------------------------------------------------------------
                        α=7.0 —— kroB100 —— 100 nodes       
------------------------------------------------------------

——————— Mon, 08 Jan 2024 08:49:09 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 4 hubs —— 1—95—98—101
total time           10                   gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             100306<=100306       subtour              129.0                
connectivity cuts    21.0                 uc strategy          4                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     1.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—95—98—101

RING
1  --- 95 | cost [672.0]
3  --- 11 | cost [1330.0]
3  --- 93 | cost [1694.0]
7  --- 58 | cost [574.0]
7  --- 84 | cost [217.0]
8  --- 29 | cost [700.0]
8  --- 99 | cost [294.0]
9  --- 25 | cost [210.0]
9  --- 46 | cost [518.0]
11 --- 93 | cost [378.0]
17 --- 36 | cost [1120.0]
17 --- 45 | cost [1008.0]
18 --- 24 | cost [1071.0]
18 --- 77 | cost [1771.0]
19 --- 92 | cost [518.0]
19 --- 96 | cost [1064.0]
20 --- 38 | cost [595.0]
20 --- 75 | cost [1722.0]
22 --- 23 | cost [329.0]
22 --- 88 | cost [791.0]
23 --- 88 | cost [896.0]
24 --- 77 | cost [1344.0]
25 --- 46 | cost [434.0]
26 --- 62 | cost [1267.0]
26 --- 100 | cost [616.0]
27 --- 61 | cost [1687.0]
27 --- 94 | cost [2128.0]
29 --- 99 | cost [903.0]
30 --- 75 | cost [413.0]
30 --- 80 | cost [1232.0]
31 --- 48 | cost [875.0]
31 --- 63 | cost [1162.0]
33 --- 64 | cost [1988.0]
33 --- 82 | cost [1981.0]
36 --- 45 | cost [539.0]
37 --- 65 | cost [2401.0]
37 --- 72 | cost [756.0]
38 --- 80 | cost [882.0]
39 --- 40 | cost [1120.0]
39 --- 70 | cost [763.0]
40 --- 70 | cost [1848.0]
48 --- 63 | cost [1267.0]
49 --- 68 | cost [2023.0]
49 --- 86 | cost [182.0]
58 --- 84 | cost [378.0]
60 --- 66 | cost [2989.0]
60 --- 74 | cost [784.0]
61 --- 94 | cost [1918.0]
62 --- 100 | cost [1624.0]
64 --- 82 | cost [1575.0]
65 --- 72 | cost [2982.0]
66 --- 74 | cost [2443.0]
68 --- 86 | cost [2009.0]
92 --- 96 | cost [966.0]
95 --- 98 | cost [1435.0]
98 --- 101 | cost [1603.0]

STAR
2  --> 63 | cost [1182.0]
4  --> 33 | cost [1395.0]
5  --> 62 | cost [918.0]
6  --> 33 | cost [834.0]
10 --> 68 | cost [387.0]
12 --> 98 | cost [561.0]
13 --> 63 | cost [795.0]
14 --> 64 | cost [363.0]
15 --> 33 | cost [558.0]
16 --> 77 | cost [780.0]
21 -->  1 | cost [774.0]
28 --> 99 | cost [978.0]
32 --> 29 | cost [519.0]
34 -->  7 | cost [882.0]
35 --> 61 | cost [318.0]
41 --> 17 | cost [486.0]
42 --> 64 | cost [762.0]
43 --> 60 | cost [1335.0]
44 --> 19 | cost [1032.0]
47 --> 65 | cost [780.0]
50 --> 77 | cost [1134.0]
51 --> 48 | cost [1383.0]
52 --> 58 | cost [738.0]
53 --> 70 | cost [690.0]
54 --> 58 | cost [1032.0]
55 --> 22 | cost [1098.0]
56 --> 100 | cost [192.0]
57 --> 94 | cost [474.0]
59 --> 29 | cost [561.0]
67 --> 40 | cost [984.0]
69 --> 26 | cost [465.0]
71 --> 27 | cost [780.0]
73 --> 93 | cost [1068.0]
76 --> 99 | cost [369.0]
78 --> 17 | cost [768.0]
79 --> 65 | cost [576.0]
81 --> 65 | cost [1065.0]
83 --> 64 | cost [1086.0]
85 --> 93 | cost [840.0]
87 --> 60 | cost [699.0]
89 --> 60 | cost [1059.0]
90 -->  1 | cost [447.0]
91 --> 99 | cost [804.0]
97 --> 99 | cost [366.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Mon, 08 Jan 2024 08:50:07 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 47 hubs —— 1-98-32-29-8-99-91-28-11-85-73-53-39-40-68-49-30-75-26-100-79-65-37-88-55-24-18-96-36-17-78-13-63-48-82-64-83-87-60-84-7-57-27-9-46-90-101-1
total time           31.38                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             118111<=118111       Master/SP costs      118111/0             
Master time          31.38                SP time              0.0                  
subtour              203.0                connectivity cuts    214.0                
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       74                   
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—98—32—29—8—99—91—28—11—85—73—53—39—40—68—49—30—75—26—100—79—65—37—88—55—24—18—96—36—17—78—13—63—48—82—64—83—87—60—84—7—57—27—9—46—90—101

RING
1  --- 98 | cost [1603.0]
1  --- 101 | cost [0.0]
7  --- 57 | cost [1862.0]
7  --- 84 | cost [217.0]
8  --- 29 | cost [700.0]
8  --- 99 | cost [294.0]
9  --- 27 | cost [2058.0]
9  --- 46 | cost [518.0]
11 --- 28 | cost [2492.0]
11 --- 85 | cost [2156.0]
13 --- 63 | cost [1855.0]
13 --- 78 | cost [1190.0]
17 --- 36 | cost [1120.0]
17 --- 78 | cost [1792.0]
18 --- 24 | cost [1071.0]
18 --- 96 | cost [2275.0]
24 --- 55 | cost [3101.0]
26 --- 75 | cost [2317.0]
26 --- 100 | cost [616.0]
27 --- 57 | cost [2576.0]
28 --- 91 | cost [448.0]
29 --- 32 | cost [1211.0]
30 --- 49 | cost [1764.0]
30 --- 75 | cost [413.0]
32 --- 98 | cost [1666.0]
36 --- 96 | cost [1274.0]
37 --- 65 | cost [2401.0]
37 --- 88 | cost [5341.0]
39 --- 40 | cost [1120.0]
39 --- 53 | cost [1673.0]
40 --- 68 | cost [3269.0]
46 --- 90 | cost [2548.0]
48 --- 63 | cost [1267.0]
48 --- 82 | cost [2835.0]
49 --- 68 | cost [2023.0]
53 --- 73 | cost [2429.0]
55 --- 88 | cost [2758.0]
60 --- 84 | cost [3059.0]
60 --- 87 | cost [1631.0]
64 --- 82 | cost [1575.0]
64 --- 83 | cost [2534.0]
65 --- 79 | cost [1344.0]
73 --- 85 | cost [616.0]
79 --- 100 | cost [3136.0]
83 --- 87 | cost [3066.0]
90 --- 101 | cost [1043.0]
91 --- 99 | cost [1876.0]

STAR
2  --> 13 | cost [552.0]
3  --> 11 | cost [570.0]
4  --> 83 | cost [663.0]
5  --> 40 | cost [1038.0]
6  --> 83 | cost [825.0]
10 --> 68 | cost [387.0]
12 --> 98 | cost [561.0]
14 --> 64 | cost [363.0]
15 --> 82 | cost [1308.0]
16 --> 78 | cost [1071.0]
19 --> 96 | cost [456.0]
20 --> 30 | cost [615.0]
21 --> 90 | cost [459.0]
22 --> 88 | cost [339.0]
23 --> 88 | cost [384.0]
25 -->  9 | cost [90.0]
31 --> 48 | cost [375.0]
33 --> 82 | cost [849.0]
34 --> 57 | cost [726.0]
35 --> 27 | cost [1011.0]
38 --> 49 | cost [765.0]
41 --> 17 | cost [486.0]
42 --> 64 | cost [762.0]
43 --> 60 | cost [1335.0]
44 --> 96 | cost [1413.0]
45 --> 36 | cost [231.0]
47 --> 79 | cost [753.0]
50 --> 55 | cost [1101.0]
51 --> 48 | cost [1383.0]
52 --> 84 | cost [846.0]
54 --> 84 | cost [1182.0]
56 --> 100 | cost [192.0]
58 --> 84 | cost [162.0]
59 --> 32 | cost [468.0]
61 --> 27 | cost [723.0]
62 --> 26 | cost [543.0]
66 --> 87 | cost [1068.0]
67 --> 40 | cost [984.0]
69 --> 26 | cost [465.0]
70 --> 39 | cost [327.0]
71 --> 27 | cost [780.0]
72 --> 37 | cost [324.0]
74 --> 60 | cost [336.0]
76 --> 99 | cost [369.0]
77 --> 24 | cost [576.0]
80 --> 30 | cost [528.0]
81 --> 79 | cost [528.0]
86 --> 49 | cost [78.0]
89 --> 87 | cost [924.0]
92 --> 96 | cost [414.0]
93 --> 11 | cost [162.0]
94 --> 57 | cost [474.0]
95 -->  1 | cost [288.0]
97 --> 99 | cost [366.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 10 Jan 2024 02:05:55 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 3 hubs —— 1—95—101
total time           13.86                gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             98143<=98143         subtour              316.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               empty                
2-opt strategy       0                                                              
explored_nodes       268                  n lazycuts edges     3.0                  
F                    0.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—95—101

RING
1  --- 95 | cost [672.0]
3  --- 11 | cost [1330.0]
3  --- 93 | cost [1694.0]
4  ---  6 | cost [1568.0]
4  --- 83 | cost [1547.0]
6  --- 83 | cost [1925.0]
7  --- 58 | cost [574.0]
7  --- 84 | cost [217.0]
8  --- 29 | cost [700.0]
8  --- 99 | cost [294.0]
9  --- 25 | cost [210.0]
9  --- 46 | cost [518.0]
11 --- 93 | cost [378.0]
14 --- 42 | cost [1624.0]
14 --- 64 | cost [847.0]
17 --- 36 | cost [1120.0]
17 --- 45 | cost [1008.0]
18 --- 24 | cost [1071.0]
18 --- 77 | cost [1771.0]
22 --- 23 | cost [329.0]
22 --- 88 | cost [791.0]
23 --- 88 | cost [896.0]
24 --- 77 | cost [1344.0]
25 --- 46 | cost [434.0]
26 --- 62 | cost [1267.0]
26 --- 100 | cost [616.0]
27 --- 61 | cost [1687.0]
27 --- 94 | cost [2128.0]
29 --- 99 | cost [903.0]
30 --- 49 | cost [1764.0]
30 --- 75 | cost [413.0]
31 --- 48 | cost [875.0]
31 --- 63 | cost [1162.0]
36 --- 45 | cost [539.0]
38 --- 49 | cost [1785.0]
38 --- 80 | cost [882.0]
39 --- 40 | cost [1120.0]
39 --- 70 | cost [763.0]
40 --- 70 | cost [1848.0]
42 --- 64 | cost [1778.0]
48 --- 63 | cost [1267.0]
58 --- 84 | cost [378.0]
61 --- 94 | cost [1918.0]
62 --- 100 | cost [1624.0]
65 --- 75 | cost [3122.0]
65 --- 80 | cost [2961.0]
95 --- 101 | cost [672.0]

STAR
2  --> 42 | cost [651.0]
5  --> 62 | cost [918.0]
10 --> 49 | cost [1158.0]
12 -->  1 | cost [789.0]
13 --> 63 | cost [795.0]
15 -->  6 | cost [774.0]
16 --> 77 | cost [780.0]
19 --> 36 | cost [864.0]
20 --> 80 | cost [126.0]
21 -->  1 | cost [774.0]
28 --> 99 | cost [978.0]
32 --> 29 | cost [519.0]
33 -->  6 | cost [834.0]
34 -->  7 | cost [882.0]
35 --> 61 | cost [318.0]
37 --> 65 | cost [1029.0]
41 --> 17 | cost [486.0]
43 --> 58 | cost [1530.0]
44 --> 36 | cost [1527.0]
47 --> 65 | cost [780.0]
50 --> 77 | cost [1134.0]
51 --> 48 | cost [1383.0]
52 --> 58 | cost [738.0]
53 --> 70 | cost [690.0]
54 --> 58 | cost [1032.0]
55 --> 22 | cost [1098.0]
56 --> 100 | cost [192.0]
57 --> 94 | cost [474.0]
59 --> 29 | cost [561.0]
60 -->  7 | cost [1302.0]
66 -->  4 | cost [1560.0]
67 --> 40 | cost [984.0]
68 --> 49 | cost [867.0]
69 --> 26 | cost [465.0]
71 --> 27 | cost [780.0]
72 --> 65 | cost [1278.0]
73 --> 93 | cost [1068.0]
74 --> 94 | cost [1191.0]
76 --> 99 | cost [369.0]
78 --> 17 | cost [768.0]
79 --> 65 | cost [576.0]
81 --> 65 | cost [1065.0]
82 --> 64 | cost [675.0]
85 --> 93 | cost [840.0]
86 --> 49 | cost [78.0]
87 -->  4 | cost [1260.0]
89 --> 83 | cost [1407.0]
90 -->  1 | cost [447.0]
91 --> 99 | cost [804.0]
92 --> 36 | cost [684.0]
96 --> 36 | cost [546.0]
97 --> 99 | cost [366.0]
98 --> 95 | cost [615.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1

       
——————— Wed, 10 Jan 2024 03:06:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 43 hubs —— 1-95-29-8-99-91-28-11-85-73-53-39-40-62-26-30-80-65-37-22-55-24-18-96-36-45-78-13-63-48-82-33-83-87-60-84-7-34-27-9-46-90-101-1
total time           3605.61 (TL 3600)    gap                  0.122                
blossom time         0                    nb blossom           0.0                  
LB <= UB             104960<=119508       Master/SP costs      119508/0             
Master time          3605.61              SP time              0.0                  
subtour              26547.0              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       43261                
F                    0.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—95—29—8—99—91—28—11—85—73—53—39—40—62—26—30—80—65—37—22—55—24—18—96—36—45—78—13—63—48—82—33—83—87—60—84—7—34—27—9—46—90—101

RING
1  --- 95 | cost [672.0]
7  --- 34 | cost [2058.0]
7  --- 84 | cost [217.0]
8  --- 29 | cost [700.0]
8  --- 99 | cost [294.0]
9  --- 27 | cost [2058.0]
9  --- 46 | cost [518.0]
11 --- 28 | cost [2492.0]
11 --- 85 | cost [2156.0]
13 --- 63 | cost [1855.0]
13 --- 78 | cost [1190.0]
18 --- 24 | cost [1071.0]
18 --- 96 | cost [2275.0]
22 --- 37 | cost [6125.0]
22 --- 55 | cost [2562.0]
24 --- 55 | cost [3101.0]
26 --- 30 | cost [2625.0]
26 --- 62 | cost [1267.0]
27 --- 34 | cost [2142.0]
28 --- 91 | cost [448.0]
29 --- 95 | cost [2835.0]
30 --- 80 | cost [1232.0]
33 --- 82 | cost [1981.0]
33 --- 83 | cost [2590.0]
36 --- 45 | cost [539.0]
36 --- 96 | cost [1274.0]
37 --- 65 | cost [2401.0]
39 --- 40 | cost [1120.0]
39 --- 53 | cost [1673.0]
40 --- 62 | cost [3423.0]
45 --- 78 | cost [2163.0]
46 --- 90 | cost [2548.0]
48 --- 63 | cost [1267.0]
48 --- 82 | cost [2835.0]
53 --- 73 | cost [2429.0]
60 --- 84 | cost [3059.0]
60 --- 87 | cost [1631.0]
65 --- 80 | cost [2961.0]
73 --- 85 | cost [616.0]
83 --- 87 | cost [3066.0]
90 --- 101 | cost [1043.0]
91 --- 99 | cost [1876.0]

STAR
2  --> 13 | cost [552.0]
3  --> 11 | cost [570.0]
4  --> 83 | cost [663.0]
5  --> 62 | cost [918.0]
6  --> 83 | cost [825.0]
10 --> 53 | cost [1455.0]
12 -->  1 | cost [789.0]
14 --> 82 | cost [954.0]
15 --> 33 | cost [558.0]
16 --> 78 | cost [1071.0]
17 --> 45 | cost [432.0]
19 --> 96 | cost [456.0]
20 --> 80 | cost [126.0]
21 --> 90 | cost [459.0]
23 --> 22 | cost [141.0]
25 -->  9 | cost [90.0]
31 --> 48 | cost [375.0]
32 --> 29 | cost [519.0]
35 --> 27 | cost [1011.0]
38 --> 80 | cost [378.0]
41 --> 36 | cost [636.0]
42 --> 82 | cost [780.0]
43 --> 60 | cost [1335.0]
44 --> 96 | cost [1413.0]
47 --> 65 | cost [780.0]
49 --> 30 | cost [756.0]
50 --> 55 | cost [1101.0]
51 --> 48 | cost [1383.0]
52 --> 84 | cost [846.0]
54 --> 84 | cost [1182.0]
56 --> 26 | cost [456.0]
57 --> 34 | cost [726.0]
58 --> 84 | cost [162.0]
59 --> 29 | cost [561.0]
61 --> 27 | cost [723.0]
64 --> 82 | cost [675.0]
66 --> 87 | cost [1068.0]
67 --> 40 | cost [984.0]
68 --> 40 | cost [1401.0]
69 --> 26 | cost [465.0]
70 --> 39 | cost [327.0]
71 --> 27 | cost [780.0]
72 --> 37 | cost [324.0]
74 --> 60 | cost [336.0]
75 --> 30 | cost [177.0]
76 --> 99 | cost [369.0]
77 --> 24 | cost [576.0]
79 --> 65 | cost [576.0]
81 --> 65 | cost [1065.0]
86 --> 30 | cost [819.0]
88 --> 22 | cost [339.0]
89 --> 87 | cost [924.0]
92 --> 96 | cost [414.0]
93 --> 11 | cost [162.0]
94 --> 27 | cost [912.0]
97 --> 99 | cost [366.0]
98 --> 95 | cost [615.0]
100 --> 26 | cost [264.0]

BACKUP RING

BACKUP STAR

B = 0.0
i★ = 1
j★ = 1
k★ = 1