------------------------------------------------------------
                         α=7.0 —— lin105 —— 105 nodes       
------------------------------------------------------------

——————— Thu, 25 Jan 2024 01:08:25 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 57 hubs —— 1—3—8—9—14—35—39—61—66—88—95—99—98—93—96—92—91—85—83—82—78—71—68—72—77—76—74—69—62—105—56—55—50—48—45—47—51—52—46—43—41—36—26—25—24—28—30—29—22—21—15—11—10—7—6—2—106
total time           115.44               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             83597<=83597         subtour              2363.0               
connectivity cuts    1169.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1156                 n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—3—8—9—14—35—39—61—66—88—95—99—98—93—96—92—91—85—83—82—78—71—68—72—77—76—74—69—62—105—56—55—50—48—45—47—51—52—46—43—41—36—26—25—24—28—30—29—22—21—15—11—10—7—6—2—106

RING
1  ---  3 | cost [2163.0]
1  --- 106 | cost [0.0]
2  ---  6 | cost [833.0]
2  --- 106 | cost [217.0]
3  ---  8 | cost [2044.0]
6  ---  7 | cost [217.0]
7  --- 10 | cost [826.0]
8  ---  9 | cost [714.0]
9  --- 14 | cost [3731.0]
10 --- 11 | cost [224.0]
11 --- 15 | cost [1120.0]
14 --- 35 | cost [2863.0]
15 --- 21 | cost [777.0]
21 --- 22 | cost [217.0]
22 --- 29 | cost [224.0]
24 --- 25 | cost [1106.0]
24 --- 28 | cost [1288.0]
25 --- 26 | cost [224.0]
26 --- 36 | cost [1988.0]
28 --- 30 | cost [770.0]
29 --- 30 | cost [700.0]
35 --- 39 | cost [2149.0]
36 --- 41 | cost [2149.0]
39 --- 61 | cost [4305.0]
41 --- 43 | cost [469.0]
43 --- 46 | cost [441.0]
45 --- 47 | cost [1498.0]
45 --- 48 | cost [441.0]
46 --- 52 | cost [441.0]
47 --- 51 | cost [441.0]
48 --- 50 | cost [441.0]
50 --- 55 | cost [441.0]
51 --- 52 | cost [1106.0]
55 --- 56 | cost [441.0]
56 --- 105 | cost [1288.0]
61 --- 66 | cost [2149.0]
62 --- 69 | cost [2149.0]
62 --- 105 | cost [2044.0]
66 --- 88 | cost [2863.0]
68 --- 71 | cost [371.0]
68 --- 72 | cost [966.0]
69 --- 74 | cost [427.0]
71 --- 78 | cost [609.0]
72 --- 77 | cost [273.0]
74 --- 76 | cost [1141.0]
76 --- 77 | cost [1267.0]
78 --- 82 | cost [217.0]
82 --- 83 | cost [301.0]
83 --- 85 | cost [553.0]
85 --- 91 | cost [1995.0]
88 --- 95 | cost [2149.0]
91 --- 92 | cost [217.0]
92 --- 96 | cost [833.0]
93 --- 96 | cost [2226.0]
93 --- 98 | cost [2044.0]
95 --- 99 | cost [3409.0]
98 --- 99 | cost [714.0]

STAR
4  --> 14 | cost [1035.0]
5  --> 14 | cost [921.0]
12 --> 15 | cost [681.0]
13 --> 14 | cost [213.0]
16 --> 25 | cost [291.0]
17 --> 25 | cost [348.0]
18 --> 25 | cost [117.0]
19 --> 24 | cost [117.0]
20 --> 28 | cost [213.0]
23 --> 28 | cost [96.0]
27 --> 24 | cost [96.0]
31 --> 30 | cost [168.0]
32 --> 30 | cost [276.0]
33 --> 28 | cost [477.0]
34 --> 35 | cost [210.0]
37 --> 36 | cost [306.0]
38 --> 39 | cost [210.0]
40 --> 45 | cost [366.0]
42 --> 43 | cost [285.0]
44 --> 47 | cost [189.0]
49 --> 48 | cost [354.0]
53 --> 52 | cost [189.0]
54 --> 51 | cost [189.0]
57 --> 51 | cost [378.0]
58 --> 52 | cost [378.0]
59 --> 56 | cost [468.0]
60 --> 61 | cost [213.0]
63 --> 62 | cost [306.0]
64 --> 72 | cost [591.0]
65 --> 66 | cost [213.0]
67 --> 68 | cost [105.0]
70 --> 74 | cost [276.0]
73 --> 76 | cost [117.0]
75 --> 74 | cost [117.0]
79 --> 77 | cost [93.0]
80 --> 76 | cost [93.0]
81 --> 74 | cost [210.0]
84 --> 83 | cost [189.0]
86 --> 77 | cost [567.0]
87 --> 88 | cost [210.0]
89 --> 98 | cost [921.0]
90 --> 99 | cost [921.0]
94 --> 95 | cost [210.0]
97 --> 96 | cost [93.0]
100 --> 95 | cost [489.0]
101 --> 96 | cost [447.0]
102 --> 96 | cost [543.0]
103 --> 21 | cost [252.0]
104 --> 45 | cost [636.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Thu, 25 Jan 2024 01:10:25 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 57 hubs —— 1-2-6-7-10-11-15-21-22-29-30-28-24-25-26-36-41-43-46-52-51-47-45-48-50-55-56-105-62-69-74-76-77-72-68-71-78-82-83-85-91-92-96-93-98-99-95-88-66-61-39-35-14-9-8-3-106-1
total time           89.61                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             83597<=83597         Master/SP costs      83597/0              
Master time          89.61                SP time              0.0                  
subtour              1509.0               connectivity cuts    1162.0               
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       1159                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—6—7—10—11—15—21—22—29—30—28—24—25—26—36—41—43—46—52—51—47—45—48—50—55—56—105—62—69—74—76—77—72—68—71—78—82—83—85—91—92—96—93—98—99—95—88—66—61—39—35—14—9—8—3—106

RING
1  ---  2 | cost [217.0]
1  --- 106 | cost [0.0]
2  ---  6 | cost [833.0]
3  ---  8 | cost [2044.0]
3  --- 106 | cost [2163.0]
6  ---  7 | cost [217.0]
7  --- 10 | cost [826.0]
8  ---  9 | cost [714.0]
9  --- 14 | cost [3731.0]
10 --- 11 | cost [224.0]
11 --- 15 | cost [1120.0]
14 --- 35 | cost [2863.0]
15 --- 21 | cost [777.0]
21 --- 22 | cost [217.0]
22 --- 29 | cost [224.0]
24 --- 25 | cost [1106.0]
24 --- 28 | cost [1288.0]
25 --- 26 | cost [224.0]
26 --- 36 | cost [1988.0]
28 --- 30 | cost [770.0]
29 --- 30 | cost [700.0]
35 --- 39 | cost [2149.0]
36 --- 41 | cost [2149.0]
39 --- 61 | cost [4305.0]
41 --- 43 | cost [469.0]
43 --- 46 | cost [441.0]
45 --- 47 | cost [1498.0]
45 --- 48 | cost [441.0]
46 --- 52 | cost [441.0]
47 --- 51 | cost [441.0]
48 --- 50 | cost [441.0]
50 --- 55 | cost [441.0]
51 --- 52 | cost [1106.0]
55 --- 56 | cost [441.0]
56 --- 105 | cost [1288.0]
61 --- 66 | cost [2149.0]
62 --- 69 | cost [2149.0]
62 --- 105 | cost [2044.0]
66 --- 88 | cost [2863.0]
68 --- 71 | cost [371.0]
68 --- 72 | cost [966.0]
69 --- 74 | cost [427.0]
71 --- 78 | cost [609.0]
72 --- 77 | cost [273.0]
74 --- 76 | cost [1141.0]
76 --- 77 | cost [1267.0]
78 --- 82 | cost [217.0]
82 --- 83 | cost [301.0]
83 --- 85 | cost [553.0]
85 --- 91 | cost [1995.0]
88 --- 95 | cost [2149.0]
91 --- 92 | cost [217.0]
92 --- 96 | cost [833.0]
93 --- 96 | cost [2226.0]
93 --- 98 | cost [2044.0]
95 --- 99 | cost [3409.0]
98 --- 99 | cost [714.0]

STAR
4  --> 14 | cost [1035.0]
5  --> 14 | cost [921.0]
12 --> 15 | cost [681.0]
13 --> 14 | cost [213.0]
16 --> 25 | cost [291.0]
17 --> 25 | cost [348.0]
18 --> 25 | cost [117.0]
19 --> 24 | cost [117.0]
20 --> 28 | cost [213.0]
23 --> 28 | cost [96.0]
27 --> 24 | cost [96.0]
31 --> 30 | cost [168.0]
32 --> 30 | cost [276.0]
33 --> 28 | cost [477.0]
34 --> 35 | cost [210.0]
37 --> 36 | cost [306.0]
38 --> 39 | cost [210.0]
40 --> 45 | cost [366.0]
42 --> 43 | cost [285.0]
44 --> 47 | cost [189.0]
49 --> 48 | cost [354.0]
53 --> 52 | cost [189.0]
54 --> 51 | cost [189.0]
57 --> 51 | cost [378.0]
58 --> 52 | cost [378.0]
59 --> 56 | cost [468.0]
60 --> 61 | cost [213.0]
63 --> 62 | cost [306.0]
64 --> 72 | cost [591.0]
65 --> 66 | cost [213.0]
67 --> 68 | cost [105.0]
70 --> 74 | cost [276.0]
73 --> 76 | cost [117.0]
75 --> 74 | cost [117.0]
79 --> 77 | cost [93.0]
80 --> 76 | cost [93.0]
81 --> 74 | cost [210.0]
84 --> 83 | cost [189.0]
86 --> 77 | cost [567.0]
87 --> 88 | cost [210.0]
89 --> 98 | cost [921.0]
90 --> 99 | cost [921.0]
94 --> 95 | cost [210.0]
97 --> 96 | cost [93.0]
100 --> 95 | cost [489.0]
101 --> 96 | cost [447.0]
102 --> 96 | cost [543.0]
103 --> 21 | cost [252.0]
104 --> 45 | cost [636.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1