------------------------------------------------------------
                        α=3.0 —— kroA200 —— 200 nodes       
------------------------------------------------------------

——————— Sun, 14 Jan 2024 15:36:12 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 6 hubs —— 1—53—111—117—115—201
total time           3605.57 (TL 3600)    gap                  0.001                
blossom time         0                    nb blossom           0.0                  
LB <= UB             86154<=86241         subtour              58803.0              
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       43578                n lazycuts edges     5.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—53—111—117—115—201

RING
1  --- 53 | cost [96.0]
2  --- 35 | cost [228.0]
2  --- 181 | cost [333.0]
3  --- 59 | cost [390.0]
3  --- 73 | cost [54.0]
4  --- 60 | cost [774.0]
4  --- 101 | cost [231.0]
5  --- 105 | cost [345.0]
5  --- 196 | cost [435.0]
6  --- 54 | cost [327.0]
6  --- 109 | cost [252.0]
7  --- 82 | cost [1023.0]
7  --- 199 | cost [642.0]
8  --- 22 | cost [384.0]
8  --- 134 | cost [420.0]
9  --- 78 | cost [249.0]
9  --- 138 | cost [351.0]
10 --- 92 | cost [204.0]
10 --- 175 | cost [30.0]
11 --- 52 | cost [81.0]
11 --- 84 | cost [285.0]
12 --- 46 | cost [975.0]
12 --- 147 | cost [633.0]
13 --- 15 | cost [702.0]
13 --- 79 | cost [390.0]
14 --- 108 | cost [669.0]
14 --- 192 | cost [330.0]
15 --- 123 | cost [111.0]
16 --- 118 | cost [369.0]
16 --- 179 | cost [480.0]
17 --- 25 | cost [306.0]
17 --- 146 | cost [726.0]
18 --- 49 | cost [321.0]
18 --- 110 | cost [120.0]
19 --- 99 | cost [300.0]
19 --- 119 | cost [594.0]
20 --- 55 | cost [576.0]
20 --- 64 | cost [75.0]
21 --- 140 | cost [174.0]
21 --- 154 | cost [237.0]
22 --- 134 | cost [45.0]
23 --- 169 | cost [723.0]
23 --- 173 | cost [345.0]
24 --- 32 | cost [456.0]
24 --- 159 | cost [564.0]
25 --- 143 | cost [285.0]
26 --- 61 | cost [513.0]
26 --- 199 | cost [474.0]
27 --- 191 | cost [303.0]
27 --- 198 | cost [321.0]
28 --- 38 | cost [327.0]
28 --- 39 | cost [285.0]
29 --- 110 | cost [219.0]
29 --- 184 | cost [246.0]
30 --- 68 | cost [417.0]
30 --- 169 | cost [648.0]
31 --- 65 | cost [777.0]
31 --- 67 | cost [390.0]
32 --- 136 | cost [540.0]
33 --- 45 | cost [321.0]
33 --- 100 | cost [147.0]
34 --- 90 | cost [270.0]
34 --- 103 | cost [750.0]
35 --- 68 | cost [459.0]
36 --- 57 | cost [126.0]
36 --- 74 | cost [309.0]
37 --- 184 | cost [411.0]
37 --- 190 | cost [1218.0]
38 --- 71 | cost [258.0]
39 --- 130 | cost [447.0]
40 --- 132 | cost [633.0]
40 --- 147 | cost [483.0]
41 --- 59 | cost [855.0]
41 --- 89 | cost [639.0]
42 --- 55 | cost [327.0]
42 --- 135 | cost [192.0]
43 --- 105 | cost [171.0]
43 --- 137 | cost [231.0]
44 --- 153 | cost [519.0]
44 --- 188 | cost [177.0]
45 --- 197 | cost [165.0]
46 --- 172 | cost [90.0]
47 --- 120 | cost [366.0]
47 --- 157 | cost [444.0]
48 --- 84 | cost [453.0]
48 --- 166 | cost [729.0]
49 --- 190 | cost [654.0]
50 --- 139 | cost [606.0]
50 --- 168 | cost [861.0]
51 --- 63 | cost [366.0]
51 --- 194 | cost [303.0]
52 --- 170 | cost [660.0]
53 --- 111 | cost [291.0]
54 --- 187 | cost [561.0]
56 --- 71 | cost [591.0]
56 --- 152 | cost [132.0]
57 --- 74 | cost [186.0]
58 --- 141 | cost [321.0]
58 --- 171 | cost [210.0]
60 --- 101 | cost [543.0]
61 --- 136 | cost [189.0]
62 --- 83 | cost [132.0]
62 --- 185 | cost [567.0]
63 --- 194 | cost [513.0]
64 --- 162 | cost [354.0]
65 --- 177 | cost [753.0]
66 --- 153 | cost [60.0]
66 --- 179 | cost [663.0]
67 --- 177 | cost [567.0]
69 --- 142 | cost [273.0]
69 --- 189 | cost [522.0]
70 --- 76 | cost [348.0]
70 --- 144 | cost [402.0]
72 --- 83 | cost [570.0]
72 --- 130 | cost [408.0]
73 --- 189 | cost [1059.0]
75 --- 155 | cost [489.0]
75 --- 183 | cost [447.0]
76 --- 182 | cost [954.0]
77 --- 80 | cost [582.0]
77 --- 158 | cost [243.0]
78 --- 82 | cost [348.0]
79 --- 160 | cost [234.0]
80 --- 158 | cost [756.0]
81 --- 97 | cost [360.0]
81 --- 197 | cost [369.0]
85 --- 132 | cost [363.0]
85 --- 145 | cost [303.0]
86 --- 95 | cost [975.0]
86 --- 139 | cost [504.0]
87 --- 96 | cost [846.0]
87 --- 126 | cost [450.0]
88 --- 114 | cost [603.0]
88 --- 148 | cost [261.0]
89 --- 154 | cost [1008.0]
90 --- 143 | cost [228.0]
91 --- 94 | cost [387.0]
91 --- 150 | cost [363.0]
92 --- 119 | cost [510.0]
93 --- 149 | cost [372.0]
93 --- 163 | cost [267.0]
94 --- 95 | cost [369.0]
96 --- 126 | cost [597.0]
97 --- 104 | cost [909.0]
98 --- 114 | cost [162.0]
98 --- 200 | cost [645.0]
99 --- 175 | cost [345.0]
100 --- 156 | cost [108.0]
102 --- 144 | cost [771.0]
102 --- 164 | cost [996.0]
103 --- 129 | cost [642.0]
104 --- 165 | cost [441.0]
106 --- 149 | cost [141.0]
106 --- 163 | cost [471.0]
107 --- 109 | cost [150.0]
107 --- 157 | cost [279.0]
108 --- 192 | cost [618.0]
111 --- 117 | cost [345.0]
112 --- 120 | cost [462.0]
112 --- 127 | cost [408.0]
113 --- 176 | cost [309.0]
113 --- 195 | cost [648.0]
115 --- 117 | cost [39.0]
115 --- 201 | cost [351.0]
116 --- 122 | cost [210.0]
116 --- 188 | cost [174.0]
118 --- 124 | cost [543.0]
121 --- 172 | cost [456.0]
121 --- 174 | cost [198.0]
122 --- 170 | cost [558.0]
123 --- 198 | cost [324.0]
124 --- 138 | cost [288.0]
125 --- 161 | cost [495.0]
125 --- 181 | cost [153.0]
127 --- 186 | cost [243.0]
128 --- 167 | cost [903.0]
128 --- 193 | cost [144.0]
129 --- 146 | cost [444.0]
131 --- 142 | cost [687.0]
131 --- 180 | cost [261.0]
133 --- 137 | cost [1224.0]
133 --- 176 | cost [276.0]
135 --- 186 | cost [423.0]
140 --- 164 | cost [240.0]
141 --- 171 | cost [249.0]
145 --- 191 | cost [537.0]
148 --- 200 | cost [756.0]
150 --- 173 | cost [540.0]
151 --- 161 | cost [558.0]
151 --- 187 | cost [438.0]
152 --- 178 | cost [120.0]
155 --- 183 | cost [69.0]
156 --- 180 | cost [843.0]
159 --- 174 | cost [267.0]
160 --- 162 | cost [453.0]
165 --- 166 | cost [345.0]
167 --- 193 | cost [1041.0]
168 --- 185 | cost [459.0]
178 --- 196 | cost [204.0]
182 --- 195 | cost [735.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sun, 14 Jan 2024 16:36:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 28 hubs —— 1-42-186-67-151-107-22-98-200-83-95-195-154-89-192-36-45-11-170-118-138-37-18-49-12-172-159-201-1
total time           3604.81 (TL 3600)    gap                  0.792                
blossom time         0                    nb blossom           0.0                  
LB <= UB             84379<=406323        Master/SP costs      406323/0             
Master time          3604.81              SP time              0.0                  
subtour              9421.0               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       6217                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—42—186—67—151—107—22—98—200—83—95—195—154—89—192—36—45—11—170—118—138—37—18—49—12—172—159—201

RING
1  --- 42 | cost [3585.0]
11 --- 45 | cost [2340.0]
11 --- 170 | cost [639.0]
12 --- 49 | cost [1179.0]
12 --- 172 | cost [1059.0]
18 --- 37 | cost [780.0]
18 --- 49 | cost [321.0]
22 --- 98 | cost [1974.0]
22 --- 107 | cost [1086.0]
36 --- 45 | cost [648.0]
36 --- 192 | cost [933.0]
37 --- 138 | cost [765.0]
42 --- 186 | cost [273.0]
67 --- 151 | cost [1440.0]
67 --- 186 | cost [882.0]
83 --- 95 | cost [1800.0]
83 --- 200 | cost [2628.0]
89 --- 154 | cost [1008.0]
89 --- 192 | cost [3342.0]
95 --- 195 | cost [1692.0]
98 --- 200 | cost [645.0]
107 --- 151 | cost [1149.0]
118 --- 138 | cost [831.0]
118 --- 170 | cost [1836.0]
154 --- 195 | cost [3375.0]
159 --- 172 | cost [864.0]
159 --- 201 | cost [1413.0]

STAR
2  --> 151 | cost [2912.0]
3  --> 89 | cost [3381.0]
4  --> 192 | cost [1995.0]
5  --> 95 | cost [3983.0]
6  --> 107 | cost [931.0]
7  --> 138 | cost [3584.0]
8  --> 22 | cost [896.0]
9  --> 138 | cost [819.0]
10 --> 36 | cost [1673.0]
13 --> 67 | cost [2226.0]
14 --> 192 | cost [770.0]
15 -->  1 | cost [3577.0]
16 --> 118 | cost [861.0]
17 --> 22 | cost [2898.0]
19 --> 36 | cost [2723.0]
20 --> 42 | cost [1701.0]
21 --> 154 | cost [553.0]
23 --> 154 | cost [3024.0]
24 --> 159 | cost [1316.0]
25 --> 98 | cost [3486.0]
26 --> 138 | cost [1421.0]
27 -->  1 | cost [3234.0]
28 --> 98 | cost [2478.0]
29 --> 18 | cost [749.0]
30 --> 89 | cost [2632.0]
31 --> 67 | cost [910.0]
32 --> 159 | cost [2359.0]
33 --> 45 | cost [749.0]
34 --> 98 | cost [2772.0]
35 --> 151 | cost [3367.0]
38 --> 98 | cost [3227.0]
39 --> 98 | cost [2674.0]
40 --> 12 | cost [1568.0]
41 --> 89 | cost [1491.0]
43 --> 95 | cost [4613.0]
44 --> 170 | cost [2100.0]
46 --> 172 | cost [210.0]
47 --> 67 | cost [1169.0]
48 --> 11 | cost [1652.0]
50 --> 83 | cost [2051.0]
51 --> 118 | cost [1687.0]
52 --> 11 | cost [189.0]
53 -->  1 | cost [224.0]
54 --> 107 | cost [1421.0]
55 --> 42 | cost [763.0]
56 --> 98 | cost [4109.0]
57 --> 36 | cost [294.0]
58 --> 200 | cost [1274.0]
59 --> 89 | cost [2555.0]
60 --> 192 | cost [2730.0]
61 --> 138 | cost [1295.0]
62 --> 83 | cost [308.0]
63 --> 118 | cost [1708.0]
64 --> 42 | cost [1645.0]
65 --> 67 | cost [2135.0]
66 --> 170 | cost [2849.0]
68 --> 89 | cost [3220.0]
69 -->  1 | cost [11193.0]
70 --> 95 | cost [2891.0]
71 --> 83 | cost [3066.0]
72 --> 83 | cost [1330.0]
73 --> 89 | cost [3402.0]
74 --> 36 | cost [721.0]
75 --> 22 | cost [1169.0]
76 --> 95 | cost [2625.0]
77 --> 151 | cost [2569.0]
78 --> 138 | cost [1309.0]
79 --> 67 | cost [2114.0]
80 --> 151 | cost [1323.0]
81 --> 45 | cost [553.0]
82 --> 138 | cost [2065.0]
84 --> 11 | cost [665.0]
85 -->  1 | cost [1512.0]
86 --> 95 | cost [2275.0]
87 --> 11 | cost [3192.0]
88 --> 98 | cost [1274.0]
90 --> 98 | cost [2919.0]
91 --> 95 | cost [1344.0]
92 --> 36 | cost [2142.0]
93 --> 49 | cost [1911.0]
94 --> 95 | cost [861.0]
96 --> 11 | cost [2079.0]
97 --> 45 | cost [1316.0]
99 --> 36 | cost [2128.0]
100 --> 45 | cost [1092.0]
101 --> 192 | cost [2121.0]
102 --> 154 | cost [2317.0]
103 --> 98 | cost [1820.0]
104 --> 45 | cost [2485.0]
105 --> 95 | cost [4312.0]
106 --> 49 | cost [2135.0]
108 --> 192 | cost [1442.0]
109 --> 107 | cost [350.0]
110 --> 18 | cost [280.0]
111 -->  1 | cost [903.0]
112 --> 186 | cost [1302.0]
113 --> 195 | cost [1512.0]
114 --> 98 | cost [378.0]
115 -->  1 | cost [819.0]
116 --> 170 | cost [1505.0]
117 -->  1 | cost [910.0]
119 --> 45 | cost [2660.0]
120 --> 186 | cost [1085.0]
121 --> 159 | cost [1057.0]
122 --> 170 | cost [1302.0]
123 -->  1 | cost [3430.0]
124 --> 138 | cost [672.0]
125 --> 151 | cost [1778.0]
126 --> 11 | cost [3213.0]
127 --> 186 | cost [567.0]
128 --> 192 | cost [4620.0]
129 --> 22 | cost [2163.0]
130 --> 83 | cost [2149.0]
131 --> 36 | cost [3304.0]
132 -->  1 | cost [1323.0]
133 --> 195 | cost [2177.0]
134 --> 22 | cost [105.0]
135 --> 42 | cost [448.0]
136 --> 138 | cost [1596.0]
137 --> 95 | cost [4116.0]
139 --> 83 | cost [2625.0]
140 --> 154 | cost [728.0]
141 --> 200 | cost [1295.0]
142 --> 36 | cost [2576.0]
143 --> 98 | cost [2856.0]
144 --> 95 | cost [2744.0]
145 -->  1 | cost [1918.0]
146 --> 22 | cost [2191.0]
147 --> 12 | cost [1477.0]
148 --> 200 | cost [1764.0]
149 --> 49 | cost [2051.0]
150 --> 95 | cost [1932.0]
152 -->  1 | cost [18781.0]
153 --> 170 | cost [2716.0]
155 --> 22 | cost [1092.0]
156 --> 45 | cost [1148.0]
157 --> 107 | cost [651.0]
158 -->  1 | cost [8288.0]
160 --> 67 | cost [1925.0]
161 --> 151 | cost [1302.0]
162 --> 67 | cost [1246.0]
163 --> 49 | cost [2359.0]
164 --> 154 | cost [1267.0]
165 --> 11 | cost [2436.0]
166 --> 11 | cost [1645.0]
167 --> 89 | cost [3493.0]
168 --> 83 | cost [2576.0]
169 --> 154 | cost [3269.0]
171 --> 200 | cost [847.0]
173 --> 95 | cost [3073.0]
174 --> 159 | cost [623.0]
175 --> 36 | cost [1603.0]
176 --> 195 | cost [1820.0]
177 --> 67 | cost [1323.0]
178 --> 83 | cost [4459.0]
179 --> 118 | cost [1610.0]
180 --> 36 | cost [2793.0]
181 --> 151 | cost [2135.0]
182 --> 195 | cost [1715.0]
183 --> 22 | cost [931.0]
184 --> 37 | cost [959.0]
185 --> 83 | cost [1568.0]
187 --> 151 | cost [1022.0]
188 --> 170 | cost [1904.0]
189 --> 36 | cost [3759.0]
190 --> 49 | cost [1526.0]
191 -->  1 | cost [2583.0]
193 --> 192 | cost [4704.0]
194 --> 170 | cost [2191.0]
196 --> 83 | cost [4060.0]
197 --> 45 | cost [385.0]
198 -->  1 | cost [3164.0]
199 --> 138 | cost [2191.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1