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

——————— Sat, 13 Jan 2024 22:58:13 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—2—106
total time           41.18                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             70517<=70517         subtour              1856.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       3476                 n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—106

RING
1  ---  2 | cost [217.0]
2  --- 106 | cost [217.0]
7  --- 10 | cost [826.0]
7  --- 11 | cost [1050.0]
10 --- 11 | cost [224.0]
14 --- 17 | cost [3409.0]
14 --- 35 | cost [2863.0]
16 --- 17 | cost [714.0]
16 --- 18 | cost [420.0]
18 --- 25 | cost [273.0]
20 --- 28 | cost [497.0]
20 --- 30 | cost [1099.0]
21 --- 22 | cost [217.0]
21 --- 29 | cost [441.0]
22 --- 29 | cost [224.0]
25 --- 26 | cost [224.0]
26 --- 37 | cost [2107.0]
28 --- 30 | cost [770.0]
35 --- 37 | cost [3409.0]
43 --- 44 | cost [1106.0]
43 --- 46 | cost [441.0]
44 --- 48 | cost [1498.0]
46 --- 52 | cost [441.0]
48 --- 50 | cost [441.0]
50 --- 55 | cost [441.0]
52 --- 53 | cost [441.0]
53 --- 54 | cost [1106.0]
54 --- 55 | cost [1435.0]
60 --- 61 | cost [497.0]
60 --- 65 | cost [2149.0]
61 --- 65 | cost [1974.0]
67 --- 68 | cost [245.0]
67 --- 71 | cost [588.0]
68 --- 71 | cost [371.0]
70 --- 74 | cost [644.0]
70 --- 75 | cost [819.0]
73 --- 76 | cost [273.0]
73 --- 80 | cost [490.0]
74 --- 75 | cost [273.0]
76 --- 80 | cost [217.0]
82 --- 83 | cost [301.0]
82 --- 84 | cost [616.0]
83 --- 84 | cost [441.0]
92 --- 96 | cost [833.0]
92 --- 97 | cost [1050.0]
94 --- 95 | cost [490.0]
94 --- 100 | cost [1267.0]
95 --- 100 | cost [1141.0]
96 --- 97 | cost [217.0]

STAR
3  -->  2 | cost [909.0]
4  --> 14 | cost [1035.0]
5  --> 14 | cost [921.0]
6  -->  7 | cost [93.0]
8  --> 16 | cost [921.0]
9  --> 17 | cost [924.0]
12 --> 20 | cost [591.0]
13 --> 14 | cost [213.0]
15 --> 21 | cost [333.0]
19 --> 16 | cost [435.0]
23 --> 20 | cost [117.0]
24 --> 25 | cost [474.0]
27 --> 26 | cost [474.0]
31 --> 30 | cost [168.0]
32 --> 30 | cost [276.0]
33 --> 28 | cost [477.0]
34 --> 35 | cost [210.0]
36 --> 37 | cost [306.0]
38 --> 35 | cost [849.0]
39 --> 35 | cost [921.0]
40 --> 48 | cost [516.0]
41 --> 43 | cost [201.0]
42 --> 43 | cost [285.0]
45 --> 48 | cost [189.0]
47 --> 44 | cost [189.0]
49 --> 48 | cost [354.0]
51 --> 54 | cost [189.0]
56 --> 55 | cost [189.0]
57 --> 54 | cost [189.0]
58 --> 53 | cost [189.0]
59 --> 55 | cost [624.0]
62 --> 70 | cost [993.0]
63 --> 70 | cost [921.0]
64 --> 67 | cost [582.0]
66 --> 65 | cost [213.0]
69 --> 74 | cost [183.0]
72 --> 68 | cost [414.0]
77 --> 84 | cost [387.0]
78 --> 82 | cost [93.0]
79 --> 84 | cost [330.0]
81 --> 75 | cost [93.0]
85 --> 83 | cost [237.0]
86 --> 84 | cost [531.0]
87 --> 94 | cost [921.0]
88 --> 94 | cost [849.0]
89 --> 80 | cost [942.0]
90 --> 75 | cost [996.0]
91 --> 92 | cost [93.0]
93 --> 92 | cost [903.0]
98 --> 97 | cost [1683.0]
99 --> 95 | cost [1461.0]
101 --> 97 | cost [354.0]
102 --> 97 | cost [450.0]
103 --> 21 | cost [252.0]
104 --> 44 | cost [702.0]
105 --> 55 | cost [726.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 13 Jan 2024 23:58:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 51 hubs —— 1-2-7-10-15-21-22-29-30-28-24-18-25-26-36-41-48-47-43-46-52-53-54-105-64-71-68-77-72-70-69-73-74-82-83-92-97-101-99-90-88-66-61-60-39-35-14-17-8-9-106-1
total time           3606.15 (TL 3600)    gap                  0.309                
blossom time         0                    nb blossom           0.0                  
LB <= UB             68934<=99730         Master/SP costs      99730/0              
Master time          3606.14              SP time              0.0                  
subtour              27869.0              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       25572                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—2—7—10—15—21—22—29—30—28—24—18—25—26—36—41—48—47—43—46—52—53—54—105—64—71—68—77—72—70—69—73—74—82—83—92—97—101—99—90—88—66—61—60—39—35—14—17—8—9—106

RING
1  ---  2 | cost [217.0]
2  ---  7 | cost [1050.0]
7  --- 10 | cost [826.0]
8  ---  9 | cost [714.0]
8  --- 17 | cost [2317.0]
9  --- 106 | cost [4879.0]
10 --- 15 | cost [1316.0]
14 --- 17 | cost [3409.0]
14 --- 35 | cost [2863.0]
15 --- 21 | cost [777.0]
18 --- 24 | cost [1141.0]
18 --- 25 | cost [273.0]
21 --- 22 | cost [217.0]
22 --- 29 | cost [224.0]
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 --- 60 | cost [4102.0]
41 --- 48 | cost [2534.0]
43 --- 46 | cost [441.0]
43 --- 47 | cost [1190.0]
46 --- 52 | cost [441.0]
47 --- 48 | cost [1435.0]
52 --- 53 | cost [441.0]
53 --- 54 | cost [1106.0]
54 --- 105 | cost [1827.0]
60 --- 61 | cost [497.0]
61 --- 66 | cost [2149.0]
64 --- 71 | cost [1939.0]
64 --- 105 | cost [2149.0]
66 --- 88 | cost [2863.0]
68 --- 71 | cost [371.0]
68 --- 77 | cost [1106.0]
69 --- 70 | cost [714.0]
69 --- 73 | cost [1015.0]
70 --- 72 | cost [2940.0]
72 --- 77 | cost [273.0]
73 --- 74 | cost [1106.0]
74 --- 82 | cost [3633.0]
82 --- 83 | cost [301.0]
83 --- 92 | cost [2765.0]
88 --- 90 | cost [3409.0]
90 --- 99 | cost [2149.0]
92 --- 97 | cost [1050.0]
97 --- 101 | cost [826.0]
99 --- 101 | cost [4704.0]

STAR
3  -->  8 | cost [876.0]
4  --> 14 | cost [1035.0]
5  --> 14 | cost [921.0]
6  -->  7 | cost [93.0]
11 --> 10 | cost [96.0]
12 --> 15 | cost [681.0]
13 --> 14 | cost [213.0]
16 --> 18 | cost [180.0]
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 --> 48 | cost [516.0]
42 --> 43 | cost [285.0]
44 --> 47 | cost [189.0]
45 --> 48 | cost [189.0]
49 --> 48 | cost [354.0]
50 --> 47 | cost [642.0]
51 --> 54 | cost [189.0]
55 --> 48 | cost [378.0]
56 --> 54 | cost [642.0]
57 --> 54 | cost [189.0]
58 --> 53 | cost [189.0]
59 --> 105 | cost [561.0]
62 --> 105 | cost [876.0]
63 --> 70 | cost [921.0]
65 --> 66 | cost [213.0]
67 --> 68 | cost [105.0]
75 --> 74 | cost [117.0]
76 --> 73 | cost [117.0]
78 --> 82 | cost [93.0]
79 --> 77 | cost [93.0]
80 --> 73 | cost [210.0]
81 --> 74 | cost [210.0]
84 --> 83 | cost [189.0]
85 --> 83 | cost [237.0]
86 --> 77 | cost [567.0]
87 --> 88 | cost [210.0]
89 --> 90 | cost [306.0]
91 --> 92 | cost [93.0]
93 --> 92 | cost [903.0]
94 --> 88 | cost [849.0]
95 --> 88 | cost [921.0]
96 --> 97 | cost [93.0]
98 --> 99 | cost [306.0]
100 --> 88 | cost [1383.0]
102 --> 101 | cost [96.0]
103 --> 21 | cost [252.0]
104 --> 48 | cost [816.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1