------------------------------------------------------------
                           α=3.0 —— d198 —— 198 nodes       
------------------------------------------------------------

——————— Wed, 24 Jan 2024 03:33:47 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 199 hubs —— 1—40—14—15—16—17—18—19—20—21—24—25—26—27—22—23—29—30—28—34—33—36—37—32—31—38—45—54—61—66—74—82—75—62—53—46—52—65—81—76—77—78—64—50—51—47—39—35—48—49—63—79—80—91—92—105—114—113—112—106—107—111—110—109—108—167—168—182—183—181—177—176—173—174—175—178—180—184—185—179—194—195—198—197—196—187—186—193—192—191—188—189—190—171—172—166—165—164—163—151—150—145—144—137—129—128—127—170—126—125—169—124—138—140—134—132—131—130—133—135—136—141—143—142—147—146—149—148—153—152—162—161—160—159—158—157—156—155—154—139—123—120—119—118—117—116—121—122—115—104—103—102—93—101—94—95—96—90—89—97—98—88—83—70—67—60—55—44—56—59—68—72—73—84—87—99—100—86—85—71—69—58—57—42—43—41—13—12—11—10—9—8—5—4—3—6—7—2—199
total time           2877.83              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             47340<=47340         subtour              13011.0              
connectivity cuts    1425.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1800                 n lazycuts edges     4.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—40—14—15—16—17—18—19—20—21—24—25—26—27—22—23—29—30—28—34—33—36—37—32—31—38—45—54—61—66—74—82—75—62—53—46—52—65—81—76—77—78—64—50—51—47—39—35—48—49—63—79—80—91—92—105—114—113—112—106—107—111—110—109—108—167—168—182—183—181—177—176—173—174—175—178—180—184—185—179—194—195—198—197—196—187—186—193—192—191—188—189—190—171—172—166—165—164—163—151—150—145—144—137—129—128—127—170—126—125—169—124—138—140—134—132—131—130—133—135—136—141—143—142—147—146—149—148—153—152—162—161—160—159—158—157—156—155—154—139—123—120—119—118—117—116—121—122—115—104—103—102—93—101—94—95—96—90—89—97—98—88—83—70—67—60—55—44—56—59—68—72—73—84—87—99—100—86—85—71—69—58—57—42—43—41—13—12—11—10—9—8—5—4—3—6—7—2—199

RING
1  --- 40 | cost [4845.0]
1  --- 199 | cost [0.0]
2  ---  7 | cost [153.0]
2  --- 199 | cost [3417.0]
3  ---  4 | cost [228.0]
3  ---  6 | cost [153.0]
4  ---  5 | cost [153.0]
5  ---  8 | cost [1059.0]
6  ---  7 | cost [228.0]
8  ---  9 | cost [153.0]
9  --- 10 | cost [75.0]
10 --- 11 | cost [75.0]
11 --- 12 | cost [75.0]
12 --- 13 | cost [75.0]
13 --- 41 | cost [540.0]
14 --- 15 | cost [108.0]
14 --- 40 | cost [456.0]
15 --- 16 | cost [306.0]
16 --- 17 | cost [75.0]
17 --- 18 | cost [456.0]
18 --- 19 | cost [153.0]
19 --- 20 | cost [228.0]
20 --- 21 | cost [306.0]
21 --- 24 | cost [108.0]
22 --- 23 | cost [153.0]
22 --- 27 | cost [240.0]
23 --- 29 | cost [240.0]
24 --- 25 | cost [108.0]
25 --- 26 | cost [108.0]
26 --- 27 | cost [75.0]
28 --- 30 | cost [108.0]
28 --- 34 | cost [171.0]
29 --- 30 | cost [108.0]
31 --- 32 | cost [75.0]
31 --- 38 | cost [108.0]
32 --- 37 | cost [75.0]
33 --- 34 | cost [75.0]
33 --- 36 | cost [108.0]
35 --- 39 | cost [171.0]
35 --- 48 | cost [216.0]
36 --- 37 | cost [75.0]
38 --- 45 | cost [171.0]
39 --- 47 | cost [75.0]
41 --- 43 | cost [444.0]
42 --- 43 | cost [75.0]
42 --- 57 | cost [108.0]
44 --- 55 | cost [75.0]
44 --- 56 | cost [108.0]
45 --- 54 | cost [75.0]
46 --- 52 | cost [108.0]
46 --- 53 | cost [108.0]
47 --- 51 | cost [108.0]
48 --- 49 | cost [108.0]
49 --- 63 | cost [108.0]
50 --- 51 | cost [153.0]
50 --- 64 | cost [153.0]
52 --- 65 | cost [153.0]
53 --- 62 | cost [75.0]
54 --- 61 | cost [75.0]
55 --- 60 | cost [75.0]
56 --- 59 | cost [75.0]
57 --- 58 | cost [75.0]
58 --- 69 | cost [75.0]
59 --- 68 | cost [75.0]
60 --- 67 | cost [75.0]
61 --- 66 | cost [75.0]
62 --- 75 | cost [153.0]
63 --- 79 | cost [228.0]
64 --- 78 | cost [75.0]
65 --- 81 | cost [171.0]
66 --- 74 | cost [75.0]
67 --- 70 | cost [69.0]
68 --- 72 | cost [75.0]
69 --- 71 | cost [75.0]
70 --- 83 | cost [207.0]
71 --- 85 | cost [108.0]
72 --- 73 | cost [75.0]
73 --- 84 | cost [75.0]
74 --- 82 | cost [108.0]
75 --- 82 | cost [108.0]
76 --- 77 | cost [75.0]
76 --- 81 | cost [108.0]
77 --- 78 | cost [75.0]
79 --- 80 | cost [75.0]
80 --- 91 | cost [75.0]
83 --- 88 | cost [75.0]
84 --- 87 | cost [75.0]
85 --- 86 | cost [108.0]
86 --- 100 | cost [108.0]
87 --- 99 | cost [75.0]
88 --- 98 | cost [75.0]
89 --- 90 | cost [75.0]
89 --- 97 | cost [108.0]
90 --- 96 | cost [108.0]
91 --- 92 | cost [75.0]
92 --- 105 | cost [276.0]
93 --- 101 | cost [108.0]
93 --- 102 | cost [75.0]
94 --- 95 | cost [75.0]
94 --- 101 | cost [75.0]
95 --- 96 | cost [153.0]
97 --- 98 | cost [75.0]
99 --- 100 | cost [228.0]
102 --- 103 | cost [171.0]
103 --- 104 | cost [75.0]
104 --- 115 | cost [444.0]
105 --- 114 | cost [108.0]
106 --- 107 | cost [75.0]
106 --- 112 | cost [75.0]
107 --- 111 | cost [108.0]
108 --- 109 | cost [108.0]
108 --- 167 | cost [444.0]
109 --- 110 | cost [75.0]
110 --- 111 | cost [75.0]
112 --- 113 | cost [75.0]
113 --- 114 | cost [75.0]
115 --- 122 | cost [120.0]
116 --- 117 | cost [75.0]
116 --- 121 | cost [120.0]
117 --- 118 | cost [153.0]
118 --- 119 | cost [75.0]
119 --- 120 | cost [75.0]
120 --- 123 | cost [255.0]
121 --- 122 | cost [153.0]
123 --- 139 | cost [342.0]
124 --- 138 | cost [342.0]
124 --- 169 | cost [240.0]
125 --- 126 | cost [114.0]
125 --- 169 | cost [75.0]
126 --- 170 | cost [204.0]
127 --- 128 | cost [180.0]
127 --- 170 | cost [75.0]
128 --- 129 | cost [234.0]
129 --- 137 | cost [261.0]
130 --- 131 | cost [75.0]
130 --- 133 | cost [75.0]
131 --- 132 | cost [75.0]
132 --- 134 | cost [75.0]
133 --- 135 | cost [75.0]
134 --- 140 | cost [75.0]
135 --- 136 | cost [75.0]
136 --- 141 | cost [108.0]
137 --- 144 | cost [213.0]
138 --- 140 | cost [306.0]
139 --- 154 | cost [498.0]
141 --- 143 | cost [75.0]
142 --- 143 | cost [75.0]
142 --- 147 | cost [75.0]
144 --- 145 | cost [108.0]
145 --- 150 | cost [108.0]
146 --- 147 | cost [75.0]
146 --- 149 | cost [75.0]
148 --- 149 | cost [75.0]
148 --- 153 | cost [75.0]
150 --- 151 | cost [153.0]
151 --- 163 | cost [171.0]
152 --- 153 | cost [75.0]
152 --- 162 | cost [75.0]
154 --- 155 | cost [75.0]
155 --- 156 | cost [75.0]
156 --- 157 | cost [75.0]
157 --- 158 | cost [75.0]
158 --- 159 | cost [153.0]
159 --- 160 | cost [324.0]
160 --- 161 | cost [132.0]
161 --- 162 | cost [75.0]
163 --- 164 | cost [153.0]
164 --- 165 | cost [228.0]
165 --- 166 | cost [75.0]
166 --- 172 | cost [450.0]
167 --- 168 | cost [381.0]
168 --- 182 | cost [4404.0]
171 --- 172 | cost [342.0]
171 --- 190 | cost [4041.0]
173 --- 174 | cost [222.0]
173 --- 176 | cost [228.0]
174 --- 175 | cost [228.0]
175 --- 178 | cost [297.0]
176 --- 177 | cost [291.0]
177 --- 181 | cost [108.0]
178 --- 180 | cost [75.0]
179 --- 185 | cost [153.0]
179 --- 194 | cost [75.0]
180 --- 184 | cost [75.0]
181 --- 183 | cost [75.0]
182 --- 183 | cost [285.0]
184 --- 185 | cost [153.0]
186 --- 187 | cost [228.0]
186 --- 193 | cost [228.0]
187 --- 196 | cost [708.0]
188 --- 189 | cost [228.0]
188 --- 191 | cost [228.0]
189 --- 190 | cost [228.0]
191 --- 192 | cost [672.0]
192 --- 193 | cost [228.0]
194 --- 195 | cost [318.0]
195 --- 198 | cost [228.0]
196 --- 197 | cost [228.0]
197 --- 198 | cost [228.0]

STAR

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 24 Jan 2024 04:34:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 6 hubs —— 1-177-48-91-23-199-1
total time           3612.56 (TL 3600)    gap                  0.989                
blossom time         0                    nb blossom           0.0                  
LB <= UB             36385<=3349568       Master/SP costs      3349568/0            
Master time          3612.56              SP time              0.0                  
subtour              20966.0              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       8777                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—177—48—91—23—199

RING
1  --- 177 | cost [11697.0]
1  --- 199 | cost [0.0]
23 --- 91 | cost [1230.0]
23 --- 199 | cost [5493.0]
48 --- 91 | cost [465.0]
48 --- 177 | cost [6264.0]

STAR
2  -->  1 | cost [7973.0]
3  -->  1 | cost [8239.0]
4  -->  1 | cost [8540.0]
5  -->  1 | cost [8834.0]
6  -->  1 | cost [8547.0]
7  -->  1 | cost [8281.0]
8  -->  1 | cost [11298.0]
9  -->  1 | cost [11494.0]
10 -->  1 | cost [11599.0]
11 -->  1 | cost [11704.0]
12 -->  1 | cost [11809.0]
13 -->  1 | cost [11914.0]
14 -->  1 | cost [12096.0]
15 -->  1 | cost [11844.0]
16 -->  1 | cost [11396.0]
17 -->  1 | cost [11536.0]
18 -->  1 | cost [12404.0]
19 -->  1 | cost [12698.0]
20 -->  1 | cost [13153.0]
21 -->  1 | cost [13538.0]
22 -->  1 | cost [13104.0]
24 -->  1 | cost [13496.0]
25 -->  1 | cost [13748.0]
26 -->  1 | cost [13706.0]
27 -->  1 | cost [13566.0]
28 -->  1 | cost [13286.0]
29 -->  1 | cost [13006.0]
30 -->  1 | cost [13258.0]
31 -->  1 | cost [13097.0]
32 -->  1 | cost [13237.0]
33 -->  1 | cost [13510.0]
34 -->  1 | cost [13643.0]
35 -->  1 | cost [14175.0]
36 -->  1 | cost [13489.0]
37 -->  1 | cost [13349.0]
38 -->  1 | cost [13083.0]
39 -->  1 | cost [14007.0]
40 -->  1 | cost [11305.0]
41 -->  1 | cost [11816.0]
42 -->  1 | cost [12691.0]
43 -->  1 | cost [12817.0]
44 -->  1 | cost [13069.0]
45 -->  1 | cost [13454.0]
46 -->  1 | cost [13853.0]
47 -->  1 | cost [14119.0]
49 -->  1 | cost [14924.0]
50 -->  1 | cost [14644.0]
51 -->  1 | cost [14371.0]
52 -->  1 | cost [14105.0]
53 -->  1 | cost [13839.0]
54 -->  1 | cost [13573.0]
55 -->  1 | cost [13195.0]
56 -->  1 | cost [13069.0]
57 -->  1 | cost [12698.0]
58 -->  1 | cost [12831.0]
59 -->  1 | cost [13195.0]
60 -->  1 | cost [13321.0]
61 -->  1 | cost [13699.0]
62 -->  1 | cost [13958.0]
63 -->  1 | cost [15176.0]
64 -->  1 | cost [14875.0]
65 -->  1 | cost [14343.0]
66 -->  1 | cost [13825.0]
67 -->  1 | cost [13447.0]
68 -->  1 | cost [13321.0]
69 -->  1 | cost [12957.0]
70 -->  1 | cost [13601.0]
71 -->  1 | cost [13090.0]
72 -->  1 | cost [13454.0]
73 -->  1 | cost [13573.0]
74 -->  1 | cost [13944.0]
75 -->  1 | cost [14203.0]
76 -->  1 | cost [14721.0]
77 -->  1 | cost [14854.0]
78 -->  1 | cost [14987.0]
79 -->  1 | cost [15512.0]
80 -->  1 | cost [15379.0]
81 -->  1 | cost [14714.0]
82 -->  1 | cost [14196.0]
83 -->  1 | cost [14070.0]
84 -->  1 | cost [13699.0]
85 -->  1 | cost [13342.0]
86 -->  1 | cost [13363.0]
87 -->  1 | cost [13832.0]
88 -->  1 | cost [14196.0]
89 -->  1 | cost [14448.0]
90 -->  1 | cost [14574.0]
92 -->  1 | cost [15624.0]
93 -->  1 | cost [15344.0]
94 -->  1 | cost [15211.0]
95 -->  1 | cost [15085.0]
96 -->  1 | cost [14826.0]
97 -->  1 | cost [14448.0]
98 -->  1 | cost [14329.0]
99 -->  1 | cost [13965.0]
100 -->  1 | cost [13615.0]
101 -->  1 | cost [15337.0]
102 -->  1 | cost [15463.0]
103 -->  1 | cost [15848.0]
104 -->  1 | cost [15981.0]
105 -->  1 | cost [16247.0]
106 -->  1 | cost [16646.0]
107 -->  1 | cost [16786.0]
108 -->  1 | cost [17339.0]
109 -->  1 | cost [17311.0]
110 -->  1 | cost [17171.0]
111 -->  1 | cost [17038.0]
112 -->  1 | cost [16765.0]
113 -->  1 | cost [16632.0]
114 -->  1 | cost [16492.0]
115 -->  1 | cost [16975.0]
116 -->  1 | cost [17101.0]
117 -->  1 | cost [17234.0]
118 -->  1 | cost [17500.0]
119 -->  1 | cost [17633.0]
120 -->  1 | cost [17766.0]
121 -->  1 | cost [17353.0]
122 -->  1 | cost [17094.0]
123 -->  1 | cost [17920.0]
124 -->  1 | cost [18522.0]
125 -->  1 | cost [18928.0]
126 -->  1 | cost [19131.0]
127 -->  1 | cost [19474.0]
128 -->  1 | cost [19803.0]
129 -->  1 | cost [19698.0]
130 -->  1 | cost [19425.0]
131 -->  1 | cost [19292.0]
132 -->  1 | cost [19404.0]
133 -->  1 | cost [19544.0]
134 -->  1 | cost [19523.0]
135 -->  1 | cost [19656.0]
136 -->  1 | cost [19789.0]
137 -->  1 | cost [20307.0]
138 -->  1 | cost [19054.0]
139 -->  1 | cost [18473.0]
140 -->  1 | cost [19642.0]
141 -->  1 | cost [19775.0]
142 -->  1 | cost [19761.0]
143 -->  1 | cost [19894.0]
144 -->  1 | cost [20160.0]
145 -->  1 | cost [20139.0]
146 -->  1 | cost [20013.0]
147 -->  1 | cost [19880.0]
148 -->  1 | cost [19999.0]
149 -->  1 | cost [20132.0]
150 -->  1 | cost [20391.0]
151 -->  1 | cost [20657.0]
152 -->  1 | cost [20251.0]
153 -->  1 | cost [20118.0]
154 -->  1 | cost [18746.0]
155 -->  1 | cost [18865.0]
156 -->  1 | cost [18991.0]
157 -->  1 | cost [19110.0]
158 -->  1 | cost [19229.0]
159 -->  1 | cost [19481.0]
160 -->  1 | cost [20013.0]
161 -->  1 | cost [20237.0]
162 -->  1 | cost [20370.0]
163 -->  1 | cost [21028.0]
164 -->  1 | cost [21294.0]
165 -->  1 | cost [21700.0]
166 -->  1 | cost [21840.0]
167 -->  1 | cost [17241.0]
168 -->  1 | cost [17976.0]
169 -->  1 | cost [18809.0]
170 -->  1 | cost [19369.0]
171 -->  1 | cost [20447.0]
172 -->  1 | cost [20930.0]
173 -->  1 | cost [26523.0]
174 -->  1 | cost [27020.0]
175 -->  1 | cost [27167.0]
176 -->  1 | cost [26670.0]
178 -->  1 | cost [27804.0]
179 -->  1 | cost [28147.0]
180 -->  1 | cost [27860.0]
181 -->  1 | cost [27181.0]
182 -->  1 | cost [26600.0]
183 -->  1 | cost [27230.0]
184 -->  1 | cost [27909.0]
185 -->  1 | cost [28252.0]
186 -->  1 | cost [29652.0]
187 -->  1 | cost [29148.0]
188 -->  1 | cost [27664.0]
189 -->  1 | cost [27160.0]
190 -->  1 | cost [27342.0]
191 -->  1 | cost [27846.0]
192 -->  1 | cost [29316.0]
193 -->  1 | cost [29820.0]
194 -->  1 | cost [28098.0]
195 -->  1 | cost [28693.0]
196 -->  1 | cost [29204.0]
197 -->  1 | cost [29071.0]
198 -->  1 | cost [28553.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1