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

——————— Tue, 23 Jan 2024 18:10:06 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 86 hubs —— 1—2—6—7—10—11—15—103—21—22—29—31—30—28—23—20—24—19—16—18—25—26—36—104—40—45—48—50—55—56—57—54—51—47—44—41—43—46—52—53—58—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—5—9—8—3—106
total time           150.12               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             69365<=69365         subtour              1800.0               
connectivity cuts    1879.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1866                 n lazycuts edges     1.0                  
F                    0.0                  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—104—40—45—48—50—55—56—57—54—51—47—44—41—43—46—52—53—58—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—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]
5  ---  9 | cost [2435.0]
5  --- 13 | cost [1410.0]
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 --- 104 | cost [1560.0]
38 --- 39 | cost [350.0]
39 --- 60 | cost [2930.0]
40 --- 45 | cost [610.0]
40 --- 104 | cost [995.0]
41 --- 43 | cost [335.0]
41 --- 44 | cost [740.0]
43 --- 46 | cost [315.0]
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 --- 57 | cost [1025.0]
58 --- 62 | cost [1500.0]
60 --- 61 | cost [355.0]
61 --- 65 | cost [1410.0]
62 --- 63 | cost [510.0]
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
4  -->  5 | cost [355.0]
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]
37 --> 36 | cost [510.0]
42 --> 43 | cost [475.0]
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]
105 --> 56 | cost [920.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 23 Jan 2024 18:15:32 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 86 hubs —— 1-2-6-7-10-11-15-103-21-22-29-31-30-28-23-20-24-19-16-18-25-26-36-104-40-45-48-50-55-56-57-54-51-47-44-41-43-46-52-53-58-62-63-70-74-75-76-80-79-77-72-67-68-71-78-82-83-85-91-92-96-97-101-93-89-98-99-95-94-88-87-66-65-61-60-39-38-35-34-14-13-5-9-8-3-106-1
total time           295.24               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             69365<=69365         Master/SP costs      69365/0              
Master time          295.24               SP time              0.0                  
subtour              7263.0               connectivity cuts    2000.0               
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       7263                 
F                    0.0                  
                                          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—104—40—45—48—50—55—56—57—54—51—47—44—41—43—46—52—53—58—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—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]
5  ---  9 | cost [2435.0]
5  --- 13 | cost [1410.0]
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 --- 104 | cost [1560.0]
38 --- 39 | cost [350.0]
39 --- 60 | cost [2930.0]
40 --- 45 | cost [610.0]
40 --- 104 | cost [995.0]
41 --- 43 | cost [335.0]
41 --- 44 | cost [740.0]
43 --- 46 | cost [315.0]
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 --- 57 | cost [1025.0]
58 --- 62 | cost [1500.0]
60 --- 61 | cost [355.0]
61 --- 65 | cost [1410.0]
62 --- 63 | cost [510.0]
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
4  -->  5 | cost [355.0]
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]
37 --> 36 | cost [510.0]
42 --> 43 | cost [475.0]
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]
105 --> 56 | cost [920.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1