------------------------------------------------------------
                        α=7.0 —— kroD100 —— 100 nodes       
------------------------------------------------------------

——————— Sat, 13 Jan 2024 17:07:50 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 44 hubs —— 1—88—24—41—71—4—44—53—60—62—37—51—100—2—92—87—26—10—21—20—18—85—59—64—96—86—65—68—33—45—99—31—57—72—74—67—36—58—70—89—17—90—50—101
total time           3676.79 (TL 3600)    gap                  0.202                
blossom time         0                    nb blossom           0.0                  
LB <= UB             100463<=125855       subtour              14399.0              
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       6044                 n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—88—24—41—71—4—44—53—60—62—37—51—100—2—92—87—26—10—21—20—18—85—59—64—96—86—65—68—33—45—99—31—57—72—74—67—36—58—70—89—17—90—50—101

RING
1  --- 88 | cost [2821.0]
2  --- 92 | cost [2716.0]
2  --- 100 | cost [714.0]
4  --- 44 | cost [1015.0]
4  --- 71 | cost [1414.0]
8  --- 52 | cost [602.0]
8  --- 66 | cost [616.0]
10 --- 21 | cost [2268.0]
10 --- 26 | cost [2261.0]
17 --- 89 | cost [1708.0]
17 --- 90 | cost [385.0]
18 --- 20 | cost [2394.0]
18 --- 85 | cost [1316.0]
20 --- 21 | cost [3605.0]
24 --- 41 | cost [1771.0]
24 --- 88 | cost [707.0]
26 --- 87 | cost [84.0]
31 --- 57 | cost [1526.0]
31 --- 99 | cost [413.0]
33 --- 45 | cost [1155.0]
33 --- 68 | cost [532.0]
36 --- 58 | cost [3612.0]
36 --- 67 | cost [875.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
38 --- 66 | cost [679.0]
38 --- 81 | cost [1323.0]
41 --- 71 | cost [5649.0]
44 --- 53 | cost [2100.0]
45 --- 99 | cost [1491.0]
50 --- 90 | cost [3976.0]
50 --- 101 | cost [651.0]
51 --- 100 | cost [798.0]
52 --- 81 | cost [2037.0]
53 --- 60 | cost [1393.0]
54 --- 63 | cost [931.0]
54 --- 91 | cost [98.0]
57 --- 72 | cost [1141.0]
58 --- 70 | cost [6468.0]
59 --- 64 | cost [1687.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
63 --- 91 | cost [1022.0]
64 --- 96 | cost [3318.0]
65 --- 68 | cost [1491.0]
65 --- 86 | cost [2044.0]
67 --- 74 | cost [3164.0]
70 --- 89 | cost [1582.0]
72 --- 74 | cost [5320.0]
86 --- 96 | cost [420.0]
87 --- 92 | cost [3080.0]

STAR
3  --> 59 | cost [696.0]
5  --> 53 | cost [654.0]
6  --> 59 | cost [519.0]
7  --> 74 | cost [795.0]
9  --> 10 | cost [609.0]
11 --> 90 | cost [576.0]
12 --> 21 | cost [1230.0]
13 --> 88 | cost [408.0]
14 --> 68 | cost [63.0]
15 --> 63 | cost [828.0]
16 --> 54 | cost [717.0]
19 -->  2 | cost [585.0]
22 --> 58 | cost [1254.0]
23 --> 66 | cost [1071.0]
25 --> 20 | cost [105.0]
27 --> 24 | cost [186.0]
28 --> 21 | cost [984.0]
29 --> 58 | cost [732.0]
30 --> 100 | cost [390.0]
32 --> 17 | cost [1020.0]
34 --> 81 | cost [150.0]
35 --> 51 | cost [708.0]
39 --> 91 | cost [690.0]
40 --> 18 | cost [750.0]
42 --> 89 | cost [1281.0]
43 --> 71 | cost [681.0]
46 --> 52 | cost [726.0]
47 --> 21 | cost [654.0]
48 --> 100 | cost [912.0]
49 --> 70 | cost [513.0]
55 --> 87 | cost [552.0]
56 --> 21 | cost [711.0]
61 --> 74 | cost [519.0]
69 --> 63 | cost [1323.0]
73 --> 91 | cost [1047.0]
75 --> 67 | cost [144.0]
76 --> 72 | cost [1128.0]
77 --> 54 | cost [489.0]
78 --> 31 | cost [297.0]
79 --> 88 | cost [381.0]
80 --> 31 | cost [921.0]
82 --> 18 | cost [1098.0]
83 --> 59 | cost [552.0]
84 --> 41 | cost [408.0]
93 --> 44 | cost [465.0]
94 --> 17 | cost [555.0]
95 --> 21 | cost [951.0]
97 --> 17 | cost [1041.0]
98 --> 70 | cost [750.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Sat, 13 Jan 2024 18:14:29 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 47 hubs —— 1-50-94-17-90-89-38-66-8-74-67-36-58-31-99-45-33-68-65-86-96-85-59-40-6-25-21-10-26-87-92-19-100-51-37-62-60-44-4-43-77-54-15-41-24-27-101-1
total time           3609.04 (TL 3600)    gap                  0.149                
blossom time         0                    nb blossom           0.0                  
LB <= UB             106085<=124716       Master/SP costs      124716/0             
Master time          3609.0               SP time              0.04                 
subtour              13796.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            0.0                  SP method            poly                 
tildeV               empty                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       28412                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—50—94—17—90—89—38—66—8—74—67—36—58—31—99—45—33—68—65—86—96—85—59—40—6—25—21—10—26—87—92—19—100—51—37—62—60—44—4—43—77—54—15—41—24—27—101

RING
1  --- 50 | cost [651.0]
4  --- 43 | cost [1764.0]
4  --- 44 | cost [1015.0]
6  --- 25 | cost [2478.0]
6  --- 40 | cost [287.0]
8  --- 66 | cost [616.0]
8  --- 74 | cost [4032.0]
10 --- 21 | cost [2268.0]
10 --- 26 | cost [2261.0]
15 --- 41 | cost [2905.0]
15 --- 54 | cost [2107.0]
17 --- 90 | cost [385.0]
17 --- 94 | cost [1295.0]
19 --- 92 | cost [2149.0]
19 --- 100 | cost [1365.0]
21 --- 25 | cost [3731.0]
24 --- 27 | cost [434.0]
24 --- 41 | cost [1771.0]
26 --- 87 | cost [84.0]
27 --- 101 | cost [2450.0]
31 --- 58 | cost [12376.0]
31 --- 99 | cost [413.0]
33 --- 45 | cost [1155.0]
33 --- 68 | cost [532.0]
36 --- 58 | cost [3612.0]
36 --- 67 | cost [875.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
38 --- 66 | cost [679.0]
38 --- 89 | cost [4116.0]
40 --- 59 | cost [1106.0]
43 --- 77 | cost [1022.0]
44 --- 60 | cost [1351.0]
45 --- 99 | cost [1491.0]
50 --- 94 | cost [3094.0]
51 --- 100 | cost [798.0]
54 --- 77 | cost [1141.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
65 --- 68 | cost [1491.0]
65 --- 86 | cost [2044.0]
67 --- 74 | cost [3164.0]
85 --- 96 | cost [3073.0]
86 --- 96 | cost [420.0]
87 --- 92 | cost [3080.0]
89 --- 90 | cost [1330.0]

STAR
2  --> 100 | cost [306.0]
3  --> 40 | cost [363.0]
5  --> 40 | cost [1134.0]
7  --> 74 | cost [795.0]
9  --> 10 | cost [609.0]
11 --> 90 | cost [576.0]
12 --> 21 | cost [1230.0]
13 --> 24 | cost [687.0]
14 --> 68 | cost [63.0]
16 --> 54 | cost [717.0]
18 --> 85 | cost [564.0]
20 --> 25 | cost [105.0]
22 --> 58 | cost [1254.0]
23 --> 66 | cost [1071.0]
28 --> 21 | cost [984.0]
29 --> 58 | cost [732.0]
30 --> 100 | cost [390.0]
32 --> 94 | cost [537.0]
34 --> 38 | cost [513.0]
35 --> 51 | cost [708.0]
39 --> 54 | cost [732.0]
42 --> 89 | cost [1281.0]
46 -->  8 | cost [858.0]
47 --> 21 | cost [654.0]
48 --> 100 | cost [912.0]
49 --> 89 | cost [999.0]
52 -->  8 | cost [258.0]
53 --> 60 | cost [597.0]
55 --> 26 | cost [549.0]
56 --> 21 | cost [711.0]
57 --> 31 | cost [654.0]
61 --> 74 | cost [519.0]
63 --> 54 | cost [399.0]
64 --> 59 | cost [723.0]
69 --> 15 | cost [1005.0]
70 --> 89 | cost [678.0]
71 -->  4 | cost [606.0]
72 --> 31 | cost [1026.0]
73 --> 15 | cost [969.0]
75 --> 67 | cost [144.0]
76 --> 31 | cost [1215.0]
78 --> 31 | cost [297.0]
79 --> 24 | cost [687.0]
80 --> 31 | cost [921.0]
81 --> 38 | cost [567.0]
82 --> 25 | cost [1140.0]
83 --> 40 | cost [93.0]
84 --> 41 | cost [408.0]
88 --> 24 | cost [303.0]
91 --> 54 | cost [42.0]
93 --> 44 | cost [465.0]
95 --> 21 | cost [951.0]
97 --> 94 | cost [903.0]
98 --> 17 | cost [1038.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1