------------------------------------------------------------
                        α=7.0 —— kroA100 —— 100 nodes       
------------------------------------------------------------

——————— Wed, 24 Jan 2024 22:38:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 56 hubs —— 1—92—8—42—80—56—97—4—65—66—70—22—16—88—18—24—38—84—72—21—74—11—32—91—98—23—60—62—86—20—57—7—83—34—46—3—14—100—48—52—78—5—37—13—95—82—50—44—64—69—81—25—61—58—28—101
total time           3606.94 (TL 3600)    gap                  0.045                
blossom time         0                    nb blossom           0.0                  
LB <= UB             110185<=115388       subtour              34085.0              
connectivity cuts    2000.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       46169                n lazycuts edges     5.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—92—8—42—80—56—97—4—65—66—70—22—16—88—18—24—38—84—72—21—74—11—32—91—98—23—60—62—86—20—57—7—83—34—46—3—14—100—48—52—78—5—37—13—95—82—50—44—64—69—81—25—61—58—28—101

RING
1  --- 92 | cost [2121.0]
3  --- 14 | cost [1547.0]
3  --- 46 | cost [973.0]
4  --- 65 | cost [1029.0]
4  --- 97 | cost [2268.0]
5  --- 37 | cost [483.0]
5  --- 78 | cost [1694.0]
7  --- 57 | cost [651.0]
7  --- 83 | cost [1890.0]
8  --- 42 | cost [1736.0]
8  --- 92 | cost [1442.0]
11 --- 32 | cost [1414.0]
11 --- 74 | cost [2303.0]
13 --- 37 | cost [3031.0]
13 --- 95 | cost [1512.0]
14 --- 100 | cost [1876.0]
16 --- 22 | cost [490.0]
16 --- 88 | cost [406.0]
18 --- 24 | cost [1267.0]
18 --- 88 | cost [2422.0]
20 --- 57 | cost [1428.0]
20 --- 86 | cost [1085.0]
21 --- 72 | cost [1064.0]
21 --- 74 | cost [462.0]
22 --- 70 | cost [1302.0]
23 --- 60 | cost [2415.0]
23 --- 98 | cost [756.0]
24 --- 38 | cost [672.0]
25 --- 61 | cost [1155.0]
25 --- 81 | cost [357.0]
28 --- 58 | cost [2121.0]
28 --- 101 | cost [2912.0]
32 --- 91 | cost [1505.0]
34 --- 46 | cost [2177.0]
34 --- 83 | cost [1022.0]
38 --- 84 | cost [2373.0]
42 --- 80 | cost [1617.0]
44 --- 50 | cost [1134.0]
44 --- 64 | cost [2450.0]
48 --- 52 | cost [2772.0]
48 --- 100 | cost [1764.0]
50 --- 82 | cost [3605.0]
52 --- 78 | cost [280.0]
56 --- 80 | cost [1967.0]
56 --- 97 | cost [1512.0]
58 --- 61 | cost [2275.0]
60 --- 62 | cost [1057.0]
62 --- 86 | cost [2156.0]
64 --- 69 | cost [2079.0]
65 --- 66 | cost [805.0]
66 --- 70 | cost [2800.0]
69 --- 81 | cost [2121.0]
72 --- 84 | cost [2198.0]
82 --- 95 | cost [1715.0]
91 --- 98 | cost [693.0]

STAR
2  --> 44 | cost [771.0]
6  --> 92 | cost [987.0]
9  -->  7 | cost [150.0]
10 --> 84 | cost [420.0]
12 --> 20 | cost [462.0]
15 --> 11 | cost [339.0]
17 --> 11 | cost [345.0]
19 --> 97 | cost [978.0]
26 --> 65 | cost [849.0]
27 --> 86 | cost [243.0]
29 --> 46 | cost [444.0]
30 --> 78 | cost [1056.0]
31 --> 80 | cost [261.0]
33 --> 13 | cost [303.0]
35 --> 86 | cost [423.0]
36 --> 38 | cost [684.0]
39 --> 78 | cost [1056.0]
40 --> 64 | cost [240.0]
41 --> 100 | cost [555.0]
43 -->  3 | cost [513.0]
45 --> 91 | cost [537.0]
47 --> 32 | cost [1083.0]
49 --> 92 | cost [1056.0]
51 --> 61 | cost [558.0]
53 --> 88 | cost [690.0]
54 --> 64 | cost [543.0]
55 --> 83 | cost [69.0]
59 --> 74 | cost [267.0]
63 -->  1 | cost [864.0]
67 --> 28 | cost [903.0]
68 --> 50 | cost [960.0]
71 --> 100 | cost [363.0]
73 --> 50 | cost [540.0]
75 --> 97 | cost [711.0]
76 --> 13 | cost [309.0]
77 --> 60 | cost [573.0]
79 --> 18 | cost [690.0]
85 --> 50 | cost [1263.0]
87 --> 57 | cost [594.0]
89 --> 42 | cost [540.0]
90 --> 84 | cost [1146.0]
93 --> 28 | cost [144.0]
94 --> 22 | cost [402.0]
96 --> 78 | cost [204.0]
99 --> 38 | cost [939.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 24 Jan 2024 22:40:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 56 hubs —— 1-92-8-42-80-56-97-4-65-66-70-22-16-88-18-24-38-84-72-21-74-11-32-91-98-23-60-62-86-20-57-7-83-34-46-3-14-100-48-52-78-5-37-13-95-82-50-44-64-69-81-25-61-58-28-101-1
total time           99.53                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             115388<=115388       Master/SP costs      115388/0             
Master time          99.53                SP time              0.0                  
subtour              956.0                connectivity cuts    1588.0               
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       1575                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—92—8—42—80—56—97—4—65—66—70—22—16—88—18—24—38—84—72—21—74—11—32—91—98—23—60—62—86—20—57—7—83—34—46—3—14—100—48—52—78—5—37—13—95—82—50—44—64—69—81—25—61—58—28—101

RING
1  --- 92 | cost [2121.0]
1  --- 101 | cost [0.0]
3  --- 14 | cost [1547.0]
3  --- 46 | cost [973.0]
4  --- 65 | cost [1029.0]
4  --- 97 | cost [2268.0]
5  --- 37 | cost [483.0]
5  --- 78 | cost [1694.0]
7  --- 57 | cost [651.0]
7  --- 83 | cost [1890.0]
8  --- 42 | cost [1736.0]
8  --- 92 | cost [1442.0]
11 --- 32 | cost [1414.0]
11 --- 74 | cost [2303.0]
13 --- 37 | cost [3031.0]
13 --- 95 | cost [1512.0]
14 --- 100 | cost [1876.0]
16 --- 22 | cost [490.0]
16 --- 88 | cost [406.0]
18 --- 24 | cost [1267.0]
18 --- 88 | cost [2422.0]
20 --- 57 | cost [1428.0]
20 --- 86 | cost [1085.0]
21 --- 72 | cost [1064.0]
21 --- 74 | cost [462.0]
22 --- 70 | cost [1302.0]
23 --- 60 | cost [2415.0]
23 --- 98 | cost [756.0]
24 --- 38 | cost [672.0]
25 --- 61 | cost [1155.0]
25 --- 81 | cost [357.0]
28 --- 58 | cost [2121.0]
28 --- 101 | cost [2912.0]
32 --- 91 | cost [1505.0]
34 --- 46 | cost [2177.0]
34 --- 83 | cost [1022.0]
38 --- 84 | cost [2373.0]
42 --- 80 | cost [1617.0]
44 --- 50 | cost [1134.0]
44 --- 64 | cost [2450.0]
48 --- 52 | cost [2772.0]
48 --- 100 | cost [1764.0]
50 --- 82 | cost [3605.0]
52 --- 78 | cost [280.0]
56 --- 80 | cost [1967.0]
56 --- 97 | cost [1512.0]
58 --- 61 | cost [2275.0]
60 --- 62 | cost [1057.0]
62 --- 86 | cost [2156.0]
64 --- 69 | cost [2079.0]
65 --- 66 | cost [805.0]
66 --- 70 | cost [2800.0]
69 --- 81 | cost [2121.0]
72 --- 84 | cost [2198.0]
82 --- 95 | cost [1715.0]
91 --- 98 | cost [693.0]

STAR
2  --> 44 | cost [771.0]
6  --> 92 | cost [987.0]
9  -->  7 | cost [150.0]
10 --> 84 | cost [420.0]
12 --> 20 | cost [462.0]
15 --> 11 | cost [339.0]
17 --> 11 | cost [345.0]
19 --> 97 | cost [978.0]
26 --> 65 | cost [849.0]
27 --> 86 | cost [243.0]
29 --> 46 | cost [444.0]
30 --> 78 | cost [1056.0]
31 --> 80 | cost [261.0]
33 --> 13 | cost [303.0]
35 --> 86 | cost [423.0]
36 --> 38 | cost [684.0]
39 --> 78 | cost [1056.0]
40 --> 64 | cost [240.0]
41 --> 100 | cost [555.0]
43 -->  3 | cost [513.0]
45 --> 91 | cost [537.0]
47 --> 32 | cost [1083.0]
49 --> 92 | cost [1056.0]
51 --> 61 | cost [558.0]
53 --> 88 | cost [690.0]
54 --> 64 | cost [543.0]
55 --> 83 | cost [69.0]
59 --> 74 | cost [267.0]
63 -->  1 | cost [864.0]
67 --> 28 | cost [903.0]
68 --> 50 | cost [960.0]
71 --> 100 | cost [363.0]
73 --> 50 | cost [540.0]
75 --> 97 | cost [711.0]
76 --> 13 | cost [309.0]
77 --> 60 | cost [573.0]
79 --> 18 | cost [690.0]
85 --> 50 | cost [1263.0]
87 --> 57 | cost [594.0]
89 --> 42 | cost [540.0]
90 --> 84 | cost [1146.0]
93 --> 28 | cost [144.0]
94 --> 22 | cost [402.0]
96 --> 78 | cost [204.0]
99 --> 38 | cost [939.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1