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

——————— Sun, 28 Jan 2024 01:35:58 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 63 hubs —— 1—50—34—38—66—8—23—42—89—49—17—94—58—75—36—67—7—80—78—57—31—99—45—33—68—14—65—86—96—16—63—54—91—43—3—83—6—40—59—85—18—25—20—21—10—87—55—92—48—2—100—51—37—62—60—44—4—93—84—24—88—27—101
total time           3633.76 (TL 3600)    gap                  0.231                
blossom time         0                    nb blossom           0.0                  
LB <= UB             110443.88<=143688.56 subtour              603.0                
connectivity cuts    177.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       82                   n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—50—34—38—66—8—23—42—89—49—17—94—58—75—36—67—7—80—78—57—31—99—45—33—68—14—65—86—96—16—63—54—91—43—3—83—6—40—59—85—18—25—20—21—10—87—55—92—48—2—100—51—37—62—60—44—4—93—84—24—88—27—101

RING
1  --- 50 | cost [651.0]
2  --- 48 | cost [1414.0]
2  --- 100 | cost [714.0]
3  --- 43 | cost [4270.0]
3  --- 83 | cost [665.0]
4  --- 44 | cost [1015.0]
4  --- 93 | cost [1246.0]
6  --- 40 | cost [287.0]
6  --- 83 | cost [420.0]
7  --- 67 | cost [2422.0]
7  --- 80 | cost [5138.0]
8  --- 23 | cost [2548.0]
8  --- 66 | cost [616.0]
10 --- 21 | cost [2268.0]
10 --- 87 | cost [2338.0]
14 --- 65 | cost [1435.0]
14 --- 68 | cost [147.0]
16 --- 63 | cost [1029.0]
16 --- 96 | cost [2205.0]
17 --- 49 | cost [2415.0]
17 --- 94 | cost [1295.0]
18 --- 25 | cost [2198.0]
18 --- 85 | cost [1316.0]
20 --- 21 | cost [3605.0]
20 --- 25 | cost [245.0]
23 --- 42 | cost [1491.0]
24 --- 84 | cost [2205.0]
24 --- 88 | cost [707.0]
27 --- 88 | cost [910.0]
27 --- 101 | cost [2450.0]
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 --- 67 | cost [875.0]
36 --- 75 | cost [1113.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
38 --- 66 | cost [679.0]
40 --- 59 | cost [1106.0]
42 --- 89 | cost [2989.0]
43 --- 91 | cost [1792.0]
44 --- 60 | cost [1351.0]
45 --- 99 | cost [1491.0]
48 --- 92 | cost [2247.0]
49 --- 89 | cost [2331.0]
51 --- 100 | cost [798.0]
54 --- 63 | cost [931.0]
54 --- 91 | cost [98.0]
55 --- 87 | cost [1288.0]
55 --- 92 | cost [2765.0]
57 --- 78 | cost [2128.0]
58 --- 75 | cost [4690.0]
58 --- 94 | cost [9464.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
65 --- 86 | cost [2044.0]
78 --- 80 | cost [1743.0]
84 --- 93 | cost [7686.0]
86 --- 96 | cost [420.0]

STAR
5  --> 83 | cost [1041.0]
9  --> 10 | cost [609.0]
11 --> 89 | cost [600.0]
12 --> 21 | cost [1230.0]
13 --> 88 | cost [408.0]
15 --> 63 | cost [828.0]
19 --> 51 | cost [426.0]
22 --> 42 | cost [1191.0]
26 --> 87 | cost [36.0]
28 --> 21 | cost [984.0]
29 --> 36 | cost [1245.0]
30 --> 51 | cost [612.0]
32 --> 94 | cost [537.0]
35 --> 51 | cost [708.0]
39 --> 91 | cost [690.0]
41 --> 24 | cost [759.0]
46 -->  8 | cost [858.0]
47 --> 21 | cost [654.0]
52 -->  8 | cost [258.0]
53 --> 60 | cost [597.0]
56 --> 21 | cost [711.0]
61 -->  7 | cost [843.0]
64 --> 59 | cost [723.0]
69 --> 63 | cost [1323.0]
70 --> 89 | cost [678.0]
71 -->  4 | cost [606.0]
72 --> 57 | cost [489.0]
73 --> 91 | cost [1047.0]
74 -->  7 | cost [795.0]
76 --> 78 | cost [1107.0]
77 --> 54 | cost [489.0]
79 --> 88 | cost [381.0]
81 --> 34 | cost [150.0]
82 --> 18 | cost [1098.0]
90 --> 17 | cost [165.0]
95 --> 21 | cost [951.0]
97 --> 94 | cost [903.0]
98 --> 17 | cost [1038.0]

BACKUP RING
1  --- 34 | cost [25.2]
2  --- 51 | cost [13.16]
2  --- 92 | cost [27.16]
3  ---  6 | cost [10.92]
3  --- 91 | cost [56.21]
4  --- 60 | cost [23.59]
4  --- 84 | cost [69.65]
6  --- 59 | cost [12.11]
7  --- 36 | cost [32.410000000000004]
7  --- 78 | cost [63.0]
8  --- 38 | cost [12.950000000000001]
8  --- 42 | cost [40.39]
10 --- 20 | cost [22.05]
10 --- 55 | cost [22.96]
14 --- 33 | cost [6.79]
14 --- 86 | cost [30.52]
16 --- 54 | cost [16.73]
16 --- 86 | cost [25.76]
17 --- 58 | cost [82.46000000000001]
17 --- 89 | cost [17.080000000000002]
18 --- 20 | cost [23.94]
18 --- 59 | cost [16.66]
21 --- 25 | cost [37.31]
21 --- 87 | cost [40.39]
23 --- 66 | cost [24.990000000000002]
23 --- 89 | cost [32.76]
24 --- 27 | cost [4.34]
24 --- 93 | cost [93.03]
25 --- 85 | cost [34.79]
31 --- 45 | cost [19.04]
31 --- 78 | cost [6.93]
33 --- 99 | cost [24.5]
34 --- 66 | cost [17.43]
36 --- 58 | cost [36.12]
37 --- 60 | cost [39.27]
37 --- 100 | cost [14.63]
38 --- 50 | cost [31.64]
40 --- 83 | cost [2.17]
40 --- 85 | cost [19.25]
42 --- 49 | cost [48.86]
43 --- 54 | cost [18.34]
43 --- 83 | cost [45.01]
44 --- 62 | cost [40.32]
44 --- 93 | cost [10.85]
45 --- 68 | cost [15.610000000000001]
48 --- 55 | cost [49.77]
48 --- 100 | cost [21.28]
49 --- 94 | cost [34.58]
51 --- 62 | cost [18.55]
57 --- 80 | cost [27.93]
57 --- 99 | cost [17.71]
63 --- 91 | cost [10.22]
63 --- 96 | cost [31.29]
65 --- 68 | cost [14.91]
65 --- 96 | cost [24.64]
67 --- 75 | cost [3.36]
67 --- 80 | cost [75.46000000000001]
75 --- 94 | cost [116.76]
84 --- 88 | cost [26.39]
87 --- 92 | cost [30.8]
88 --- 101 | cost [28.21]

BACKUP STAR
5  -->  3 | cost [8.040000000000001]
9  --> 55 | cost [6.2700000000000005]
11 --> 17 | cost [6.93]
12 --> 10 | cost [20.64]
13 --> 24 | cost [6.87]
15 --> 54 | cost [9.03]
19 --> 37 | cost [3.54]
22 --> 58 | cost [12.540000000000001]
26 --> 55 | cost [5.49]
28 --> 10 | cost [19.38]
29 --> 58 | cost [7.32]
30 --> 100 | cost [3.9]
32 --> 17 | cost [10.200000000000001]
35 --> 37 | cost [7.71]
39 --> 54 | cost [7.32]
41 --> 84 | cost [4.08]
46 --> 66 | cost [10.950000000000001]
47 --> 10 | cost [13.8]
52 --> 66 | cost [3.93]
53 --> 44 | cost [9.0]
56 --> 10 | cost [13.620000000000001]
61 --> 67 | cost [17.16]
64 --> 85 | cost [7.95]
69 --> 84 | cost [14.4]
70 --> 49 | cost [5.13]
71 --> 43 | cost [6.8100000000000005]
72 --> 31 | cost [10.26]
73 --> 54 | cost [10.83]
74 --> 67 | cost [13.56]
76 --> 80 | cost [4.05]
77 --> 43 | cost [4.38]
79 --> 24 | cost [6.87]
81 --> 38 | cost [5.67]
82 --> 25 | cost [11.4]
90 --> 89 | cost [5.7]
95 --> 10 | cost [13.44]
97 --> 17 | cost [10.41]
98 --> 49 | cost [2.46]

B = 116.76
i★ = 75
j★ = 58
k★ = 94

       
——————— Sun, 28 Jan 2024 01:45:14 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 54 hubs —— 1-50-94-17-90-11-38-66-23-42-58-36-67-7-61-76-80-78-31-99-45-33-68-65-86-96-85-59-40-6-25-20-47-21-10-26-87-92-2-100-51-37-62-60-44-4-43-77-54-15-84-24-88-101-1
total time           489.09               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             119429.97<=119429.97 Master/SP costs      117295/2134.97       
Master time          426.21               SP time              62.89                
subtour              898.0                connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            378.0                SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       28731                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—50—94—17—90—11—38—66—23—42—58—36—67—7—61—76—80—78—31—99—45—33—68—65—86—96—85—59—40—6—25—20—47—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  --- 61 | cost [1967.0]
7  --- 67 | cost [2422.0]
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]
17 --- 90 | cost [385.0]
17 --- 94 | cost [1295.0]
20 --- 25 | cost [245.0]
20 --- 47 | cost [3647.0]
21 --- 47 | cost [1526.0]
23 --- 42 | cost [1491.0]
23 --- 66 | cost [2499.0]
24 --- 84 | cost [2205.0]
24 --- 88 | cost [707.0]
26 --- 87 | cost [84.0]
31 --- 78 | cost [693.0]
31 --- 99 | cost [413.0]
33 --- 45 | cost [1155.0]
33 --- 68 | cost [532.0]
36 --- 58 | cost [3612.0]
36 --- 67 | cost [875.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
38 --- 66 | cost [679.0]
40 --- 59 | cost [1106.0]
42 --- 58 | cost [4018.0]
43 --- 77 | cost [1022.0]
44 --- 60 | cost [1351.0]
45 --- 99 | cost [1491.0]
50 --- 94 | cost [3094.0]
51 --- 100 | cost [798.0]
54 --- 77 | cost [1141.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
61 --- 76 | cost [3367.0]
65 --- 68 | cost [1491.0]
65 --- 86 | cost [2044.0]
76 --- 80 | cost [945.0]
78 --- 80 | cost [1743.0]
85 --- 96 | cost [3073.0]
86 --- 96 | cost [420.0]
87 --- 92 | cost [3080.0]
88 --- 101 | cost [2821.0]

STAR
3  --> 40 | cost [363.0]
5  --> 40 | cost [1134.0]
8  --> 66 | cost [264.0]
9  --> 10 | cost [609.0]
12 --> 47 | cost [690.0]
13 --> 88 | cost [408.0]
14 --> 68 | cost [63.0]
16 --> 54 | cost [717.0]
18 --> 85 | cost [564.0]
19 --> 37 | cost [354.0]
22 --> 42 | cost [1191.0]
27 --> 24 | cost [186.0]
28 --> 47 | cost [750.0]
29 --> 58 | cost [732.0]
30 --> 100 | cost [390.0]
32 --> 94 | cost [537.0]
34 --> 38 | cost [513.0]
35 --> 51 | cost [708.0]
39 --> 54 | cost [732.0]
41 --> 84 | cost [408.0]
46 --> 66 | cost [1095.0]
48 -->  2 | cost [606.0]
49 --> 90 | cost [1011.0]
52 --> 66 | cost [393.0]
53 --> 60 | cost [597.0]
55 --> 26 | cost [549.0]
56 --> 21 | cost [711.0]
57 --> 31 | cost [654.0]
63 --> 54 | cost [399.0]
64 --> 59 | cost [723.0]
69 --> 15 | cost [1005.0]
70 --> 90 | cost [975.0]
71 -->  4 | cost [606.0]
72 --> 31 | cost [1026.0]
73 --> 15 | cost [969.0]
74 --> 61 | cost [519.0]
75 --> 67 | cost [144.0]
79 --> 88 | cost [381.0]
81 --> 38 | cost [567.0]
82 --> 25 | cost [1140.0]
83 --> 40 | cost [93.0]
89 --> 90 | cost [570.0]
91 --> 54 | cost [42.0]
93 --> 44 | cost [465.0]
95 --> 21 | cost [951.0]
97 --> 94 | cost [903.0]
98 --> 17 | cost [1038.0]

BACKUP RING
1  --- 94 | cost [35.63]
2  --- 51 | cost [13.16]
2  --- 87 | cost [57.89]
4  --- 60 | cost [23.59]
4  --- 77 | cost [27.580000000000002]
6  --- 20 | cost [25.48]
6  --- 59 | cost [12.11]
7  --- 36 | cost [32.410000000000004]
7  --- 76 | cost [42.56]
10 --- 47 | cost [32.2]
10 --- 87 | cost [23.38]
11 --- 17 | cost [16.17]
11 --- 66 | cost [34.230000000000004]
15 --- 24 | cost [44.24]
15 --- 77 | cost [32.410000000000004]
17 --- 50 | cost [38.71]
20 --- 21 | cost [36.050000000000004]
21 --- 26 | cost [39.62]
23 --- 38 | cost [26.740000000000002]
23 --- 58 | cost [51.870000000000005]
24 --- 101 | cost [28.490000000000002]
25 --- 40 | cost [27.580000000000002]
25 --- 47 | cost [36.75]
26 --- 92 | cost [31.5]
31 --- 45 | cost [19.04]
31 --- 80 | cost [21.490000000000002]
33 --- 65 | cost [18.76]
33 --- 99 | cost [24.5]
36 --- 42 | cost [56.42]
37 --- 60 | cost [39.27]
37 --- 100 | cost [14.63]
38 --- 90 | cost [42.14]
40 --- 85 | cost [19.25]
42 --- 66 | cost [39.62]
43 --- 44 | cost [26.6]
43 --- 54 | cost [18.34]
44 --- 62 | cost [40.32]
45 --- 68 | cost [15.610000000000001]
51 --- 62 | cost [18.55]
54 --- 84 | cost [41.51]
58 --- 67 | cost [43.89]
59 --- 96 | cost [39.62]
61 --- 67 | cost [40.04]
61 --- 80 | cost [43.19]
65 --- 96 | cost [24.64]
68 --- 86 | cost [31.71]
76 --- 78 | cost [25.830000000000002]
78 --- 99 | cost [8.47]
84 --- 88 | cost [26.39]
85 --- 86 | cost [33.6]
90 --- 94 | cost [16.38]
92 --- 100 | cost [31.92]

BACKUP STAR
3  -->  6 | cost [4.68]
5  -->  6 | cost [12.06]
8  --> 38 | cost [5.55]
9  --> 20 | cost [8.25]
12 --> 21 | cost [12.3]
13 --> 24 | cost [6.87]
14 --> 33 | cost [2.91]
16 --> 77 | cost [7.5600000000000005]
18 -->  6 | cost [6.57]
19 --> 51 | cost [4.26]
22 --> 58 | cost [12.540000000000001]
27 --> 88 | cost [3.9]
28 --> 21 | cost [9.84]
29 --> 36 | cost [12.450000000000001]
30 --> 51 | cost [6.12]
32 --> 17 | cost [10.200000000000001]
34 --> 66 | cost [7.47]
35 --> 37 | cost [7.71]
39 --> 43 | cost [9.72]
41 --> 24 | cost [7.59]
46 --> 61 | cost [12.66]
48 --> 100 | cost [9.120000000000001]
49 --> 17 | cost [10.35]
52 --> 38 | cost [6.33]
53 --> 44 | cost [9.0]
55 --> 87 | cost [5.5200000000000005]
56 --> 47 | cost [12.75]
57 --> 99 | cost [7.59]
63 --> 77 | cost [7.23]
64 --> 77 | cost [7.83]
69 --> 84 | cost [14.4]
70 --> 17 | cost [10.74]
71 --> 43 | cost [6.8100000000000005]
72 --> 76 | cost [11.28]
73 --> 54 | cost [10.83]
74 -->  7 | cost [7.95]
75 --> 36 | cost [4.7700000000000005]
79 --> 24 | cost [6.87]
81 --> 66 | cost [7.5600000000000005]
82 --> 20 | cost [12.39]
83 -->  6 | cost [1.8]
89 --> 11 | cost [6.0]
91 --> 77 | cost [4.92]
93 -->  4 | cost [5.34]
95 --> 10 | cost [13.44]
97 --> 17 | cost [10.41]
98 --> 90 | cost [10.53]

B = 68.87
i★ = 36
j★ = 58
k★ = 42