------------------------------------------------------------
                           α=7.0 —— d198 —— 198 nodes       
------------------------------------------------------------

——————— Wed, 24 Jan 2024 07:37:07 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 5 hubs —— 1—198—197—196—199
total time           3611.34 (TL 3600)    gap                  0.936                
blossom time         0                    nb blossom           0.0                  
LB <= UB             70000.07<=1091178    subtour              13192.0              
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       12958                n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—198—197—196—199

RING
1  --- 198 | cost [28553.0]
196 --- 197 | cost [532.0]
196 --- 199 | cost [29204.0]
197 --- 198 | cost [532.0]

STAR
2  -->  1 | cost [3417.0]
3  -->  1 | cost [3531.0]
4  -->  1 | cost [3660.0]
5  -->  1 | cost [3786.0]
6  -->  1 | cost [3663.0]
7  -->  1 | cost [3549.0]
8  -->  1 | cost [4842.0]
9  -->  1 | cost [4926.0]
10 -->  1 | cost [4971.0]
11 -->  1 | cost [5016.0]
12 -->  1 | cost [5061.0]
13 -->  1 | cost [5106.0]
14 -->  1 | cost [5184.0]
15 -->  1 | cost [5076.0]
16 -->  1 | cost [4884.0]
17 -->  1 | cost [4944.0]
18 -->  1 | cost [5316.0]
19 -->  1 | cost [5442.0]
20 -->  1 | cost [5637.0]
21 -->  1 | cost [5802.0]
22 -->  1 | cost [5616.0]
23 -->  1 | cost [5493.0]
24 -->  1 | cost [5784.0]
25 -->  1 | cost [5892.0]
26 -->  1 | cost [5874.0]
27 -->  1 | cost [5814.0]
28 -->  1 | cost [5694.0]
29 -->  1 | cost [5574.0]
30 -->  1 | cost [5682.0]
31 -->  1 | cost [5613.0]
32 -->  1 | cost [5673.0]
33 -->  1 | cost [5790.0]
34 -->  1 | cost [5847.0]
35 -->  1 | cost [6075.0]
36 -->  1 | cost [5781.0]
37 -->  1 | cost [5721.0]
38 -->  1 | cost [5607.0]
39 -->  1 | cost [6003.0]
40 -->  1 | cost [4845.0]
41 -->  1 | cost [5064.0]
42 -->  1 | cost [5439.0]
43 -->  1 | cost [5493.0]
44 -->  1 | cost [5601.0]
45 -->  1 | cost [5766.0]
46 -->  1 | cost [5937.0]
47 -->  1 | cost [6051.0]
48 -->  1 | cost [6288.0]
49 -->  1 | cost [6396.0]
50 -->  1 | cost [6276.0]
51 -->  1 | cost [6159.0]
52 -->  1 | cost [6045.0]
53 -->  1 | cost [5931.0]
54 -->  1 | cost [5817.0]
55 -->  1 | cost [5655.0]
56 -->  1 | cost [5601.0]
57 -->  1 | cost [5442.0]
58 -->  1 | cost [5499.0]
59 -->  1 | cost [5655.0]
60 -->  1 | cost [5709.0]
61 -->  1 | cost [5871.0]
62 -->  1 | cost [5982.0]
63 -->  1 | cost [6504.0]
64 -->  1 | cost [6375.0]
65 -->  1 | cost [6147.0]
66 -->  1 | cost [5925.0]
67 -->  1 | cost [5763.0]
68 -->  1 | cost [5709.0]
69 -->  1 | cost [5553.0]
70 -->  1 | cost [5829.0]
71 -->  1 | cost [5610.0]
72 -->  1 | cost [5766.0]
73 -->  1 | cost [5817.0]
74 -->  1 | cost [5976.0]
75 -->  1 | cost [6087.0]
76 -->  1 | cost [6309.0]
77 -->  1 | cost [6366.0]
78 -->  1 | cost [6423.0]
79 -->  1 | cost [6648.0]
80 -->  1 | cost [6591.0]
81 -->  1 | cost [6306.0]
82 -->  1 | cost [6084.0]
83 -->  1 | cost [6030.0]
84 -->  1 | cost [5871.0]
85 -->  1 | cost [5718.0]
86 -->  1 | cost [5727.0]
87 -->  1 | cost [5928.0]
88 -->  1 | cost [6084.0]
89 -->  1 | cost [6192.0]
90 -->  1 | cost [6246.0]
91 -->  1 | cost [6639.0]
92 -->  1 | cost [6696.0]
93 -->  1 | cost [6576.0]
94 -->  1 | cost [6519.0]
95 -->  1 | cost [6465.0]
96 -->  1 | cost [6354.0]
97 -->  1 | cost [6192.0]
98 -->  1 | cost [6141.0]
99 -->  1 | cost [5985.0]
100 -->  1 | cost [5835.0]
101 -->  1 | cost [6573.0]
102 -->  1 | cost [6627.0]
103 -->  1 | cost [6792.0]
104 -->  1 | cost [6849.0]
105 --> 198 | cost [6801.0]
106 --> 198 | cost [6579.0]
107 --> 198 | cost [6507.0]
108 --> 198 | cost [6210.0]
109 --> 198 | cost [6303.0]
110 --> 198 | cost [6378.0]
111 --> 198 | cost [6450.0]
112 --> 198 | cost [6597.0]
113 --> 198 | cost [6672.0]
114 --> 198 | cost [6747.0]
115 --> 198 | cost [6825.0]
116 --> 198 | cost [6753.0]
117 --> 198 | cost [6681.0]
118 --> 198 | cost [6534.0]
119 --> 198 | cost [6462.0]
120 --> 198 | cost [6390.0]
121 --> 198 | cost [6750.0]
122 --> 198 | cost [6897.0]
123 --> 198 | cost [6570.0]
124 --> 198 | cost [6249.0]
125 --> 198 | cost [6033.0]
126 --> 198 | cost [5928.0]
127 --> 198 | cost [5751.0]
128 --> 198 | cost [5586.0]
129 --> 198 | cost [5808.0]
130 --> 198 | cost [5949.0]
131 --> 198 | cost [6021.0]
132 --> 198 | cost [6051.0]
133 --> 198 | cost [5979.0]
134 --> 198 | cost [6081.0]
135 --> 198 | cost [6012.0]
136 --> 198 | cost [5940.0]
137 --> 198 | cost [5727.0]
138 --> 198 | cost [6375.0]
139 --> 198 | cost [6690.0]
140 --> 198 | cost [6111.0]
141 --> 198 | cost [6042.0]
142 --> 198 | cost [6144.0]
143 --> 198 | cost [6075.0]
144 --> 198 | cost [5937.0]
145 --> 198 | cost [6039.0]
146 --> 198 | cost [6108.0]
147 --> 198 | cost [6177.0]
148 --> 198 | cost [6210.0]
149 --> 198 | cost [6141.0]
150 --> 198 | cost [6006.0]
151 --> 198 | cost [5871.0]
152 --> 198 | cost [6177.0]
153 --> 198 | cost [6246.0]
154 --> 198 | cost [7101.0]
155 --> 198 | cost [7032.0]
156 --> 198 | cost [6963.0]
157 --> 198 | cost [6894.0]
158 --> 198 | cost [6825.0]
159 --> 198 | cost [6687.0]
160 --> 198 | cost [6399.0]
161 --> 198 | cost [6279.0]
162 --> 198 | cost [6213.0]
163 --> 198 | cost [5880.0]
164 --> 198 | cost [5748.0]
165 --> 198 | cost [5553.0]
166 --> 198 | cost [5487.0]
167 --> 198 | cost [5901.0]
168 --> 198 | cost [5529.0]
169 --> 198 | cost [6006.0]
170 --> 198 | cost [5721.0]
171 --> 198 | cost [5271.0]
172 --> 198 | cost [5421.0]
173 --> 198 | cost [900.0]
174 --> 198 | cost [678.0]
175 --> 198 | cost [717.0]
176 --> 198 | cost [930.0]
177 --> 198 | cost [795.0]
178 --> 198 | cost [612.0]
179 --> 198 | cost [510.0]
180 --> 198 | cost [666.0]
181 --> 198 | cost [900.0]
182 --> 198 | cost [1185.0]
183 --> 198 | cost [945.0]
184 --> 198 | cost [723.0]
185 --> 196 | cost [624.0]
186 --> 196 | cost [672.0]
187 --> 196 | cost [708.0]
188 --> 198 | cost [1122.0]
189 --> 198 | cost [1272.0]
190 --> 198 | cost [1443.0]
191 --> 196 | cost [1272.0]
192 --> 196 | cost [930.0]
193 --> 196 | cost [900.0]
194 --> 198 | cost [450.0]
195 --> 198 | cost [228.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 24 Jan 2024 07:46:55 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 102 hubs —— 1-16-15-14-31-32-30-28-22-24-27-34-39-47-51-50-64-78-80-92-105-114-113-112-111-110-109-120-124-125-131-132-134-135-136-129-127-128-171-182-181-177-180-179-195-187-191-190-166-165-164-163-151-150-145-146-147-148-153-160-159-158-157-156-139-123-121-116-115-104-103-102-101-95-96-90-89-82-83-74-66-61-54-55-60-67-73-84-85-71-69-58-57-13-12-11-10-9-5-6-2-199-1
total time           548.29               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             94300<=94300         Master/SP costs      94300/0              
Master time          548.29               SP time              0.0                  
subtour              855.0                connectivity cuts    1698.0               
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       1861                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—16—15—14—31—32—30—28—22—24—27—34—39—47—51—50—64—78—80—92—105—114—113—112—111—110—109—120—124—125—131—132—134—135—136—129—127—128—171—182—181—177—180—179—195—187—191—190—166—165—164—163—151—150—145—146—147—148—153—160—159—158—157—156—139—123—121—116—115—104—103—102—101—95—96—90—89—82—83—74—66—61—54—55—60—67—73—84—85—71—69—58—57—13—12—11—10—9—5—6—2—199

RING
1  --- 16 | cost [11396.0]
1  --- 199 | cost [0.0]
2  ---  6 | cost [644.0]
2  --- 199 | cost [7973.0]
5  ---  6 | cost [532.0]
5  ---  9 | cost [2667.0]
9  --- 10 | cost [175.0]
10 --- 11 | cost [175.0]
11 --- 12 | cost [175.0]
12 --- 13 | cost [175.0]
13 --- 57 | cost [1435.0]
14 --- 15 | cost [252.0]
14 --- 31 | cost [1008.0]
15 --- 16 | cost [714.0]
22 --- 24 | cost [399.0]
22 --- 28 | cost [560.0]
24 --- 27 | cost [399.0]
27 --- 34 | cost [399.0]
28 --- 30 | cost [252.0]
30 --- 32 | cost [252.0]
31 --- 32 | cost [175.0]
34 --- 39 | cost [399.0]
39 --- 47 | cost [175.0]
47 --- 51 | cost [252.0]
50 --- 51 | cost [357.0]
50 --- 64 | cost [357.0]
54 --- 55 | cost [532.0]
54 --- 61 | cost [175.0]
55 --- 60 | cost [175.0]
57 --- 58 | cost [175.0]
58 --- 69 | cost [175.0]
60 --- 67 | cost [175.0]
61 --- 66 | cost [175.0]
64 --- 78 | cost [175.0]
66 --- 74 | cost [175.0]
67 --- 73 | cost [175.0]
69 --- 71 | cost [175.0]
71 --- 85 | cost [252.0]
73 --- 84 | cost [175.0]
74 --- 83 | cost [175.0]
78 --- 80 | cost [399.0]
80 --- 92 | cost [252.0]
82 --- 83 | cost [175.0]
82 --- 89 | cost [252.0]
84 --- 85 | cost [532.0]
89 --- 90 | cost [175.0]
90 --- 96 | cost [252.0]
92 --- 105 | cost [644.0]
95 --- 96 | cost [357.0]
95 --- 101 | cost [252.0]
101 --- 102 | cost [175.0]
102 --- 103 | cost [399.0]
103 --- 104 | cost [175.0]
104 --- 115 | cost [1036.0]
105 --- 114 | cost [252.0]
109 --- 110 | cost [175.0]
109 --- 120 | cost [714.0]
110 --- 111 | cost [175.0]
111 --- 112 | cost [357.0]
112 --- 113 | cost [175.0]
113 --- 114 | cost [175.0]
115 --- 116 | cost [175.0]
116 --- 121 | cost [280.0]
120 --- 124 | cost [756.0]
121 --- 123 | cost [595.0]
123 --- 139 | cost [798.0]
124 --- 125 | cost [532.0]
125 --- 131 | cost [399.0]
127 --- 128 | cost [420.0]
127 --- 129 | cost [357.0]
128 --- 171 | cost [798.0]
129 --- 136 | cost [399.0]
131 --- 132 | cost [175.0]
132 --- 134 | cost [175.0]
134 --- 135 | cost [175.0]
135 --- 136 | cost [175.0]
139 --- 156 | cost [1015.0]
145 --- 146 | cost [175.0]
145 --- 150 | cost [252.0]
146 --- 147 | cost [175.0]
147 --- 148 | cost [175.0]
148 --- 153 | cost [175.0]
150 --- 151 | cost [357.0]
151 --- 163 | cost [399.0]
153 --- 160 | cost [357.0]
156 --- 157 | cost [175.0]
157 --- 158 | cost [175.0]
158 --- 159 | cost [357.0]
159 --- 160 | cost [756.0]
163 --- 164 | cost [357.0]
164 --- 165 | cost [532.0]
165 --- 166 | cost [175.0]
166 --- 190 | cost [9688.0]
171 --- 182 | cost [9541.0]
177 --- 180 | cost [560.0]
177 --- 181 | cost [252.0]
179 --- 180 | cost [399.0]
179 --- 195 | cost [819.0]
181 --- 182 | cost [693.0]
187 --- 191 | cost [1652.0]
187 --- 195 | cost [1568.0]
190 --- 191 | cost [532.0]

STAR
3  -->  6 | cost [153.0]
4  -->  5 | cost [153.0]
7  -->  2 | cost [153.0]
8  -->  9 | cost [153.0]
17 --> 16 | cost [75.0]
18 --> 22 | cost [342.0]
19 --> 22 | cost [306.0]
20 --> 22 | cost [381.0]
21 --> 24 | cost [108.0]
23 --> 22 | cost [153.0]
25 --> 24 | cost [108.0]
26 --> 27 | cost [75.0]
29 --> 30 | cost [108.0]
33 --> 34 | cost [75.0]
35 --> 39 | cost [171.0]
36 --> 32 | cost [108.0]
37 --> 32 | cost [75.0]
38 --> 31 | cost [108.0]
40 --> 15 | cost [390.0]
41 --> 57 | cost [381.0]
42 --> 57 | cost [108.0]
43 --> 57 | cost [171.0]
44 --> 55 | cost [75.0]
45 --> 54 | cost [75.0]
46 --> 47 | cost [153.0]
48 --> 50 | cost [108.0]
49 --> 50 | cost [153.0]
52 --> 47 | cost [108.0]
53 --> 54 | cost [153.0]
56 --> 55 | cost [75.0]
59 --> 60 | cost [75.0]
62 --> 61 | cost [153.0]
63 --> 80 | cost [240.0]
65 --> 51 | cost [216.0]
68 --> 67 | cost [75.0]
70 --> 67 | cost [69.0]
72 --> 73 | cost [75.0]
75 --> 82 | cost [108.0]
76 --> 78 | cost [153.0]
77 --> 78 | cost [75.0]
79 --> 92 | cost [75.0]
81 --> 96 | cost [171.0]
86 --> 85 | cost [108.0]
87 --> 84 | cost [75.0]
88 --> 83 | cost [75.0]
91 --> 80 | cost [75.0]
93 --> 102 | cost [75.0]
94 --> 101 | cost [75.0]
97 --> 89 | cost [108.0]
98 --> 83 | cost [153.0]
99 --> 84 | cost [153.0]
100 --> 85 | cost [153.0]
106 --> 112 | cost [75.0]
107 --> 112 | cost [108.0]
108 --> 109 | cost [108.0]
117 --> 116 | cost [75.0]
118 --> 120 | cost [153.0]
119 --> 120 | cost [75.0]
122 --> 115 | cost [120.0]
126 --> 125 | cost [114.0]
130 --> 131 | cost [75.0]
133 --> 132 | cost [75.0]
137 --> 136 | cost [258.0]
138 --> 134 | cost [306.0]
140 --> 134 | cost [75.0]
141 --> 135 | cost [75.0]
142 --> 147 | cost [75.0]
143 --> 146 | cost [75.0]
144 --> 145 | cost [108.0]
149 --> 146 | cost [75.0]
152 --> 153 | cost [75.0]
154 --> 156 | cost [153.0]
155 --> 156 | cost [75.0]
161 --> 153 | cost [75.0]
162 --> 153 | cost [108.0]
167 --> 109 | cost [549.0]
168 --> 109 | cost [825.0]
169 --> 125 | cost [75.0]
170 --> 127 | cost [75.0]
172 --> 171 | cost [342.0]
173 --> 177 | cost [471.0]
174 --> 177 | cost [417.0]
175 --> 177 | cost [186.0]
176 --> 177 | cost [291.0]
178 --> 180 | cost [75.0]
183 --> 181 | cost [75.0]
184 --> 180 | cost [75.0]
185 --> 179 | cost [153.0]
186 --> 187 | cost [228.0]
188 --> 191 | cost [228.0]
189 --> 190 | cost [228.0]
192 --> 187 | cost [228.0]
193 --> 187 | cost [324.0]
194 --> 179 | cost [75.0]
196 --> 195 | cost [228.0]
197 --> 195 | cost [324.0]
198 --> 195 | cost [228.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1