------------------------------------------------------------
                        α=7.0 —— kroC100 —— 100 nodes       
------------------------------------------------------------

——————— Tue, 30 Jan 2024 15:00:38 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 65 hubs —— 1—53—29—9—78—26—37—16—51—44—48—100—33—45—81—36—57—74—87—96—84—52—11—99—92—10—19—14—4—59—3—73—41—89—30—68—35—23—91—70—76—94—86—5—43—56—38—88—98—34—25—17—22—72—62—75—6—31—67—55—64—79—15—85—101
total time           3632.8 (TL 3600)     gap                  0.394                
blossom time         0                    nb blossom           0.0                  
LB <= UB             110234.25<=182048.37 subtour              353.0                
connectivity cuts    189.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       119                  n lazycuts edges     0.0                  
F                    183.0                post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—53—29—9—78—26—37—16—51—44—48—100—33—45—81—36—57—74—87—96—84—52—11—99—92—10—19—14—4—59—3—73—41—89—30—68—35—23—91—70—76—94—86—5—43—56—38—88—98—34—25—17—22—72—62—75—6—31—67—55—64—79—15—85—101

RING
1  --- 53 | cost [224.0]
1  --- 101 | cost [0.0]
3  --- 59 | cost [910.0]
3  --- 73 | cost [126.0]
4  --- 14 | cost [2688.0]
4  --- 59 | cost [6650.0]
5  --- 43 | cost [1190.0]
5  --- 86 | cost [1764.0]
6  --- 31 | cost [2198.0]
6  --- 75 | cost [1876.0]
9  --- 29 | cost [3724.0]
9  --- 78 | cost [581.0]
10 --- 19 | cost [1106.0]
10 --- 92 | cost [476.0]
11 --- 52 | cost [189.0]
11 --- 99 | cost [6097.0]
14 --- 19 | cost [2415.0]
15 --- 79 | cost [1715.0]
15 --- 85 | cost [2163.0]
16 --- 37 | cost [2317.0]
16 --- 51 | cost [1099.0]
17 --- 22 | cost [2898.0]
17 --- 25 | cost [714.0]
22 --- 72 | cost [4221.0]
23 --- 35 | cost [2016.0]
23 --- 91 | cost [2450.0]
25 --- 34 | cost [1239.0]
26 --- 37 | cost [2863.0]
26 --- 78 | cost [1484.0]
29 --- 53 | cost [5698.0]
30 --- 68 | cost [973.0]
30 --- 89 | cost [2632.0]
31 --- 67 | cost [910.0]
33 --- 45 | cost [749.0]
33 --- 100 | cost [343.0]
34 --- 98 | cost [2772.0]
35 --- 68 | cost [1071.0]
36 --- 57 | cost [294.0]
36 --- 81 | cost [1883.0]
38 --- 56 | cost [1239.0]
38 --- 88 | cost [2177.0]
41 --- 73 | cost [2968.0]
41 --- 89 | cost [1491.0]
43 --- 56 | cost [2373.0]
44 --- 48 | cost [2205.0]
44 --- 51 | cost [1491.0]
45 --- 81 | cost [553.0]
48 --- 100 | cost [5397.0]
52 --- 84 | cost [826.0]
55 --- 64 | cost [1218.0]
55 --- 67 | cost [1512.0]
57 --- 74 | cost [434.0]
62 --- 72 | cost [1561.0]
62 --- 75 | cost [3241.0]
64 --- 79 | cost [2044.0]
70 --- 76 | cost [812.0]
70 --- 91 | cost [1652.0]
74 --- 87 | cost [7644.0]
76 --- 94 | cost [1778.0]
84 --- 96 | cost [2352.0]
85 --- 101 | cost [1512.0]
86 --- 94 | cost [3038.0]
87 --- 96 | cost [1974.0]
88 --- 98 | cost [1274.0]
92 --- 99 | cost [742.0]

STAR
2  --> 35 | cost [228.0]
7  --> 26 | cost [1113.0]
8  --> 22 | cost [384.0]
12 --> 53 | cost [1566.0]
13 --> 79 | cost [390.0]
18 --> 29 | cost [321.0]
20 --> 64 | cost [75.0]
21 --> 23 | cost [1062.0]
24 --> 53 | cost [1881.0]
27 --> 15 | cost [750.0]
28 --> 38 | cost [327.0]
32 --> 53 | cost [2328.0]
39 --> 38 | cost [345.0]
40 --> 85 | cost [918.0]
42 --> 55 | cost [327.0]
46 --> 53 | cost [1638.0]
47 --> 31 | cost [261.0]
49 --> 19 | cost [1353.0]
50 --> 91 | cost [1260.0]
54 -->  6 | cost [327.0]
58 --> 98 | cost [618.0]
60 --> 10 | cost [2244.0]
61 --> 19 | cost [2670.0]
63 --> 48 | cost [1269.0]
65 --> 31 | cost [777.0]
66 --> 19 | cost [1158.0]
69 --> 74 | cost [1074.0]
71 --> 38 | cost [258.0]
77 --> 30 | cost [1152.0]
80 --> 31 | cost [1293.0]
82 -->  9 | cost [537.0]
83 --> 72 | cost [570.0]
90 --> 17 | cost [555.0]
93 --> 19 | cost [1086.0]
95 --> 76 | cost [1125.0]
97 --> 45 | cost [564.0]

BACKUP RING
1  --- 29 | cost [59.15]
3  ---  4 | cost [68.32000000000001]
3  --- 41 | cost [28.98]
4  --- 19 | cost [39.2]
5  --- 56 | cost [15.33]
5  --- 94 | cost [46.76]
6  --- 62 | cost [39.62]
6  --- 67 | cost [30.59]
9  --- 26 | cost [15.47]
9  --- 53 | cost [83.65]
10 --- 14 | cost [18.41]
10 --- 99 | cost [7.5600000000000005]
11 --- 84 | cost [6.65]
11 --- 92 | cost [53.9]
14 --- 59 | cost [62.370000000000005]
15 --- 64 | cost [36.19]
15 --- 101 | cost [35.77]
16 --- 26 | cost [42.21]
16 --- 44 | cost [15.47]
17 --- 34 | cost [19.11]
17 --- 72 | cost [59.99]
19 --- 92 | cost [7.42]
22 --- 25 | cost [35.07]
22 --- 62 | cost [34.09]
23 --- 68 | cost [23.45]
23 --- 70 | cost [23.59]
25 --- 98 | cost [34.86]
29 --- 78 | cost [42.0]
30 --- 35 | cost [20.16]
30 --- 41 | cost [26.88]
31 --- 55 | cost [21.14]
31 --- 75 | cost [35.42]
33 --- 48 | cost [50.54]
33 --- 81 | cost [8.19]
34 --- 88 | cost [40.46]
35 --- 91 | cost [40.81]
36 --- 45 | cost [15.120000000000001]
36 --- 74 | cost [7.21]
37 --- 51 | cost [33.6]
37 --- 78 | cost [30.73]
38 --- 43 | cost [35.07]
38 --- 98 | cost [32.27]
43 --- 86 | cost [26.39]
44 --- 100 | cost [66.5]
45 --- 100 | cost [10.92]
48 --- 51 | cost [35.42]
52 --- 96 | cost [21.490000000000002]
52 --- 99 | cost [62.86]
55 --- 79 | cost [27.72]
56 --- 88 | cost [28.91]
57 --- 81 | cost [19.25]
57 --- 87 | cost [76.09]
59 --- 73 | cost [9.73]
64 --- 67 | cost [19.6]
68 --- 89 | cost [32.2]
70 --- 94 | cost [21.490000000000002]
72 --- 75 | cost [44.17]
73 --- 89 | cost [34.02]
74 --- 96 | cost [60.13]
76 --- 86 | cost [47.95]
76 --- 91 | cost [16.52]
79 --- 85 | cost [38.5]
84 --- 87 | cost [37.45]

BACKUP STAR
2  --> 68 | cost [6.2700000000000005]
7  --> 78 | cost [10.8]
8  --> 75 | cost [7.890000000000001]
12 -->  4 | cost [13.35]
13 --> 15 | cost [7.0200000000000005]
18 --> 37 | cost [7.8]
20 --> 55 | cost [5.76]
21 --> 89 | cost [11.07]
24 --> 26 | cost [11.82]
27 --> 85 | cost [7.71]
28 --> 88 | cost [6.09]
32 --> 26 | cost [7.68]
39 --> 88 | cost [7.95]
40 --> 53 | cost [11.07]
42 --> 64 | cost [7.05]
46 --> 29 | cost [8.040000000000001]
47 --> 67 | cost [5.01]
49 --> 29 | cost [6.18]
50 --> 72 | cost [7.71]
54 --> 75 | cost [7.08]
58 --> 34 | cost [9.96]
60 -->  4 | cost [7.74]
61 --> 26 | cost [5.13]
63 --> 44 | cost [3.27]
65 --> 67 | cost [9.15]
66 --> 44 | cost [5.7]
69 --> 57 | cost [11.94]
71 --> 56 | cost [5.91]
77 --> 68 | cost [13.59]
80 -->  6 | cost [13.38]
82 --> 78 | cost [3.48]
83 --> 62 | cost [1.32]
90 --> 34 | cost [2.7]
93 -->  4 | cost [8.700000000000001]
95 --> 94 | cost [3.69]
97 --> 81 | cost [3.6]

B = 100.04
i★ = 1
j★ = 53
k★ = 29

       
——————— Tue, 30 Jan 2024 16:01:54 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 54 hubs —— 1-85-15-79-64-55-67-31-6-75-22-8-17-25-90-98-88-28-38-71-72-50-95-91-23-35-68-30-41-59-3-69-74-100-33-45-10-92-48-11-84-44-63-16-9-26-61-29-18-49-93-12-40-101-1
total time           3604.12 (TL 3600)    gap                  0.073                
blossom time         0                    nb blossom           0.0                  
LB <= UB             115947.16<=125067.79 Master/SP costs      114430/10637.79      
Master time          3185.51              SP time              418.61               
subtour              3197.0               connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            2587.0               SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       125734               
F                    183.0                
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—85—15—79—64—55—67—31—6—75—22—8—17—25—90—98—88—28—38—71—72—50—95—91—23—35—68—30—41—59—3—69—74—100—33—45—10—92—48—11—84—44—63—16—9—26—61—29—18—49—93—12—40—101

RING
1  --- 85 | cost [1512.0]
1  --- 101 | cost [0.0]
3  --- 59 | cost [910.0]
3  --- 69 | cost [2905.0]
6  --- 31 | cost [2198.0]
6  --- 75 | cost [1876.0]
8  --- 17 | cost [2156.0]
8  --- 22 | cost [896.0]
9  --- 16 | cost [2989.0]
9  --- 26 | cost [1547.0]
10 --- 45 | cost [1953.0]
10 --- 92 | cost [476.0]
11 --- 48 | cost [1652.0]
11 --- 84 | cost [665.0]
12 --- 40 | cost [1568.0]
12 --- 93 | cost [2681.0]
15 --- 79 | cost [1715.0]
15 --- 85 | cost [2163.0]
16 --- 63 | cost [847.0]
17 --- 25 | cost [714.0]
18 --- 29 | cost [749.0]
18 --- 49 | cost [749.0]
22 --- 75 | cost [1169.0]
23 --- 35 | cost [2016.0]
23 --- 91 | cost [2450.0]
25 --- 90 | cost [672.0]
26 --- 61 | cost [1197.0]
28 --- 38 | cost [763.0]
28 --- 88 | cost [1421.0]
29 --- 61 | cost [2275.0]
30 --- 41 | cost [2688.0]
30 --- 68 | cost [973.0]
31 --- 67 | cost [910.0]
33 --- 45 | cost [749.0]
33 --- 100 | cost [343.0]
35 --- 68 | cost [1071.0]
38 --- 71 | cost [602.0]
40 --- 101 | cost [2653.0]
41 --- 59 | cost [1995.0]
44 --- 63 | cost [763.0]
44 --- 84 | cost [2667.0]
48 --- 92 | cost [3822.0]
49 --- 93 | cost [1911.0]
50 --- 72 | cost [1799.0]
50 --- 95 | cost [2163.0]
55 --- 64 | cost [1218.0]
55 --- 67 | cost [1512.0]
64 --- 79 | cost [2044.0]
69 --- 74 | cost [2506.0]
71 --- 72 | cost [1764.0]
74 --- 100 | cost [840.0]
88 --- 98 | cost [1274.0]
90 --- 98 | cost [2919.0]
91 --- 95 | cost [1344.0]

STAR
2  --> 35 | cost [228.0]
4  --> 93 | cost [870.0]
5  --> 71 | cost [948.0]
7  --> 26 | cost [1113.0]
13 --> 79 | cost [390.0]
14 --> 10 | cost [789.0]
19 --> 92 | cost [318.0]
20 --> 64 | cost [75.0]
21 --> 23 | cost [1062.0]
24 --> 61 | cost [966.0]
27 --> 15 | cost [750.0]
32 --> 61 | cost [717.0]
34 --> 90 | cost [270.0]
36 --> 74 | cost [309.0]
37 --> 29 | cost [648.0]
39 --> 28 | cost [285.0]
42 --> 55 | cost [327.0]
43 --> 71 | cost [1434.0]
46 --> 29 | cost [804.0]
47 --> 31 | cost [261.0]
51 --> 63 | cost [366.0]
52 --> 11 | cost [81.0]
53 -->  1 | cost [96.0]
54 -->  6 | cost [327.0]
56 --> 38 | cost [531.0]
57 --> 74 | cost [186.0]
58 --> 98 | cost [618.0]
60 --> 93 | cost [1641.0]
62 --> 72 | cost [669.0]
65 --> 31 | cost [777.0]
66 --> 44 | cost [570.0]
70 --> 91 | cost [708.0]
73 -->  3 | cost [54.0]
76 --> 91 | cost [708.0]
77 --> 30 | cost [1152.0]
78 -->  9 | cost [249.0]
80 --> 31 | cost [1293.0]
81 --> 45 | cost [237.0]
82 -->  9 | cost [537.0]
83 --> 72 | cost [570.0]
86 --> 50 | cost [933.0]
87 --> 11 | cost [1368.0]
89 --> 41 | cost [639.0]
94 --> 95 | cost [369.0]
96 --> 11 | cost [891.0]
97 --> 45 | cost [564.0]
99 --> 92 | cost [318.0]

BACKUP RING
1  --- 15 | cost [35.77]
3  --- 41 | cost [28.98]
3  --- 74 | cost [53.410000000000004]
6  --- 22 | cost [30.38]
6  --- 67 | cost [30.59]
8  --- 25 | cost [28.21]
8  --- 75 | cost [18.41]
9  --- 61 | cost [19.6]
9  --- 63 | cost [37.660000000000004]
10 --- 33 | cost [22.54]
10 --- 48 | cost [41.58]
11 --- 44 | cost [32.97]
11 --- 92 | cost [53.9]
12 --- 49 | cost [27.51]
12 --- 101 | cost [38.01]
15 --- 64 | cost [36.19]
16 --- 26 | cost [42.21]
16 --- 44 | cost [15.47]
17 --- 22 | cost [28.98]
17 --- 90 | cost [12.950000000000001]
18 --- 61 | cost [29.89]
18 --- 93 | cost [26.53]
23 --- 68 | cost [23.45]
23 --- 95 | cost [36.12]
25 --- 98 | cost [34.86]
26 --- 29 | cost [34.72]
28 --- 71 | cost [13.23]
28 --- 98 | cost [24.78]
29 --- 49 | cost [14.42]
30 --- 35 | cost [20.16]
30 --- 59 | cost [46.410000000000004]
31 --- 55 | cost [21.14]
31 --- 75 | cost [35.42]
33 --- 74 | cost [10.85]
35 --- 91 | cost [40.81]
38 --- 72 | cost [22.05]
38 --- 88 | cost [21.77]
40 --- 93 | cost [41.230000000000004]
41 --- 68 | cost [35.7]
45 --- 92 | cost [22.47]
45 --- 100 | cost [10.92]
48 --- 84 | cost [10.57]
50 --- 71 | cost [29.96]
50 --- 91 | cost [29.400000000000002]
55 --- 79 | cost [27.72]
59 --- 69 | cost [32.97]
63 --- 84 | cost [33.39]
64 --- 67 | cost [19.6]
69 --- 100 | cost [31.5]
72 --- 95 | cost [38.22]
79 --- 85 | cost [38.5]
88 --- 90 | cost [41.72]

BACKUP STAR
2  --> 68 | cost [6.2700000000000005]
4  --> 12 | cost [13.35]
5  --> 38 | cost [10.53]
7  -->  9 | cost [13.17]
13 --> 15 | cost [7.0200000000000005]
14 --> 74 | cost [8.22]
19 --> 10 | cost [4.74]
20 --> 55 | cost [5.76]
21 --> 68 | cost [14.25]
24 --> 26 | cost [11.82]
27 --> 85 | cost [7.71]
32 --> 26 | cost [7.68]
34 --> 25 | cost [5.3100000000000005]
36 --> 100 | cost [4.7700000000000005]
37 --> 18 | cost [7.8]
39 --> 38 | cost [3.45]
42 --> 64 | cost [7.05]
43 --> 38 | cost [15.030000000000001]
46 --> 18 | cost [9.39]
47 --> 67 | cost [5.01]
51 --> 16 | cost [4.71]
52 --> 84 | cost [3.54]
54 --> 75 | cost [7.08]
56 --> 71 | cost [5.91]
57 --> 100 | cost [4.32]
58 --> 88 | cost [10.200000000000001]
60 --> 69 | cost [17.16]
62 --> 50 | cost [8.55]
65 --> 67 | cost [9.15]
66 --> 63 | cost [8.07]
70 --> 23 | cost [10.11]
73 --> 59 | cost [4.17]
76 --> 95 | cost [11.25]
77 --> 68 | cost [13.59]
78 --> 26 | cost [6.36]
80 -->  6 | cost [13.38]
81 --> 33 | cost [3.5100000000000002]
82 --> 26 | cost [9.48]
83 --> 50 | cost [8.790000000000001]
86 --> 95 | cost [9.75]
87 --> 84 | cost [16.05]
89 --> 59 | cost [10.950000000000001]
94 --> 91 | cost [3.87]
96 --> 84 | cost [10.08]
97 --> 33 | cost [6.96]
99 --> 10 | cost [3.24]

B = 58.13
i★ = 6
j★ = 31
k★ = 67