------------------------------------------------------------
                        α=5.0 —— kroD100 —— 100 nodes       
------------------------------------------------------------

——————— Tue, 16 Jan 2024 12:48:47 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—50—101
total time           1843.49              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             97455<=97455         subtour              68006.0              
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       23022                n lazycuts edges     3.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—50—101

RING
1  --- 50 | cost [465.0]
2  --- 19 | cost [975.0]
2  --- 100 | cost [510.0]
4  --- 44 | cost [725.0]
4  --- 71 | cost [1010.0]
6  --- 40 | cost [205.0]
6  --- 83 | cost [300.0]
7  --- 61 | cost [1405.0]
7  --- 74 | cost [1325.0]
8  --- 46 | cost [1430.0]
8  --- 52 | cost [430.0]
9  --- 10 | cost [1015.0]
9  --- 20 | cost [1375.0]
10 --- 21 | cost [1620.0]
12 --- 28 | cost [905.0]
12 --- 47 | cost [1150.0]
14 --- 33 | cost [485.0]
14 --- 68 | cost [105.0]
15 --- 39 | cost [1685.0]
15 --- 73 | cost [1615.0]
16 --- 63 | cost [735.0]
16 --- 86 | cost [1840.0]
17 --- 90 | cost [275.0]
17 --- 94 | cost [925.0]
18 --- 25 | cost [1570.0]
18 --- 85 | cost [940.0]
19 --- 92 | cost [1535.0]
20 --- 25 | cost [175.0]
21 --- 56 | cost [1185.0]
22 --- 42 | cost [1985.0]
22 --- 58 | cost [2090.0]
24 --- 27 | cost [310.0]
24 --- 84 | cost [1575.0]
26 --- 55 | cost [915.0]
26 --- 95 | cost [2455.0]
27 --- 88 | cost [650.0]
28 --- 47 | cost [1250.0]
31 --- 57 | cost [1090.0]
31 --- 78 | cost [495.0]
33 --- 68 | cost [380.0]
34 --- 38 | cost [855.0]
34 --- 66 | cost [1245.0]
36 --- 67 | cost [625.0]
36 --- 75 | cost [795.0]
37 --- 51 | cost [500.0]
37 --- 62 | cost [880.0]
38 --- 66 | cost [485.0]
39 --- 73 | cost [750.0]
40 --- 83 | cost [155.0]
41 --- 84 | cost [680.0]
41 --- 88 | cost [1410.0]
42 --- 58 | cost [2870.0]
43 --- 71 | cost [1135.0]
43 --- 77 | cost [730.0]
44 --- 60 | cost [965.0]
46 --- 52 | cost [1210.0]
49 --- 70 | cost [855.0]
49 --- 98 | cost [410.0]
50 --- 101 | cost [465.0]
51 --- 100 | cost [570.0]
53 --- 60 | cost [995.0]
53 --- 62 | cost [1840.0]
54 --- 63 | cost [665.0]
54 --- 77 | cost [815.0]
55 --- 92 | cost [1975.0]
56 --- 95 | cost [590.0]
57 --- 72 | cost [815.0]
59 --- 64 | cost [1205.0]
59 --- 85 | cost [740.0]
61 --- 74 | cost [865.0]
64 --- 96 | cost [2370.0]
67 --- 75 | cost [240.0]
70 --- 98 | cost [1250.0]
72 --- 76 | cost [1880.0]
76 --- 80 | cost [675.0]
78 --- 80 | cost [1245.0]
86 --- 96 | cost [300.0]
90 --- 94 | cost [1170.0]

STAR
3  --> 83 | cost [475.0]
5  --> 53 | cost [1090.0]
11 --> 90 | cost [960.0]
13 --> 88 | cost [680.0]
23 --> 42 | cost [1065.0]
29 --> 58 | cost [1220.0]
30 --> 100 | cost [650.0]
32 --> 94 | cost [895.0]
35 --> 51 | cost [1180.0]
45 --> 33 | cost [825.0]
48 -->  2 | cost [1010.0]
65 --> 14 | cost [1025.0]
69 --> 15 | cost [1675.0]
79 --> 88 | cost [635.0]
81 --> 34 | cost [250.0]
82 --> 18 | cost [1830.0]
87 --> 26 | cost [60.0]
89 --> 90 | cost [950.0]
91 --> 54 | cost [70.0]
93 --> 44 | cost [775.0]
97 --> 94 | cost [1505.0]
99 --> 31 | cost [295.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Tue, 16 Jan 2024 13:50:51 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 81 hubs —— 1-50-88-24-41-84-15-73-39-71-4-44-60-53-62-37-51-100-2-19-92-87-26-55-9-10-21-56-28-12-47-20-25-83-40-6-18-85-64-77-91-54-63-16-96-86-65-14-68-33-45-99-31-57-72-76-61-74-7-75-67-36-29-58-22-42-89-70-49-98-97-32-94-17-90-11-66-46-52-34-101-1
total time           3604.94 (TL 3600)    gap                  0.083                
blossom time         0                    nb blossom           0.0                  
LB <= UB             97060<=105900        Master/SP costs      105900/0             
Master time          3604.91              SP time              0.04                 
subtour              27962.0              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       14002                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—50—88—24—41—84—15—73—39—71—4—44—60—53—62—37—51—100—2—19—92—87—26—55—9—10—21—56—28—12—47—20—25—83—40—6—18—85—64—77—91—54—63—16—96—86—65—14—68—33—45—99—31—57—72—76—61—74—7—75—67—36—29—58—22—42—89—70—49—98—97—32—94—17—90—11—66—46—52—34—101

RING
1  --- 50 | cost [465.0]
2  --- 19 | cost [975.0]
2  --- 100 | cost [510.0]
4  --- 44 | cost [725.0]
4  --- 71 | cost [1010.0]
6  --- 18 | cost [1095.0]
6  --- 40 | cost [205.0]
7  --- 74 | cost [1325.0]
7  --- 75 | cost [1690.0]
9  --- 10 | cost [1015.0]
9  --- 55 | cost [1045.0]
10 --- 21 | cost [1620.0]
11 --- 66 | cost [2445.0]
11 --- 90 | cost [960.0]
12 --- 28 | cost [905.0]
12 --- 47 | cost [1150.0]
14 --- 65 | cost [1025.0]
14 --- 68 | cost [105.0]
15 --- 73 | cost [1615.0]
15 --- 84 | cost [1585.0]
16 --- 63 | cost [735.0]
16 --- 96 | cost [1575.0]
17 --- 90 | cost [275.0]
17 --- 94 | cost [925.0]
18 --- 85 | cost [940.0]
19 --- 92 | cost [1535.0]
20 --- 25 | cost [175.0]
20 --- 47 | cost [2605.0]
21 --- 56 | cost [1185.0]
22 --- 42 | cost [1985.0]
22 --- 58 | cost [2090.0]
24 --- 41 | cost [1265.0]
24 --- 88 | cost [505.0]
25 --- 83 | cost [1995.0]
26 --- 55 | cost [915.0]
26 --- 87 | cost [60.0]
28 --- 56 | cost [1995.0]
29 --- 36 | cost [2075.0]
29 --- 58 | cost [1220.0]
31 --- 57 | cost [1090.0]
31 --- 99 | cost [295.0]
32 --- 94 | cost [895.0]
32 --- 97 | cost [1150.0]
33 --- 45 | cost [825.0]
33 --- 68 | cost [380.0]
34 --- 52 | cost [1550.0]
34 --- 101 | cost [1800.0]
36 --- 67 | cost [625.0]
37 --- 51 | cost [500.0]
37 --- 62 | cost [880.0]
39 --- 71 | cost [1525.0]
39 --- 73 | cost [750.0]
40 --- 83 | cost [155.0]
41 --- 84 | cost [680.0]
42 --- 89 | cost [2135.0]
44 --- 60 | cost [965.0]
45 --- 99 | cost [1065.0]
46 --- 52 | cost [1210.0]
46 --- 66 | cost [1825.0]
49 --- 70 | cost [855.0]
49 --- 98 | cost [410.0]
50 --- 88 | cost [2385.0]
51 --- 100 | cost [570.0]
53 --- 60 | cost [995.0]
53 --- 62 | cost [1840.0]
54 --- 63 | cost [665.0]
54 --- 91 | cost [70.0]
57 --- 72 | cost [815.0]
61 --- 74 | cost [865.0]
61 --- 76 | cost [2405.0]
64 --- 77 | cost [1305.0]
64 --- 85 | cost [1325.0]
65 --- 86 | cost [1460.0]
67 --- 75 | cost [240.0]
70 --- 89 | cost [1130.0]
72 --- 76 | cost [1880.0]
77 --- 91 | cost [820.0]
86 --- 96 | cost [300.0]
87 --- 92 | cost [2200.0]
97 --- 98 | cost [1770.0]

STAR
3  --> 83 | cost [475.0]
5  --> 53 | cost [1090.0]
8  --> 52 | cost [430.0]
13 --> 88 | cost [680.0]
23 --> 42 | cost [1065.0]
27 --> 24 | cost [310.0]
30 --> 100 | cost [650.0]
35 --> 51 | cost [1180.0]
38 --> 66 | cost [485.0]
43 --> 77 | cost [730.0]
48 -->  2 | cost [1010.0]
59 --> 85 | cost [740.0]
69 --> 15 | cost [1675.0]
78 --> 31 | cost [495.0]
79 --> 88 | cost [635.0]
80 --> 76 | cost [675.0]
81 --> 34 | cost [250.0]
82 --> 18 | cost [1830.0]
93 --> 44 | cost [775.0]
95 --> 56 | cost [590.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1