------------------------------------------------------------
                          α=5.0 —— rd100 —— 100 nodes       
------------------------------------------------------------

——————— Fri, 26 Jan 2024 10:55:14 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 77 hubs —— 1—60—8—71—68—83—51—65—80—81—5—61—22—41—34—7—42—43—40—55—39—96—29—44—45—52—36—57—47—99—53—6—94—98—66—31—84—23—2—89—58—76—59—77—28—37—19—46—50—73—54—38—72—17—92—27—10—33—78—20—74—26—9—32—4—85—82—75—21—49—67—97—63—15—62—18—101
total time           2379.25              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             38102.75<=38102.75   subtour              393.0                
connectivity cuts    163.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       141                  n lazycuts edges     3.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—60—8—71—68—83—51—65—80—81—5—61—22—41—34—7—42—43—40—55—39—96—29—44—45—52—36—57—47—99—53—6—94—98—66—31—84—23—2—89—58—76—59—77—28—37—19—46—50—73—54—38—72—17—92—27—10—33—78—20—74—26—9—32—4—85—82—75—21—49—67—97—63—15—62—18—101

RING
1  --- 60 | cost [110.0]
1  --- 101 | cost [0.0]
2  --- 23 | cost [435.0]
2  --- 89 | cost [540.0]
4  --- 32 | cost [210.0]
4  --- 85 | cost [520.0]
5  --- 61 | cost [250.0]
5  --- 81 | cost [640.0]
6  --- 53 | cost [295.0]
6  --- 94 | cost [605.0]
7  --- 34 | cost [285.0]
7  --- 42 | cost [365.0]
8  --- 60 | cost [170.0]
8  --- 71 | cost [630.0]
9  --- 26 | cost [210.0]
9  --- 32 | cost [600.0]
10 --- 27 | cost [595.0]
10 --- 33 | cost [205.0]
15 --- 62 | cost [555.0]
15 --- 63 | cost [150.0]
17 --- 72 | cost [270.0]
17 --- 92 | cost [750.0]
18 --- 62 | cost [335.0]
18 --- 101 | cost [440.0]
19 --- 37 | cost [470.0]
19 --- 46 | cost [420.0]
20 --- 74 | cost [95.0]
20 --- 78 | cost [195.0]
21 --- 49 | cost [175.0]
21 --- 75 | cost [125.0]
22 --- 41 | cost [250.0]
22 --- 61 | cost [575.0]
23 --- 84 | cost [910.0]
26 --- 74 | cost [195.0]
27 --- 92 | cost [185.0]
28 --- 37 | cost [180.0]
28 --- 77 | cost [370.0]
29 --- 44 | cost [430.0]
29 --- 96 | cost [800.0]
31 --- 66 | cost [475.0]
31 --- 84 | cost [270.0]
33 --- 78 | cost [575.0]
34 --- 41 | cost [485.0]
36 --- 52 | cost [970.0]
36 --- 57 | cost [500.0]
38 --- 54 | cost [355.0]
38 --- 72 | cost [335.0]
39 --- 55 | cost [560.0]
39 --- 96 | cost [200.0]
40 --- 43 | cost [605.0]
40 --- 55 | cost [595.0]
42 --- 43 | cost [330.0]
44 --- 45 | cost [695.0]
45 --- 52 | cost [630.0]
46 --- 50 | cost [25.0]
47 --- 57 | cost [500.0]
47 --- 99 | cost [460.0]
49 --- 67 | cost [435.0]
50 --- 73 | cost [135.0]
51 --- 65 | cost [415.0]
51 --- 83 | cost [170.0]
53 --- 99 | cost [240.0]
54 --- 73 | cost [400.0]
58 --- 76 | cost [480.0]
58 --- 89 | cost [1215.0]
59 --- 76 | cost [650.0]
59 --- 77 | cost [240.0]
63 --- 97 | cost [40.0]
65 --- 80 | cost [300.0]
66 --- 98 | cost [360.0]
67 --- 97 | cost [160.0]
68 --- 71 | cost [705.0]
68 --- 83 | cost [405.0]
75 --- 82 | cost [180.0]
80 --- 81 | cost [335.0]
82 --- 85 | cost [205.0]
94 --- 98 | cost [380.0]

STAR
3  --> 33 | cost [575.0]
11 --> 61 | cost [405.0]
12 --> 85 | cost [205.0]
13 --> 67 | cost [295.0]
14 --> 85 | cost [205.0]
16 --> 45 | cost [510.0]
24 --> 43 | cost [225.0]
25 --> 43 | cost [210.0]
30 --> 80 | cost [420.0]
35 --> 29 | cost [290.0]
48 --> 80 | cost [385.0]
56 --> 46 | cost [125.0]
64 --> 36 | cost [680.0]
69 -->  8 | cost [305.0]
70 --> 72 | cost [285.0]
79 -->  6 | cost [230.0]
86 --> 97 | cost [65.0]
87 --> 62 | cost [420.0]
88 --> 84 | cost [95.0]
90 --> 51 | cost [210.0]
91 --> 65 | cost [600.0]
93 --> 77 | cost [220.0]
95 --> 59 | cost [95.0]
100 --> 44 | cost [365.0]

BACKUP RING
1  ---  8 | cost [2.75]
2  --- 58 | cost [15.4]
2  --- 84 | cost [11.85]
4  ---  9 | cost [8.1]
4  --- 82 | cost [4.0]
5  --- 22 | cost [4.65]
5  --- 80 | cost [9.35]
6  --- 98 | cost [9.450000000000001]
6  --- 99 | cost [4.55]
7  --- 41 | cost [5.3]
7  --- 43 | cost [6.75]
8  --- 68 | cost [8.5]
9  --- 74 | cost [4.05]
10 --- 78 | cost [7.8]
10 --- 92 | cost [7.3500000000000005]
15 --- 18 | cost [8.45]
15 --- 97 | cost [1.9000000000000001]
17 --- 27 | cost [9.35]
17 --- 38 | cost [3.7]
19 --- 28 | cost [6.45]
19 --- 50 | cost [4.45]
20 --- 26 | cost [2.6]
20 --- 33 | cost [6.05]
21 --- 67 | cost [5.1000000000000005]
21 --- 82 | cost [2.1]
22 --- 34 | cost [6.3]
23 --- 31 | cost [10.3]
23 --- 89 | cost [8.05]
26 --- 32 | cost [6.15]
27 --- 33 | cost [6.8500000000000005]
28 --- 59 | cost [5.95]
29 --- 39 | cost [8.5]
29 --- 45 | cost [11.200000000000001]
31 --- 98 | cost [7.15]
32 --- 85 | cost [5.65]
34 --- 42 | cost [6.4]
36 --- 45 | cost [14.450000000000001]
36 --- 47 | cost [8.2]
37 --- 46 | cost [6.4]
37 --- 77 | cost [5.3]
38 --- 73 | cost [5.55]
39 --- 40 | cost [9.35]
40 --- 42 | cost [4.4]
41 --- 61 | cost [6.6000000000000005]
43 --- 55 | cost [10.4]
44 --- 52 | cost [8.65]
44 --- 96 | cost [11.25]
46 --- 73 | cost [1.45]
47 --- 53 | cost [4.95]
49 --- 75 | cost [1.9000000000000001]
49 --- 97 | cost [4.7]
50 --- 54 | cost [5.05]
51 --- 68 | cost [5.45]
51 --- 80 | cost [6.8500000000000005]
52 --- 57 | cost [8.15]
53 --- 94 | cost [5.7]
54 --- 72 | cost [6.9]
55 --- 96 | cost [5.8]
57 --- 99 | cost [9.6]
58 --- 59 | cost [10.25]
60 --- 71 | cost [6.4]
61 --- 81 | cost [8.9]
62 --- 63 | cost [6.8]
62 --- 101 | cost [4.7]
63 --- 67 | cost [1.9000000000000001]
65 --- 81 | cost [4.9]
65 --- 83 | cost [5.15]
66 --- 84 | cost [5.8]
66 --- 94 | cost [7.3500000000000005]
71 --- 83 | cost [10.450000000000001]
72 --- 92 | cost [9.950000000000001]
74 --- 78 | cost [2.7]
75 --- 85 | cost [3.85]
76 --- 77 | cost [8.65]
76 --- 89 | cost [16.15]

BACKUP STAR
3  --> 10 | cost [6.5]
11 -->  5 | cost [5.9]
12 --> 82 | cost [3.95]
13 --> 49 | cost [4.4]
14 --> 82 | cost [3.85]
16 --> 98 | cost [5.9]
24 --> 42 | cost [3.4]
25 --> 42 | cost [5.45]
30 --> 81 | cost [6.0]
35 --> 44 | cost [4.8500000000000005]
48 --> 65 | cost [5.15]
56 --> 50 | cost [1.4000000000000001]
64 --> 47 | cost [10.1]
69 --> 60 | cost [4.15]
70 --> 38 | cost [4.3500000000000005]
79 --> 53 | cost [3.25]
86 --> 63 | cost [0.75]
87 --> 15 | cost [6.0]
88 --> 31 | cost [2.95]
90 --> 83 | cost [3.6]
91 --> 81 | cost [6.45]
93 --> 59 | cost [3.85]
95 --> 77 | cost [2.6]
100 --> 29 | cost [4.7]

B = 18.25
i★ = 52
j★ = 36
k★ = 57

       
——————— Fri, 26 Jan 2024 11:01:46 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 77 hubs —— 1-18-62-15-63-97-67-49-21-75-82-85-4-32-9-26-74-20-78-33-10-27-92-17-72-38-54-73-50-46-19-37-28-77-59-76-58-89-2-23-84-31-66-98-94-6-53-99-47-57-36-52-45-44-29-96-39-55-40-43-42-7-34-41-22-61-5-81-80-65-51-83-68-71-8-60-101-1
total time           329.91               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             38102.75<=38102.75   Master/SP costs      37975/127.75         
Master time          327.3                SP time              2.61                 
subtour              7236.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            12.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       3367                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—18—62—15—63—97—67—49—21—75—82—85—4—32—9—26—74—20—78—33—10—27—92—17—72—38—54—73—50—46—19—37—28—77—59—76—58—89—2—23—84—31—66—98—94—6—53—99—47—57—36—52—45—44—29—96—39—55—40—43—42—7—34—41—22—61—5—81—80—65—51—83—68—71—8—60—101

RING
1  --- 18 | cost [440.0]
1  --- 101 | cost [0.0]
2  --- 23 | cost [435.0]
2  --- 89 | cost [540.0]
4  --- 32 | cost [210.0]
4  --- 85 | cost [520.0]
5  --- 61 | cost [250.0]
5  --- 81 | cost [640.0]
6  --- 53 | cost [295.0]
6  --- 94 | cost [605.0]
7  --- 34 | cost [285.0]
7  --- 42 | cost [365.0]
8  --- 60 | cost [170.0]
8  --- 71 | cost [630.0]
9  --- 26 | cost [210.0]
9  --- 32 | cost [600.0]
10 --- 27 | cost [595.0]
10 --- 33 | cost [205.0]
15 --- 62 | cost [555.0]
15 --- 63 | cost [150.0]
17 --- 72 | cost [270.0]
17 --- 92 | cost [750.0]
18 --- 62 | cost [335.0]
19 --- 37 | cost [470.0]
19 --- 46 | cost [420.0]
20 --- 74 | cost [95.0]
20 --- 78 | cost [195.0]
21 --- 49 | cost [175.0]
21 --- 75 | cost [125.0]
22 --- 41 | cost [250.0]
22 --- 61 | cost [575.0]
23 --- 84 | cost [910.0]
26 --- 74 | cost [195.0]
27 --- 92 | cost [185.0]
28 --- 37 | cost [180.0]
28 --- 77 | cost [370.0]
29 --- 44 | cost [430.0]
29 --- 96 | cost [800.0]
31 --- 66 | cost [475.0]
31 --- 84 | cost [270.0]
33 --- 78 | cost [575.0]
34 --- 41 | cost [485.0]
36 --- 52 | cost [970.0]
36 --- 57 | cost [500.0]
38 --- 54 | cost [355.0]
38 --- 72 | cost [335.0]
39 --- 55 | cost [560.0]
39 --- 96 | cost [200.0]
40 --- 43 | cost [605.0]
40 --- 55 | cost [595.0]
42 --- 43 | cost [330.0]
44 --- 45 | cost [695.0]
45 --- 52 | cost [630.0]
46 --- 50 | cost [25.0]
47 --- 57 | cost [500.0]
47 --- 99 | cost [460.0]
49 --- 67 | cost [435.0]
50 --- 73 | cost [135.0]
51 --- 65 | cost [415.0]
51 --- 83 | cost [170.0]
53 --- 99 | cost [240.0]
54 --- 73 | cost [400.0]
58 --- 76 | cost [480.0]
58 --- 89 | cost [1215.0]
59 --- 76 | cost [650.0]
59 --- 77 | cost [240.0]
60 --- 101 | cost [110.0]
63 --- 97 | cost [40.0]
65 --- 80 | cost [300.0]
66 --- 98 | cost [360.0]
67 --- 97 | cost [160.0]
68 --- 71 | cost [705.0]
68 --- 83 | cost [405.0]
75 --- 82 | cost [180.0]
80 --- 81 | cost [335.0]
82 --- 85 | cost [205.0]
94 --- 98 | cost [380.0]

STAR
3  --> 33 | cost [575.0]
11 --> 61 | cost [405.0]
12 --> 85 | cost [205.0]
13 --> 67 | cost [295.0]
14 --> 85 | cost [205.0]
16 --> 45 | cost [510.0]
24 --> 43 | cost [225.0]
25 --> 43 | cost [210.0]
30 --> 80 | cost [420.0]
35 --> 29 | cost [290.0]
48 --> 80 | cost [385.0]
56 --> 46 | cost [125.0]
64 --> 36 | cost [680.0]
69 -->  8 | cost [305.0]
70 --> 72 | cost [285.0]
79 -->  6 | cost [230.0]
86 --> 97 | cost [65.0]
87 --> 62 | cost [420.0]
88 --> 84 | cost [95.0]
90 --> 51 | cost [210.0]
91 --> 65 | cost [600.0]
93 --> 77 | cost [220.0]
95 --> 59 | cost [95.0]
100 --> 44 | cost [365.0]

BACKUP RING
1  --- 62 | cost [4.7]
2  --- 58 | cost [15.4]
2  --- 84 | cost [11.85]
4  ---  9 | cost [8.1]
4  --- 82 | cost [4.0]
5  --- 22 | cost [4.65]
5  --- 80 | cost [9.35]
6  --- 98 | cost [9.450000000000001]
6  --- 99 | cost [4.55]
7  --- 41 | cost [5.3]
7  --- 43 | cost [6.75]
8  --- 68 | cost [8.5]
8  --- 101 | cost [2.75]
9  --- 74 | cost [4.05]
10 --- 78 | cost [7.8]
10 --- 92 | cost [7.3500000000000005]
15 --- 18 | cost [8.45]
15 --- 97 | cost [1.9000000000000001]
17 --- 27 | cost [9.35]
17 --- 38 | cost [3.7]
19 --- 28 | cost [6.45]
19 --- 50 | cost [4.45]
20 --- 26 | cost [2.6]
20 --- 33 | cost [6.05]
21 --- 67 | cost [5.1000000000000005]
21 --- 82 | cost [2.1]
22 --- 34 | cost [6.3]
23 --- 31 | cost [10.3]
23 --- 89 | cost [8.05]
26 --- 32 | cost [6.15]
27 --- 33 | cost [6.8500000000000005]
28 --- 59 | cost [5.95]
29 --- 39 | cost [8.5]
29 --- 45 | cost [11.200000000000001]
31 --- 98 | cost [7.15]
32 --- 85 | cost [5.65]
34 --- 42 | cost [6.4]
36 --- 45 | cost [14.450000000000001]
36 --- 47 | cost [8.2]
37 --- 46 | cost [6.4]
37 --- 77 | cost [5.3]
38 --- 73 | cost [5.55]
39 --- 40 | cost [9.35]
40 --- 42 | cost [4.4]
41 --- 61 | cost [6.6000000000000005]
43 --- 55 | cost [10.4]
44 --- 52 | cost [8.65]
44 --- 96 | cost [11.25]
46 --- 73 | cost [1.45]
47 --- 53 | cost [4.95]
49 --- 75 | cost [1.9000000000000001]
49 --- 97 | cost [4.7]
50 --- 54 | cost [5.05]
51 --- 68 | cost [5.45]
51 --- 80 | cost [6.8500000000000005]
52 --- 57 | cost [8.15]
53 --- 94 | cost [5.7]
54 --- 72 | cost [6.9]
55 --- 96 | cost [5.8]
57 --- 99 | cost [9.6]
58 --- 59 | cost [10.25]
60 --- 71 | cost [6.4]
61 --- 81 | cost [8.9]
62 --- 63 | cost [6.8]
63 --- 67 | cost [1.9000000000000001]
65 --- 81 | cost [4.9]
65 --- 83 | cost [5.15]
66 --- 84 | cost [5.8]
66 --- 94 | cost [7.3500000000000005]
71 --- 83 | cost [10.450000000000001]
72 --- 92 | cost [9.950000000000001]
74 --- 78 | cost [2.7]
75 --- 85 | cost [3.85]
76 --- 77 | cost [8.65]
76 --- 89 | cost [16.15]

BACKUP STAR
3  --> 10 | cost [6.5]
11 -->  5 | cost [5.9]
12 --> 82 | cost [3.95]
13 --> 49 | cost [4.4]
14 --> 82 | cost [3.85]
16 --> 98 | cost [5.9]
24 --> 42 | cost [3.4]
25 --> 42 | cost [5.45]
30 --> 81 | cost [6.0]
35 --> 44 | cost [4.8500000000000005]
48 --> 65 | cost [5.15]
56 --> 50 | cost [1.4000000000000001]
64 --> 47 | cost [10.1]
69 --> 60 | cost [4.15]
70 --> 38 | cost [4.3500000000000005]
79 --> 53 | cost [3.25]
86 --> 63 | cost [0.75]
87 --> 15 | cost [6.0]
88 --> 31 | cost [2.95]
90 --> 83 | cost [3.6]
91 --> 81 | cost [6.45]
93 --> 59 | cost [3.85]
95 --> 77 | cost [2.6]
100 --> 29 | cost [4.7]

B = 18.25
i★ = 52
j★ = 36
k★ = 57