------------------------------------------------------------
                        α=5.0 —— kroA200 —— 200 nodes       
------------------------------------------------------------

——————— Sun, 14 Jan 2024 16:47:38 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—53—201
total time           617.05               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             127820<=127820       subtour              2904.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       4045                 n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—53—201

RING
1  --- 53 | cost [160.0]
2  --- 35 | cost [380.0]
2  --- 181 | cost [555.0]
3  --- 59 | cost [650.0]
3  --- 73 | cost [90.0]
4  --- 101 | cost [385.0]
4  --- 192 | cost [1425.0]
5  --- 86 | cost [1260.0]
5  --- 196 | cost [725.0]
6  --- 107 | cost [665.0]
6  --- 109 | cost [420.0]
8  --- 22 | cost [640.0]
8  --- 183 | cost [725.0]
9  --- 78 | cost [415.0]
9  --- 138 | cost [585.0]
10 --- 92 | cost [340.0]
10 --- 175 | cost [50.0]
11 --- 52 | cost [135.0]
11 --- 84 | cost [475.0]
12 --- 40 | cost [1120.0]
12 --- 147 | cost [1055.0]
13 --- 79 | cost [650.0]
13 --- 177 | cost [650.0]
15 --- 123 | cost [185.0]
15 --- 198 | cost [725.0]
16 --- 63 | cost [605.0]
16 --- 179 | cost [800.0]
20 --- 64 | cost [125.0]
20 --- 162 | cost [705.0]
21 --- 140 | cost [290.0]
21 --- 154 | cost [395.0]
22 --- 183 | cost [665.0]
23 --- 144 | cost [1050.0]
23 --- 173 | cost [575.0]
24 --- 32 | cost [760.0]
24 --- 159 | cost [940.0]
25 --- 90 | cost [480.0]
25 --- 143 | cost [475.0]
26 --- 136 | cost [735.0]
26 --- 199 | cost [790.0]
28 --- 88 | cost [1015.0]
28 --- 148 | cost [975.0]
29 --- 110 | cost [365.0]
29 --- 184 | cost [410.0]
30 --- 68 | cost [695.0]
30 --- 89 | cost [1880.0]
31 --- 47 | cost [435.0]
31 --- 67 | cost [650.0]
32 --- 136 | cost [900.0]
33 --- 100 | cost [245.0]
33 --- 156 | cost [315.0]
35 --- 169 | cost [715.0]
36 --- 57 | cost [210.0]
36 --- 74 | cost [515.0]
37 --- 124 | cost [1120.0]
37 --- 184 | cost [685.0]
38 --- 39 | cost [575.0]
38 --- 71 | cost [430.0]
39 --- 130 | cost [745.0]
40 --- 147 | cost [805.0]
41 --- 89 | cost [1065.0]
41 --- 167 | cost [1505.0]
42 --- 127 | cost [755.0]
42 --- 186 | cost [455.0]
43 --- 105 | cost [285.0]
43 --- 137 | cost [385.0]
44 --- 153 | cost [865.0]
44 --- 188 | cost [295.0]
45 --- 81 | cost [395.0]
45 --- 197 | cost [275.0]
46 --- 121 | cost [750.0]
46 --- 172 | cost [150.0]
47 --- 67 | cost [835.0]
50 --- 139 | cost [1010.0]
50 --- 185 | cost [930.0]
51 --- 63 | cost [610.0]
51 --- 194 | cost [505.0]
52 --- 84 | cost [590.0]
53 --- 201 | cost [160.0]
56 --- 71 | cost [985.0]
56 --- 152 | cost [220.0]
57 --- 74 | cost [310.0]
58 --- 141 | cost [535.0]
58 --- 171 | cost [350.0]
59 --- 73 | cost [695.0]
62 --- 83 | cost [220.0]
62 --- 185 | cost [945.0]
64 --- 162 | cost [590.0]
66 --- 153 | cost [100.0]
66 --- 179 | cost [1105.0]
68 --- 169 | cost [475.0]
69 --- 142 | cost [455.0]
69 --- 189 | cost [870.0]
70 --- 76 | cost [580.0]
70 --- 144 | cost [670.0]
72 --- 83 | cost [950.0]
72 --- 130 | cost [680.0]
76 --- 94 | cost [1270.0]
77 --- 80 | cost [970.0]
77 --- 158 | cost [405.0]
78 --- 199 | cost [1045.0]
79 --- 177 | cost [825.0]
80 --- 161 | cost [845.0]
81 --- 197 | cost [615.0]
85 --- 132 | cost [605.0]
85 --- 145 | cost [505.0]
86 --- 139 | cost [840.0]
88 --- 148 | cost [435.0]
90 --- 143 | cost [380.0]
91 --- 94 | cost [645.0]
91 --- 150 | cost [605.0]
92 --- 175 | cost [385.0]
93 --- 106 | cost [435.0]
93 --- 149 | cost [620.0]
96 --- 165 | cost [615.0]
96 --- 166 | cost [620.0]
100 --- 156 | cost [180.0]
101 --- 192 | cost [1515.0]
103 --- 114 | cost [1105.0]
103 --- 146 | cost [695.0]
105 --- 137 | cost [345.0]
106 --- 149 | cost [235.0]
107 --- 109 | cost [250.0]
110 --- 172 | cost [1350.0]
111 --- 115 | cost [565.0]
111 --- 117 | cost [575.0]
113 --- 133 | cost [505.0]
113 --- 176 | cost [515.0]
114 --- 129 | cost [1505.0]
115 --- 117 | cost [65.0]
116 --- 122 | cost [350.0]
116 --- 188 | cost [290.0]
121 --- 174 | cost [330.0]
122 --- 194 | cost [670.0]
123 --- 198 | cost [540.0]
124 --- 138 | cost [480.0]
125 --- 161 | cost [825.0]
125 --- 181 | cost [255.0]
127 --- 186 | cost [405.0]
128 --- 167 | cost [1505.0]
128 --- 193 | cost [240.0]
129 --- 146 | cost [740.0]
131 --- 142 | cost [1145.0]
131 --- 189 | cost [940.0]
132 --- 145 | cost [1110.0]
133 --- 176 | cost [460.0]
140 --- 154 | cost [520.0]
141 --- 171 | cost [415.0]
150 --- 173 | cost [900.0]
152 --- 178 | cost [200.0]
158 --- 193 | cost [1555.0]
159 --- 174 | cost [445.0]
165 --- 166 | cost [575.0]
178 --- 196 | cost [340.0]

STAR
7  --> 199 | cost [1070.0]
14 --> 192 | cost [550.0]
17 --> 25 | cost [510.0]
18 --> 110 | cost [200.0]
19 --> 92 | cost [530.0]
27 --> 198 | cost [535.0]
34 --> 90 | cost [450.0]
48 --> 84 | cost [755.0]
49 --> 110 | cost [660.0]
54 -->  6 | cost [545.0]
55 --> 42 | cost [545.0]
60 --> 101 | cost [905.0]
61 --> 136 | cost [315.0]
65 --> 177 | cost [1255.0]
75 --> 183 | cost [745.0]
82 --> 78 | cost [580.0]
87 --> 96 | cost [1410.0]
95 --> 94 | cost [615.0]
97 --> 81 | cost [600.0]
98 --> 114 | cost [270.0]
99 --> 92 | cost [530.0]
102 --> 70 | cost [925.0]
104 --> 165 | cost [735.0]
108 --> 192 | cost [1030.0]
112 --> 127 | cost [680.0]
118 --> 16 | cost [615.0]
119 --> 92 | cost [850.0]
120 --> 47 | cost [610.0]
126 --> 96 | cost [995.0]
134 --> 22 | cost [75.0]
135 --> 42 | cost [320.0]
151 --> 161 | cost [930.0]
155 --> 183 | cost [115.0]
157 --> 107 | cost [465.0]
160 --> 79 | cost [390.0]
163 --> 93 | cost [445.0]
164 --> 140 | cost [400.0]
168 --> 185 | cost [765.0]
170 --> 84 | cost [800.0]
180 --> 131 | cost [435.0]
182 --> 94 | cost [1440.0]
187 -->  6 | cost [605.0]
190 --> 149 | cost [1040.0]
191 --> 198 | cost [495.0]
195 --> 113 | cost [1080.0]
200 --> 171 | cost [605.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 14 Jan 2024 17:48:20 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 42 hubs —— 1-123-145-15-181-120-183-186-67-42-146-103-141-130-71-113-95-72-127-54-47-83-144-169-164-3-14-49-136-138-118-16-153-122-52-45-142-101-198-53-191-201-1
total time           3609.75 (TL 3600)    gap                  0.565                
blossom time         0                    nb blossom           0.0                  
LB <= UB             126765<=291335       Master/SP costs      291335/0             
Master time          3609.75              SP time              0.0                  
subtour              10882.0              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       20607                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—123—145—15—181—120—183—186—67—42—146—103—141—130—71—113—95—72—127—54—47—83—144—169—164—3—14—49—136—138—118—16—153—122—52—45—142—101—198—53—191—201

RING
1  --- 123 | cost [2450.0]
3  --- 14 | cost [4315.0]
3  --- 164 | cost [4185.0]
14 --- 49 | cost [3215.0]
15 --- 145 | cost [1190.0]
15 --- 181 | cost [5635.0]
16 --- 118 | cost [615.0]
16 --- 153 | cost [1630.0]
42 --- 67 | cost [1600.0]
42 --- 146 | cost [4310.0]
45 --- 52 | cost [4025.0]
45 --- 142 | cost [2580.0]
47 --- 54 | cost [1935.0]
47 --- 83 | cost [4265.0]
49 --- 136 | cost [2870.0]
52 --- 122 | cost [2025.0]
53 --- 191 | cost [1920.0]
53 --- 198 | cost [2350.0]
54 --- 127 | cost [2735.0]
67 --- 186 | cost [1470.0]
71 --- 113 | cost [4330.0]
71 --- 130 | cost [700.0]
72 --- 95 | cost [2730.0]
72 --- 127 | cost [5355.0]
83 --- 144 | cost [3990.0]
95 --- 113 | cost [3050.0]
101 --- 142 | cost [3305.0]
101 --- 198 | cost [3915.0]
103 --- 141 | cost [2255.0]
103 --- 146 | cost [695.0]
118 --- 138 | cost [1385.0]
120 --- 181 | cost [3875.0]
120 --- 183 | cost [1955.0]
122 --- 153 | cost [1625.0]
123 --- 145 | cost [1105.0]
130 --- 141 | cost [3970.0]
136 --- 138 | cost [1140.0]
144 --- 169 | cost [2240.0]
164 --- 169 | cost [1485.0]
183 --- 186 | cost [2140.0]
191 --- 201 | cost [1845.0]

STAR
2  --> 54 | cost [2495.0]
4  --> 101 | cost [385.0]
5  --> 71 | cost [1580.0]
6  --> 54 | cost [545.0]
7  --> 136 | cost [2545.0]
8  --> 183 | cost [725.0]
9  --> 138 | cost [585.0]
10 --> 14 | cost [1315.0]
11 --> 52 | cost [135.0]
12 --> 49 | cost [1965.0]
13 --> 67 | cost [1590.0]
17 --> 146 | cost [1210.0]
18 --> 49 | cost [535.0]
19 --> 14 | cost [1725.0]
20 --> 42 | cost [1215.0]
21 --> 164 | cost [570.0]
22 --> 183 | cost [665.0]
23 --> 144 | cost [1050.0]
24 --> 136 | cost [1405.0]
25 --> 103 | cost [1330.0]
26 --> 136 | cost [735.0]
27 --> 191 | cost [505.0]
28 --> 71 | cost [945.0]
29 --> 49 | cost [1030.0]
30 --> 169 | cost [1080.0]
31 --> 47 | cost [435.0]
32 --> 136 | cost [900.0]
33 --> 45 | cost [535.0]
34 --> 103 | cost [1250.0]
35 --> 169 | cost [715.0]
36 --> 14 | cost [1050.0]
37 --> 118 | cost [1250.0]
38 --> 71 | cost [430.0]
39 --> 130 | cost [745.0]
40 --> 191 | cost [1455.0]
41 -->  3 | cost [2070.0]
43 --> 71 | cost [2390.0]
44 --> 122 | cost [855.0]
46 --> 49 | cost [1675.0]
48 --> 52 | cost [1310.0]
50 --> 72 | cost [1285.0]
51 --> 16 | cost [785.0]
55 --> 67 | cost [1080.0]
56 --> 71 | cost [985.0]
57 --> 14 | cost [1125.0]
58 --> 141 | cost [535.0]
59 -->  3 | cost [650.0]
60 --> 101 | cost [905.0]
61 --> 136 | cost [315.0]
62 --> 83 | cost [220.0]
63 --> 16 | cost [605.0]
64 --> 42 | cost [1175.0]
65 --> 67 | cost [1525.0]
66 --> 153 | cost [100.0]
68 --> 169 | cost [475.0]
69 -->  3 | cost [2075.0]
70 --> 144 | cost [670.0]
73 -->  3 | cost [90.0]
74 --> 45 | cost [1235.0]
75 --> 183 | cost [745.0]
76 --> 144 | cost [1155.0]
77 --> 181 | cost [2140.0]
78 --> 138 | cost [935.0]
79 --> 15 | cost [1225.0]
80 --> 181 | cost [1865.0]
81 --> 14 | cost [2360.0]
82 --> 138 | cost [1475.0]
84 --> 52 | cost [590.0]
85 --> 145 | cost [505.0]
86 --> 95 | cost [1625.0]
87 --> 52 | cost [2240.0]
88 --> 71 | cost [1960.0]
89 --> 164 | cost [1835.0]
90 --> 103 | cost [1070.0]
91 --> 95 | cost [960.0]
92 --> 14 | cost [1585.0]
93 --> 49 | cost [1365.0]
94 --> 95 | cost [615.0]
96 --> 52 | cost [1535.0]
97 --> 45 | cost [940.0]
98 --> 103 | cost [1300.0]
99 --> 14 | cost [1225.0]
100 --> 45 | cost [780.0]
102 --> 144 | cost [1285.0]
104 --> 45 | cost [1775.0]
105 --> 71 | cost [2135.0]
106 --> 49 | cost [1525.0]
107 --> 54 | cost [1015.0]
108 -->  3 | cost [3215.0]
109 --> 54 | cost [785.0]
110 --> 49 | cost [660.0]
111 --> 53 | cost [485.0]
112 --> 127 | cost [680.0]
114 --> 103 | cost [1105.0]
115 --> 53 | cost [475.0]
116 --> 122 | cost [350.0]
117 --> 53 | cost [535.0]
119 --> 153 | cost [1400.0]
121 --> 53 | cost [2215.0]
124 --> 138 | cost [480.0]
125 --> 181 | cost [255.0]
126 --> 52 | cost [2300.0]
128 --> 101 | cost [2080.0]
129 --> 146 | cost [740.0]
131 --> 142 | cost [1145.0]
132 -->  1 | cost [945.0]
133 --> 113 | cost [505.0]
134 --> 183 | cost [730.0]
135 --> 42 | cost [320.0]
137 --> 113 | cost [2165.0]
139 --> 72 | cost [1120.0]
140 --> 164 | cost [400.0]
143 --> 103 | cost [855.0]
147 --> 191 | cost [1830.0]
148 --> 71 | cost [1885.0]
149 --> 49 | cost [1465.0]
150 --> 144 | cost [810.0]
151 --> 181 | cost [1525.0]
152 --> 71 | cost [1145.0]
154 --> 164 | cost [905.0]
155 --> 183 | cost [115.0]
156 --> 45 | cost [820.0]
157 --> 47 | cost [740.0]
158 --> 181 | cost [2540.0]
159 --> 53 | cost [2200.0]
160 --> 67 | cost [1375.0]
161 --> 181 | cost [1035.0]
162 --> 67 | cost [890.0]
163 --> 101 | cost [1440.0]
165 --> 52 | cost [1830.0]
166 --> 52 | cost [1270.0]
167 -->  3 | cost [2985.0]
168 --> 83 | cost [1840.0]
170 --> 122 | cost [930.0]
171 --> 141 | cost [415.0]
172 --> 49 | cost [1680.0]
173 --> 144 | cost [1165.0]
174 --> 53 | cost [2090.0]
175 --> 14 | cost [1295.0]
176 --> 113 | cost [515.0]
177 --> 67 | cost [945.0]
178 --> 71 | cost [1060.0]
179 --> 16 | cost [800.0]
180 --> 142 | cost [1155.0]
182 --> 95 | cost [1840.0]
184 --> 49 | cost [1335.0]
185 --> 83 | cost [1120.0]
187 --> 54 | cost [935.0]
188 --> 122 | cost [595.0]
189 --> 142 | cost [900.0]
190 --> 49 | cost [1090.0]
192 --> 14 | cost [550.0]
193 --> 101 | cost [2065.0]
194 --> 122 | cost [670.0]
195 --> 113 | cost [1080.0]
196 --> 71 | cost [875.0]
197 --> 45 | cost [275.0]
199 --> 136 | cost [1500.0]
200 --> 141 | cost [925.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1