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

——————— Tue, 23 Jan 2024 16:34:25 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 48 hubs —— 1—50—34—38—11—90—89—42—58—36—67—7—72—57—31—99—45—33—68—65—86—96—85—59—40—6—25—21—10—26—87—92—2—100—51—37—62—60—44—4—43—77—54—15—84—24—88—101
total time           122.85               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             116849<=116849       subtour              1230.0               
connectivity cuts    1549.0               uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1517                 n lazycuts edges     2.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—50—34—38—11—90—89—42—58—36—67—7—72—57—31—99—45—33—68—65—86—96—85—59—40—6—25—21—10—26—87—92—2—100—51—37—62—60—44—4—43—77—54—15—84—24—88—101

RING
1  --- 50 | cost [651.0]
1  --- 101 | cost [0.0]
2  --- 92 | cost [2716.0]
2  --- 100 | cost [714.0]
4  --- 43 | cost [1764.0]
4  --- 44 | cost [1015.0]
6  --- 25 | cost [2478.0]
6  --- 40 | cost [287.0]
7  --- 67 | cost [2422.0]
7  --- 72 | cost [4046.0]
10 --- 21 | cost [2268.0]
10 --- 26 | cost [2261.0]
11 --- 38 | cost [2926.0]
11 --- 90 | cost [1344.0]
15 --- 54 | cost [2107.0]
15 --- 84 | cost [2219.0]
21 --- 25 | cost [3731.0]
24 --- 84 | cost [2205.0]
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]
34 --- 38 | cost [1197.0]
34 --- 50 | cost [2121.0]
36 --- 58 | cost [3612.0]
36 --- 67 | cost [875.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
40 --- 59 | cost [1106.0]
42 --- 58 | cost [4018.0]
42 --- 89 | cost [2989.0]
43 --- 77 | cost [1022.0]
44 --- 60 | cost [1351.0]
45 --- 99 | cost [1491.0]
51 --- 100 | cost [798.0]
54 --- 77 | cost [1141.0]
57 --- 72 | cost [1141.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
65 --- 68 | cost [1491.0]
65 --- 86 | cost [2044.0]
85 --- 96 | cost [3073.0]
86 --- 96 | cost [420.0]
87 --- 92 | cost [3080.0]
88 --- 101 | cost [2821.0]
89 --- 90 | cost [1330.0]

STAR
3  --> 40 | cost [363.0]
5  --> 40 | cost [1134.0]
8  --> 38 | cost [555.0]
9  --> 10 | cost [609.0]
12 --> 21 | cost [1230.0]
13 --> 88 | cost [408.0]
14 --> 68 | cost [63.0]
16 --> 54 | cost [717.0]
17 --> 90 | cost [165.0]
18 --> 85 | cost [564.0]
19 --> 37 | cost [354.0]
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 --> 58 | cost [732.0]
30 --> 100 | cost [390.0]
32 --> 90 | cost [1182.0]
35 --> 51 | cost [708.0]
39 --> 54 | cost [732.0]
41 --> 84 | cost [408.0]
46 --> 38 | cost [1359.0]
47 --> 21 | cost [654.0]
48 -->  2 | cost [606.0]
49 --> 89 | cost [999.0]
52 --> 38 | cost [633.0]
53 --> 60 | cost [597.0]
55 --> 26 | cost [549.0]
56 --> 21 | cost [711.0]
61 -->  7 | cost [843.0]
63 --> 54 | cost [399.0]
64 --> 59 | cost [723.0]
66 --> 38 | cost [291.0]
69 --> 15 | cost [1005.0]
70 --> 89 | cost [678.0]
71 -->  4 | cost [606.0]
73 --> 15 | cost [969.0]
74 -->  7 | cost [795.0]
75 --> 67 | cost [144.0]
76 --> 72 | cost [1128.0]
78 --> 31 | cost [297.0]
79 --> 88 | cost [381.0]
80 --> 31 | cost [921.0]
81 --> 34 | cost [150.0]
82 --> 25 | cost [1140.0]
83 --> 40 | cost [93.0]
91 --> 54 | cost [42.0]
93 --> 44 | cost [465.0]
94 --> 90 | cost [702.0]
95 --> 21 | cost [951.0]
97 --> 90 | cost [1191.0]
98 --> 90 | cost [1053.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 23 Jan 2024 16:36:33 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 48 hubs —— 1-88-24-84-15-54-77-43-4-44-60-62-37-51-100-2-92-87-26-10-21-25-6-40-59-85-96-86-65-68-33-45-99-31-57-72-7-67-36-58-42-89-90-11-38-34-50-101-1
total time           97.57                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             116843<=116849       Master/SP costs      116849/0             
Master time          97.57                SP time              0.0                  
subtour              1015.0               connectivity cuts    1276.0               
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       1242                 
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—88—24—84—15—54—77—43—4—44—60—62—37—51—100—2—92—87—26—10—21—25—6—40—59—85—96—86—65—68—33—45—99—31—57—72—7—67—36—58—42—89—90—11—38—34—50—101

RING
1  --- 88 | cost [2821.0]
1  --- 101 | cost [0.0]
2  --- 92 | cost [2716.0]
2  --- 100 | cost [714.0]
4  --- 43 | cost [1764.0]
4  --- 44 | cost [1015.0]
6  --- 25 | cost [2478.0]
6  --- 40 | cost [287.0]
7  --- 67 | cost [2422.0]
7  --- 72 | cost [4046.0]
10 --- 21 | cost [2268.0]
10 --- 26 | cost [2261.0]
11 --- 38 | cost [2926.0]
11 --- 90 | cost [1344.0]
15 --- 54 | cost [2107.0]
15 --- 84 | cost [2219.0]
21 --- 25 | cost [3731.0]
24 --- 84 | cost [2205.0]
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]
34 --- 38 | cost [1197.0]
34 --- 50 | cost [2121.0]
36 --- 58 | cost [3612.0]
36 --- 67 | cost [875.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
40 --- 59 | cost [1106.0]
42 --- 58 | cost [4018.0]
42 --- 89 | cost [2989.0]
43 --- 77 | cost [1022.0]
44 --- 60 | cost [1351.0]
45 --- 99 | cost [1491.0]
50 --- 101 | cost [651.0]
51 --- 100 | cost [798.0]
54 --- 77 | cost [1141.0]
57 --- 72 | cost [1141.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
65 --- 68 | cost [1491.0]
65 --- 86 | cost [2044.0]
85 --- 96 | cost [3073.0]
86 --- 96 | cost [420.0]
87 --- 92 | cost [3080.0]
89 --- 90 | cost [1330.0]

STAR
3  --> 40 | cost [363.0]
5  --> 40 | cost [1134.0]
8  --> 38 | cost [555.0]
9  --> 10 | cost [609.0]
12 --> 21 | cost [1230.0]
13 --> 88 | cost [408.0]
14 --> 68 | cost [63.0]
16 --> 54 | cost [717.0]
17 --> 90 | cost [165.0]
18 --> 85 | cost [564.0]
19 --> 37 | cost [354.0]
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 --> 58 | cost [732.0]
30 --> 100 | cost [390.0]
32 --> 90 | cost [1182.0]
35 --> 51 | cost [708.0]
39 --> 54 | cost [732.0]
41 --> 84 | cost [408.0]
46 --> 38 | cost [1359.0]
47 --> 21 | cost [654.0]
48 -->  2 | cost [606.0]
49 --> 89 | cost [999.0]
52 --> 38 | cost [633.0]
53 --> 60 | cost [597.0]
55 --> 26 | cost [549.0]
56 --> 21 | cost [711.0]
61 -->  7 | cost [843.0]
63 --> 54 | cost [399.0]
64 --> 59 | cost [723.0]
66 --> 38 | cost [291.0]
69 --> 15 | cost [1005.0]
70 --> 89 | cost [678.0]
71 -->  4 | cost [606.0]
73 --> 15 | cost [969.0]
74 -->  7 | cost [795.0]
75 --> 67 | cost [144.0]
76 --> 72 | cost [1128.0]
78 --> 31 | cost [297.0]
79 --> 88 | cost [381.0]
80 --> 31 | cost [921.0]
81 --> 34 | cost [150.0]
82 --> 25 | cost [1140.0]
83 --> 40 | cost [93.0]
91 --> 54 | cost [42.0]
93 --> 44 | cost [465.0]
94 --> 90 | cost [702.0]
95 --> 21 | cost [951.0]
97 --> 90 | cost [1191.0]
98 --> 90 | cost [1053.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1