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

——————— Thu, 25 Jan 2024 17:37:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 141 hubs —— 1—132—85—145—191—198—123—15—79—162—64—20—55—42—186—127—112—120—47—67—157—107—109—6—54—22—183—8—25—90—34—143—17—146—129—98—114—141—58—171—200—148—28—38—56—71—72—83—62—185—50—139—196—178—152—105—5—137—133—176—113—195—182—94—91—150—23—70—76—102—21—30—68—169—35—2—181—125—80—77—167—41—59—3—73—189—131—69—108—14—36—74—156—100—81—165—96—166—52—11—84—122—51—82—199—78—9—138—26—136—190—147—40—128—60—101—4—163—49—110—16—63—188—116—66—153—48—119—92—175—149—18—184—29—172—121—174—111—115—53—201
total time           3606.01 (TL 3600)    gap                  0.261                
blossom time         0                    nb blossom           0.0                  
LB <= UB             131755<=178355       subtour              16793.0              
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       12240                n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—132—85—145—191—198—123—15—79—162—64—20—55—42—186—127—112—120—47—67—157—107—109—6—54—22—183—8—25—90—34—143—17—146—129—98—114—141—58—171—200—148—28—38—56—71—72—83—62—185—50—139—196—178—152—105—5—137—133—176—113—195—182—94—91—150—23—70—76—102—21—30—68—169—35—2—181—125—80—77—167—41—59—3—73—189—131—69—108—14—36—74—156—100—81—165—96—166—52—11—84—122—51—82—199—78—9—138—26—136—190—147—40—128—60—101—4—163—49—110—16—63—188—116—66—153—48—119—92—175—149—18—184—29—172—121—174—111—115—53—201

RING
1  --- 132 | cost [945.0]
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  --- 163 | cost [1055.0]
5  --- 105 | cost [575.0]
5  --- 137 | cost [815.0]
6  --- 54 | cost [545.0]
6  --- 109 | cost [420.0]
8  --- 25 | cost [2015.0]
8  --- 183 | cost [725.0]
9  --- 78 | cost [415.0]
9  --- 138 | cost [585.0]
11 --- 52 | cost [135.0]
11 --- 84 | cost [475.0]
14 --- 36 | cost [1050.0]
14 --- 108 | cost [1115.0]
15 --- 79 | cost [1225.0]
15 --- 123 | cost [185.0]
16 --- 63 | cost [605.0]
16 --- 110 | cost [2725.0]
17 --- 143 | cost [710.0]
17 --- 146 | cost [1210.0]
18 --- 149 | cost [1930.0]
18 --- 184 | cost [800.0]
20 --- 55 | cost [960.0]
20 --- 64 | cost [125.0]
21 --- 30 | cost [2500.0]
21 --- 102 | cost [1435.0]
22 --- 54 | cost [1990.0]
22 --- 183 | cost [665.0]
23 --- 70 | cost [1685.0]
23 --- 150 | cost [1205.0]
25 --- 90 | cost [480.0]
26 --- 136 | cost [735.0]
26 --- 138 | cost [1015.0]
28 --- 38 | cost [545.0]
28 --- 148 | cost [975.0]
29 --- 172 | cost [1255.0]
29 --- 184 | cost [410.0]
30 --- 68 | cost [695.0]
34 --- 90 | cost [450.0]
34 --- 143 | cost [800.0]
35 --- 169 | cost [715.0]
36 --- 74 | cost [515.0]
38 --- 56 | cost [885.0]
40 --- 128 | cost [3555.0]
40 --- 147 | cost [805.0]
41 --- 59 | cost [1425.0]
41 --- 167 | cost [1505.0]
42 --- 55 | cost [545.0]
42 --- 186 | cost [455.0]
47 --- 67 | cost [835.0]
47 --- 120 | cost [610.0]
48 --- 119 | cost [1900.0]
48 --- 153 | cost [1380.0]
49 --- 110 | cost [660.0]
49 --- 163 | cost [1685.0]
50 --- 139 | cost [1010.0]
50 --- 185 | cost [930.0]
51 --- 82 | cost [2780.0]
51 --- 122 | cost [1055.0]
52 --- 166 | cost [1270.0]
53 --- 115 | cost [475.0]
53 --- 201 | cost [160.0]
56 --- 71 | cost [985.0]
58 --- 141 | cost [535.0]
58 --- 171 | cost [350.0]
60 --- 101 | cost [905.0]
60 --- 128 | cost [1350.0]
62 --- 83 | cost [220.0]
62 --- 185 | cost [945.0]
63 --- 188 | cost [515.0]
64 --- 162 | cost [590.0]
66 --- 116 | cost [1375.0]
66 --- 153 | cost [100.0]
67 --- 157 | cost [1565.0]
68 --- 169 | cost [475.0]
69 --- 108 | cost [1255.0]
69 --- 131 | cost [1450.0]
70 --- 76 | cost [580.0]
71 --- 72 | cost [1260.0]
72 --- 83 | cost [950.0]
73 --- 189 | cost [1765.0]
74 --- 156 | cost [740.0]
76 --- 102 | cost [1315.0]
77 --- 80 | cost [970.0]
77 --- 167 | cost [1955.0]
78 --- 199 | cost [1045.0]
79 --- 162 | cost [1080.0]
80 --- 125 | cost [1635.0]
81 --- 100 | cost [790.0]
81 --- 165 | cost [2390.0]
82 --- 199 | cost [1305.0]
84 --- 122 | cost [1620.0]
85 --- 132 | cost [605.0]
85 --- 145 | cost [505.0]
91 --- 94 | cost [645.0]
91 --- 150 | cost [605.0]
92 --- 119 | cost [850.0]
92 --- 175 | cost [385.0]
94 --- 182 | cost [1440.0]
96 --- 165 | cost [615.0]
96 --- 166 | cost [620.0]
98 --- 114 | cost [270.0]
98 --- 129 | cost [1775.0]
100 --- 156 | cost [180.0]
105 --- 152 | cost [1295.0]
107 --- 109 | cost [250.0]
107 --- 157 | cost [465.0]
111 --- 115 | cost [565.0]
111 --- 174 | cost [1645.0]
112 --- 120 | cost [770.0]
112 --- 127 | cost [680.0]
113 --- 176 | cost [515.0]
113 --- 195 | cost [1080.0]
114 --- 141 | cost [1720.0]
116 --- 188 | cost [290.0]
121 --- 172 | cost [760.0]
121 --- 174 | cost [330.0]
123 --- 198 | cost [540.0]
125 --- 181 | cost [255.0]
127 --- 186 | cost [405.0]
129 --- 146 | cost [740.0]
131 --- 189 | cost [940.0]
133 --- 137 | cost [2040.0]
133 --- 176 | cost [460.0]
136 --- 190 | cost [3515.0]
139 --- 196 | cost [1420.0]
145 --- 191 | cost [895.0]
147 --- 190 | cost [3680.0]
148 --- 200 | cost [1260.0]
149 --- 175 | cost [1745.0]
152 --- 178 | cost [200.0]
171 --- 200 | cost [605.0]
178 --- 196 | cost [340.0]
182 --- 195 | cost [1225.0]
191 --- 198 | cost [495.0]

STAR
7  --> 199 | cost [1070.0]
10 --> 175 | cost [50.0]
12 --> 147 | cost [1055.0]
13 --> 79 | cost [650.0]
19 --> 199 | cost [5925.0]
24 --> 174 | cost [1145.0]
27 --> 191 | cost [505.0]
31 --> 47 | cost [435.0]
32 --> 199 | cost [1780.0]
33 --> 100 | cost [245.0]
37 --> 184 | cost [685.0]
39 --> 28 | cost [475.0]
43 --> 105 | cost [285.0]
44 --> 116 | cost [515.0]
45 --> 81 | cost [395.0]
46 --> 172 | cost [150.0]
57 --> 36 | cost [210.0]
61 --> 136 | cost [315.0]
65 --> 80 | cost [1285.0]
75 --> 183 | cost [745.0]
86 --> 139 | cost [840.0]
87 --> 96 | cost [1410.0]
88 --> 148 | cost [435.0]
89 --> 41 | cost [1065.0]
93 --> 163 | cost [445.0]
95 --> 91 | cost [960.0]
97 --> 81 | cost [600.0]
99 --> 92 | cost [530.0]
103 --> 146 | cost [695.0]
104 --> 165 | cost [735.0]
106 --> 149 | cost [235.0]
117 --> 115 | cost [65.0]
118 --> 16 | cost [615.0]
124 --> 138 | cost [480.0]
126 --> 96 | cost [995.0]
130 --> 72 | cost [680.0]
134 --> 22 | cost [75.0]
135 --> 42 | cost [320.0]
140 --> 21 | cost [290.0]
142 --> 69 | cost [455.0]
144 --> 70 | cost [670.0]
151 --> 80 | cost [945.0]
154 --> 21 | cost [395.0]
155 --> 183 | cost [115.0]
158 --> 77 | cost [405.0]
159 --> 174 | cost [445.0]
160 --> 79 | cost [390.0]
161 --> 125 | cost [825.0]
164 --> 21 | cost [570.0]
168 --> 185 | cost [765.0]
170 --> 84 | cost [800.0]
173 --> 23 | cost [575.0]
177 --> 79 | cost [825.0]
179 --> 16 | cost [800.0]
180 --> 131 | cost [435.0]
187 -->  6 | cost [605.0]
192 --> 14 | cost [550.0]
193 --> 128 | cost [240.0]
194 --> 51 | cost [505.0]
197 --> 81 | cost [615.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Thu, 25 Jan 2024 18:38:18 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 41 hubs —— 1-145-198-67-20-120-112-155-17-133-157-83-130-140-41-142-14-10-33-81-97-96-166-122-188-179-118-9-7-24-159-174-121-184-29-49-93-163-147-115-201-1
total time           3613.0 (TL 3600)     gap                  0.539                
blossom time         0                    nb blossom           0.0                  
LB <= UB             133360<=289120       Master/SP costs      289120/0             
Master time          3613.0               SP time              0.0                  
subtour              18472.0              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       11045                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—145—198—67—20—120—112—155—17—133—157—83—130—140—41—142—14—10—33—81—97—96—166—122—188—179—118—9—7—24—159—174—121—184—29—49—93—163—147—115—201

RING
1  --- 145 | cost [1370.0]
7  ---  9 | cost [2195.0]
7  --- 24 | cost [3390.0]
9  --- 118 | cost [1545.0]
10 --- 14 | cost [1315.0]
10 --- 33 | cost [1610.0]
14 --- 142 | cost [2140.0]
17 --- 133 | cost [8960.0]
17 --- 155 | cost [2255.0]
20 --- 67 | cost [1525.0]
20 --- 120 | cost [1900.0]
24 --- 159 | cost [940.0]
29 --- 49 | cost [1030.0]
29 --- 184 | cost [410.0]
33 --- 81 | cost [585.0]
41 --- 140 | cost [2625.0]
41 --- 142 | cost [3695.0]
49 --- 93 | cost [1365.0]
67 --- 198 | cost [3205.0]
81 --- 97 | cost [600.0]
83 --- 130 | cost [1535.0]
83 --- 157 | cost [3525.0]
93 --- 163 | cost [445.0]
96 --- 97 | cost [2545.0]
96 --- 166 | cost [620.0]
112 --- 120 | cost [770.0]
112 --- 155 | cost [1150.0]
115 --- 147 | cost [2975.0]
115 --- 201 | cost [585.0]
118 --- 179 | cost [1150.0]
121 --- 174 | cost [330.0]
121 --- 184 | cost [2240.0]
122 --- 166 | cost [2745.0]
122 --- 188 | cost [595.0]
130 --- 140 | cost [6455.0]
133 --- 157 | cost [9095.0]
145 --- 198 | cost [1070.0]
147 --- 163 | cost [2105.0]
159 --- 174 | cost [445.0]
179 --- 188 | cost [1295.0]

STAR
2  --> 140 | cost [2880.0]
3  --> 41 | cost [2070.0]
4  --> 163 | cost [1055.0]
5  --> 130 | cost [2195.0]
6  --> 157 | cost [695.0]
8  --> 155 | cost [770.0]
11 --> 166 | cost [1175.0]
12 --> 147 | cost [1055.0]
13 --> 67 | cost [1590.0]
15 --> 198 | cost [725.0]
16 --> 118 | cost [615.0]
18 --> 49 | cost [535.0]
19 --> 10 | cost [790.0]
21 --> 140 | cost [290.0]
22 --> 155 | cost [780.0]
23 --> 140 | cost [1700.0]
25 --> 17 | cost [510.0]
26 -->  9 | cost [1105.0]
27 --> 198 | cost [535.0]
28 --> 130 | cost [1180.0]
30 --> 41 | cost [1920.0]
31 --> 67 | cost [650.0]
32 --> 24 | cost [760.0]
34 --> 17 | cost [1365.0]
35 --> 140 | cost [2500.0]
36 --> 33 | cost [825.0]
37 --> 184 | cost [685.0]
38 --> 130 | cost [920.0]
39 --> 130 | cost [745.0]
40 --> 147 | cost [805.0]
42 --> 120 | cost [1170.0]
43 --> 133 | cost [2245.0]
44 --> 188 | cost [295.0]
45 --> 81 | cost [395.0]
46 --> 121 | cost [750.0]
47 --> 120 | cost [610.0]
48 --> 166 | cost [1215.0]
50 --> 83 | cost [1465.0]
51 --> 188 | cost [880.0]
52 --> 166 | cost [1270.0]
53 -->  1 | cost [160.0]
54 --> 157 | cost [1205.0]
55 --> 20 | cost [960.0]
56 --> 130 | cost [1680.0]
57 --> 33 | cost [810.0]
58 --> 17 | cost [2825.0]
59 --> 41 | cost [1425.0]
60 --> 163 | cost [2345.0]
61 --> 184 | cost [1355.0]
62 --> 83 | cost [220.0]
63 --> 188 | cost [515.0]
64 --> 20 | cost [125.0]
65 --> 67 | cost [1525.0]
66 --> 179 | cost [1105.0]
68 --> 140 | cost [2120.0]
69 --> 142 | cost [455.0]
70 --> 140 | cost [2245.0]
71 --> 130 | cost [700.0]
72 --> 130 | cost [680.0]
73 --> 41 | cost [2120.0]
74 --> 33 | cost [775.0]
75 --> 155 | cost [815.0]
76 --> 140 | cost [2805.0]
77 --> 41 | cost [2880.0]
78 -->  9 | cost [415.0]
79 --> 67 | cost [1510.0]
80 --> 157 | cost [2400.0]
82 -->  9 | cost [895.0]
84 --> 166 | cost [1205.0]
85 --> 145 | cost [505.0]
86 --> 130 | cost [2025.0]
87 --> 96 | cost [1410.0]
88 --> 130 | cost [2065.0]
89 --> 41 | cost [1065.0]
90 --> 17 | cost [925.0]
91 --> 140 | cost [3035.0]
92 --> 10 | cost [340.0]
94 --> 133 | cost [3450.0]
95 --> 83 | cost [3000.0]
98 --> 130 | cost [2555.0]
99 --> 10 | cost [540.0]
100 --> 33 | cost [245.0]
101 --> 163 | cost [1440.0]
102 --> 140 | cost [1685.0]
103 --> 17 | cost [1435.0]
104 --> 166 | cost [1080.0]
105 --> 133 | cost [2375.0]
106 --> 93 | cost [435.0]
107 --> 157 | cost [465.0]
108 --> 14 | cost [1115.0]
109 --> 157 | cost [500.0]
110 --> 29 | cost [365.0]
111 --> 115 | cost [565.0]
113 --> 133 | cost [505.0]
114 --> 130 | cost [2410.0]
116 --> 188 | cost [290.0]
117 --> 115 | cost [65.0]
119 --> 10 | cost [1135.0]
123 --> 198 | cost [540.0]
124 -->  9 | cost [755.0]
125 --> 157 | cost [2680.0]
126 --> 96 | cost [995.0]
127 --> 112 | cost [680.0]
128 --> 147 | cost [2855.0]
129 --> 17 | cost [1945.0]
131 --> 142 | cost [1145.0]
132 -->  1 | cost [945.0]
134 --> 155 | cost [845.0]
135 --> 20 | cost [1310.0]
136 --> 24 | cost [1405.0]
137 --> 133 | cost [2040.0]
138 -->  9 | cost [585.0]
139 --> 130 | cost [1305.0]
141 --> 17 | cost [3280.0]
143 --> 17 | cost [710.0]
144 --> 140 | cost [2035.0]
146 --> 17 | cost [1210.0]
148 --> 130 | cost [2135.0]
149 --> 93 | cost [620.0]
150 --> 140 | cost [2680.0]
151 --> 157 | cost [1650.0]
152 --> 130 | cost [1845.0]
153 --> 179 | cost [1115.0]
154 --> 140 | cost [520.0]
156 --> 33 | cost [315.0]
158 --> 41 | cost [2830.0]
160 --> 20 | cost [1120.0]
161 --> 157 | cost [2575.0]
162 --> 20 | cost [705.0]
164 --> 140 | cost [400.0]
165 --> 166 | cost [575.0]
167 --> 41 | cost [1505.0]
168 --> 83 | cost [1840.0]
169 --> 140 | cost [1820.0]
170 --> 122 | cost [930.0]
171 --> 17 | cost [3160.0]
172 --> 121 | cost [760.0]
173 --> 140 | cost [2275.0]
175 --> 10 | cost [50.0]
176 --> 133 | cost [460.0]
177 --> 67 | cost [945.0]
178 --> 130 | cost [1760.0]
180 --> 142 | cost [1155.0]
181 --> 157 | cost [2895.0]
182 --> 133 | cost [2495.0]
183 --> 155 | cost [115.0]
185 --> 83 | cost [1120.0]
186 --> 120 | cost [775.0]
187 --> 157 | cost [990.0]
189 --> 142 | cost [900.0]
190 --> 49 | cost [1090.0]
191 --> 198 | cost [495.0]
192 --> 14 | cost [550.0]
193 --> 147 | cost [2665.0]
194 --> 122 | cost [670.0]
195 --> 133 | cost [1555.0]
196 --> 130 | cost [1535.0]
197 --> 81 | cost [615.0]
199 -->  7 | cost [1070.0]
200 --> 130 | cost [3220.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1