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

——————— Tue, 30 Jan 2024 19:54:22 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 75 hubs —— 1—32—97—98—89—17—90—70—42—29—67—75—7—23—79—13—27—24—88—41—84—54—91—4—93—44—53—60—37—92—51—2—100—30—35—5—40—83—6—59—85—18—25—20—12—9—55—87—26—56—95—21—82—33—68—14—45—31—78—80—76—96—16—69—46—8—61—74—52—66—38—34—81—50—101
total time           3633.89 (TL 3600)    gap                  0.531                
blossom time         0                    nb blossom           0.0                  
LB <= UB             109089.82<=232719.52 subtour              246.0                
connectivity cuts    128.0                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—32—97—98—89—17—90—70—42—29—67—75—7—23—79—13—27—24—88—41—84—54—91—4—93—44—53—60—37—92—51—2—100—30—35—5—40—83—6—59—85—18—25—20—12—9—55—87—26—56—95—21—82—33—68—14—45—31—78—80—76—96—16—69—46—8—61—74—52—66—38—34—81—50—101

RING
1  --- 32 | cost [3927.0]
2  --- 51 | cost [1316.0]
2  --- 100 | cost [714.0]
4  --- 91 | cost [3493.0]
4  --- 93 | cost [1246.0]
5  --- 35 | cost [4802.0]
5  --- 40 | cost [2646.0]
6  --- 59 | cost [1211.0]
6  --- 83 | cost [420.0]
7  --- 23 | cost [5831.0]
7  --- 75 | cost [2366.0]
8  --- 46 | cost [2002.0]
8  --- 61 | cost [4074.0]
9  --- 12 | cost [6027.0]
9  --- 55 | cost [1463.0]
12 --- 20 | cost [5110.0]
13 --- 27 | cost [1624.0]
13 --- 79 | cost [525.0]
14 --- 45 | cost [1701.0]
14 --- 68 | cost [147.0]
16 --- 69 | cost [3514.0]
16 --- 96 | cost [2205.0]
17 --- 89 | cost [1708.0]
17 --- 90 | cost [385.0]
18 --- 25 | cost [2198.0]
18 --- 85 | cost [1316.0]
20 --- 25 | cost [245.0]
21 --- 82 | cost [4886.0]
21 --- 95 | cost [2219.0]
23 --- 79 | cost [8358.0]
24 --- 27 | cost [434.0]
24 --- 88 | cost [707.0]
26 --- 56 | cost [3976.0]
26 --- 87 | cost [84.0]
29 --- 42 | cost [5537.0]
29 --- 67 | cost [3780.0]
30 --- 35 | cost [1981.0]
30 --- 100 | cost [910.0]
31 --- 45 | cost [1904.0]
31 --- 78 | cost [693.0]
32 --- 97 | cost [1610.0]
33 --- 68 | cost [532.0]
33 --- 82 | cost [4333.0]
34 --- 38 | cost [1197.0]
34 --- 81 | cost [350.0]
37 --- 60 | cost [3927.0]
37 --- 92 | cost [2905.0]
38 --- 66 | cost [679.0]
40 --- 83 | cost [217.0]
41 --- 84 | cost [952.0]
41 --- 88 | cost [1974.0]
42 --- 70 | cost [3724.0]
44 --- 53 | cost [2100.0]
44 --- 93 | cost [1085.0]
46 --- 69 | cost [3703.0]
50 --- 81 | cost [2275.0]
50 --- 101 | cost [651.0]
51 --- 92 | cost [3115.0]
52 --- 66 | cost [917.0]
52 --- 74 | cost [4291.0]
53 --- 60 | cost [1393.0]
54 --- 84 | cost [4151.0]
54 --- 91 | cost [98.0]
55 --- 87 | cost [1288.0]
56 --- 95 | cost [826.0]
59 --- 85 | cost [1036.0]
61 --- 74 | cost [1211.0]
67 --- 75 | cost [336.0]
70 --- 90 | cost [2275.0]
76 --- 80 | cost [945.0]
76 --- 96 | cost [5285.0]
78 --- 80 | cost [1743.0]
89 --- 98 | cost [2709.0]
97 --- 98 | cost [2478.0]

STAR
3  --> 68 | cost [3318.0]
10 --> 92 | cost [2157.0]
11 --> 90 | cost [576.0]
15 -->  1 | cost [3069.0]
19 --> 51 | cost [426.0]
22 --> 90 | cost [2316.0]
28 --> 68 | cost [3762.0]
36 --> 75 | cost [477.0]
39 --> 84 | cost [1530.0]
43 --> 68 | cost [3498.0]
47 --> 68 | cost [3231.0]
48 --> 55 | cost [2133.0]
49 --> 90 | cost [1011.0]
57 --> 31 | cost [654.0]
58 --> 90 | cost [3372.0]
62 --> 37 | cost [528.0]
63 --> 68 | cost [2841.0]
64 --> 68 | cost [2745.0]
65 --> 68 | cost [639.0]
71 -->  4 | cost [606.0]
72 --> 31 | cost [1026.0]
73 -->  4 | cost [1848.0]
77 --> 18 | cost [2091.0]
86 --> 68 | cost [1359.0]
94 --> 90 | cost [702.0]
99 --> 68 | cost [1134.0]

BACKUP RING
1  --- 97 | cost [54.53]
2  --- 30 | cost [14.49]
2  --- 92 | cost [27.16]
4  --- 44 | cost [10.15]
4  --- 54 | cost [35.49]
5  --- 30 | cost [57.26]
5  --- 83 | cost [24.29]
6  --- 40 | cost [2.87]
6  --- 85 | cost [18.900000000000002]
7  --- 67 | cost [24.22]
7  --- 79 | cost [118.44]
8  --- 69 | cost [53.2]
8  --- 74 | cost [40.32]
9  --- 20 | cost [19.25]
9  --- 87 | cost [22.82]
12 --- 25 | cost [50.96]
12 --- 55 | cost [71.12]
13 --- 23 | cost [79.94]
13 --- 24 | cost [16.03]
14 --- 31 | cost [30.87]
14 --- 33 | cost [6.79]
16 --- 46 | cost [72.10000000000001]
16 --- 76 | cost [62.93]
17 --- 70 | cost [25.060000000000002]
17 --- 98 | cost [24.22]
18 --- 20 | cost [23.94]
18 --- 59 | cost [16.66]
21 --- 33 | cost [89.32000000000001]
21 --- 56 | cost [16.59]
23 --- 75 | cost [63.21]
24 --- 41 | cost [17.71]
25 --- 85 | cost [34.79]
26 --- 55 | cost [12.81]
26 --- 95 | cost [34.37]
27 --- 79 | cost [17.57]
27 --- 88 | cost [9.1]
29 --- 70 | cost [81.76]
29 --- 75 | cost [40.04]
31 --- 80 | cost [21.490000000000002]
32 --- 98 | cost [36.89]
34 --- 50 | cost [21.21]
34 --- 66 | cost [17.43]
35 --- 40 | cost [73.5]
35 --- 100 | cost [21.21]
37 --- 51 | cost [7.0]
37 --- 53 | cost [37.17]
38 --- 52 | cost [14.77]
38 --- 81 | cost [13.23]
41 --- 54 | cost [45.92]
42 --- 67 | cost [59.08]
42 --- 90 | cost [42.07]
44 --- 60 | cost [13.51]
45 --- 68 | cost [15.610000000000001]
45 --- 78 | cost [20.51]
46 --- 61 | cost [29.54]
51 --- 100 | cost [7.98]
52 --- 61 | cost [41.72]
53 --- 93 | cost [30.240000000000002]
56 --- 87 | cost [40.32]
59 --- 83 | cost [12.88]
60 --- 92 | cost [57.96]
66 --- 74 | cost [45.71]
68 --- 82 | cost [40.53]
69 --- 96 | cost [42.0]
76 --- 78 | cost [25.830000000000002]
80 --- 96 | cost [44.94]
81 --- 101 | cost [26.04]
82 --- 95 | cost [70.14]
84 --- 88 | cost [26.39]
84 --- 91 | cost [41.230000000000004]
89 --- 90 | cost [13.3]
89 --- 97 | cost [39.13]
91 --- 93 | cost [45.92]

BACKUP STAR
3  --> 83 | cost [2.85]
10 -->  9 | cost [6.09]
11 --> 89 | cost [6.0]
19 --> 37 | cost [3.54]
22 --> 42 | cost [11.91]
28 --> 12 | cost [5.43]
36 --> 67 | cost [3.75]
39 --> 91 | cost [6.9]
43 -->  4 | cost [7.5600000000000005]
47 --> 21 | cost [6.54]
48 -->  2 | cost [6.0600000000000005]
49 --> 98 | cost [2.46]
57 --> 78 | cost [9.120000000000001]
58 --> 29 | cost [7.32]
62 --> 51 | cost [7.95]
63 --> 54 | cost [3.99]
64 --> 59 | cost [7.23]
65 --> 14 | cost [6.15]
71 --> 93 | cost [8.700000000000001]
72 --> 76 | cost [11.28]
73 --> 91 | cost [10.47]
77 --> 54 | cost [4.89]
86 --> 96 | cost [1.8]
94 --> 32 | cost [5.37]
99 --> 31 | cost [1.77]

B = 118.44
i★ = 7
j★ = 23
k★ = 79

       
——————— Tue, 30 Jan 2024 20:55:30 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 55 hubs —— 1-50-94-17-90-11-38-66-23-42-58-29-36-67-7-61-76-80-78-31-99-45-33-68-65-86-96-85-59-40-6-25-20-47-21-10-26-87-92-2-100-51-37-62-60-44-4-43-77-54-15-84-24-88-101-1
total time           3604.54 (TL 3600)    gap                  0.088                
blossom time         0                    nb blossom           0.0                  
LB <= UB             118505.05<=129939.24 Master/SP costs      117627/12312.24      
Master time          3254.58              SP time              349.96               
subtour              5157.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            2109.0               SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       86583                
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—50—94—17—90—11—38—66—23—42—58—29—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]
29 --- 36 | cost [2905.0]
29 --- 58 | cost [1708.0]
31 --- 78 | cost [693.0]
31 --- 99 | cost [413.0]
33 --- 45 | cost [1155.0]
33 --- 68 | cost [532.0]
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 --> 58 | cost [1254.0]
27 --> 24 | cost [186.0]
28 --> 47 | cost [750.0]
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]
29 --- 42 | cost [55.370000000000005]
29 --- 67 | cost [37.800000000000004]
31 --- 45 | cost [19.04]
31 --- 80 | cost [21.490000000000002]
33 --- 65 | cost [18.76]
33 --- 99 | cost [24.5]
36 --- 58 | cost [36.12]
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]
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 --> 42 | cost [11.91]
27 --> 88 | cost [3.9]
28 --> 21 | cost [9.84]
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 = 67.28
i★ = 29
j★ = 58
k★ = 42