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

——————— Thu, 25 Jan 2024 15:36:05 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 5 hubs —— 1—200—199—198—201
total time           3606.05 (TL 3600)    gap                  0.935                
blossom time         0                    nb blossom           0.0                  
LB <= UB             83441<=1274890       subtour              11665.0              
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       4852                 n lazycuts edges     0.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—200—199—198—201

RING
1  --- 200 | cost [7848.0]
198 --- 199 | cost [4605.0]
198 --- 201 | cost [1356.0]
199 --- 200 | cost [11280.0]

STAR
2  --> 198 | cost [8750.0]
3  --> 198 | cost [10752.0]
4  --> 198 | cost [5572.0]
5  --> 200 | cost [5775.0]
6  --> 198 | cost [7035.0]
7  --> 199 | cost [1498.0]
8  --> 200 | cost [6055.0]
9  --> 199 | cost [1876.0]
10 --> 199 | cost [9387.0]
11 --> 199 | cost [9499.0]
12 -->  1 | cost [3801.0]
13 --> 198 | cost [2268.0]
14 --> 198 | cost [8253.0]
15 --> 198 | cost [1015.0]
16 --> 199 | cost [4851.0]
17 --> 200 | cost [4991.0]
18 --> 199 | cost [5264.0]
19 --> 199 | cost [8295.0]
20 --> 198 | cost [4641.0]
21 --> 198 | cost [11788.0]
22 --> 200 | cost [6104.0]
23 --> 198 | cost [11004.0]
24 --> 199 | cost [3549.0]
25 --> 200 | cost [4543.0]
26 --> 199 | cost [1106.0]
27 --> 198 | cost [749.0]
28 --> 200 | cost [3017.0]
29 --> 199 | cost [4578.0]
30 --> 198 | cost [8309.0]
31 --> 198 | cost [5019.0]
32 --> 199 | cost [2492.0]
33 --> 198 | cost [10871.0]
34 --> 200 | cost [3542.0]
35 --> 198 | cost [9044.0]
36 --> 198 | cost [9723.0]
37 --> 199 | cost [3864.0]
38 --> 200 | cost [3752.0]
39 --> 200 | cost [3479.0]
40 -->  1 | cost [2653.0]
41 --> 198 | cost [8869.0]
42 --> 198 | cost [6090.0]
43 --> 200 | cost [6426.0]
44 --> 199 | cost [6384.0]
45 --> 198 | cost [11067.0]
46 -->  1 | cost [4039.0]
47 --> 198 | cost [5544.0]
48 --> 199 | cost [8589.0]
49 --> 199 | cost [6006.0]
50 --> 200 | cost [7098.0]
51 --> 199 | cost [5271.0]
52 --> 199 | cost [9576.0]
53 -->  1 | cost [224.0]
54 --> 198 | cost [7756.0]
55 --> 198 | cost [5390.0]
56 --> 200 | cost [4242.0]
57 --> 198 | cost [9786.0]
58 --> 200 | cost [1274.0]
59 --> 198 | cost [10164.0]
60 --> 198 | cost [5600.0]
61 --> 199 | cost [2303.0]
62 --> 200 | cost [6440.0]
63 --> 199 | cost [5642.0]
64 --> 198 | cost [4606.0]
65 --> 198 | cost [4018.0]
66 --> 199 | cost [7014.0]
67 --> 198 | cost [4487.0]
68 --> 198 | cost [8771.0]
69 --> 198 | cost [9597.0]
70 --> 200 | cost [11564.0]
71 --> 200 | cost [4340.0]
72 --> 200 | cost [5376.0]
73 --> 198 | cost [10871.0]
74 --> 198 | cost [10038.0]
75 --> 200 | cost [7154.0]
76 --> 200 | cost [11382.0]
77 --> 198 | cost [5628.0]
78 --> 199 | cost [1463.0]
79 --> 198 | cost [2625.0]
80 --> 198 | cost [5418.0]
81 --> 198 | cost [11550.0]
82 --> 199 | cost [1827.0]
83 --> 200 | cost [6132.0]
84 --> 199 | cost [8946.0]
85 -->  1 | cost [1512.0]
86 --> 200 | cost [6741.0]
87 --> 199 | cost [12684.0]
88 --> 200 | cost [1624.0]
89 --> 198 | cost [10080.0]
90 --> 200 | cost [3899.0]
91 --> 200 | cost [9912.0]
92 --> 199 | cost [8960.0]
93 --> 198 | cost [6440.0]
94 --> 200 | cost [9611.0]
95 --> 200 | cost [8757.0]
96 --> 199 | cost [11130.0]
97 --> 199 | cost [11942.0]
98 --> 200 | cost [1505.0]
99 --> 198 | cost [8750.0]
100 --> 198 | cost [10794.0]
101 --> 198 | cost [5481.0]
102 --> 200 | cost [12817.0]
103 --> 200 | cost [3178.0]
104 --> 199 | cost [10493.0]
105 --> 200 | cost [6258.0]
106 --> 198 | cost [7021.0]
107 --> 198 | cost [7070.0]
108 --> 198 | cost [8400.0]
109 --> 198 | cost [7098.0]
110 --> 199 | cost [5082.0]
111 -->  1 | cost [903.0]
112 --> 198 | cost [7042.0]
113 --> 200 | cost [9772.0]
114 --> 200 | cost [1876.0]
115 -->  1 | cost [819.0]
116 --> 199 | cost [6657.0]
117 -->  1 | cost [910.0]
118 --> 199 | cost [4011.0]
119 --> 199 | cost [8470.0]
120 --> 198 | cost [5971.0]
121 -->  1 | cost [3325.0]
122 --> 199 | cost [6748.0]
123 --> 198 | cost [756.0]
124 --> 199 | cost [2779.0]
125 --> 198 | cost [7693.0]
126 --> 199 | cost [12502.0]
127 --> 198 | cost [6797.0]
128 --> 198 | cost [4788.0]
129 --> 200 | cost [3983.0]
130 --> 200 | cost [4508.0]
131 --> 198 | cost [11543.0]
132 -->  1 | cost [1323.0]
133 --> 200 | cost [9569.0]
134 --> 200 | cost [6062.0]
135 --> 198 | cost [6370.0]
136 --> 199 | cost [2100.0]
137 --> 200 | cost [6741.0]
138 --> 199 | cost [2191.0]
139 --> 200 | cost [6125.0]
140 --> 198 | cost [11389.0]
141 --> 200 | cost [1295.0]
142 --> 198 | cost [9940.0]
143 --> 200 | cost [4004.0]
144 --> 200 | cost [11109.0]
145 --> 198 | cost [1498.0]
146 --> 200 | cost [4088.0]
147 --> 198 | cost [3010.0]
148 --> 200 | cost [1764.0]
149 -->  1 | cost [7266.0]
150 --> 200 | cost [9989.0]
151 --> 198 | cost [6202.0]
152 --> 200 | cost [4494.0]
153 --> 199 | cost [7007.0]
154 --> 198 | cost [11928.0]
155 --> 200 | cost [7049.0]
156 --> 198 | cost [11032.0]
157 --> 198 | cost [6433.0]
158 --> 198 | cost [5313.0]
159 -->  1 | cost [3297.0]
160 --> 198 | cost [3122.0]
161 --> 198 | cost [6601.0]
162 --> 198 | cost [4130.0]
163 --> 198 | cost [5936.0]
164 --> 198 | cost [11158.0]
165 --> 199 | cost [10850.0]
166 --> 199 | cost [10290.0]
167 --> 198 | cost [6818.0]
168 --> 200 | cost [8589.0]
169 --> 198 | cost [9415.0]
170 --> 199 | cost [8050.0]
171 --> 200 | cost [847.0]
172 -->  1 | cost [4172.0]
173 --> 200 | cost [10339.0]
174 -->  1 | cost [3150.0]
175 --> 198 | cost [9464.0]
176 --> 200 | cost [10199.0]
177 --> 198 | cost [3185.0]
178 --> 200 | cost [4697.0]
179 --> 199 | cost [5481.0]
180 --> 198 | cost [11452.0]
181 --> 198 | cost [8029.0]
182 --> 200 | cost [10584.0]
183 --> 200 | cost [6930.0]
184 --> 199 | cost [4151.0]
185 --> 200 | cost [7518.0]
186 --> 198 | cost [6251.0]
187 --> 198 | cost [6531.0]
188 --> 199 | cost [6335.0]
189 --> 198 | cost [10759.0]
190 --> 199 | cost [6685.0]
191 --> 198 | cost [693.0]
192 --> 198 | cost [7553.0]
193 --> 198 | cost [4452.0]
194 --> 199 | cost [5894.0]
195 --> 200 | cost [10822.0]
196 --> 200 | cost [4921.0]
197 --> 199 | cost [10717.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Thu, 25 Jan 2024 16:36:51 ————————— 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           3612.53 (TL 3600)    gap                  0.778                
blossom time         0                    nb blossom           0.0                  
LB <= UB             84105.04<=378575     Master/SP costs      378575/0             
Master time          3612.53              SP time              0.0                  
subtour              16406.0              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       7147                 
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 --> 36 | cost [3059.0]
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 --> 98 | cost [4410.0]
153 --> 170 | cost [2716.0]
155 --> 22 | cost [1092.0]
156 --> 45 | cost [1148.0]
157 --> 107 | cost [651.0]
158 --> 151 | cost [3045.0]
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