------------------------------------------------------------
                           α=7.0 —— d198 —— 198 nodes       
------------------------------------------------------------

——————— Sun, 14 Jan 2024 13:34:48 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 4 hubs —— 1—2—3—199
total time           50.55                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             61209<=61209         subtour              240.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       2484                 n lazycuts edges     3.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—2—3—199

RING
1  ---  2 | cost [7973.0]
2  ---  3 | cost [532.0]
3  --- 199 | cost [8239.0]
10 --- 11 | cost [175.0]
10 --- 12 | cost [357.0]
11 --- 12 | cost [175.0]
15 --- 16 | cost [714.0]
15 --- 17 | cost [735.0]
16 --- 17 | cost [175.0]
24 --- 25 | cost [252.0]
24 --- 26 | cost [357.0]
25 --- 26 | cost [252.0]
29 --- 30 | cost [252.0]
29 --- 32 | cost [357.0]
30 --- 32 | cost [252.0]
42 --- 43 | cost [175.0]
42 --- 56 | cost [399.0]
43 --- 56 | cost [252.0]
46 --- 52 | cost [252.0]
46 --- 53 | cost [252.0]
52 --- 53 | cost [357.0]
64 --- 77 | cost [252.0]
64 --- 78 | cost [175.0]
67 --- 70 | cost [161.0]
67 --- 73 | cost [175.0]
70 --- 73 | cost [161.0]
71 --- 85 | cost [252.0]
71 --- 86 | cost [357.0]
77 --- 78 | cost [175.0]
79 --- 91 | cost [252.0]
79 --- 92 | cost [175.0]
82 --- 83 | cost [175.0]
82 --- 88 | cost [252.0]
83 --- 88 | cost [175.0]
85 --- 86 | cost [252.0]
91 --- 92 | cost [175.0]
94 --- 95 | cost [175.0]
94 --- 101 | cost [175.0]
95 --- 101 | cost [252.0]
106 --- 112 | cost [175.0]
106 --- 113 | cost [252.0]
108 --- 109 | cost [252.0]
108 --- 110 | cost [399.0]
109 --- 110 | cost [175.0]
112 --- 113 | cost [175.0]
115 --- 116 | cost [175.0]
115 --- 117 | cost [357.0]
116 --- 117 | cost [175.0]
118 --- 119 | cost [175.0]
118 --- 120 | cost [357.0]
119 --- 120 | cost [175.0]
127 --- 128 | cost [420.0]
127 --- 170 | cost [175.0]
128 --- 170 | cost [455.0]
131 --- 132 | cost [175.0]
131 --- 133 | cost [252.0]
132 --- 133 | cost [175.0]
143 --- 145 | cost [252.0]
143 --- 146 | cost [175.0]
145 --- 146 | cost [175.0]
149 --- 152 | cost [175.0]
149 --- 153 | cost [252.0]
152 --- 153 | cost [175.0]
155 --- 156 | cost [175.0]
155 --- 157 | cost [357.0]
156 --- 157 | cost [175.0]
164 --- 165 | cost [532.0]
164 --- 166 | cost [714.0]
165 --- 166 | cost [175.0]
177 --- 181 | cost [252.0]
177 --- 183 | cost [399.0]
178 --- 180 | cost [175.0]
178 --- 184 | cost [357.0]
180 --- 184 | cost [175.0]
181 --- 183 | cost [175.0]
186 --- 187 | cost [532.0]
186 --- 192 | cost [756.0]
187 --- 192 | cost [532.0]
188 --- 189 | cost [532.0]
188 --- 191 | cost [532.0]
189 --- 190 | cost [532.0]
190 --- 191 | cost [532.0]
195 --- 196 | cost [532.0]
195 --- 198 | cost [532.0]
196 --- 197 | cost [532.0]
197 --- 198 | cost [532.0]

STAR
4  -->  3 | cost [228.0]
5  -->  3 | cost [276.0]
6  -->  3 | cost [153.0]
7  -->  2 | cost [153.0]
8  --> 10 | cost [228.0]
9  --> 10 | cost [75.0]
13 --> 12 | cost [75.0]
14 --> 15 | cost [108.0]
18 --> 17 | cost [456.0]
19 --> 24 | cost [411.0]
20 --> 24 | cost [390.0]
21 --> 24 | cost [108.0]
22 --> 24 | cost [171.0]
23 --> 29 | cost [240.0]
27 --> 26 | cost [75.0]
28 --> 30 | cost [108.0]
31 --> 32 | cost [75.0]
33 --> 30 | cost [108.0]
34 --> 30 | cost [171.0]
35 --> 26 | cost [240.0]
36 --> 32 | cost [108.0]
37 --> 32 | cost [75.0]
38 --> 32 | cost [171.0]
39 --> 52 | cost [171.0]
40 --> 15 | cost [390.0]
41 --> 42 | cost [381.0]
44 --> 56 | cost [108.0]
45 --> 53 | cost [171.0]
47 --> 52 | cost [108.0]
48 --> 64 | cost [240.0]
49 --> 64 | cost [216.0]
50 --> 64 | cost [153.0]
51 --> 52 | cost [153.0]
54 --> 53 | cost [153.0]
55 --> 56 | cost [75.0]
57 --> 42 | cost [108.0]
58 --> 71 | cost [153.0]
59 --> 56 | cost [75.0]
60 --> 67 | cost [75.0]
61 --> 53 | cost [171.0]
62 --> 53 | cost [75.0]
63 --> 79 | cost [228.0]
65 --> 52 | cost [153.0]
66 --> 83 | cost [153.0]
68 --> 67 | cost [75.0]
69 --> 71 | cost [75.0]
72 --> 73 | cost [75.0]
74 --> 83 | cost [75.0]
75 --> 82 | cost [108.0]
76 --> 77 | cost [75.0]
80 --> 91 | cost [75.0]
81 --> 77 | cost [171.0]
84 --> 73 | cost [75.0]
87 --> 73 | cost [153.0]
89 --> 82 | cost [108.0]
90 --> 82 | cost [171.0]
93 --> 94 | cost [75.0]
96 --> 95 | cost [153.0]
97 --> 88 | cost [108.0]
98 --> 88 | cost [75.0]
99 --> 73 | cost [228.0]
100 --> 86 | cost [108.0]
102 --> 101 | cost [75.0]
103 --> 91 | cost [228.0]
104 --> 92 | cost [228.0]
105 --> 113 | cost [171.0]
107 --> 106 | cost [75.0]
111 --> 110 | cost [75.0]
114 --> 113 | cost [75.0]
121 --> 116 | cost [120.0]
122 --> 115 | cost [120.0]
123 --> 118 | cost [231.0]
124 --> 120 | cost [324.0]
125 --> 131 | cost [171.0]
126 --> 131 | cost [156.0]
129 --> 127 | cost [153.0]
130 --> 133 | cost [75.0]
134 --> 132 | cost [75.0]
135 --> 133 | cost [75.0]
136 --> 133 | cost [108.0]
137 --> 145 | cost [318.0]
138 --> 132 | cost [327.0]
139 --> 157 | cost [420.0]
140 --> 143 | cost [108.0]
141 --> 143 | cost [75.0]
142 --> 143 | cost [75.0]
144 --> 145 | cost [108.0]
147 --> 146 | cost [75.0]
148 --> 153 | cost [75.0]
150 --> 145 | cost [108.0]
151 --> 145 | cost [240.0]
154 --> 155 | cost [75.0]
158 --> 157 | cost [75.0]
159 --> 157 | cost [228.0]
160 --> 153 | cost [153.0]
161 --> 153 | cost [75.0]
162 --> 152 | cost [75.0]
163 --> 164 | cost [153.0]
167 --> 108 | cost [444.0]
168 --> 108 | cost [720.0]
169 --> 131 | cost [240.0]
171 --> 128 | cost [342.0]
172 --> 165 | cost [429.0]
173 --> 177 | cost [471.0]
174 --> 177 | cost [417.0]
175 --> 177 | cost [186.0]
176 --> 177 | cost [291.0]
179 --> 178 | cost [153.0]
182 --> 183 | cost [285.0]
185 --> 184 | cost [153.0]
193 --> 186 | cost [228.0]
194 --> 178 | cost [171.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 14 Jan 2024 14:35:35 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 26 hubs —— 1-177-195-176-164-152-142-120-119-109-113-91-94-96-78-64-48-51-36-28-23-14-44-68-11-199-1
total time           3613.32 (TL 3600)    gap                  0.518                
blossom time         0                    nb blossom           0.0                  
LB <= UB             61904<=128442        Master/SP costs      128442/0             
Master time          3613.32              SP time              0.0                  
subtour              24350.0              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       10389                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—177—195—176—164—152—142—120—119—109—113—91—94—96—78—64—48—51—36—28—23—14—44—68—11—199

RING
1  --- 177 | cost [27293.0]
11 --- 68 | cost [2317.0]
11 --- 199 | cost [11704.0]
14 --- 23 | cost [1085.0]
14 --- 44 | cost [1260.0]
23 --- 28 | cost [560.0]
28 --- 36 | cost [560.0]
36 --- 51 | cost [889.0]
44 --- 68 | cost [560.0]
48 --- 51 | cost [560.0]
48 --- 64 | cost [560.0]
64 --- 78 | cost [175.0]
78 --- 96 | cost [889.0]
91 --- 94 | cost [560.0]
91 --- 113 | cost [1141.0]
94 --- 96 | cost [532.0]
109 --- 113 | cost [889.0]
109 --- 119 | cost [735.0]
119 --- 120 | cost [175.0]
120 --- 142 | cost [2030.0]
142 --- 152 | cost [560.0]
152 --- 164 | cost [1260.0]
164 --- 176 | cost [11347.0]
176 --- 195 | cost [2100.0]
177 --- 195 | cost [1638.0]

STAR
2  --> 11 | cost [1677.0]
3  --> 11 | cost [1509.0]
4  --> 11 | cost [1356.0]
5  --> 11 | cost [1239.0]
6  --> 11 | cost [1404.0]
7  --> 11 | cost [1587.0]
8  --> 11 | cost [306.0]
9  --> 11 | cost [153.0]
10 --> 11 | cost [75.0]
12 --> 11 | cost [75.0]
13 --> 11 | cost [153.0]
15 --> 14 | cost [108.0]
16 --> 14 | cost [390.0]
17 --> 14 | cost [381.0]
18 --> 23 | cost [306.0]
19 --> 23 | cost [342.0]
20 --> 23 | cost [489.0]
21 --> 28 | cost [381.0]
22 --> 23 | cost [153.0]
24 --> 28 | cost [276.0]
25 --> 28 | cost [315.0]
26 --> 28 | cost [228.0]
27 --> 28 | cost [153.0]
29 --> 28 | cost [153.0]
30 --> 28 | cost [108.0]
31 --> 36 | cost [171.0]
32 --> 36 | cost [108.0]
33 --> 36 | cost [108.0]
34 --> 28 | cost [171.0]
35 --> 48 | cost [216.0]
37 --> 36 | cost [75.0]
38 --> 44 | cost [216.0]
39 --> 51 | cost [171.0]
40 --> 14 | cost [456.0]
41 --> 14 | cost [549.0]
42 --> 44 | cost [228.0]
43 --> 44 | cost [153.0]
45 --> 36 | cost [216.0]
46 --> 36 | cost [171.0]
47 --> 51 | cost [108.0]
49 --> 48 | cost [108.0]
50 --> 48 | cost [108.0]
52 --> 51 | cost [153.0]
53 --> 36 | cost [228.0]
54 --> 44 | cost [240.0]
55 --> 44 | cost [75.0]
56 --> 44 | cost [108.0]
57 --> 68 | cost [276.0]
58 --> 68 | cost [240.0]
59 --> 68 | cost [75.0]
60 --> 23 | cost [852.0]
61 --> 44 | cost [276.0]
62 --> 36 | cost [306.0]
63 --> 48 | cost [216.0]
65 --> 51 | cost [216.0]
66 --> 68 | cost [306.0]
67 --> 68 | cost [75.0]
69 --> 68 | cost [228.0]
70 --> 68 | cost [138.0]
71 --> 68 | cost [240.0]
72 --> 68 | cost [75.0]
73 --> 68 | cost [108.0]
74 --> 68 | cost [315.0]
75 --> 96 | cost [276.0]
76 --> 78 | cost [153.0]
77 --> 78 | cost [75.0]
79 --> 91 | cost [108.0]
80 --> 91 | cost [75.0]
81 --> 96 | cost [171.0]
82 --> 96 | cost [276.0]
83 --> 68 | cost [342.0]
84 --> 68 | cost [171.0]
85 --> 68 | cost [216.0]
86 --> 68 | cost [324.0]
87 --> 68 | cost [240.0]
88 --> 96 | cost [315.0]
89 --> 96 | cost [171.0]
90 --> 96 | cost [108.0]
92 --> 91 | cost [75.0]
93 --> 94 | cost [75.0]
95 --> 94 | cost [75.0]
97 --> 96 | cost [228.0]
98 --> 96 | cost [306.0]
99 --> 91 | cost [993.0]
100 --> 68 | cost [342.0]
101 --> 94 | cost [75.0]
102 --> 94 | cost [108.0]
103 --> 91 | cost [228.0]
104 --> 91 | cost [240.0]
105 --> 113 | cost [171.0]
106 --> 113 | cost [108.0]
107 --> 113 | cost [171.0]
108 --> 109 | cost [108.0]
110 --> 109 | cost [75.0]
111 --> 109 | cost [153.0]
112 --> 113 | cost [75.0]
114 --> 113 | cost [75.0]
115 --> 113 | cost [315.0]
116 --> 113 | cost [306.0]
117 --> 119 | cost [228.0]
118 --> 119 | cost [75.0]
121 --> 119 | cost [291.0]
122 --> 113 | cost [435.0]
123 --> 119 | cost [231.0]
124 --> 120 | cost [324.0]
125 --> 142 | cost [465.0]
126 --> 142 | cost [459.0]
127 --> 142 | cost [510.0]
128 --> 142 | cost [612.0]
129 --> 142 | cost [381.0]
130 --> 142 | cost [315.0]
131 --> 142 | cost [306.0]
132 --> 142 | cost [228.0]
133 --> 142 | cost [240.0]
134 --> 142 | cost [153.0]
135 --> 142 | cost [171.0]
136 --> 142 | cost [216.0]
137 --> 142 | cost [423.0]
138 --> 142 | cost [327.0]
139 --> 119 | cost [573.0]
140 --> 142 | cost [75.0]
141 --> 142 | cost [108.0]
143 --> 142 | cost [75.0]
144 --> 142 | cost [228.0]
145 --> 152 | cost [171.0]
146 --> 142 | cost [108.0]
147 --> 142 | cost [75.0]
148 --> 152 | cost [108.0]
149 --> 152 | cost [75.0]
150 --> 152 | cost [171.0]
151 --> 164 | cost [276.0]
153 --> 152 | cost [75.0]
154 --> 142 | cost [963.0]
155 --> 91 | cost [1665.0]
156 --> 142 | cost [822.0]
157 --> 142 | cost [750.0]
158 --> 142 | cost [681.0]
159 --> 152 | cost [540.0]
160 --> 152 | cost [222.0]
161 --> 152 | cost [108.0]
162 --> 152 | cost [75.0]
163 --> 164 | cost [153.0]
165 --> 164 | cost [228.0]
166 --> 164 | cost [306.0]
167 --> 109 | cost [549.0]
168 --> 109 | cost [825.0]
169 --> 120 | cost [483.0]
170 --> 142 | cost [579.0]
171 --> 164 | cost [774.0]
172 --> 164 | cost [441.0]
173 --> 176 | cost [228.0]
174 --> 176 | cost [318.0]
175 --> 177 | cost [186.0]
178 --> 177 | cost [228.0]
179 --> 195 | cost [351.0]
180 --> 177 | cost [240.0]
181 --> 177 | cost [108.0]
182 --> 176 | cost [366.0]
183 --> 177 | cost [171.0]
184 --> 177 | cost [276.0]
185 --> 177 | cost [411.0]
186 --> 195 | cost [708.0]
187 --> 195 | cost [672.0]
188 --> 177 | cost [486.0]
189 --> 177 | cost [534.0]
190 --> 177 | cost [747.0]
191 --> 177 | cost [714.0]
192 --> 195 | cost [900.0]
193 --> 195 | cost [930.0]
194 --> 195 | cost [318.0]
196 --> 195 | cost [228.0]
197 --> 195 | cost [324.0]
198 --> 195 | cost [228.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1