------------------------------------------------------------
                         α=7.0 —— rat195 —— 195 nodes       
------------------------------------------------------------

——————— Wed, 24 Jan 2024 01:44:28 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 91 hubs —— 1—15—16—17—30—44—32—20—31—29—40—41—42—57—58—71—70—69—92—93—105—79—66—67—80—81—100—127—126—146—178—176—186—170—185—171—159—177—169—150—189—164—151—131—147—144—148—191—194—182—195—181—179—143—142—129—130—104—103—117—91—116—102—158—133—120—109—94—95—88—76—75—62—63—49—51—26—38—37—36—22—8—10—13—12—9—6—5—4—3—196
total time           3615.04 (TL 3600)    gap                  0.463                
blossom time         0                    nb blossom           0.0                  
LB <= UB             11756<=21910         subtour              22704.0              
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       9499                 n lazycuts edges     3.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—15—16—17—30—44—32—20—31—29—40—41—42—57—58—71—70—69—92—93—105—79—66—67—80—81—100—127—126—146—178—176—186—170—185—171—159—177—169—150—189—164—151—131—147—144—148—191—194—182—195—181—179—143—142—129—130—104—103—117—91—116—102—158—133—120—109—94—95—88—76—75—62—63—49—51—26—38—37—36—22—8—10—13—12—9—6—5—4—3—196

RING
1  --- 15 | cost [161.0]
3  ---  4 | cost [77.0]
3  --- 196 | cost [140.0]
4  ---  5 | cost [91.0]
5  ---  6 | cost [49.0]
6  ---  9 | cost [231.0]
8  --- 10 | cost [133.0]
8  --- 22 | cost [203.0]
9  --- 12 | cost [210.0]
10 --- 13 | cost [210.0]
12 --- 13 | cost [56.0]
15 --- 16 | cost [77.0]
16 --- 17 | cost [49.0]
17 --- 30 | cost [140.0]
20 --- 31 | cost [168.0]
20 --- 32 | cost [119.0]
22 --- 36 | cost [147.0]
26 --- 38 | cost [112.0]
26 --- 51 | cost [224.0]
29 --- 31 | cost [154.0]
29 --- 40 | cost [224.0]
30 --- 44 | cost [126.0]
32 --- 44 | cost [161.0]
36 --- 37 | cost [42.0]
37 --- 38 | cost [98.0]
40 --- 41 | cost [63.0]
41 --- 42 | cost [84.0]
42 --- 57 | cost [168.0]
49 --- 51 | cost [175.0]
49 --- 63 | cost [140.0]
57 --- 58 | cost [70.0]
58 --- 71 | cost [70.0]
62 --- 63 | cost [63.0]
62 --- 75 | cost [98.0]
66 --- 67 | cost [63.0]
66 --- 79 | cost [91.0]
67 --- 80 | cost [98.0]
69 --- 70 | cost [56.0]
69 --- 92 | cost [371.0]
70 --- 71 | cost [105.0]
75 --- 76 | cost [56.0]
76 --- 88 | cost [119.0]
79 --- 105 | cost [259.0]
80 --- 81 | cost [91.0]
81 --- 100 | cost [441.0]
88 --- 95 | cost [455.0]
91 --- 116 | cost [259.0]
91 --- 117 | cost [245.0]
92 --- 93 | cost [70.0]
93 --- 105 | cost [147.0]
94 --- 95 | cost [77.0]
94 --- 109 | cost [182.0]
100 --- 127 | cost [224.0]
102 --- 116 | cost [147.0]
102 --- 158 | cost [910.0]
103 --- 104 | cost [77.0]
103 --- 117 | cost [126.0]
104 --- 130 | cost [329.0]
109 --- 120 | cost [224.0]
120 --- 133 | cost [98.0]
126 --- 127 | cost [63.0]
126 --- 146 | cost [525.0]
129 --- 130 | cost [84.0]
129 --- 142 | cost [91.0]
131 --- 147 | cost [238.0]
131 --- 151 | cost [525.0]
133 --- 158 | cost [266.0]
142 --- 143 | cost [84.0]
143 --- 179 | cost [490.0]
144 --- 147 | cost [196.0]
144 --- 148 | cost [259.0]
146 --- 178 | cost [476.0]
148 --- 191 | cost [553.0]
150 --- 169 | cost [441.0]
150 --- 189 | cost [413.0]
151 --- 164 | cost [91.0]
159 --- 171 | cost [147.0]
159 --- 177 | cost [343.0]
164 --- 189 | cost [287.0]
169 --- 177 | cost [364.0]
170 --- 185 | cost [196.0]
170 --- 186 | cost [231.0]
171 --- 185 | cost [105.0]
176 --- 178 | cost [140.0]
176 --- 186 | cost [266.0]
179 --- 181 | cost [147.0]
181 --- 195 | cost [154.0]
182 --- 194 | cost [175.0]
182 --- 195 | cost [119.0]
191 --- 194 | cost [189.0]

STAR
2  -->  3 | cost [21.0]
7  -->  8 | cost [39.0]
11 --> 12 | cost [27.0]
14 --> 15 | cost [36.0]
18 --> 17 | cost [27.0]
19 --> 20 | cost [39.0]
21 --> 20 | cost [30.0]
23 --> 22 | cost [36.0]
24 --> 12 | cost [48.0]
25 --> 26 | cost [36.0]
27 --> 29 | cost [69.0]
28 --> 29 | cost [36.0]
33 --> 32 | cost [39.0]
34 --> 22 | cost [42.0]
35 --> 37 | cost [48.0]
39 --> 38 | cost [36.0]
43 --> 42 | cost [27.0]
45 --> 44 | cost [24.0]
46 --> 44 | cost [57.0]
47 --> 49 | cost [63.0]
48 --> 49 | cost [39.0]
50 --> 51 | cost [30.0]
52 --> 51 | cost [27.0]
53 --> 40 | cost [27.0]
54 --> 67 | cost [48.0]
55 --> 67 | cost [60.0]
56 --> 57 | cost [30.0]
59 --> 58 | cost [39.0]
60 --> 62 | cost [51.0]
61 --> 62 | cost [39.0]
64 --> 63 | cost [36.0]
65 --> 63 | cost [60.0]
68 --> 67 | cost [27.0]
72 --> 71 | cost [33.0]
73 --> 71 | cost [54.0]
74 --> 75 | cost [36.0]
77 --> 76 | cost [39.0]
78 --> 76 | cost [66.0]
82 --> 81 | cost [33.0]
83 --> 81 | cost [51.0]
84 --> 70 | cost [69.0]
85 --> 71 | cost [60.0]
86 --> 88 | cost [57.0]
87 --> 88 | cost [45.0]
89 --> 88 | cost [21.0]
90 --> 91 | cost [33.0]
96 --> 109 | cost [45.0]
97 --> 95 | cost [63.0]
98 --> 109 | cost [72.0]
99 --> 100 | cost [36.0]
101 --> 100 | cost [18.0]
106 --> 105 | cost [45.0]
107 --> 94 | cost [36.0]
108 --> 109 | cost [33.0]
110 --> 109 | cost [30.0]
111 --> 109 | cost [60.0]
112 --> 126 | cost [57.0]
113 --> 127 | cost [39.0]
114 --> 126 | cost [51.0]
115 --> 100 | cost [72.0]
118 --> 131 | cost [51.0]
119 --> 120 | cost [33.0]
121 --> 120 | cost [45.0]
122 --> 133 | cost [84.0]
123 --> 120 | cost [87.0]
124 --> 126 | cost [57.0]
125 --> 126 | cost [27.0]
128 --> 129 | cost [21.0]
132 --> 133 | cost [30.0]
134 --> 133 | cost [30.0]
135 --> 133 | cost [57.0]
136 --> 148 | cost [57.0]
137 --> 150 | cost [48.0]
138 --> 150 | cost [54.0]
139 --> 150 | cost [72.0]
140 --> 142 | cost [63.0]
141 --> 142 | cost [42.0]
145 --> 144 | cost [21.0]
149 --> 148 | cost [36.0]
152 --> 151 | cost [39.0]
153 --> 151 | cost [60.0]
154 --> 142 | cost [72.0]
155 --> 143 | cost [57.0]
156 --> 143 | cost [63.0]
157 --> 158 | cost [27.0]
160 --> 159 | cost [33.0]
161 --> 148 | cost [63.0]
162 --> 164 | cost [48.0]
163 --> 164 | cost [24.0]
165 --> 164 | cost [42.0]
166 --> 178 | cost [60.0]
167 --> 179 | cost [51.0]
168 --> 169 | cost [42.0]
172 --> 171 | cost [33.0]
173 --> 159 | cost [48.0]
174 --> 186 | cost [63.0]
175 --> 176 | cost [39.0]
180 --> 181 | cost [36.0]
183 --> 185 | cost [48.0]
184 --> 185 | cost [27.0]
187 --> 186 | cost [33.0]
188 --> 189 | cost [48.0]
190 --> 189 | cost [18.0]
192 --> 191 | cost [33.0]
193 --> 194 | cost [30.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 24 Jan 2024 02:45:16 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 31 hubs —— 1-16-41-31-32-18-9-24-51-49-78-89-90-103-99-107-136-146-160-157-183-187-178-165-153-143-169-195-194-193-196-1
total time           3615.35 (TL 3600)    gap                  0.38                 
blossom time         0                    nb blossom           0.0                  
LB <= UB             11647<=18793         Master/SP costs      18793/0              
Master time          3615.35              SP time              0.0                  
subtour              22192.0              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       10477                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—16—41—31—32—18—9—24—51—49—78—89—90—103—99—107—136—146—160—157—183—187—178—165—153—143—169—195—194—193—196

RING
1  --- 16 | cost [224.0]
9  --- 18 | cost [364.0]
9  --- 24 | cost [182.0]
16 --- 41 | cost [294.0]
18 --- 32 | cost [119.0]
24 --- 51 | cost [294.0]
31 --- 32 | cost [49.0]
31 --- 41 | cost [287.0]
49 --- 51 | cost [175.0]
49 --- 78 | cost [329.0]
78 --- 89 | cost [203.0]
89 --- 90 | cost [98.0]
90 --- 103 | cost [161.0]
99 --- 103 | cost [294.0]
99 --- 107 | cost [364.0]
107 --- 136 | cost [378.0]
136 --- 146 | cost [252.0]
143 --- 153 | cost [287.0]
143 --- 169 | cost [308.0]
146 --- 160 | cost [91.0]
153 --- 165 | cost [112.0]
157 --- 160 | cost [189.0]
157 --- 183 | cost [266.0]
165 --- 178 | cost [105.0]
169 --- 195 | cost [259.0]
178 --- 187 | cost [350.0]
183 --- 187 | cost [252.0]
193 --- 194 | cost [70.0]
193 --- 196 | cost [2079.0]
194 --- 195 | cost [98.0]

STAR
2  -->  1 | cost [42.0]
3  -->  1 | cost [60.0]
4  --> 18 | cost [72.0]
5  --> 18 | cost [72.0]
6  --> 18 | cost [75.0]
7  -->  9 | cost [66.0]
8  -->  9 | cost [33.0]
10 -->  9 | cost [24.0]
11 --> 24 | cost [48.0]
12 --> 24 | cost [48.0]
13 --> 24 | cost [63.0]
14 -->  1 | cost [60.0]
15 --> 16 | cost [33.0]
17 --> 16 | cost [21.0]
19 --> 18 | cost [42.0]
20 --> 32 | cost [51.0]
21 --> 32 | cost [72.0]
22 -->  9 | cost [84.0]
23 --> 24 | cost [27.0]
25 --> 24 | cost [33.0]
26 --> 24 | cost [69.0]
27 --> 16 | cost [81.0]
28 --> 16 | cost [48.0]
29 --> 16 | cost [48.0]
30 --> 31 | cost [39.0]
33 --> 32 | cost [39.0]
34 --> 32 | cost [63.0]
35 --> 49 | cost [78.0]
36 --> 51 | cost [72.0]
37 --> 51 | cost [54.0]
38 --> 51 | cost [54.0]
39 --> 51 | cost [57.0]
40 --> 41 | cost [27.0]
42 --> 41 | cost [36.0]
43 --> 41 | cost [63.0]
44 --> 31 | cost [54.0]
45 --> 31 | cost [69.0]
46 --> 32 | cost [75.0]
47 --> 49 | cost [63.0]
48 --> 49 | cost [39.0]
50 --> 51 | cost [30.0]
52 --> 51 | cost [27.0]
53 --> 41 | cost [39.0]
54 --> 41 | cost [60.0]
55 --> 41 | cost [63.0]
56 --> 41 | cost [72.0]
57 --> 41 | cost [102.0]
58 --> 41 | cost [129.0]
59 --> 49 | cost [99.0]
60 --> 49 | cost [75.0]
61 --> 49 | cost [57.0]
62 --> 49 | cost [63.0]
63 --> 49 | cost [60.0]
64 --> 78 | cost [54.0]
65 --> 78 | cost [48.0]
66 --> 41 | cost [120.0]
67 --> 41 | cost [108.0]
68 --> 41 | cost [114.0]
69 --> 41 | cost [117.0]
70 --> 41 | cost [138.0]
71 --> 49 | cost [147.0]
72 --> 99 | cost [123.0]
73 --> 89 | cost [99.0]
74 --> 89 | cost [75.0]
75 --> 89 | cost [57.0]
76 --> 89 | cost [39.0]
77 --> 78 | cost [33.0]
79 --> 107 | cost [126.0]
80 --> 107 | cost [123.0]
81 --> 107 | cost [93.0]
82 --> 107 | cost [120.0]
83 --> 99 | cost [111.0]
84 --> 99 | cost [84.0]
85 --> 99 | cost [90.0]
86 --> 99 | cost [72.0]
87 --> 99 | cost [54.0]
88 --> 89 | cost [21.0]
91 --> 90 | cost [33.0]
92 --> 107 | cost [66.0]
93 --> 107 | cost [60.0]
94 --> 107 | cost [36.0]
95 --> 107 | cost [51.0]
96 --> 107 | cost [69.0]
97 --> 99 | cost [63.0]
98 --> 99 | cost [39.0]
100 --> 99 | cost [36.0]
101 --> 99 | cost [57.0]
102 --> 103 | cost [39.0]
104 --> 103 | cost [33.0]
105 --> 107 | cost [66.0]
106 --> 107 | cost [33.0]
108 --> 107 | cost [42.0]
109 --> 107 | cost [57.0]
110 --> 107 | cost [87.0]
111 --> 99 | cost [60.0]
112 --> 99 | cost [60.0]
113 --> 99 | cost [75.0]
114 --> 103 | cost [90.0]
115 --> 103 | cost [57.0]
116 --> 103 | cost [48.0]
117 --> 103 | cost [54.0]
118 --> 107 | cost [99.0]
119 --> 107 | cost [75.0]
120 --> 107 | cost [90.0]
121 --> 107 | cost [72.0]
122 --> 136 | cost [72.0]
123 --> 136 | cost [51.0]
124 --> 136 | cost [69.0]
125 --> 136 | cost [93.0]
126 --> 99 | cost [114.0]
127 --> 99 | cost [114.0]
128 --> 143 | cost [81.0]
129 --> 143 | cost [63.0]
130 --> 143 | cost [42.0]
131 --> 146 | cost [105.0]
132 --> 146 | cost [75.0]
133 --> 146 | cost [78.0]
134 --> 136 | cost [60.0]
135 --> 136 | cost [33.0]
137 --> 136 | cost [33.0]
138 --> 136 | cost [63.0]
139 --> 153 | cost [75.0]
140 --> 153 | cost [78.0]
141 --> 153 | cost [66.0]
142 --> 143 | cost [36.0]
144 --> 157 | cost [60.0]
145 --> 146 | cost [45.0]
147 --> 146 | cost [39.0]
148 --> 136 | cost [57.0]
149 --> 136 | cost [42.0]
150 --> 136 | cost [69.0]
151 --> 165 | cost [57.0]
152 --> 153 | cost [27.0]
154 --> 153 | cost [36.0]
155 --> 143 | cost [57.0]
156 --> 143 | cost [63.0]
158 --> 157 | cost [27.0]
159 --> 160 | cost [33.0]
161 --> 160 | cost [42.0]
162 --> 160 | cost [78.0]
163 --> 165 | cost [66.0]
164 --> 165 | cost [42.0]
166 --> 165 | cost [24.0]
167 --> 165 | cost [54.0]
168 --> 169 | cost [42.0]
170 --> 157 | cost [51.0]
171 --> 183 | cost [48.0]
172 --> 160 | cost [69.0]
173 --> 160 | cost [60.0]
174 --> 187 | cost [63.0]
175 --> 187 | cost [75.0]
176 --> 178 | cost [60.0]
177 --> 178 | cost [39.0]
179 --> 178 | cost [33.0]
180 --> 178 | cost [57.0]
181 --> 169 | cost [60.0]
182 --> 195 | cost [51.0]
184 --> 183 | cost [36.0]
185 --> 183 | cost [48.0]
186 --> 187 | cost [33.0]
188 --> 187 | cost [36.0]
189 --> 187 | cost [72.0]
190 --> 178 | cost [78.0]
191 --> 193 | cost [51.0]
192 --> 193 | cost [36.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1