------------------------------------------------------------
                        α=7.0 —— kroA200 —— 200 nodes       
------------------------------------------------------------

——————— Wed, 17 Jan 2024 15:08:58 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—53—201
total time           58.21                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             130155<=130167       subtour              419.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       517                  n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—53—201

RING
1  --- 53 | cost [224.0]
2  --- 125 | cost [1141.0]
2  --- 181 | cost [777.0]
3  --- 59 | cost [910.0]
3  --- 73 | cost [126.0]
6  --- 109 | cost [588.0]
6  --- 187 | cost [847.0]
9  --- 124 | cost [1057.0]
9  --- 138 | cost [819.0]
10 --- 92 | cost [476.0]
10 --- 175 | cost [70.0]
11 --- 52 | cost [189.0]
11 --- 84 | cost [665.0]
13 --- 79 | cost [910.0]
13 --- 177 | cost [910.0]
20 --- 64 | cost [175.0]
20 --- 162 | cost [987.0]
21 --- 140 | cost [406.0]
21 --- 154 | cost [553.0]
22 --- 134 | cost [105.0]
22 --- 183 | cost [931.0]
25 --- 90 | cost [672.0]
25 --- 143 | cost [665.0]
26 --- 61 | cost [1197.0]
26 --- 136 | cost [1029.0]
28 --- 38 | cost [763.0]
28 --- 39 | cost [665.0]
29 --- 37 | cost [1512.0]
29 --- 184 | cost [574.0]
33 --- 45 | cost [749.0]
33 --- 100 | cost [343.0]
36 --- 57 | cost [294.0]
36 --- 74 | cost [721.0]
37 --- 184 | cost [959.0]
38 --- 39 | cost [805.0]
42 --- 135 | cost [448.0]
42 --- 186 | cost [637.0]
43 --- 105 | cost [399.0]
43 --- 137 | cost [539.0]
44 --- 63 | cost [763.0]
44 --- 188 | cost [413.0]
45 --- 100 | cost [1092.0]
52 --- 84 | cost [826.0]
53 --- 201 | cost [224.0]
57 --- 74 | cost [434.0]
58 --- 141 | cost [749.0]
58 --- 171 | cost [490.0]
59 --- 73 | cost [973.0]
61 --- 136 | cost [441.0]
62 --- 83 | cost [308.0]
62 --- 185 | cost [1323.0]
63 --- 188 | cost [721.0]
64 --- 162 | cost [826.0]
69 --- 142 | cost [637.0]
69 --- 189 | cost [1218.0]
79 --- 160 | cost [546.0]
83 --- 185 | cost [1568.0]
85 --- 191 | cost [1106.0]
85 --- 198 | cost [1652.0]
90 --- 143 | cost [532.0]
91 --- 144 | cost [1407.0]
91 --- 150 | cost [847.0]
92 --- 175 | cost [539.0]
93 --- 106 | cost [609.0]
93 --- 163 | cost [623.0]
96 --- 126 | cost [1393.0]
96 --- 165 | cost [861.0]
105 --- 137 | cost [483.0]
106 --- 163 | cost [1099.0]
107 --- 109 | cost [350.0]
107 --- 157 | cost [651.0]
113 --- 133 | cost [707.0]
113 --- 176 | cost [721.0]
121 --- 159 | cost [1057.0]
121 --- 174 | cost [462.0]
124 --- 138 | cost [672.0]
125 --- 161 | cost [1155.0]
126 --- 165 | cost [1981.0]
128 --- 158 | cost [2121.0]
128 --- 193 | cost [336.0]
133 --- 176 | cost [644.0]
134 --- 183 | cost [1022.0]
135 --- 186 | cost [987.0]
140 --- 154 | cost [728.0]
141 --- 171 | cost [581.0]
142 --- 189 | cost [1260.0]
144 --- 150 | cost [1134.0]
152 --- 178 | cost [280.0]
152 --- 196 | cost [742.0]
157 --- 187 | cost [1386.0]
158 --- 193 | cost [2177.0]
159 --- 174 | cost [623.0]
160 --- 177 | cost [1337.0]
161 --- 181 | cost [1449.0]
178 --- 196 | cost [476.0]
191 --- 198 | cost [693.0]

STAR
4  --> 163 | cost [633.0]
5  --> 105 | cost [345.0]
7  --> 26 | cost [1113.0]
8  --> 22 | cost [384.0]
12 --> 163 | cost [1038.0]
14 --> 36 | cost [630.0]
15 --> 198 | cost [435.0]
16 --> 63 | cost [363.0]
17 --> 25 | cost [306.0]
18 --> 29 | cost [321.0]
19 --> 92 | cost [318.0]
23 --> 144 | cost [630.0]
24 --> 159 | cost [564.0]
27 --> 191 | cost [303.0]
30 -->  2 | cost [993.0]
31 --> 157 | cost [612.0]
32 --> 136 | cost [540.0]
34 --> 90 | cost [270.0]
35 -->  2 | cost [228.0]
40 --> 191 | cost [873.0]
41 --> 59 | cost [855.0]
46 --> 121 | cost [450.0]
47 --> 157 | cost [444.0]
48 --> 84 | cost [453.0]
49 --> 29 | cost [618.0]
50 --> 185 | cost [558.0]
51 --> 63 | cost [366.0]
54 -->  6 | cost [327.0]
55 --> 42 | cost [327.0]
56 --> 152 | cost [132.0]
60 --> 128 | cost [810.0]
65 --> 177 | cost [753.0]
66 --> 44 | cost [570.0]
67 --> 162 | cost [534.0]
68 -->  2 | cost [627.0]
70 --> 144 | cost [402.0]
71 --> 38 | cost [258.0]
72 --> 83 | cost [570.0]
75 --> 183 | cost [447.0]
76 --> 144 | cost [693.0]
77 --> 158 | cost [243.0]
78 -->  9 | cost [249.0]
80 --> 161 | cost [507.0]
81 --> 45 | cost [237.0]
82 -->  9 | cost [537.0]
86 --> 196 | cost [846.0]
87 --> 126 | cost [450.0]
88 --> 28 | cost [609.0]
89 --> 140 | cost [978.0]
94 --> 91 | cost [387.0]
95 --> 91 | cost [576.0]
97 --> 45 | cost [564.0]
98 --> 58 | cost [618.0]
99 --> 92 | cost [318.0]
101 --> 163 | cost [864.0]
102 --> 144 | cost [771.0]
103 --> 143 | cost [513.0]
104 --> 165 | cost [441.0]
108 --> 142 | cost [744.0]
110 --> 29 | cost [219.0]
111 --> 53 | cost [291.0]
112 --> 186 | cost [558.0]
114 --> 58 | cost [741.0]
115 --> 53 | cost [285.0]
116 --> 188 | cost [174.0]
117 --> 53 | cost [321.0]
118 --> 124 | cost [543.0]
119 --> 92 | cost [510.0]
120 --> 186 | cost [465.0]
122 --> 188 | cost [357.0]
123 --> 198 | cost [324.0]
127 --> 186 | cost [243.0]
129 --> 134 | cost [903.0]
130 --> 39 | cost [447.0]
131 --> 189 | cost [564.0]
132 --> 85 | cost [363.0]
139 --> 196 | cost [852.0]
145 --> 85 | cost [303.0]
146 --> 143 | cost [594.0]
147 --> 191 | cost [1098.0]
148 --> 28 | cost [585.0]
149 --> 106 | cost [141.0]
151 --> 187 | cost [438.0]
153 --> 44 | cost [519.0]
155 --> 183 | cost [69.0]
156 --> 100 | cost [108.0]
164 --> 140 | cost [240.0]
166 --> 165 | cost [345.0]
167 --> 128 | cost [903.0]
168 --> 185 | cost [459.0]
169 -->  2 | cost [651.0]
170 --> 84 | cost [480.0]
172 --> 121 | cost [456.0]
173 --> 150 | cost [540.0]
179 --> 63 | cost [573.0]
180 --> 142 | cost [693.0]
182 --> 91 | cost [1182.0]
190 --> 106 | cost [747.0]
192 --> 36 | cost [933.0]
194 --> 188 | cost [483.0]
195 --> 113 | cost [648.0]
197 --> 45 | cost [165.0]
199 --> 26 | cost [474.0]
200 --> 171 | cost [363.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 17 Jan 2024 16:10:32 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 37 hubs —— 1-79-160-67-120-157-54-83-146-25-200-56-152-5-137-176-195-182-76-91-2-30-41-59-69-97-52-170-190-49-110-118-9-199-24-174-201-1
total time           3613.12 (TL 3600)    gap                  0.385                
blossom time         0                    nb blossom           0.0                  
LB <= UB             132640<=215512       Master/SP costs      215512/0             
Master time          3613.12              SP time              0.0                  
subtour              14173.0              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       14799                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—79—160—67—120—157—54—83—146—25—200—56—152—5—137—176—195—182—76—91—2—30—41—59—69—97—52—170—190—49—110—118—9—199—24—174—201

RING
1  --- 79 | cost [5187.0]
2  --- 30 | cost [2317.0]
2  --- 91 | cost [4312.0]
5  --- 137 | cost [1141.0]
5  --- 152 | cost [1281.0]
9  --- 118 | cost [2163.0]
9  --- 199 | cost [1876.0]
24 --- 174 | cost [1603.0]
24 --- 199 | cost [3549.0]
25 --- 146 | cost [1911.0]
25 --- 200 | cost [4543.0]
30 --- 41 | cost [2688.0]
41 --- 59 | cost [1995.0]
49 --- 110 | cost [924.0]
49 --- 190 | cost [1526.0]
52 --- 97 | cost [5292.0]
52 --- 170 | cost [1540.0]
54 --- 83 | cost [3388.0]
54 --- 157 | cost [1687.0]
56 --- 152 | cost [308.0]
56 --- 200 | cost [4242.0]
59 --- 69 | cost [3297.0]
67 --- 120 | cost [1491.0]
67 --- 160 | cost [1925.0]
69 --- 97 | cost [4900.0]
76 --- 91 | cost [1652.0]
76 --- 182 | cost [2226.0]
79 --- 160 | cost [546.0]
83 --- 146 | cost [4081.0]
110 --- 118 | cost [3451.0]
120 --- 157 | cost [1428.0]
137 --- 176 | cost [3472.0]
170 --- 190 | cost [5628.0]
174 --- 201 | cost [3150.0]
176 --- 195 | cost [1820.0]
182 --- 195 | cost [1715.0]

STAR
3  --> 59 | cost [390.0]
4  --> 49 | cost [1644.0]
6  --> 54 | cost [327.0]
7  --> 199 | cost [642.0]
8  --> 146 | cost [846.0]
10 --> 190 | cost [1221.0]
11 --> 52 | cost [81.0]
12 --> 49 | cost [1179.0]
13 --> 79 | cost [390.0]
14 --> 69 | cost [1377.0]
15 --> 79 | cost [735.0]
16 --> 118 | cost [369.0]
17 --> 25 | cost [306.0]
18 --> 110 | cost [120.0]
19 --> 190 | cost [753.0]
20 --> 160 | cost [672.0]
21 --> 30 | cost [1500.0]
22 --> 146 | cost [939.0]
23 -->  2 | cost [1047.0]
26 --> 199 | cost [474.0]
27 -->  1 | cost [1386.0]
28 --> 56 | cost [747.0]
29 --> 110 | cost [219.0]
31 --> 67 | cost [390.0]
32 --> 24 | cost [456.0]
33 --> 97 | cost [696.0]
34 --> 25 | cost [531.0]
35 -->  2 | cost [228.0]
36 --> 97 | cost [1167.0]
37 --> 118 | cost [750.0]
38 --> 56 | cost [531.0]
39 --> 56 | cost [873.0]
40 -->  1 | cost [1137.0]
42 --> 120 | cost [702.0]
43 --> 137 | cost [231.0]
44 --> 170 | cost [900.0]
45 --> 97 | cost [564.0]
46 --> 174 | cost [648.0]
47 --> 120 | cost [366.0]
48 --> 170 | cost [720.0]
50 --> 83 | cost [879.0]
51 --> 118 | cost [723.0]
53 -->  1 | cost [96.0]
55 --> 120 | cost [582.0]
57 --> 97 | cost [1179.0]
58 --> 200 | cost [546.0]
60 --> 69 | cost [1716.0]
61 -->  9 | cost [840.0]
62 --> 83 | cost [132.0]
63 --> 118 | cost [732.0]
64 --> 160 | cost [645.0]
65 --> 67 | cost [915.0]
66 --> 190 | cost [1194.0]
68 --> 30 | cost [417.0]
70 --> 76 | cost [348.0]
71 --> 56 | cost [591.0]
72 --> 83 | cost [570.0]
73 --> 59 | cost [417.0]
74 --> 69 | cost [1074.0]
75 --> 54 | cost [708.0]
77 --> 30 | cost [1152.0]
78 -->  9 | cost [249.0]
80 -->  2 | cost [1428.0]
81 --> 97 | cost [360.0]
82 -->  9 | cost [537.0]
84 --> 52 | cost [354.0]
85 -->  1 | cost [648.0]
86 -->  5 | cost [756.0]
87 --> 52 | cost [1344.0]
88 --> 200 | cost [696.0]
89 --> 41 | cost [639.0]
90 --> 25 | cost [288.0]
92 --> 190 | cost [1068.0]
93 --> 49 | cost [819.0]
94 --> 91 | cost [387.0]
95 --> 91 | cost [576.0]
96 --> 52 | cost [921.0]
98 --> 200 | cost [645.0]
99 --> 190 | cost [960.0]
100 --> 97 | cost [798.0]
101 --> 49 | cost [1872.0]
102 --> 76 | cost [789.0]
103 --> 146 | cost [417.0]
104 --> 97 | cost [909.0]
105 --> 137 | cost [207.0]
106 --> 190 | cost [747.0]
107 --> 157 | cost [279.0]
108 --> 69 | cost [753.0]
109 --> 157 | cost [300.0]
111 -->  1 | cost [387.0]
112 --> 120 | cost [462.0]
113 --> 176 | cost [309.0]
114 --> 200 | cost [804.0]
115 -->  1 | cost [351.0]
116 --> 170 | cost [645.0]
117 -->  1 | cost [390.0]
119 --> 190 | cost [1128.0]
121 --> 174 | cost [198.0]
122 --> 170 | cost [558.0]
123 --> 79 | cost [834.0]
124 -->  9 | cost [453.0]
125 -->  2 | cost [489.0]
126 --> 52 | cost [1380.0]
127 --> 120 | cost [543.0]
128 --> 41 | cost [1803.0]
129 --> 146 | cost [444.0]
130 --> 83 | cost [921.0]
131 --> 69 | cost [870.0]
132 -->  1 | cost [567.0]
133 --> 176 | cost [276.0]
134 --> 146 | cost [933.0]
135 --> 120 | cost [879.0]
136 --> 24 | cost [843.0]
138 -->  9 | cost [351.0]
139 -->  5 | cost [1005.0]
140 --> 30 | cost [1329.0]
141 --> 200 | cost [555.0]
142 --> 69 | cost [273.0]
143 --> 25 | cost [285.0]
144 --> 91 | cost [603.0]
145 -->  1 | cost [822.0]
147 -->  1 | cost [1614.0]
148 --> 200 | cost [756.0]
149 --> 190 | cost [624.0]
150 --> 91 | cost [363.0]
151 --> 54 | cost [927.0]
153 --> 170 | cost [1164.0]
154 --> 30 | cost [1587.0]
155 --> 157 | cost [1044.0]
156 --> 97 | cost [738.0]
158 --> 30 | cost [1293.0]
159 --> 174 | cost [267.0]
161 -->  2 | cost [921.0]
162 --> 160 | cost [453.0]
163 --> 49 | cost [1011.0]
164 --> 30 | cost [1221.0]
165 --> 52 | cost [1098.0]
166 --> 52 | cost [762.0]
167 --> 41 | cost [903.0]
168 -->  2 | cost [1023.0]
169 --> 30 | cost [648.0]
171 --> 200 | cost [363.0]
172 --> 174 | cost [645.0]
173 --> 91 | cost [903.0]
175 --> 190 | cost [1248.0]
177 --> 79 | cost [495.0]
178 --> 152 | cost [120.0]
179 --> 118 | cost [690.0]
180 --> 69 | cost [933.0]
181 -->  2 | cost [333.0]
183 --> 157 | cost [1068.0]
184 --> 110 | cost [420.0]
185 --> 83 | cost [672.0]
186 --> 120 | cost [465.0]
187 --> 54 | cost [561.0]
188 --> 170 | cost [816.0]
189 --> 69 | cost [522.0]
191 -->  1 | cost [1107.0]
192 --> 69 | cost [1371.0]
193 --> 41 | cost [1941.0]
194 --> 170 | cost [939.0]
196 --> 152 | cost [318.0]
197 --> 97 | cost [639.0]
198 --> 79 | cost [1125.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1