------------------------------------------------------------
                         α=5.0 —— lin105 —— 105 nodes       
------------------------------------------------------------

——————— Sun, 28 Jan 2024 05:05:23 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 87 hubs —— 1—2—6—7—10—11—15—103—21—22—29—31—30—28—23—20—24—19—16—18—25—26—36—37—42—43—46—52—53—58—57—54—51—47—44—45—48—50—55—56—105—62—63—70—74—75—76—80—79—77—72—67—68—71—78—82—83—85—91—92—96—97—101—93—89—98—99—95—94—88—87—66—65—61—60—39—38—35—34—14—13—4—5—9—8—3—106
total time           1543.05              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             70676.43<=70680.8    subtour              168.0                
connectivity cuts    72.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               2:105                
2-opt strategy       0                                                              
explored_nodes       324                  n lazycuts edges     5.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—6—7—10—11—15—103—21—22—29—31—30—28—23—20—24—19—16—18—25—26—36—37—42—43—46—52—53—58—57—54—51—47—44—45—48—50—55—56—105—62—63—70—74—75—76—80—79—77—72—67—68—71—78—82—83—85—91—92—96—97—101—93—89—98—99—95—94—88—87—66—65—61—60—39—38—35—34—14—13—4—5—9—8—3—106

RING
1  ---  2 | cost [155.0]
1  --- 106 | cost [0.0]
2  ---  6 | cost [595.0]
3  ---  8 | cost [1460.0]
3  --- 106 | cost [1545.0]
4  ---  5 | cost [355.0]
4  --- 13 | cost [1535.0]
5  ---  9 | cost [2435.0]
6  ---  7 | cost [155.0]
7  --- 10 | cost [590.0]
8  ---  9 | cost [510.0]
10 --- 11 | cost [160.0]
11 --- 15 | cost [800.0]
13 --- 14 | cost [355.0]
14 --- 34 | cost [1915.0]
15 --- 103 | cost [500.0]
16 --- 18 | cost [300.0]
16 --- 19 | cost [725.0]
18 --- 25 | cost [195.0]
19 --- 24 | cost [195.0]
20 --- 23 | cost [195.0]
20 --- 24 | cost [930.0]
21 --- 22 | cost [155.0]
21 --- 103 | cost [420.0]
22 --- 29 | cost [160.0]
23 --- 28 | cost [160.0]
25 --- 26 | cost [160.0]
26 --- 36 | cost [1420.0]
28 --- 30 | cost [550.0]
29 --- 31 | cost [600.0]
30 --- 31 | cost [280.0]
34 --- 35 | cost [350.0]
35 --- 38 | cost [1415.0]
36 --- 37 | cost [510.0]
37 --- 42 | cost [1535.0]
38 --- 39 | cost [350.0]
39 --- 60 | cost [2930.0]
42 --- 43 | cost [475.0]
43 --- 46 | cost [315.0]
44 --- 45 | cost [1025.0]
44 --- 47 | cost [315.0]
45 --- 48 | cost [315.0]
46 --- 52 | cost [315.0]
47 --- 51 | cost [315.0]
48 --- 50 | cost [315.0]
50 --- 55 | cost [315.0]
51 --- 54 | cost [315.0]
52 --- 53 | cost [315.0]
53 --- 58 | cost [315.0]
54 --- 57 | cost [315.0]
55 --- 56 | cost [315.0]
56 --- 105 | cost [920.0]
57 --- 58 | cost [790.0]
60 --- 61 | cost [355.0]
61 --- 65 | cost [1410.0]
62 --- 63 | cost [510.0]
62 --- 105 | cost [1460.0]
63 --- 70 | cost [1535.0]
65 --- 66 | cost [355.0]
66 --- 87 | cost [1915.0]
67 --- 68 | cost [175.0]
67 --- 72 | cost [700.0]
68 --- 71 | cost [265.0]
70 --- 74 | cost [460.0]
71 --- 78 | cost [435.0]
72 --- 77 | cost [195.0]
74 --- 75 | cost [195.0]
75 --- 76 | cost [790.0]
76 --- 80 | cost [155.0]
77 --- 79 | cost [155.0]
78 --- 82 | cost [155.0]
79 --- 80 | cost [905.0]
82 --- 83 | cost [215.0]
83 --- 85 | cost [395.0]
85 --- 91 | cost [1425.0]
87 --- 88 | cost [350.0]
88 --- 94 | cost [1415.0]
89 --- 93 | cost [1560.0]
89 --- 98 | cost [1535.0]
91 --- 92 | cost [155.0]
92 --- 96 | cost [595.0]
93 --- 101 | cost [1965.0]
94 --- 95 | cost [350.0]
95 --- 99 | cost [2435.0]
96 --- 97 | cost [155.0]
97 --- 101 | cost [590.0]
98 --- 99 | cost [510.0]

STAR
12 --> 20 | cost [985.0]
17 --> 18 | cost [455.0]
27 --> 24 | cost [160.0]
32 --> 31 | cost [180.0]
33 --> 28 | cost [795.0]
40 --> 45 | cost [610.0]
41 --> 43 | cost [335.0]
49 --> 48 | cost [590.0]
59 --> 56 | cost [780.0]
64 --> 67 | cost [970.0]
69 --> 74 | cost [305.0]
73 --> 76 | cost [195.0]
81 --> 75 | cost [155.0]
84 --> 83 | cost [315.0]
86 --> 79 | cost [800.0]
90 --> 89 | cost [510.0]
100 --> 95 | cost [815.0]
102 --> 101 | cost [160.0]
104 --> 45 | cost [1060.0]

BACKUP RING
1  ---  6 | cost [7.5]
2  ---  7 | cost [7.5]
3  ---  9 | cost [19.400000000000002]
4  ---  9 | cost [27.75]
4  --- 14 | cost [17.25]
5  ---  8 | cost [29.35]
5  --- 13 | cost [14.1]
6  --- 10 | cost [7.45]
7  --- 11 | cost [7.5]
8  --- 106 | cost [29.900000000000002]
10 --- 15 | cost [9.4]
11 --- 103 | cost [13.0]
13 --- 34 | cost [20.5]
14 --- 35 | cost [20.45]
15 --- 21 | cost [5.55]
16 --- 24 | cost [8.2]
16 --- 25 | cost [4.8500000000000005]
18 --- 19 | cost [7.9]
18 --- 26 | cost [3.5500000000000003]
19 --- 20 | cost [9.1]
20 --- 28 | cost [3.5500000000000003]
21 --- 29 | cost [3.15]
22 --- 31 | cost [7.5]
22 --- 103 | cost [5.0]
23 --- 24 | cost [9.05]
23 --- 30 | cost [6.45]
25 --- 36 | cost [15.8]
26 --- 37 | cost [15.05]
28 --- 31 | cost [8.1]
29 --- 30 | cost [5.0]
34 --- 38 | cost [15.35]
35 --- 39 | cost [15.35]
36 --- 42 | cost [16.55]
37 --- 43 | cost [18.5]
38 --- 60 | cost [30.7]
39 --- 61 | cost [30.75]
42 --- 46 | cost [7.05]
43 --- 52 | cost [6.3]
44 --- 48 | cost [10.700000000000001]
44 --- 51 | cost [6.3]
45 --- 47 | cost [10.700000000000001]
45 --- 50 | cost [6.3]
46 --- 53 | cost [6.3]
47 --- 54 | cost [6.3]
48 --- 55 | cost [6.3]
50 --- 56 | cost [6.3]
51 --- 57 | cost [6.3]
52 --- 58 | cost [6.3]
53 --- 57 | cost [8.5]
54 --- 58 | cost [8.5]
55 --- 105 | cost [12.1]
56 --- 62 | cost [22.6]
60 --- 65 | cost [15.35]
61 --- 66 | cost [15.35]
62 --- 70 | cost [16.55]
63 --- 74 | cost [18.150000000000002]
63 --- 105 | cost [19.400000000000002]
65 --- 87 | cost [20.5]
66 --- 88 | cost [20.45]
67 --- 71 | cost [4.2]
67 --- 77 | cost [8.35]
68 --- 72 | cost [6.9]
68 --- 78 | cost [6.05]
70 --- 75 | cost [5.8500000000000005]
71 --- 82 | cost [5.9]
72 --- 79 | cost [3.5]
74 --- 76 | cost [8.15]
75 --- 80 | cost [8.05]
76 --- 79 | cost [9.200000000000001]
77 --- 80 | cost [9.200000000000001]
78 --- 83 | cost [3.65]
82 --- 85 | cost [5.9]
83 --- 91 | cost [18.25]
85 --- 92 | cost [15.8]
87 --- 94 | cost [15.35]
88 --- 95 | cost [15.35]
89 --- 99 | cost [16.55]
89 --- 101 | cost [35.2]
91 --- 96 | cost [7.5]
92 --- 97 | cost [7.5]
93 --- 97 | cost [16.45]
93 --- 98 | cost [14.6]
94 --- 99 | cost [27.75]
95 --- 98 | cost [29.35]
96 --- 101 | cost [7.45]

BACKUP STAR
12 --> 103 | cost [10.85]
17 --> 16 | cost [5.1000000000000005]
27 --> 19 | cost [3.5500000000000003]
32 --> 30 | cost [4.6000000000000005]
33 --> 30 | cost [8.85]
40 --> 48 | cost [8.6]
41 --> 42 | cost [5.1000000000000005]
49 --> 45 | cost [6.5]
59 --> 105 | cost [9.35]
64 --> 72 | cost [9.85]
69 --> 75 | cost [4.9]
73 --> 80 | cost [3.5]
81 --> 74 | cost [3.5]
84 --> 82 | cost [4.4]
86 --> 77 | cost [9.450000000000001]
90 --> 99 | cost [15.35]
100 --> 94 | cost [9.05]
102 --> 97 | cost [7.5]
104 --> 44 | cost [11.700000000000001]

B = 36.8
i★ = 94
j★ = 95
k★ = 99

       
——————— Sun, 28 Jan 2024 05:40:10 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 85 hubs —— 1-2-6-7-10-11-15-103-21-22-29-31-30-28-23-20-24-19-16-18-25-26-36-37-42-43-46-52-53-54-51-47-44-45-48-50-55-56-105-62-63-70-74-75-76-80-79-77-72-67-68-71-78-82-83-85-91-92-96-97-101-93-89-98-99-95-94-88-87-66-65-61-60-39-38-35-34-14-13-4-5-9-8-3-106-1
total time           2008.21              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             70680.8<=70680.8     Master/SP costs      69540/1140.8         
Master time          1991.4               SP time              16.81                
subtour              26253.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            83.0                 SP method            poly                 
tildeV               2:105                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       22737                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—6—7—10—11—15—103—21—22—29—31—30—28—23—20—24—19—16—18—25—26—36—37—42—43—46—52—53—54—51—47—44—45—48—50—55—56—105—62—63—70—74—75—76—80—79—77—72—67—68—71—78—82—83—85—91—92—96—97—101—93—89—98—99—95—94—88—87—66—65—61—60—39—38—35—34—14—13—4—5—9—8—3—106

RING
1  ---  2 | cost [155.0]
2  ---  6 | cost [595.0]
3  ---  8 | cost [1460.0]
3  --- 106 | cost [1545.0]
4  ---  5 | cost [355.0]
4  --- 13 | cost [1535.0]
5  ---  9 | cost [2435.0]
6  ---  7 | cost [155.0]
7  --- 10 | cost [590.0]
8  ---  9 | cost [510.0]
10 --- 11 | cost [160.0]
11 --- 15 | cost [800.0]
13 --- 14 | cost [355.0]
14 --- 34 | cost [1915.0]
15 --- 103 | cost [500.0]
16 --- 18 | cost [300.0]
16 --- 19 | cost [725.0]
18 --- 25 | cost [195.0]
19 --- 24 | cost [195.0]
20 --- 23 | cost [195.0]
20 --- 24 | cost [930.0]
21 --- 22 | cost [155.0]
21 --- 103 | cost [420.0]
22 --- 29 | cost [160.0]
23 --- 28 | cost [160.0]
25 --- 26 | cost [160.0]
26 --- 36 | cost [1420.0]
28 --- 30 | cost [550.0]
29 --- 31 | cost [600.0]
30 --- 31 | cost [280.0]
34 --- 35 | cost [350.0]
35 --- 38 | cost [1415.0]
36 --- 37 | cost [510.0]
37 --- 42 | cost [1535.0]
38 --- 39 | cost [350.0]
39 --- 60 | cost [2930.0]
42 --- 43 | cost [475.0]
43 --- 46 | cost [315.0]
44 --- 45 | cost [1025.0]
44 --- 47 | cost [315.0]
45 --- 48 | cost [315.0]
46 --- 52 | cost [315.0]
47 --- 51 | cost [315.0]
48 --- 50 | cost [315.0]
50 --- 55 | cost [315.0]
51 --- 54 | cost [315.0]
52 --- 53 | cost [315.0]
53 --- 54 | cost [790.0]
55 --- 56 | cost [315.0]
56 --- 105 | cost [920.0]
60 --- 61 | cost [355.0]
61 --- 65 | cost [1410.0]
62 --- 63 | cost [510.0]
62 --- 105 | cost [1460.0]
63 --- 70 | cost [1535.0]
65 --- 66 | cost [355.0]
66 --- 87 | cost [1915.0]
67 --- 68 | cost [175.0]
67 --- 72 | cost [700.0]
68 --- 71 | cost [265.0]
70 --- 74 | cost [460.0]
71 --- 78 | cost [435.0]
72 --- 77 | cost [195.0]
74 --- 75 | cost [195.0]
75 --- 76 | cost [790.0]
76 --- 80 | cost [155.0]
77 --- 79 | cost [155.0]
78 --- 82 | cost [155.0]
79 --- 80 | cost [905.0]
82 --- 83 | cost [215.0]
83 --- 85 | cost [395.0]
85 --- 91 | cost [1425.0]
87 --- 88 | cost [350.0]
88 --- 94 | cost [1415.0]
89 --- 93 | cost [1560.0]
89 --- 98 | cost [1535.0]
91 --- 92 | cost [155.0]
92 --- 96 | cost [595.0]
93 --- 101 | cost [1965.0]
94 --- 95 | cost [350.0]
95 --- 99 | cost [2435.0]
96 --- 97 | cost [155.0]
97 --- 101 | cost [590.0]
98 --- 99 | cost [510.0]

STAR
12 --> 20 | cost [985.0]
17 --> 18 | cost [455.0]
27 --> 24 | cost [160.0]
32 --> 31 | cost [180.0]
33 --> 28 | cost [795.0]
40 --> 45 | cost [610.0]
41 --> 43 | cost [335.0]
49 --> 48 | cost [590.0]
57 --> 54 | cost [315.0]
58 --> 53 | cost [315.0]
59 --> 56 | cost [780.0]
64 --> 67 | cost [970.0]
69 --> 74 | cost [305.0]
73 --> 76 | cost [195.0]
81 --> 75 | cost [155.0]
84 --> 83 | cost [315.0]
86 --> 79 | cost [800.0]
90 --> 89 | cost [510.0]
100 --> 95 | cost [815.0]
102 --> 101 | cost [160.0]
104 --> 45 | cost [1060.0]

BACKUP RING
1  ---  6 | cost [7.5]
2  ---  7 | cost [7.5]
3  ---  9 | cost [19.400000000000002]
4  ---  9 | cost [27.75]
4  --- 14 | cost [17.25]
5  ---  8 | cost [29.35]
5  --- 13 | cost [14.1]
6  --- 10 | cost [7.45]
7  --- 11 | cost [7.5]
8  --- 106 | cost [29.900000000000002]
10 --- 15 | cost [9.4]
11 --- 103 | cost [13.0]
13 --- 34 | cost [20.5]
14 --- 35 | cost [20.45]
15 --- 21 | cost [5.55]
16 --- 24 | cost [8.2]
16 --- 25 | cost [4.8500000000000005]
18 --- 19 | cost [7.9]
18 --- 26 | cost [3.5500000000000003]
19 --- 20 | cost [9.1]
20 --- 28 | cost [3.5500000000000003]
21 --- 29 | cost [3.15]
22 --- 31 | cost [7.5]
22 --- 103 | cost [5.0]
23 --- 24 | cost [9.05]
23 --- 30 | cost [6.45]
25 --- 36 | cost [15.8]
26 --- 37 | cost [15.05]
28 --- 31 | cost [8.1]
29 --- 30 | cost [5.0]
34 --- 38 | cost [15.35]
35 --- 39 | cost [15.35]
36 --- 42 | cost [16.55]
37 --- 43 | cost [18.5]
38 --- 60 | cost [30.7]
39 --- 61 | cost [30.75]
42 --- 46 | cost [7.05]
43 --- 52 | cost [6.3]
44 --- 48 | cost [10.700000000000001]
44 --- 51 | cost [6.3]
45 --- 47 | cost [10.700000000000001]
45 --- 50 | cost [6.3]
46 --- 53 | cost [6.3]
47 --- 54 | cost [6.3]
48 --- 55 | cost [6.3]
50 --- 56 | cost [6.3]
51 --- 53 | cost [8.5]
52 --- 54 | cost [8.5]
55 --- 105 | cost [12.1]
56 --- 62 | cost [22.6]
60 --- 65 | cost [15.35]
61 --- 66 | cost [15.35]
62 --- 70 | cost [16.55]
63 --- 74 | cost [18.150000000000002]
63 --- 105 | cost [19.400000000000002]
65 --- 87 | cost [20.5]
66 --- 88 | cost [20.45]
67 --- 71 | cost [4.2]
67 --- 77 | cost [8.35]
68 --- 72 | cost [6.9]
68 --- 78 | cost [6.05]
70 --- 75 | cost [5.8500000000000005]
71 --- 82 | cost [5.9]
72 --- 79 | cost [3.5]
74 --- 76 | cost [8.15]
75 --- 80 | cost [8.05]
76 --- 79 | cost [9.200000000000001]
77 --- 80 | cost [9.200000000000001]
78 --- 83 | cost [3.65]
82 --- 85 | cost [5.9]
83 --- 91 | cost [18.25]
85 --- 92 | cost [15.8]
87 --- 94 | cost [15.35]
88 --- 95 | cost [15.35]
89 --- 99 | cost [16.55]
89 --- 101 | cost [35.2]
91 --- 96 | cost [7.5]
92 --- 97 | cost [7.5]
93 --- 97 | cost [16.45]
93 --- 98 | cost [14.6]
94 --- 99 | cost [27.75]
95 --- 98 | cost [29.35]
96 --- 101 | cost [7.45]

BACKUP STAR
12 --> 103 | cost [10.85]
17 --> 16 | cost [5.1000000000000005]
27 --> 19 | cost [3.5500000000000003]
32 --> 30 | cost [4.6000000000000005]
33 --> 30 | cost [8.85]
40 --> 48 | cost [8.6]
41 --> 42 | cost [5.1000000000000005]
49 --> 45 | cost [6.5]
57 --> 51 | cost [6.3]
58 --> 52 | cost [6.3]
59 --> 105 | cost [9.35]
64 --> 72 | cost [9.85]
69 --> 75 | cost [4.9]
73 --> 80 | cost [3.5]
81 --> 74 | cost [3.5]
84 --> 82 | cost [4.4]
86 --> 77 | cost [9.450000000000001]
90 --> 99 | cost [15.35]
100 --> 94 | cost [9.05]
102 --> 97 | cost [7.5]
104 --> 44 | cost [11.700000000000001]

B = 36.8
i★ = 94
j★ = 95
k★ = 99