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

——————— Fri, 26 Jan 2024 09:55:06 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 49 hubs —— 1—88—24—84—15—54—77—43—4—44—60—62—37—51—19—92—87—26—10—21—20—25—6—40—59—85—96—86—65—14—68—33—45—99—31—57—72—7—67—74—23—66—38—11—90—17—94—50—101
total time           3636.45 (TL 3600)    gap                  0.056                
blossom time         0                    nb blossom           0.0                  
LB <= UB             111589.47<=118232.51 subtour              190.0                
connectivity cuts    263.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       220                  n lazycuts edges     1.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—88—24—84—15—54—77—43—4—44—60—62—37—51—19—92—87—26—10—21—20—25—6—40—59—85—96—86—65—14—68—33—45—99—31—57—72—7—67—74—23—66—38—11—90—17—94—50—101

RING
1  --- 88 | cost [2821.0]
1  --- 101 | cost [0.0]
4  --- 43 | cost [1764.0]
4  --- 44 | cost [1015.0]
6  --- 25 | cost [2478.0]
6  --- 40 | cost [287.0]
7  --- 67 | cost [2422.0]
7  --- 72 | cost [4046.0]
10 --- 21 | cost [2268.0]
10 --- 26 | cost [2261.0]
11 --- 38 | cost [2926.0]
11 --- 90 | cost [1344.0]
14 --- 65 | cost [1435.0]
14 --- 68 | cost [147.0]
15 --- 54 | cost [2107.0]
15 --- 84 | cost [2219.0]
17 --- 90 | cost [385.0]
17 --- 94 | cost [1295.0]
19 --- 51 | cost [994.0]
19 --- 92 | cost [2149.0]
20 --- 21 | cost [3605.0]
20 --- 25 | cost [245.0]
23 --- 66 | cost [2499.0]
23 --- 74 | cost [4032.0]
24 --- 84 | cost [2205.0]
24 --- 88 | cost [707.0]
26 --- 87 | cost [84.0]
31 --- 57 | cost [1526.0]
31 --- 99 | cost [413.0]
33 --- 45 | cost [1155.0]
33 --- 68 | cost [532.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
38 --- 66 | cost [679.0]
40 --- 59 | cost [1106.0]
43 --- 77 | cost [1022.0]
44 --- 60 | cost [1351.0]
45 --- 99 | cost [1491.0]
50 --- 94 | cost [3094.0]
50 --- 101 | cost [651.0]
54 --- 77 | cost [1141.0]
57 --- 72 | cost [1141.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
65 --- 86 | cost [2044.0]
67 --- 74 | cost [3164.0]
85 --- 96 | cost [3073.0]
86 --- 96 | cost [420.0]
87 --- 92 | cost [3080.0]

STAR
2  --> 51 | cost [564.0]
3  --> 40 | cost [363.0]
5  --> 40 | cost [1134.0]
8  --> 66 | cost [264.0]
9  --> 10 | cost [609.0]
12 --> 21 | cost [1230.0]
13 --> 88 | cost [408.0]
16 --> 54 | cost [717.0]
18 --> 85 | cost [564.0]
22 --> 23 | cost [1830.0]
27 --> 24 | cost [186.0]
28 --> 21 | cost [984.0]
29 --> 67 | cost [1620.0]
30 --> 51 | cost [612.0]
32 --> 94 | cost [537.0]
34 --> 38 | cost [513.0]
35 --> 51 | cost [708.0]
36 --> 67 | cost [375.0]
39 --> 54 | cost [732.0]
41 --> 84 | cost [408.0]
42 --> 23 | cost [639.0]
46 --> 66 | cost [1095.0]
47 --> 21 | cost [654.0]
48 --> 19 | cost [960.0]
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]
58 --> 67 | cost [1881.0]
61 --> 74 | cost [519.0]
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]
73 --> 15 | cost [969.0]
75 --> 67 | cost [144.0]
76 --> 72 | cost [1128.0]
78 --> 31 | cost [297.0]
79 --> 88 | cost [381.0]
80 --> 31 | cost [921.0]
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]
100 --> 51 | cost [342.0]

BACKUP RING
1  --- 24 | cost [28.490000000000002]
4  --- 60 | cost [23.59]
4  --- 77 | cost [27.580000000000002]
6  --- 20 | cost [25.48]
6  --- 59 | cost [12.11]
7  --- 57 | cost [51.870000000000005]
7  --- 74 | cost [18.55]
10 --- 20 | cost [22.05]
10 --- 87 | cost [23.38]
11 --- 17 | cost [16.17]
11 --- 66 | cost [34.230000000000004]
14 --- 33 | cost [6.79]
14 --- 86 | cost [30.52]
15 --- 24 | cost [44.24]
15 --- 77 | cost [32.410000000000004]
17 --- 50 | cost [38.71]
19 --- 37 | cost [8.26]
19 --- 87 | cost [51.24]
21 --- 25 | cost [37.31]
21 --- 26 | cost [39.62]
23 --- 38 | cost [26.740000000000002]
23 --- 67 | cost [60.27]
25 --- 40 | cost [27.580000000000002]
26 --- 92 | cost [31.5]
31 --- 45 | cost [19.04]
31 --- 72 | cost [23.94]
33 --- 99 | cost [24.5]
37 --- 60 | cost [39.27]
38 --- 90 | cost [42.14]
40 --- 85 | cost [19.25]
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]
51 --- 92 | cost [31.150000000000002]
54 --- 84 | cost [41.51]
57 --- 99 | cost [17.71]
59 --- 96 | cost [39.62]
65 --- 68 | cost [14.91]
65 --- 96 | cost [24.64]
66 --- 74 | cost [45.71]
67 --- 72 | cost [61.25]
84 --- 88 | cost [26.39]
85 --- 86 | cost [33.6]
90 --- 94 | cost [16.38]
94 --- 101 | cost [35.63]

BACKUP STAR
2  --> 19 | cost [5.8500000000000005]
3  -->  6 | cost [4.68]
5  -->  6 | cost [12.06]
8  --> 38 | cost [5.55]
9  --> 20 | cost [8.25]
12 --> 10 | cost [20.64]
13 --> 24 | cost [6.87]
16 --> 77 | cost [7.5600000000000005]
18 -->  6 | cost [6.57]
22 --> 11 | cost [22.32]
27 --> 88 | cost [3.9]
28 --> 10 | cost [19.38]
29 --> 74 | cost [25.47]
30 --> 37 | cost [9.09]
32 --> 17 | cost [10.200000000000001]
34 --> 66 | cost [7.47]
35 --> 37 | cost [7.71]
36 -->  7 | cost [13.89]
39 --> 43 | cost [9.72]
41 --> 24 | cost [7.59]
42 --> 11 | cost [14.46]
46 --> 38 | cost [13.59]
47 --> 10 | cost [13.8]
48 --> 92 | cost [9.63]
49 --> 17 | cost [10.35]
52 --> 38 | cost [6.33]
53 --> 44 | cost [9.0]
55 --> 87 | cost [5.5200000000000005]
56 --> 10 | cost [13.620000000000001]
58 --> 23 | cost [22.23]
61 -->  7 | cost [8.43]
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]
73 --> 54 | cost [10.83]
75 -->  7 | cost [10.14]
76 --> 31 | cost [12.15]
78 --> 99 | cost [3.63]
79 --> 24 | cost [6.87]
80 --> 99 | cost [10.68]
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]
100 --> 19 | cost [5.8500000000000005]

B = 102.92999999999999
i★ = 10
j★ = 21
k★ = 20

       
——————— Fri, 26 Jan 2024 09:58:23 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 49 hubs —— 1-50-34-38-11-90-89-42-58-36-67-7-72-57-31-99-45-33-68-65-86-96-85-59-40-6-25-47-21-10-26-87-92-2-100-51-37-62-60-44-4-43-77-54-15-84-24-88-101-1
total time           124.84               gap                  0.0                  
blossom time         0                    nb blossom           0.0                  
LB <= UB             117534.79<=117534.79 Master/SP costs      116891/643.79        
Master time          116.58               SP time              8.26                 
subtour              512.0                connectivity cuts    1359.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            46.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       1845                 
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—50—34—38—11—90—89—42—58—36—67—7—72—57—31—99—45—33—68—65—86—96—85—59—40—6—25—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  --- 67 | cost [2422.0]
7  --- 72 | cost [4046.0]
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]
21 --- 47 | cost [1526.0]
24 --- 84 | cost [2205.0]
24 --- 88 | cost [707.0]
25 --- 47 | cost [3675.0]
26 --- 87 | cost [84.0]
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 --- 58 | cost [3612.0]
36 --- 67 | cost [875.0]
37 --- 51 | cost [700.0]
37 --- 62 | cost [1232.0]
40 --- 59 | cost [1106.0]
42 --- 58 | cost [4018.0]
42 --- 89 | cost [2989.0]
43 --- 77 | cost [1022.0]
44 --- 60 | cost [1351.0]
45 --- 99 | cost [1491.0]
51 --- 100 | cost [798.0]
54 --- 77 | cost [1141.0]
57 --- 72 | cost [1141.0]
59 --- 85 | cost [1036.0]
60 --- 62 | cost [2695.0]
65 --- 68 | cost [1491.0]
65 --- 86 | cost [2044.0]
85 --- 96 | cost [3073.0]
86 --- 96 | cost [420.0]
87 --- 92 | cost [3080.0]
88 --- 101 | cost [2821.0]
89 --- 90 | cost [1330.0]

STAR
3  --> 40 | cost [363.0]
5  --> 40 | cost [1134.0]
8  --> 38 | cost [555.0]
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]
17 --> 90 | cost [165.0]
18 --> 85 | cost [564.0]
19 --> 37 | cost [354.0]
20 --> 25 | cost [105.0]
22 --> 42 | cost [1191.0]
23 --> 42 | cost [639.0]
27 --> 24 | cost [186.0]
28 --> 47 | cost [750.0]
29 --> 58 | cost [732.0]
30 --> 100 | cost [390.0]
32 --> 90 | cost [1182.0]
35 --> 51 | cost [708.0]
39 --> 54 | cost [732.0]
41 --> 84 | cost [408.0]
46 --> 38 | cost [1359.0]
48 -->  2 | cost [606.0]
49 --> 89 | cost [999.0]
52 --> 38 | cost [633.0]
53 --> 60 | cost [597.0]
55 --> 26 | cost [549.0]
56 --> 21 | cost [711.0]
61 -->  7 | cost [843.0]
63 --> 54 | cost [399.0]
64 --> 59 | cost [723.0]
66 --> 38 | cost [291.0]
69 --> 15 | cost [1005.0]
70 --> 89 | cost [678.0]
71 -->  4 | cost [606.0]
73 --> 15 | cost [969.0]
74 -->  7 | cost [795.0]
75 --> 67 | cost [144.0]
76 --> 72 | cost [1128.0]
78 --> 31 | cost [297.0]
79 --> 88 | cost [381.0]
80 --> 31 | cost [921.0]
81 --> 34 | cost [150.0]
82 --> 25 | cost [1140.0]
83 --> 40 | cost [93.0]
91 --> 54 | cost [42.0]
93 --> 44 | cost [465.0]
94 --> 90 | cost [702.0]
95 --> 21 | cost [951.0]
97 --> 90 | cost [1191.0]
98 --> 90 | cost [1053.0]

BACKUP RING
1  --- 34 | cost [25.2]
2  --- 51 | cost [13.16]
2  --- 87 | cost [57.89]
4  --- 60 | cost [23.59]
4  --- 77 | cost [27.580000000000002]
6  --- 47 | cost [61.46]
6  --- 59 | cost [12.11]
7  --- 36 | cost [32.410000000000004]
7  --- 57 | cost [51.870000000000005]
10 --- 47 | cost [32.2]
10 --- 87 | cost [23.38]
11 --- 34 | cost [32.13]
11 --- 89 | cost [14.0]
15 --- 24 | cost [44.24]
15 --- 77 | cost [32.410000000000004]
21 --- 25 | cost [37.31]
21 --- 26 | cost [39.62]
24 --- 101 | cost [28.490000000000002]
25 --- 40 | cost [27.580000000000002]
26 --- 92 | cost [31.5]
31 --- 45 | cost [19.04]
31 --- 72 | cost [23.94]
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 --- 50 | cost [31.64]
38 --- 90 | cost [42.14]
40 --- 85 | cost [19.25]
42 --- 90 | cost [42.07]
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]
57 --- 99 | cost [17.71]
58 --- 67 | cost [43.89]
58 --- 89 | cost [65.38]
59 --- 96 | cost [39.62]
65 --- 96 | cost [24.64]
67 --- 72 | cost [61.25]
68 --- 86 | cost [31.71]
84 --- 88 | cost [26.39]
85 --- 86 | cost [33.6]
92 --- 100 | cost [31.92]

BACKUP STAR
3  -->  6 | cost [4.68]
5  -->  6 | cost [12.06]
8  --> 34 | cost [9.75]
9  --> 25 | cost [9.3]
12 --> 21 | cost [12.3]
13 --> 24 | cost [6.87]
14 --> 33 | cost [2.91]
16 --> 77 | cost [7.5600000000000005]
17 --> 11 | cost [6.93]
18 -->  6 | cost [6.57]
19 --> 51 | cost [4.26]
20 --> 10 | cost [9.450000000000001]
22 --> 58 | cost [12.540000000000001]
23 --> 38 | cost [11.46]
27 --> 88 | cost [3.9]
28 --> 21 | cost [9.84]
29 --> 36 | cost [12.450000000000001]
30 --> 51 | cost [6.12]
32 --> 50 | cost [15.540000000000001]
35 --> 37 | cost [7.71]
39 --> 43 | cost [9.72]
41 --> 24 | cost [7.59]
46 --> 34 | cost [16.2]
48 --> 100 | cost [9.120000000000001]
49 --> 90 | cost [10.11]
52 --> 34 | cost [9.3]
53 --> 44 | cost [9.0]
55 --> 87 | cost [5.5200000000000005]
56 --> 47 | cost [12.75]
61 --> 67 | cost [17.16]
63 --> 77 | cost [7.23]
64 --> 77 | cost [7.83]
66 --> 34 | cost [7.47]
69 --> 84 | cost [14.4]
70 --> 90 | cost [9.75]
71 --> 43 | cost [6.8100000000000005]
73 --> 54 | cost [10.83]
74 --> 67 | cost [13.56]
75 --> 36 | cost [4.7700000000000005]
76 --> 31 | cost [12.15]
78 --> 99 | cost [3.63]
79 --> 24 | cost [6.87]
80 --> 99 | cost [10.68]
81 --> 38 | cost [5.67]
82 --> 85 | cost [15.15]
83 -->  6 | cost [1.8]
91 --> 77 | cost [4.92]
93 -->  4 | cost [5.34]
94 --> 11 | cost [10.200000000000001]
95 --> 10 | cost [13.44]
97 --> 89 | cost [16.77]
98 --> 89 | cost [11.61]

B = 91.97
i★ = 67
j★ = 7
k★ = 72