------------------------------------------------------------
                          α=7.0 —— rd100 —— 100 nodes       
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——————— Sat, 13 Jan 2024 20:26:58 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—60—101
total time           163.26               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             37232<=37232         subtour              4717.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       22767                n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—60—101

RING
1  --- 60 | cost [154.0]
4  --- 32 | cost [294.0]
4  --- 33 | cost [1309.0]
6  --- 53 | cost [413.0]
6  --- 99 | cost [637.0]
7  --- 41 | cost [742.0]
7  --- 42 | cost [511.0]
20 --- 74 | cost [133.0]
20 --- 78 | cost [273.0]
21 --- 82 | cost [294.0]
21 --- 85 | cost [532.0]
26 --- 32 | cost [861.0]
26 --- 74 | cost [273.0]
29 --- 96 | cost [1120.0]
29 --- 100 | cost [658.0]
33 --- 78 | cost [805.0]
36 --- 47 | cost [1148.0]
36 --- 57 | cost [700.0]
38 --- 46 | cost [973.0]
38 --- 54 | cost [497.0]
41 --- 42 | cost [938.0]
46 --- 50 | cost [35.0]
47 --- 57 | cost [700.0]
50 --- 73 | cost [189.0]
51 --- 65 | cost [581.0]
51 --- 90 | cost [294.0]
53 --- 99 | cost [336.0]
54 --- 73 | cost [560.0]
59 --- 77 | cost [336.0]
59 --- 93 | cost [539.0]
60 --- 101 | cost [154.0]
63 --- 86 | cost [105.0]
63 --- 97 | cost [56.0]
65 --- 90 | cost [672.0]
66 --- 84 | cost [812.0]
66 --- 88 | cost [714.0]
77 --- 93 | cost [308.0]
82 --- 85 | cost [287.0]
84 --- 88 | cost [133.0]
86 --- 97 | cost [91.0]
96 --- 100 | cost [1225.0]

STAR
2  --> 84 | cost [711.0]
3  --> 33 | cost [345.0]
5  --> 41 | cost [384.0]
8  --> 60 | cost [102.0]
9  --> 26 | cost [126.0]
10 --> 33 | cost [123.0]
11 --> 36 | cost [507.0]
12 --> 85 | cost [123.0]
13 --> 97 | cost [270.0]
14 --> 85 | cost [123.0]
15 --> 63 | cost [90.0]
16 --> 66 | cost [420.0]
17 --> 38 | cost [222.0]
18 -->  1 | cost [264.0]
19 --> 46 | cost [252.0]
22 --> 41 | cost [150.0]
23 --> 84 | cost [546.0]
24 --> 42 | cost [204.0]
25 --> 42 | cost [327.0]
27 --> 50 | cost [285.0]
28 --> 77 | cost [222.0]
30 --> 65 | cost [423.0]
31 --> 84 | cost [162.0]
34 -->  7 | cost [171.0]
35 --> 29 | cost [174.0]
37 --> 77 | cost [318.0]
39 --> 96 | cost [120.0]
40 -->  7 | cost [213.0]
43 --> 42 | cost [198.0]
44 --> 100 | cost [219.0]
45 --> 100 | cost [504.0]
48 --> 65 | cost [309.0]
49 --> 21 | cost [105.0]
52 --> 100 | cost [429.0]
55 --> 96 | cost [348.0]
56 --> 46 | cost [75.0]
58 --> 88 | cost [345.0]
61 --> 41 | cost [396.0]
62 -->  1 | cost [282.0]
64 --> 36 | cost [408.0]
67 --> 97 | cost [96.0]
68 --> 51 | cost [327.0]
69 --> 60 | cost [249.0]
70 --> 38 | cost [261.0]
71 --> 60 | cost [384.0]
72 --> 38 | cost [201.0]
75 --> 21 | cost [75.0]
76 --> 66 | cost [204.0]
79 --> 99 | cost [207.0]
80 --> 65 | cost [180.0]
81 --> 65 | cost [294.0]
83 --> 51 | cost [102.0]
87 --> 86 | cost [381.0]
89 --> 84 | cost [663.0]
91 --> 65 | cost [360.0]
92 --> 50 | cost [246.0]
94 --> 53 | cost [342.0]
95 --> 59 | cost [57.0]
98 --> 66 | cost [216.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 13 Jan 2024 21:27:34 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 47 hubs —— 1-8-51-65-80-81-5-61-34-7-42-40-55-96-29-44-45-31-84-88-66-98-94-53-99-77-28-37-19-54-38-73-50-27-10-33-78-32-12-85-82-21-86-97-63-15-101-1
total time           3606.21 (TL 3600)    gap                  0.129                
blossom time         0                    nb blossom           0.0                  
LB <= UB             36722<=42167         Master/SP costs      42167/0              
Master time          3606.21              SP time              0.0                  
subtour              24631.0              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       27793                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—8—51—65—80—81—5—61—34—7—42—40—55—96—29—44—45—31—84—88—66—98—94—53—99—77—28—37—19—54—38—73—50—27—10—33—78—32—12—85—82—21—86—97—63—15—101

RING
1  ---  8 | cost [385.0]
5  --- 61 | cost [350.0]
5  --- 81 | cost [896.0]
7  --- 34 | cost [399.0]
7  --- 42 | cost [511.0]
8  --- 51 | cost [1302.0]
10 --- 27 | cost [833.0]
10 --- 33 | cost [287.0]
12 --- 32 | cost [798.0]
12 --- 85 | cost [287.0]
15 --- 63 | cost [210.0]
15 --- 101 | cost [910.0]
19 --- 37 | cost [658.0]
19 --- 54 | cost [679.0]
21 --- 82 | cost [294.0]
21 --- 86 | cost [609.0]
27 --- 50 | cost [665.0]
28 --- 37 | cost [252.0]
28 --- 77 | cost [518.0]
29 --- 44 | cost [602.0]
29 --- 96 | cost [1120.0]
31 --- 45 | cost [1190.0]
31 --- 84 | cost [378.0]
32 --- 78 | cost [658.0]
33 --- 78 | cost [805.0]
34 --- 61 | cost [756.0]
38 --- 54 | cost [497.0]
38 --- 73 | cost [777.0]
40 --- 42 | cost [616.0]
40 --- 55 | cost [833.0]
44 --- 45 | cost [973.0]
50 --- 73 | cost [189.0]
51 --- 65 | cost [581.0]
53 --- 94 | cost [798.0]
53 --- 99 | cost [336.0]
55 --- 96 | cost [812.0]
63 --- 97 | cost [56.0]
65 --- 80 | cost [420.0]
66 --- 88 | cost [714.0]
66 --- 98 | cost [504.0]
77 --- 99 | cost [2037.0]
80 --- 81 | cost [469.0]
82 --- 85 | cost [287.0]
84 --- 88 | cost [133.0]
86 --- 97 | cost [91.0]
94 --- 98 | cost [532.0]

STAR
2  --> 84 | cost [711.0]
3  --> 33 | cost [345.0]
4  --> 32 | cost [126.0]
6  --> 53 | cost [177.0]
9  --> 78 | cost [297.0]
11 --> 61 | cost [243.0]
13 --> 97 | cost [270.0]
14 --> 85 | cost [123.0]
16 --> 45 | cost [306.0]
17 --> 38 | cost [222.0]
18 -->  1 | cost [264.0]
20 --> 78 | cost [117.0]
22 -->  5 | cost [279.0]
23 --> 84 | cost [546.0]
24 --> 42 | cost [204.0]
25 --> 42 | cost [327.0]
26 --> 78 | cost [204.0]
30 --> 80 | cost [252.0]
35 --> 29 | cost [174.0]
36 --> 61 | cost [669.0]
39 --> 96 | cost [120.0]
41 --> 34 | cost [291.0]
43 --> 42 | cost [198.0]
46 --> 50 | cost [15.0]
47 --> 99 | cost [276.0]
48 --> 80 | cost [231.0]
49 --> 21 | cost [105.0]
52 --> 45 | cost [378.0]
56 --> 50 | cost [84.0]
57 --> 53 | cost [573.0]
58 --> 88 | cost [345.0]
59 --> 77 | cost [144.0]
60 -->  1 | cost [66.0]
62 -->  1 | cost [282.0]
64 --> 81 | cost [726.0]
67 --> 97 | cost [96.0]
68 --> 51 | cost [327.0]
69 -->  8 | cost [183.0]
70 --> 38 | cost [261.0]
71 -->  8 | cost [378.0]
72 --> 38 | cost [201.0]
74 --> 78 | cost [162.0]
75 --> 21 | cost [75.0]
76 --> 66 | cost [204.0]
79 --> 10 | cost [354.0]
83 --> 51 | cost [102.0]
87 --> 15 | cost [360.0]
89 --> 84 | cost [663.0]
90 --> 51 | cost [126.0]
91 --> 65 | cost [360.0]
92 --> 27 | cost [111.0]
93 --> 77 | cost [132.0]
95 --> 77 | cost [156.0]
100 --> 44 | cost [219.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1