost [45.0]
51 --- 53 | cost [80.0]
54 --- 60 | cost [185.0]
57 --- 58 | cost [65.0]
57 --- 65 | cost [95.0]
58 --- 59 | cost [40.0]
59 --- 67 | cost [90.0]
60 --- 61 | cost [80.0]
61 --- 62 | cost [45.0]
62 --- 71 | cost [85.0]
65 --- 74 | cost [75.0]
66 --- 67 | cost [65.0]
66 --- 69 | cost [160.0]
69 --- 95 | cost [250.0]
70 --- 71 | cost [35.0]
70 --- 79 | cost [115.0]
73 --- 82 | cost [90.0]
73 --- 83 | cost [105.0]
74 --- 93 | cost [245.0]
76 --- 84 | cost [70.0]
76 --- 85 | cost [50.0]
79 --- 88 | cost [70.0]
83 --- 93 | cost [80.0]
84 --- 86 | cost [95.0]
85 --- 95 | cost [90.0]
86 --- 94 | cost [120.0]
87 --- 88 | cost [40.0]
87 --- 99 | cost [150.0]
89 --- 92 | cost [345.0]
89 --- 97 | cost [85.0]
90 --- 98 | cost [85.0]
90 --- 99 | cost [50.0]
92 --- 94 | cost [110.0]
97 --- 98 | cost [65.0]

STAR
2  -->  3 | cost [45.0]
4  -->  3 | cost [55.0]
16 --> 15 | cost [50.0]
19 --> 20 | cost [65.0]
27 --> 35 | cost [65.0]
28 --> 29 | cost [65.0]
33 --> 42 | cost [60.0]
37 --> 29 | cost [45.0]
38 --> 39 | cost [45.0]
40 --> 39 | cost [30.0]
49 --> 58 | cost [60.0]
50 --> 51 | cost [60.0]
56 --> 57 | cost [40.0]
63 --> 62 | cost [80.0]
64 --> 65 | cost [70.0]
68 --> 67 | cost [25.0]
72 --> 71 | cost [65.0]
75 --> 76 | cost [65.0]
77 --> 76 | cost [60.0]
78 --> 69 | cost [60.0]
80 --> 71 | cost [50.0]
81 --> 90 | cost [160.0]
91 --> 92 | cost [35.0]
96 --> 97 | cost [55.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1