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

——————— Tue, 16 Jan 2024 14:26:06 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 5 hubs —— 1—27—24—88—101
total time           2028.77              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             106498<=106498       subtour              16398.0              
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       20767                n lazycuts edges     4.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—27—24—88—101

RING
1  --- 27 | cost [2450.0]
2  --- 92 | cost [2716.0]
2  --- 100 | cost [714.0]
3  --- 53 | cost [2380.0]
3  --- 83 | cost [665.0]
7  --- 74 | cost [1855.0]
7  --- 75 | cost [2366.0]
8  --- 52 | cost [602.0]
8  --- 66 | cost [616.0]
10 --- 21 | cost [2268.0]
10 --- 87 | cost [2338.0]
11 --- 89 | cost [1400.0]
11 --- 90 | cost [1344.0]
14 --- 65 | cost [1435.0]
14 --- 68 | cost [147.0]
18 --- 25 | cost [2198.0]
18 --- 59 | cost [1666.0]
21 --- 47 | cost [1526.0]
24 --- 27 | cost [434.0]
24 --- 88 | cost [707.0]
25 --- 47 | cost [3675.0]
31 --- 57 | cost [1526.0]
31 --- 99 | cost [413.0]
34 --- 38 | cost [1197.0]
34 --- 52 | cost [2170.0]
36 --- 67 | cost [875.0]
36 --- 74 | cost [3682.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
38 --- 66 | cost [679.0]
40 --- 59 | cost [1106.0]
40 --- 83 | cost [217.0]
51 --- 100 | cost [798.0]
53 --- 60 | cost [1393.0]
54 --- 63 | cost [931.0]
54 --- 91 | cost [98.0]
57 --- 99 | cost [1771.0]
60 --- 62 | cost [2695.0]
63 --- 91 | cost [1022.0]
65 --- 68 | cost [1491.0]
67 --- 75 | cost [336.0]
87 --- 92 | cost [3080.0]
88 --- 101 | cost [2821.0]
89 --- 90 | cost [1330.0]

STAR
4  --> 60 | cost [1011.0]
5  --> 53 | cost [654.0]
6  --> 40 | cost [123.0]
9  --> 10 | cost [609.0]
12 --> 47 | cost [690.0]
13 --> 88 | cost [408.0]
15 --> 63 | cost [828.0]
16 --> 63 | cost [441.0]
17 --> 90 | cost [165.0]
19 --> 37 | cost [354.0]
20 --> 25 | cost [105.0]
22 --> 89 | cost [1761.0]
23 --> 66 | cost [1071.0]
26 --> 87 | cost [36.0]
28 --> 47 | cost [750.0]
29 --> 36 | cost [1245.0]
30 --> 100 | cost [390.0]
32 --> 90 | cost [1182.0]
33 --> 68 | cost [228.0]
35 --> 51 | cost [708.0]
39 --> 91 | cost [690.0]
41 --> 24 | cost [759.0]
42 --> 89 | cost [1281.0]
43 --> 91 | cost [768.0]
44 --> 60 | cost [579.0]
45 --> 99 | cost [639.0]
46 --> 52 | cost [726.0]
48 -->  2 | cost [606.0]
49 --> 89 | cost [999.0]
50 -->  1 | cost [279.0]
55 --> 87 | cost [552.0]
56 --> 21 | cost [711.0]
58 --> 36 | cost [1548.0]
61 --> 74 | cost [519.0]
64 --> 59 | cost [723.0]
69 --> 63 | cost [1323.0]
70 --> 89 | cost [678.0]
71 --> 91 | cost [1182.0]
72 --> 57 | cost [489.0]
73 --> 91 | cost [1047.0]
76 --> 31 | cost [1215.0]
77 --> 54 | cost [489.0]
78 --> 31 | cost [297.0]
79 --> 88 | cost [381.0]
80 --> 31 | cost [921.0]
81 --> 34 | cost [150.0]
82 --> 18 | cost [1098.0]
84 --> 24 | cost [945.0]
85 --> 59 | cost [444.0]
86 --> 65 | cost [876.0]
93 --> 60 | cost [807.0]
94 --> 90 | cost [702.0]
95 --> 21 | cost [951.0]
96 --> 65 | cost [1056.0]
97 --> 90 | cost [1191.0]
98 --> 90 | cost [1053.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 16 Jan 2024 15:28:12 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 44 hubs —— 1-88-24-84-73-39-91-77-43-4-44-60-62-37-51-100-19-92-26-10-21-25-18-6-40-59-85-96-86-68-33-99-31-67-74-8-66-42-70-89-90-17-94-101-1
total time           3609.72 (TL 3600)    gap                  0.135                
blossom time         0                    nb blossom           0.0                  
LB <= UB             106634<=123267       Master/SP costs      123267/0             
Master time          3609.67              SP time              0.05                 
subtour              23640.0              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       45257                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—88—24—84—73—39—91—77—43—4—44—60—62—37—51—100—19—92—26—10—21—25—18—6—40—59—85—96—86—68—33—99—31—67—74—8—66—42—70—89—90—17—94—101

RING
1  --- 88 | cost [2821.0]
4  --- 43 | cost [1764.0]
4  --- 44 | cost [1015.0]
6  --- 18 | cost [1533.0]
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]
17 --- 90 | cost [385.0]
17 --- 94 | cost [1295.0]
18 --- 25 | cost [2198.0]
19 --- 92 | cost [2149.0]
19 --- 100 | cost [1365.0]
21 --- 25 | cost [3731.0]
24 --- 84 | cost [2205.0]
24 --- 88 | cost [707.0]
26 --- 92 | cost [3150.0]
31 --- 67 | cost [8400.0]
31 --- 99 | cost [413.0]
33 --- 68 | cost [532.0]
33 --- 99 | cost [2450.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
39 --- 73 | cost [1050.0]
39 --- 91 | cost [1610.0]
40 --- 59 | cost [1106.0]
42 --- 66 | cost [3962.0]
42 --- 70 | cost [3724.0]
43 --- 77 | cost [1022.0]
44 --- 60 | cost [1351.0]
51 --- 100 | cost [798.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
67 --- 74 | cost [3164.0]
68 --- 86 | cost [3171.0]
70 --- 89 | cost [1582.0]
73 --- 84 | cost [2765.0]
77 --- 91 | cost [1148.0]
85 --- 96 | cost [3073.0]
86 --- 96 | cost [420.0]
89 --- 90 | cost [1330.0]
94 --- 101 | cost [3563.0]

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 --> 88 | cost [408.0]
14 --> 68 | cost [63.0]
15 --> 91 | cost [903.0]
16 --> 91 | cost [756.0]
20 --> 25 | cost [105.0]
22 --> 42 | cost [1191.0]
23 --> 42 | cost [639.0]
27 --> 24 | cost [186.0]
28 --> 21 | cost [984.0]
29 --> 67 | cost [1620.0]
30 --> 100 | cost [390.0]
32 --> 94 | cost [537.0]
34 --> 66 | cost [747.0]
35 --> 51 | cost [708.0]
36 --> 67 | cost [375.0]
38 --> 66 | cost [291.0]
41 --> 84 | cost [408.0]
45 --> 33 | cost [495.0]
46 -->  8 | cost [858.0]
47 --> 21 | cost [654.0]
48 --> 100 | cost [912.0]
49 --> 70 | cost [513.0]
50 -->  1 | cost [279.0]
52 -->  8 | cost [258.0]
53 --> 60 | cost [597.0]
54 --> 91 | cost [42.0]
55 --> 26 | cost [549.0]
56 --> 21 | cost [711.0]
57 --> 31 | cost [654.0]
58 --> 42 | cost [1722.0]
61 --> 74 | cost [519.0]
63 --> 91 | cost [438.0]
64 --> 59 | cost [723.0]
65 --> 68 | cost [639.0]
69 --> 91 | cost [1659.0]
71 -->  4 | cost [606.0]
72 --> 31 | cost [1026.0]
75 --> 67 | cost [144.0]
76 --> 31 | cost [1215.0]
78 --> 31 | cost [297.0]
79 --> 88 | cost [381.0]
80 --> 31 | cost [921.0]
81 --> 66 | cost [756.0]
82 --> 18 | cost [1098.0]
83 --> 40 | cost [93.0]
87 --> 26 | cost [36.0]
93 --> 44 | cost [465.0]
95 --> 21 | cost [951.0]
97 --> 94 | cost [903.0]
98 --> 70 | cost [750.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1