------------------------------------------------------------
                        α=3.0 —— kroD100 —— 100 nodes       
------------------------------------------------------------

——————— Fri, 19 Jan 2024 00:48:47 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 100 hubs —— 1—50—90—17—32—98—70—11—34—66—52—8—38—81—24—27—88—13—79—41—84—73—71—93—60—62—5—19—92—48—2—51—100—30—35—37—53—4—43—64—85—3—83—6—40—59—18—25—20—10—9—55—87—26—95—56—21—28—12—47—82—96—86—16—63—91—77—54—39—15—69—46—76—80—31—65—78—45—68—14—33—99—57—72—61—74—7—75—67—36—29—58—22—42—23—89—49—97—94—101
total time           3671.01 (TL 3600)    gap                  0.25                 
blossom time         0                    nb blossom           0.0                  
LB <= UB             62022.96<=82751.35   subtour              2106.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1060                 n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—50—90—17—32—98—70—11—34—66—52—8—38—81—24—27—88—13—79—41—84—73—71—93—60—62—5—19—92—48—2—51—100—30—35—37—53—4—43—64—85—3—83—6—40—59—18—25—20—10—9—55—87—26—95—56—21—28—12—47—82—96—86—16—63—91—77—54—39—15—69—46—76—80—31—65—78—45—68—14—33—99—57—72—61—74—7—75—67—36—29—58—22—42—23—89—49—97—94—101

RING
1  --- 50 | cost [279.0]
2  --- 48 | cost [606.0]
2  --- 51 | cost [564.0]
3  --- 83 | cost [285.0]
3  --- 85 | cost [1116.0]
4  --- 43 | cost [756.0]
4  --- 53 | cost [1284.0]
5  --- 19 | cost [1593.0]
5  --- 62 | cost [1212.0]
6  --- 40 | cost [123.0]
6  --- 83 | cost [180.0]
7  --- 74 | cost [795.0]
7  --- 75 | cost [1014.0]
8  --- 38 | cost [555.0]
8  --- 52 | cost [258.0]
9  --- 10 | cost [609.0]
9  --- 55 | cost [627.0]
10 --- 20 | cost [945.0]
11 --- 34 | cost [1377.0]
11 --- 70 | cost [1260.0]
12 --- 28 | cost [543.0]
12 --- 47 | cost [690.0]
13 --- 79 | cost [225.0]
13 --- 88 | cost [408.0]
14 --- 33 | cost [291.0]
14 --- 68 | cost [63.0]
15 --- 39 | cost [1011.0]
15 --- 69 | cost [1005.0]
16 --- 63 | cost [441.0]
16 --- 86 | cost [1104.0]
17 --- 32 | cost [1020.0]
17 --- 90 | cost [165.0]
18 --- 25 | cost [942.0]
18 --- 59 | cost [714.0]
19 --- 92 | cost [921.0]
20 --- 25 | cost [105.0]
21 --- 28 | cost [984.0]
21 --- 56 | cost [711.0]
22 --- 42 | cost [1191.0]
22 --- 58 | cost [1254.0]
23 --- 42 | cost [639.0]
23 --- 89 | cost [1404.0]
24 --- 27 | cost [186.0]
24 --- 81 | cost [1344.0]
26 --- 87 | cost [36.0]
26 --- 95 | cost [1473.0]
27 --- 88 | cost [390.0]
29 --- 36 | cost [1245.0]
29 --- 58 | cost [732.0]
30 --- 35 | cost [849.0]
30 --- 100 | cost [390.0]
31 --- 65 | cost [1140.0]
31 --- 80 | cost [921.0]
32 --- 98 | cost [1581.0]
33 --- 99 | cost [1050.0]
34 --- 66 | cost [747.0]
35 --- 37 | cost [771.0]
36 --- 67 | cost [375.0]
37 --- 53 | cost [1593.0]
38 --- 81 | cost [567.0]
39 --- 54 | cost [732.0]
40 --- 59 | cost [474.0]
41 --- 79 | cost [1065.0]
41 --- 84 | cost [408.0]
43 --- 64 | cost [927.0]
45 --- 68 | cost [669.0]
45 --- 78 | cost [879.0]
46 --- 69 | cost [1587.0]
46 --- 76 | cost [1815.0]
47 --- 82 | cost [1683.0]
48 --- 92 | cost [963.0]
49 --- 89 | cost [999.0]
49 --- 97 | cost [1263.0]
50 --- 90 | cost [1704.0]
51 --- 100 | cost [342.0]
52 --- 66 | cost [393.0]
54 --- 77 | cost [489.0]
55 --- 87 | cost [552.0]
56 --- 95 | cost [354.0]
57 --- 72 | cost [489.0]
57 --- 99 | cost [759.0]
60 --- 62 | cost [1155.0]
60 --- 93 | cost [807.0]
61 --- 72 | cost [1893.0]
61 --- 74 | cost [519.0]
63 --- 91 | cost [438.0]
64 --- 85 | cost [795.0]
65 --- 78 | cost [912.0]
67 --- 75 | cost [144.0]
70 --- 98 | cost [750.0]
71 --- 73 | cost [1266.0]
71 --- 93 | cost [870.0]
73 --- 84 | cost [1185.0]
76 --- 80 | cost [405.0]
77 --- 91 | cost [492.0]
82 --- 96 | cost [2031.0]
86 --- 96 | cost [180.0]
94 --- 97 | cost [903.0]
94 --- 101 | cost [1527.0]

STAR
44 -->  4 | cost [1015.0]

BACKUP RING
1  --- 90 | cost [19.62]
2  --- 92 | cost [11.64]
2  --- 100 | cost [3.06]
3  ---  6 | cost [4.68]
3  --- 64 | cost [12.36]
4  --- 37 | cost [26.91]
4  --- 64 | cost [13.59]
5  --- 60 | cost [12.33]
5  --- 92 | cost [16.29]
6  --- 59 | cost [5.19]
7  --- 61 | cost [8.43]
7  --- 67 | cost [10.38]
8  --- 66 | cost [2.64]
8  --- 81 | cost [9.57]
9  --- 20 | cost [8.25]
9  --- 87 | cost [9.78]
10 --- 25 | cost [10.41]
10 --- 55 | cost [9.84]
11 --- 66 | cost [14.67]
11 --- 98 | cost [15.75]
12 --- 21 | cost [12.3]
12 --- 82 | cost [19.86]
13 --- 27 | cost [6.96]
13 --- 41 | cost [12.120000000000001]
14 --- 45 | cost [7.29]
14 --- 99 | cost [11.790000000000001]
15 --- 46 | cost [23.580000000000002]
15 --- 54 | cost [9.03]
16 --- 91 | cost [7.5600000000000005]
16 --- 96 | cost [9.450000000000001]
17 --- 50 | cost [16.59]
17 --- 98 | cost [10.38]
18 --- 20 | cost [10.26]
18 --- 40 | cost [7.5]
19 --- 48 | cost [9.6]
19 --- 62 | cost [8.16]
21 --- 95 | cost [9.51]
22 --- 23 | cost [18.3]
22 --- 29 | cost [19.740000000000002]
23 --- 49 | cost [23.67]
24 --- 38 | cost [18.990000000000002]
24 --- 88 | cost [3.0300000000000002]
25 --- 59 | cost [14.76]
26 --- 55 | cost [5.49]
26 --- 56 | cost [17.04]
27 --- 81 | cost [11.85]
28 --- 47 | cost [7.5]
28 --- 56 | cost [11.97]
29 --- 67 | cost [16.2]
30 --- 37 | cost [9.09]
30 --- 51 | cost [6.12]
31 --- 76 | cost [12.15]
31 --- 78 | cost [2.97]
32 --- 70 | cost [19.8]
32 --- 90 | cost [11.82]
33 --- 57 | cost [17.7]
33 --- 68 | cost [2.2800000000000002]
34 --- 52 | cost [9.3]
34 --- 70 | cost [26.34]
35 --- 53 | cost [18.6]
35 --- 100 | cost [9.09]
36 --- 58 | cost [15.48]
36 --- 75 | cost [4.7700000000000005]
38 --- 52 | cost [6.33]
39 --- 69 | cost [19.92]
39 --- 77 | cost [10.08]
40 --- 83 | cost [0.93]
41 --- 73 | cost [11.55]
42 --- 58 | cost [17.22]
42 --- 89 | cost [12.81]
43 --- 53 | cost [18.06]
43 --- 85 | cost [17.22]
45 --- 65 | cost [9.75]
46 --- 80 | cost [21.150000000000002]
47 --- 96 | cost [37.050000000000004]
48 --- 51 | cost [11.31]
49 --- 94 | cost [14.82]
54 --- 91 | cost [0.42]
57 --- 61 | cost [23.25]
60 --- 71 | cost [15.72]
62 --- 93 | cost [19.2]
63 --- 77 | cost [7.23]
63 --- 86 | cost [14.85]
65 --- 80 | cost [13.59]
68 --- 78 | cost [11.88]
69 --- 76 | cost [17.79]
71 --- 84 | cost [24.330000000000002]
72 --- 74 | cost [22.8]
72 --- 99 | cost [11.73]
73 --- 93 | cost [21.150000000000002]
74 --- 75 | cost [14.16]
79 --- 84 | cost [14.16]
79 --- 88 | cost [3.81]
82 --- 86 | cost [20.16]
83 --- 85 | cost [9.15]
87 --- 95 | cost [14.97]
89 --- 97 | cost [16.77]
97 --- 101 | cost [23.37]

BACKUP STAR
44 --> 93 | cost [10.85]

B = 37.050000000000004
i★ = 47
j★ = 82
k★ = 96

       
——————— Fri, 19 Jan 2024 01:17:37 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 101 hubs —— 1-50-34-81-38-66-8-52-46-23-42-89-11-90-17-94-32-97-98-49-70-22-58-29-36-67-75-7-74-61-76-80-72-57-31-78-99-45-33-68-14-65-86-96-16-63-54-91-77-43-64-85-59-3-83-40-6-18-82-25-20-9-10-21-47-12-28-56-95-26-87-55-92-48-2-100-30-35-51-19-37-62-5-53-60-44-93-4-71-39-73-15-69-84-41-24-27-88-79-13-101-1
total time           1647.94              gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             64076.04<=64076.04   Master/SP costs      63882/194.04         
Master time          1639.64              SP time              8.3                  
subtour              22788.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            25.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       6547                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—50—34—81—38—66—8—52—46—23—42—89—11—90—17—94—32—97—98—49—70—22—58—29—36—67—75—7—74—61—76—80—72—57—31—78—99—45—33—68—14—65—86—96—16—63—54—91—77—43—64—85—59—3—83—40—6—18—82—25—20—9—10—21—47—12—28—56—95—26—87—55—92—48—2—100—30—35—51—19—37—62—5—53—60—44—93—4—71—39—73—15—69—84—41—24—27—88—79—13—101

RING
1  --- 50 | cost [279.0]
2  --- 48 | cost [606.0]
2  --- 100 | cost [306.0]
3  --- 59 | cost [696.0]
3  --- 83 | cost [285.0]
4  --- 71 | cost [606.0]
4  --- 93 | cost [534.0]
5  --- 53 | cost [654.0]
5  --- 62 | cost [1212.0]
6  --- 18 | cost [657.0]
6  --- 40 | cost [123.0]
7  --- 74 | cost [795.0]
7  --- 75 | cost [1014.0]
8  --- 52 | cost [258.0]
8  --- 66 | cost [264.0]
9  --- 10 | cost [609.0]
9  --- 20 | cost [825.0]
10 --- 21 | cost [972.0]
11 --- 89 | cost [600.0]
11 --- 90 | cost [576.0]
12 --- 28 | cost [543.0]
12 --- 47 | cost [690.0]
13 --- 79 | cost [225.0]
13 --- 101 | cost [1095.0]
14 --- 65 | cost [615.0]
14 --- 68 | cost [63.0]
15 --- 69 | cost [1005.0]
15 --- 73 | cost [969.0]
16 --- 63 | cost [441.0]
16 --- 96 | cost [945.0]
17 --- 90 | cost [165.0]
17 --- 94 | cost [555.0]
18 --- 82 | cost [1098.0]
19 --- 37 | cost [354.0]
19 --- 51 | cost [426.0]
20 --- 25 | cost [105.0]
21 --- 47 | cost [654.0]
22 --- 58 | cost [1254.0]
22 --- 70 | cost [1566.0]
23 --- 42 | cost [639.0]
23 --- 46 | cost [1782.0]
24 --- 27 | cost [186.0]
24 --- 41 | cost [759.0]
25 --- 82 | cost [1140.0]
26 --- 87 | cost [36.0]
26 --- 95 | cost [1473.0]
27 --- 88 | cost [390.0]
28 --- 56 | cost [1197.0]
29 --- 36 | cost [1245.0]
29 --- 58 | cost [732.0]
30 --- 35 | cost [849.0]
30 --- 100 | cost [390.0]
31 --- 57 | cost [654.0]
31 --- 78 | cost [297.0]
32 --- 94 | cost [537.0]
32 --- 97 | cost [690.0]
33 --- 45 | cost [495.0]
33 --- 68 | cost [228.0]
34 --- 50 | cost [909.0]
34 --- 81 | cost [150.0]
35 --- 51 | cost [708.0]
36 --- 67 | cost [375.0]
37 --- 62 | cost [528.0]
38 --- 66 | cost [291.0]
38 --- 81 | cost [567.0]
39 --- 71 | cost [915.0]
39 --- 73 | cost [450.0]
40 --- 83 | cost [93.0]
41 --- 84 | cost [408.0]
42 --- 89 | cost [1281.0]
43 --- 64 | cost [927.0]
43 --- 77 | cost [438.0]
44 --- 60 | cost [579.0]
44 --- 93 | cost [465.0]
45 --- 99 | cost [639.0]
46 --- 52 | cost [726.0]
48 --- 92 | cost [963.0]
49 --- 70 | cost [513.0]
49 --- 98 | cost [246.0]
53 --- 60 | cost [597.0]
54 --- 63 | cost [399.0]
54 --- 91 | cost [42.0]
55 --- 87 | cost [552.0]
55 --- 92 | cost [1185.0]
56 --- 95 | cost [354.0]
57 --- 72 | cost [489.0]
59 --- 85 | cost [444.0]
61 --- 74 | cost [519.0]
61 --- 76 | cost [1443.0]
64 --- 85 | cost [795.0]
65 --- 86 | cost [876.0]
67 --- 75 | cost [144.0]
69 --- 84 | cost [1440.0]
72 --- 80 | cost [1191.0]
76 --- 80 | cost [405.0]
77 --- 91 | cost [492.0]
78 --- 99 | cost [363.0]
79 --- 88 | cost [381.0]
86 --- 96 | cost [180.0]
97 --- 98 | cost [1062.0]

STAR

BACKUP RING
1  --- 34 | cost [10.8]
2  --- 30 | cost [6.21]
2  --- 92 | cost [11.64]
3  --- 40 | cost [3.63]
3  --- 85 | cost [11.16]
4  --- 39 | cost [14.52]
4  --- 44 | cost [4.3500000000000005]
5  --- 37 | cost [15.450000000000001]
5  --- 60 | cost [12.33]
6  --- 82 | cost [16.95]
6  --- 83 | cost [1.8]
7  --- 61 | cost [8.43]
7  --- 67 | cost [10.38]
8  --- 38 | cost [5.55]
8  --- 46 | cost [8.58]
9  --- 21 | cost [15.69]
9  --- 25 | cost [9.3]
10 --- 20 | cost [9.450000000000001]
10 --- 47 | cost [13.8]
11 --- 17 | cost [6.93]
11 --- 42 | cost [14.46]
12 --- 21 | cost [12.3]
12 --- 56 | cost [16.5]
13 --- 88 | cost [4.08]
14 --- 33 | cost [2.91]
14 --- 86 | cost [13.08]
15 --- 39 | cost [10.11]
15 --- 84 | cost [9.51]
16 --- 54 | cost [7.17]
16 --- 86 | cost [11.040000000000001]
17 --- 32 | cost [10.200000000000001]
18 --- 25 | cost [9.42]
18 --- 40 | cost [7.5]
19 --- 35 | cost [10.86]
19 --- 62 | cost [8.16]
20 --- 82 | cost [12.39]
22 --- 29 | cost [19.740000000000002]
22 --- 49 | cost [20.31]
23 --- 52 | cost [13.5]
23 --- 89 | cost [14.040000000000001]
24 --- 84 | cost [9.450000000000001]
24 --- 88 | cost [3.0300000000000002]
26 --- 55 | cost [5.49]
26 --- 56 | cost [17.04]
27 --- 41 | cost [9.36]
27 --- 79 | cost [7.53]
28 --- 47 | cost [7.5]
28 --- 95 | cost [15.51]
29 --- 67 | cost [16.2]
30 --- 51 | cost [6.12]
31 --- 72 | cost [10.26]
31 --- 99 | cost [1.77]
32 --- 98 | cost [15.81]
33 --- 99 | cost [10.5]
34 --- 38 | cost [5.13]
35 --- 100 | cost [9.09]
36 --- 58 | cost [15.48]
36 --- 75 | cost [4.7700000000000005]
37 --- 51 | cost [3.0]
41 --- 69 | cost [18.45]
42 --- 46 | cost [23.85]
43 --- 85 | cost [17.22]
43 --- 91 | cost [7.68]
44 --- 53 | cost [9.0]
45 --- 68 | cost [6.69]
45 --- 78 | cost [8.790000000000001]
48 --- 55 | cost [21.330000000000002]
48 --- 100 | cost [9.120000000000001]
49 --- 97 | cost [12.63]
50 --- 81 | cost [9.75]
52 --- 66 | cost [3.93]
53 --- 62 | cost [11.040000000000001]
54 --- 77 | cost [4.89]
57 --- 78 | cost [9.120000000000001]
57 --- 80 | cost [11.97]
58 --- 70 | cost [27.72]
59 --- 64 | cost [7.23]
59 --- 83 | cost [5.5200000000000005]
60 --- 93 | cost [8.07]
61 --- 80 | cost [18.51]
63 --- 91 | cost [4.38]
63 --- 96 | cost [13.41]
64 --- 77 | cost [7.83]
65 --- 68 | cost [6.390000000000001]
65 --- 96 | cost [10.56]
66 --- 81 | cost [7.5600000000000005]
69 --- 73 | cost [19.650000000000002]
70 --- 98 | cost [7.5]
71 --- 73 | cost [12.66]
71 --- 93 | cost [8.700000000000001]
72 --- 76 | cost [11.28]
74 --- 75 | cost [14.16]
74 --- 76 | cost [19.56]
79 --- 101 | cost [13.14]
87 --- 92 | cost [13.200000000000001]
87 --- 95 | cost [14.97]
89 --- 90 | cost [5.7]
90 --- 94 | cost [7.0200000000000005]
94 --- 97 | cost [9.03]

BACKUP STAR

B = 27.72
i★ = 58
j★ = 22
k★ = 70