------------------------------------------------------------
                        α=7.0 —— kroA100 —— 100 nodes       
------------------------------------------------------------

——————— Tue, 30 Jan 2024 10:09:05 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 61 hubs —— 1—28—58—61—25—81—69—64—40—44—50—82—95—13—33—37—5—52—78—48—100—14—3—46—34—83—7—57—20—86—62—60—23—98—91—32—11—74—21—72—84—38—24—18—88—22—16—66—65—4—75—97—56—80—31—42—8—49—6—63—101
total time           3635.46 (TL 3600)    gap                  0.167                
blossom time         0                    nb blossom           0.0                  
LB <= UB             115993.61<=139243.23 subtour              179.0                
connectivity cuts    136.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—28—58—61—25—81—69—64—40—44—50—82—95—13—33—37—5—52—78—48—100—14—3—46—34—83—7—57—20—86—62—60—23—98—91—32—11—74—21—72—84—38—24—18—88—22—16—66—65—4—75—97—56—80—31—42—8—49—6—63—101

RING
1  --- 28 | cost [2912.0]
3  --- 14 | cost [1547.0]
3  --- 46 | cost [973.0]
4  --- 65 | cost [1029.0]
4  --- 75 | cost [3339.0]
5  --- 37 | cost [483.0]
5  --- 52 | cost [1813.0]
6  --- 49 | cost [329.0]
6  --- 63 | cost [1099.0]
7  --- 57 | cost [651.0]
7  --- 83 | cost [1890.0]
8  --- 42 | cost [1736.0]
8  --- 49 | cost [3871.0]
11 --- 32 | cost [1414.0]
11 --- 74 | cost [2303.0]
13 --- 33 | cost [707.0]
13 --- 95 | cost [1512.0]
14 --- 100 | cost [1876.0]
16 --- 22 | cost [490.0]
16 --- 66 | cost [3738.0]
18 --- 24 | cost [1267.0]
18 --- 88 | cost [2422.0]
20 --- 57 | cost [1428.0]
20 --- 86 | cost [1085.0]
21 --- 72 | cost [1064.0]
21 --- 74 | cost [462.0]
22 --- 88 | cost [833.0]
23 --- 60 | cost [2415.0]
23 --- 98 | cost [756.0]
24 --- 38 | cost [672.0]
25 --- 61 | cost [1155.0]
25 --- 81 | cost [357.0]
28 --- 58 | cost [2121.0]
31 --- 42 | cost [1603.0]
31 --- 80 | cost [609.0]
32 --- 91 | cost [1505.0]
33 --- 37 | cost [2856.0]
34 --- 46 | cost [2177.0]
34 --- 83 | cost [1022.0]
38 --- 84 | cost [2373.0]
40 --- 44 | cost [2849.0]
40 --- 64 | cost [560.0]
44 --- 50 | cost [1134.0]
48 --- 78 | cost [2954.0]
48 --- 100 | cost [1764.0]
50 --- 82 | cost [3605.0]
52 --- 78 | cost [280.0]
56 --- 80 | cost [1967.0]
56 --- 97 | cost [1512.0]
58 --- 61 | cost [2275.0]
60 --- 62 | cost [1057.0]
62 --- 86 | cost [2156.0]
63 --- 101 | cost [2016.0]
64 --- 69 | cost [2079.0]
65 --- 66 | cost [805.0]
69 --- 81 | cost [2121.0]
72 --- 84 | cost [2198.0]
75 --- 97 | cost [1659.0]
82 --- 95 | cost [1715.0]
91 --- 98 | cost [693.0]

STAR
2  --> 44 | cost [771.0]
9  -->  7 | cost [150.0]
10 --> 84 | cost [420.0]
12 --> 20 | cost [462.0]
15 --> 11 | cost [339.0]
17 --> 11 | cost [345.0]
19 --> 97 | cost [978.0]
26 --> 65 | cost [849.0]
27 --> 86 | cost [243.0]
29 -->  3 | cost [642.0]
30 --> 78 | cost [1056.0]
35 --> 86 | cost [423.0]
36 --> 24 | cost [939.0]
39 --> 78 | cost [1056.0]
41 --> 100 | cost [555.0]
43 --> 46 | cost [594.0]
45 --> 91 | cost [537.0]
47 --> 32 | cost [1083.0]
51 --> 61 | cost [558.0]
53 --> 88 | cost [690.0]
54 --> 64 | cost [543.0]
55 --> 83 | cost [69.0]
59 --> 74 | cost [267.0]
67 --> 28 | cost [903.0]
68 --> 50 | cost [960.0]
70 --> 88 | cost [816.0]
71 --> 14 | cost [804.0]
73 --> 44 | cost [699.0]
76 --> 33 | cost [276.0]
77 --> 60 | cost [573.0]
79 --> 18 | cost [690.0]
85 --> 50 | cost [1263.0]
87 --> 57 | cost [594.0]
89 -->  8 | cost [1248.0]
90 --> 49 | cost [624.0]
92 -->  1 | cost [909.0]
93 --> 28 | cost [144.0]
94 --> 88 | cost [483.0]
96 --> 78 | cost [204.0]
99 --> 38 | cost [939.0]

BACKUP RING
1  --- 58 | cost [50.26]
3  --- 34 | cost [31.36]
3  --- 100 | cost [31.78]
4  --- 66 | cost [15.120000000000001]
4  --- 97 | cost [22.68]
5  --- 33 | cost [33.25]
5  --- 78 | cost [16.94]
6  ---  8 | cost [37.38]
6  --- 101 | cost [27.79]
7  --- 20 | cost [16.94]
7  --- 34 | cost [25.69]
8  --- 31 | cost [32.55]
11 --- 21 | cost [24.43]
11 --- 91 | cost [29.05]
13 --- 37 | cost [30.310000000000002]
13 --- 82 | cost [28.0]
14 --- 46 | cost [23.1]
14 --- 48 | cost [20.16]
16 --- 65 | cost [44.17]
16 --- 88 | cost [4.0600000000000005]
18 --- 22 | cost [30.240000000000002]
18 --- 38 | cost [19.39]
20 --- 62 | cost [22.12]
21 --- 84 | cost [31.36]
22 --- 66 | cost [38.43]
23 --- 62 | cost [34.51]
23 --- 91 | cost [13.44]
24 --- 84 | cost [23.73]
24 --- 88 | cost [36.82]
25 --- 58 | cost [33.46]
25 --- 69 | cost [24.29]
28 --- 61 | cost [43.96]
31 --- 56 | cost [25.69]
32 --- 74 | cost [34.72]
32 --- 98 | cost [21.84]
33 --- 95 | cost [21.77]
37 --- 52 | cost [22.82]
38 --- 72 | cost [40.32]
40 --- 50 | cost [37.52]
40 --- 69 | cost [25.48]
42 --- 49 | cost [54.39]
42 --- 80 | cost [16.17]
44 --- 64 | cost [24.5]
44 --- 82 | cost [36.26]
46 --- 83 | cost [28.98]
48 --- 52 | cost [27.72]
49 --- 63 | cost [14.14]
50 --- 95 | cost [52.71]
56 --- 75 | cost [25.900000000000002]
57 --- 83 | cost [24.92]
57 --- 86 | cost [24.64]
60 --- 86 | cost [32.13]
60 --- 98 | cost [31.220000000000002]
61 --- 81 | cost [14.49]
64 --- 81 | cost [41.93]
65 --- 75 | cost [43.61]
72 --- 74 | cost [15.05]
78 --- 100 | cost [46.97]
80 --- 97 | cost [34.79]

BACKUP STAR
2  --> 64 | cost [9.96]
9  --> 57 | cost [3.0]
10 --> 72 | cost [8.1]
12 --> 86 | cost [5.58]
15 --> 32 | cost [8.4]
17 --> 32 | cost [8.67]
19 --> 75 | cost [7.0200000000000005]
26 --> 66 | cost [9.69]
27 --> 20 | cost [5.43]
29 --> 46 | cost [4.44]
30 --> 52 | cost [11.07]
35 --> 20 | cost [8.790000000000001]
36 --> 38 | cost [6.84]
39 --> 52 | cost [11.67]
41 --> 14 | cost [10.32]
43 -->  3 | cost [5.13]
45 --> 98 | cost [6.42]
47 --> 91 | cost [10.98]
51 --> 25 | cost [7.62]
53 --> 16 | cost [7.68]
54 --> 40 | cost [3.12]
55 --> 34 | cost [5.07]
59 --> 21 | cost [4.53]
67 --> 58 | cost [10.35]
68 --> 81 | cost [12.21]
70 --> 22 | cost [5.58]
71 --> 100 | cost [3.63]
73 --> 50 | cost [5.4]
76 --> 13 | cost [3.09]
77 --> 62 | cost [6.63]
79 --> 88 | cost [7.7700000000000005]
85 --> 81 | cost [15.42]
87 -->  7 | cost [7.140000000000001]
89 --> 42 | cost [5.4]
90 -->  6 | cost [7.47]
93 --> 58 | cost [9.33]
94 --> 22 | cost [4.0200000000000005]
96 --> 52 | cost [3.18]
99 --> 24 | cost [11.91]

B = 69.94
i★ = 1
j★ = 28
k★ = 58

       
——————— Tue, 30 Jan 2024 11:10:27 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 55 hubs —— 1-92-8-42-80-56-97-4-65-66-70-22-16-88-18-24-84-10-72-21-74-17-32-91-98-23-62-20-27-86-12-7-55-83-34-46-3-14-48-52-78-5-37-13-95-82-44-73-64-69-25-61-58-93-101-1
total time           3608.1 (TL 3600)     gap                  0.198                
blossom time         0                    nb blossom           0.0                  
LB <= UB             105958.62<=132180.88 Master/SP costs      120220/11960.88      
Master time          3586.08              SP time              22.02                
subtour              30397.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            119.0                SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       36616                
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—92—8—42—80—56—97—4—65—66—70—22—16—88—18—24—84—10—72—21—74—17—32—91—98—23—62—20—27—86—12—7—55—83—34—46—3—14—48—52—78—5—37—13—95—82—44—73—64—69—25—61—58—93—101

RING
1  --- 92 | cost [2121.0]
1  --- 101 | cost [0.0]
3  --- 14 | cost [1547.0]
3  --- 46 | cost [973.0]
4  --- 65 | cost [1029.0]
4  --- 97 | cost [2268.0]
5  --- 37 | cost [483.0]
5  --- 78 | cost [1694.0]
7  --- 12 | cost [1512.0]
7  --- 55 | cost [1848.0]
8  --- 42 | cost [1736.0]
8  --- 92 | cost [1442.0]
10 --- 72 | cost [1890.0]
10 --- 84 | cost [980.0]
12 --- 86 | cost [1302.0]
13 --- 37 | cost [3031.0]
13 --- 95 | cost [1512.0]
14 --- 48 | cost [2016.0]
16 --- 22 | cost [490.0]
16 --- 88 | cost [406.0]
17 --- 32 | cost [2023.0]
17 --- 74 | cost [2478.0]
18 --- 24 | cost [1267.0]
18 --- 88 | cost [2422.0]
20 --- 27 | cost [1267.0]
20 --- 62 | cost [2212.0]
21 --- 72 | cost [1064.0]
21 --- 74 | cost [462.0]
22 --- 70 | cost [1302.0]
23 --- 62 | cost [3451.0]
23 --- 98 | cost [756.0]
24 --- 84 | cost [2373.0]
25 --- 61 | cost [1155.0]
25 --- 69 | cost [2429.0]
27 --- 86 | cost [567.0]
32 --- 91 | cost [1505.0]
34 --- 46 | cost [2177.0]
34 --- 83 | cost [1022.0]
42 --- 80 | cost [1617.0]
44 --- 73 | cost [1631.0]
44 --- 82 | cost [3626.0]
48 --- 52 | cost [2772.0]
52 --- 78 | cost [280.0]
55 --- 83 | cost [161.0]
56 --- 80 | cost [1967.0]
56 --- 97 | cost [1512.0]
58 --- 61 | cost [2275.0]
58 --- 93 | cost [2177.0]
64 --- 69 | cost [2079.0]
64 --- 73 | cost [2632.0]
65 --- 66 | cost [805.0]
66 --- 70 | cost [2800.0]
82 --- 95 | cost [1715.0]
91 --- 98 | cost [693.0]
93 --- 101 | cost [2891.0]

STAR
2  --> 44 | cost [771.0]
6  --> 92 | cost [987.0]
9  -->  7 | cost [150.0]
11 --> 17 | cost [345.0]
15 --> 17 | cost [39.0]
19 --> 97 | cost [978.0]
26 --> 65 | cost [849.0]
28 --> 93 | cost [144.0]
29 --> 46 | cost [444.0]
30 --> 78 | cost [1056.0]
31 --> 80 | cost [261.0]
33 --> 13 | cost [303.0]
35 --> 86 | cost [423.0]
36 --> 24 | cost [939.0]
38 --> 24 | cost [288.0]
39 --> 78 | cost [1056.0]
40 --> 64 | cost [240.0]
41 --> 14 | cost [1032.0]
43 -->  3 | cost [513.0]
45 --> 91 | cost [537.0]
47 --> 32 | cost [1083.0]
49 --> 92 | cost [1056.0]
50 --> 44 | cost [486.0]
51 --> 61 | cost [558.0]
53 --> 88 | cost [690.0]
54 --> 64 | cost [543.0]
57 -->  7 | cost [279.0]
59 --> 74 | cost [267.0]
60 --> 27 | cost [1617.0]
63 -->  1 | cost [864.0]
67 --> 58 | cost [1035.0]
68 --> 73 | cost [801.0]
71 --> 14 | cost [804.0]
75 --> 97 | cost [711.0]
76 --> 13 | cost [309.0]
77 --> 62 | cost [663.0]
79 --> 18 | cost [690.0]
81 --> 61 | cost [621.0]
85 --> 73 | cost [1236.0]
87 -->  7 | cost [714.0]
89 --> 42 | cost [540.0]
90 --> 10 | cost [900.0]
94 --> 22 | cost [402.0]
96 --> 78 | cost [204.0]
99 --> 24 | cost [1191.0]
100 --> 48 | cost [756.0]

BACKUP RING
1  ---  8 | cost [29.75]
3  --- 34 | cost [31.36]
3  --- 48 | cost [35.49]
4  --- 56 | cost [35.0]
4  --- 66 | cost [15.120000000000001]
5  --- 13 | cost [35.14]
5  --- 52 | cost [18.13]
7  --- 83 | cost [18.900000000000002]
7  --- 86 | cost [25.830000000000002]
8  --- 80 | cost [30.73]
10 --- 21 | cost [29.400000000000002]
10 --- 24 | cost [33.18]
12 --- 27 | cost [9.52]
12 --- 55 | cost [16.1]
13 --- 82 | cost [28.0]
14 --- 46 | cost [23.1]
14 --- 52 | cost [44.38]
16 --- 18 | cost [27.93]
16 --- 70 | cost [15.05]
17 --- 21 | cost [27.51]
17 --- 91 | cost [34.300000000000004]
18 --- 84 | cost [27.09]
20 --- 23 | cost [53.9]
20 --- 86 | cost [10.85]
22 --- 66 | cost [38.43]
22 --- 88 | cost [8.33]
23 --- 91 | cost [13.44]
24 --- 88 | cost [36.82]
25 --- 58 | cost [33.46]
25 --- 64 | cost [45.08]
27 --- 62 | cost [27.16]
32 --- 74 | cost [34.72]
32 --- 98 | cost [21.84]
34 --- 55 | cost [11.83]
37 --- 78 | cost [21.42]
37 --- 95 | cost [42.21]
42 --- 56 | cost [25.900000000000002]
42 --- 92 | cost [31.29]
44 --- 64 | cost [24.5]
44 --- 95 | cost [53.410000000000004]
46 --- 83 | cost [28.98]
48 --- 78 | cost [29.54]
58 --- 101 | cost [50.26]
61 --- 69 | cost [30.45]
61 --- 93 | cost [44.38]
62 --- 98 | cost [41.300000000000004]
65 --- 70 | cost [35.84]
65 --- 97 | cost [32.69]
69 --- 73 | cost [20.51]
72 --- 74 | cost [15.05]
72 --- 84 | cost [21.98]
73 --- 82 | cost [48.370000000000005]
80 --- 97 | cost [34.79]

BACKUP STAR
2  --> 64 | cost [9.96]
6  -->  1 | cost [11.91]
9  --> 12 | cost [7.98]
11 --> 32 | cost [6.0600000000000005]
15 --> 32 | cost [8.4]
19 -->  4 | cost [11.16]
26 --> 66 | cost [9.69]
28 --> 58 | cost [9.09]
29 -->  3 | cost [6.42]
30 --> 52 | cost [11.07]
31 --> 42 | cost [6.87]
33 --> 95 | cost [9.33]
35 --> 27 | cost [5.34]
36 --> 84 | cost [9.66]
38 --> 18 | cost [8.31]
39 --> 52 | cost [11.67]
40 --> 69 | cost [10.92]
41 --> 48 | cost [12.99]
43 --> 46 | cost [5.94]
45 --> 98 | cost [6.42]
47 --> 91 | cost [10.98]
49 --> 10 | cost [12.63]
50 --> 73 | cost [5.4]
51 --> 25 | cost [7.62]
53 --> 16 | cost [7.68]
54 --> 44 | cost [13.89]
57 --> 20 | cost [6.12]
59 --> 21 | cost [4.53]
60 --> 62 | cost [4.53]
67 --> 93 | cost [10.41]
68 --> 25 | cost [13.35]
71 --> 48 | cost [10.71]
75 --> 92 | cost [10.74]
76 --> 95 | cost [7.8]
77 --> 23 | cost [11.46]
79 --> 88 | cost [7.7700000000000005]
81 --> 25 | cost [1.53]
85 --> 25 | cost [16.26]
87 --> 61 | cost [9.72]
89 --> 80 | cost [7.59]
90 --> 84 | cost [11.46]
94 --> 16 | cost [4.83]
96 --> 52 | cost [3.18]
99 --> 18 | cost [17.19]
100 --> 14 | cost [8.040000000000001]

B = 65.36
i★ = 20
j★ = 62
k★ = 23