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

——————— Thu, 18 Jan 2024 17:35:35 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 23 hubs —— 1—8—16—38—90—49—79—47—23—77—61—9—46—68—39—96—52—33—2—44—40—67—101
total time           3635.32 (TL 3600)    gap                  0.676                
blossom time         0                    nb blossom           0.0                  
LB <= UB             108807.92<=335672.24 subtour              598.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       348                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—8—16—38—90—49—79—47—23—77—61—9—46—68—39—96—52—33—2—44—40—67—101

RING
1  ---  8 | cost [2975.0]
2  --- 33 | cost [7483.0]
2  --- 44 | cost [1799.0]
8  --- 16 | cost [8477.0]
9  --- 46 | cost [4837.0]
9  --- 61 | cost [3619.0]
16 --- 38 | cost [4718.0]
23 --- 47 | cost [3766.0]
23 --- 77 | cost [2674.0]
33 --- 52 | cost [5131.0]
38 --- 90 | cost [4620.0]
39 --- 68 | cost [3423.0]
39 --- 96 | cost [1988.0]
40 --- 44 | cost [2849.0]
40 --- 67 | cost [5397.0]
46 --- 68 | cost [6552.0]
47 --- 79 | cost [7448.0]
49 --- 79 | cost [3976.0]
49 --- 90 | cost [1456.0]
52 --- 96 | cost [742.0]
61 --- 77 | cost [4606.0]
67 --- 101 | cost [4151.0]

STAR
3  --> 40 | cost [5193.0]
4  -->  1 | cost [3312.0]
5  --> 40 | cost [4239.0]
6  -->  1 | cost [1191.0]
7  --> 67 | cost [3393.0]
10 -->  1 | cost [2247.0]
11 -->  1 | cost [2706.0]
12 --> 40 | cost [4422.0]
13 --> 40 | cost [3825.0]
14 --> 40 | cost [5181.0]
15 -->  1 | cost [3045.0]
17 -->  1 | cost [3054.0]
18 -->  1 | cost [3501.0]
19 -->  1 | cost [2442.0]
20 -->  1 | cost [4215.0]
21 -->  1 | cost [2655.0]
22 -->  1 | cost [3990.0]
24 -->  1 | cost [3618.0]
25 --> 67 | cost [2118.0]
26 -->  1 | cost [4533.0]
27 -->  1 | cost [4716.0]
28 -->  1 | cost [1248.0]
29 --> 40 | cost [4551.0]
30 --> 96 | cost [921.0]
31 -->  1 | cost [2661.0]
32 -->  1 | cost [2370.0]
34 --> 67 | cost [4317.0]
35 -->  1 | cost [4728.0]
36 --> 47 | cost [2934.0]
37 --> 40 | cost [4143.0]
41 --> 40 | cost [6198.0]
42 -->  1 | cost [1983.0]
43 --> 40 | cost [5499.0]
45 -->  1 | cost [2769.0]
48 --> 40 | cost [5148.0]
50 --> 44 | cost [486.0]
51 --> 67 | cost [2256.0]
53 --> 79 | cost [669.0]
54 --> 40 | cost [312.0]
55 --> 67 | cost [4170.0]
56 -->  1 | cost [2385.0]
57 --> 67 | cost [3192.0]
58 --> 67 | cost [1035.0]
59 -->  1 | cost [3093.0]
60 -->  1 | cost [3456.0]
62 -->  1 | cost [3780.0]
63 -->  1 | cost [864.0]
64 --> 40 | cost [240.0]
65 -->  1 | cost [3750.0]
66 -->  1 | cost [3858.0]
69 --> 40 | cost [1092.0]
70 -->  1 | cost [4161.0]
71 -->  1 | cost [7905.0]
72 -->  1 | cost [2406.0]
73 --> 44 | cost [699.0]
74 -->  1 | cost [2826.0]
75 -->  1 | cost [1884.0]
76 --> 40 | cost [4074.0]
78 --> 40 | cost [4326.0]
80 -->  1 | cost [2589.0]
81 --> 40 | cost [2001.0]
82 --> 40 | cost [2637.0]
83 --> 67 | cost [4170.0]
84 -->  1 | cost [2664.0]
85 --> 39 | cost [1116.0]
86 -->  1 | cost [4524.0]
87 --> 67 | cost [2694.0]
88 -->  1 | cost [3657.0]
89 -->  1 | cost [2418.0]
91 -->  1 | cost [2259.0]
92 -->  1 | cost [909.0]
93 -->  1 | cost [1239.0]
94 -->  1 | cost [4077.0]
95 --> 40 | cost [3345.0]
97 -->  1 | cost [2445.0]
98 -->  1 | cost [2349.0]
99 -->  1 | cost [4404.0]
100 --> 40 | cost [5793.0]

BACKUP RING
1  --- 16 | cost [88.13]
2  --- 40 | cost [23.59]
2  --- 52 | cost [91.14]
8  --- 38 | cost [97.79]
9  --- 68 | cost [48.79]
9  --- 77 | cost [39.9]
16 --- 90 | cost [44.800000000000004]
23 --- 61 | cost [65.38]
23 --- 79 | cost [110.25]
33 --- 44 | cost [69.16]
33 --- 96 | cost [49.56]
38 --- 49 | cost [59.43]
39 --- 46 | cost [58.24]
39 --- 52 | cost [27.23]
40 --- 101 | cost [95.06]
44 --- 67 | cost [75.39]
46 --- 61 | cost [80.29]
47 --- 49 | cost [42.980000000000004]
47 --- 77 | cost [57.68]
68 --- 96 | cost [53.9]
79 --- 90 | cost [25.55]

BACKUP STAR
3  --> 46 | cost [4.17]
5  --> 96 | cost [7.59]
7  -->  9 | cost [1.5]
12 -->  9 | cost [7.98]
13 --> 33 | cost [3.0300000000000002]
14 --> 46 | cost [9.9]
25 --> 61 | cost [4.95]
29 --> 46 | cost [4.44]
30 --> 39 | cost [7.83]
34 --> 46 | cost [9.33]
36 --> 38 | cost [6.84]
37 --> 96 | cost [9.24]
41 --> 46 | cost [17.7]
43 --> 46 | cost [5.94]
48 --> 52 | cost [11.88]
50 --> 68 | cost [9.6]
51 --> 61 | cost [5.58]
53 --> 16 | cost [7.68]
54 -->  2 | cost [9.93]
55 -->  9 | cost [8.94]
57 -->  9 | cost [3.0]
58 --> 61 | cost [9.75]
64 -->  2 | cost [9.96]
69 --> 61 | cost [13.05]
73 --> 68 | cost [8.01]
76 --> 33 | cost [2.7600000000000002]
78 --> 52 | cost [1.2]
81 --> 61 | cost [6.21]
82 --> 33 | cost [14.97]
83 -->  9 | cost [9.0]
85 --> 68 | cost [4.59]
87 -->  9 | cost [5.8500000000000005]
95 --> 33 | cost [9.33]
100 --> 46 | cost [17.52]

B = 242.19000000000003
i★ = 44
j★ = 40
k★ = 67

       
——————— Thu, 18 Jan 2024 18:36:59 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 48 hubs —— 1-63-6-92-8-42-56-97-66-70-22-16-18-24-38-36-72-21-74-11-32-45-23-62-86-20-57-83-34-46-14-100-48-52-78-5-37-13-95-50-73-64-40-69-81-58-93-101-1
total time           3606.82 (TL 3600)    gap                  0.122                
blossom time         0                    nb blossom           0.0                  
LB <= UB             107240.5<=122201.52  Master/SP costs      121499/702.52        
Master time          3591.63              SP time              15.19                
subtour              31039.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            45.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       29855                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—63—6—92—8—42—56—97—66—70—22—16—18—24—38—36—72—21—74—11—32—45—23—62—86—20—57—83—34—46—14—100—48—52—78—5—37—13—95—50—73—64—40—69—81—58—93—101

RING
1  --- 63 | cost [2016.0]
5  --- 37 | cost [483.0]
5  --- 78 | cost [1694.0]
6  --- 63 | cost [1099.0]
6  --- 92 | cost [2303.0]
8  --- 42 | cost [1736.0]
8  --- 92 | cost [1442.0]
11 --- 32 | cost [1414.0]
11 --- 74 | cost [2303.0]
13 --- 37 | cost [3031.0]
13 --- 95 | cost [1512.0]
14 --- 46 | cost [2310.0]
14 --- 100 | cost [1876.0]
16 --- 18 | cost [2793.0]
16 --- 22 | cost [490.0]
18 --- 24 | cost [1267.0]
20 --- 57 | cost [1428.0]
20 --- 86 | cost [1085.0]
21 --- 72 | cost [1064.0]
21 --- 74 | cost [462.0]
22 --- 70 | cost [1302.0]
23 --- 45 | cost [1547.0]
23 --- 62 | cost [3451.0]
24 --- 38 | cost [672.0]
32 --- 45 | cost [1554.0]
34 --- 46 | cost [2177.0]
34 --- 83 | cost [1022.0]
36 --- 38 | cost [1596.0]
36 --- 72 | cost [2968.0]
40 --- 64 | cost [560.0]
40 --- 69 | cost [2548.0]
42 --- 56 | cost [2590.0]
48 --- 52 | cost [2772.0]
48 --- 100 | cost [1764.0]
50 --- 73 | cost [1260.0]
50 --- 95 | cost [5271.0]
52 --- 78 | cost [280.0]
56 --- 97 | cost [1512.0]
57 --- 83 | cost [2492.0]
58 --- 81 | cost [3556.0]
58 --- 93 | cost [2177.0]
62 --- 86 | cost [2156.0]
64 --- 73 | cost [2632.0]
66 --- 70 | cost [2800.0]
66 --- 97 | cost [3759.0]
69 --- 81 | cost [2121.0]
93 --- 101 | cost [2891.0]

STAR
2  --> 64 | cost [996.0]
3  --> 46 | cost [417.0]
4  --> 66 | cost [648.0]
7  --> 57 | cost [279.0]
9  --> 57 | cost [300.0]
10 --> 72 | cost [810.0]
12 --> 20 | cost [462.0]
15 --> 11 | cost [339.0]
17 --> 11 | cost [345.0]
19 --> 97 | cost [978.0]
25 --> 81 | cost [153.0]
26 --> 66 | cost [969.0]
27 --> 86 | cost [243.0]
28 --> 93 | cost [144.0]
29 --> 46 | cost [444.0]
30 --> 78 | cost [1056.0]
31 --> 42 | cost [687.0]
33 --> 13 | cost [303.0]
35 --> 86 | cost [423.0]
39 --> 78 | cost [1056.0]
41 --> 100 | cost [555.0]
43 --> 46 | cost [594.0]
44 --> 50 | cost [486.0]
47 --> 32 | cost [1083.0]
49 -->  6 | cost [141.0]
51 --> 81 | cost [915.0]
53 --> 16 | cost [768.0]
54 --> 40 | cost [312.0]
55 --> 83 | cost [69.0]
59 --> 74 | cost [267.0]
60 --> 62 | cost [453.0]
61 --> 81 | cost [621.0]
65 --> 66 | cost [345.0]
67 --> 58 | cost [1035.0]
68 --> 73 | cost [801.0]
71 --> 100 | cost [363.0]
75 --> 97 | cost [711.0]
76 --> 13 | cost [309.0]
77 --> 62 | cost [663.0]
79 --> 18 | cost [690.0]
80 --> 42 | cost [693.0]
82 --> 95 | cost [735.0]
84 --> 72 | cost [942.0]
85 --> 73 | cost [1236.0]
87 --> 57 | cost [594.0]
88 --> 16 | cost [174.0]
89 --> 42 | cost [540.0]
90 -->  6 | cost [747.0]
91 --> 45 | cost [537.0]
94 --> 22 | cost [402.0]
96 --> 78 | cost [204.0]
98 --> 23 | cost [324.0]
99 --> 36 | cost [900.0]

BACKUP RING
1  ---  6 | cost [27.79]
5  --- 13 | cost [35.14]
5  --- 52 | cost [18.13]
6  ---  8 | cost [37.38]
8  --- 56 | cost [29.47]
11 --- 21 | cost [24.43]
11 --- 45 | cost [25.900000000000002]
13 --- 50 | cost [59.5]
14 --- 34 | cost [41.86]
14 --- 48 | cost [20.16]
16 --- 24 | cost [40.46]
16 --- 70 | cost [15.05]
18 --- 22 | cost [30.240000000000002]
18 --- 38 | cost [19.39]
20 --- 62 | cost [22.12]
20 --- 83 | cost [27.37]
21 --- 36 | cost [32.62]
22 --- 66 | cost [38.43]
23 --- 32 | cost [26.810000000000002]
23 --- 86 | cost [55.93]
24 --- 36 | cost [21.91]
32 --- 74 | cost [34.72]
34 --- 57 | cost [32.2]
37 --- 78 | cost [21.42]
37 --- 95 | cost [42.21]
38 --- 72 | cost [40.32]
40 --- 73 | cost [31.85]
40 --- 81 | cost [46.69]
42 --- 92 | cost [31.29]
42 --- 97 | cost [39.06]
45 --- 62 | cost [46.83]
46 --- 83 | cost [28.98]
46 --- 100 | cost [40.88]
48 --- 78 | cost [29.54]
50 --- 64 | cost [32.69]
52 --- 100 | cost [44.94]
56 --- 66 | cost [50.120000000000005]
57 --- 86 | cost [24.64]
58 --- 69 | cost [42.7]
58 --- 101 | cost [50.26]
63 --- 92 | cost [24.71]
64 --- 69 | cost [20.79]
70 --- 97 | cost [56.56]
72 --- 74 | cost [15.05]
73 --- 95 | cost [65.24]
81 --- 93 | cost [57.33]

BACKUP STAR
2  --> 40 | cost [10.11]
3  --> 14 | cost [6.63]
4  --> 97 | cost [9.72]
7  --> 20 | cost [7.26]
9  --> 20 | cost [8.43]
10 --> 21 | cost [12.6]
12 --> 86 | cost [5.58]
15 --> 32 | cost [8.4]
17 --> 32 | cost [8.67]
19 -->  6 | cost [14.22]
25 --> 69 | cost [10.41]
26 --> 70 | cost [20.07]
27 --> 20 | cost [5.43]
28 --> 58 | cost [9.09]
29 --> 14 | cost [9.03]
30 --> 52 | cost [11.07]
31 --> 56 | cost [11.01]
33 --> 95 | cost [9.33]
35 --> 20 | cost [8.790000000000001]
39 --> 52 | cost [11.67]
41 --> 14 | cost [10.32]
43 --> 14 | cost [11.370000000000001]
44 --> 73 | cost [6.99]
47 --> 63 | cost [12.63]
49 --> 63 | cost [6.0600000000000005]
51 --> 57 | cost [9.9]
53 --> 22 | cost [9.75]
54 --> 64 | cost [5.43]
55 --> 34 | cost [5.07]
59 --> 21 | cost [4.53]
60 --> 23 | cost [10.35]
61 --> 58 | cost [9.75]
65 --> 97 | cost [14.01]
67 --> 93 | cost [10.41]
68 --> 50 | cost [9.6]
71 --> 14 | cost [8.040000000000001]
75 --> 92 | cost [10.74]
76 --> 95 | cost [7.8]
77 --> 23 | cost [11.46]
79 --> 16 | cost [9.48]
80 --> 56 | cost [8.43]
82 --> 13 | cost [12.0]
84 --> 36 | cost [9.66]
85 --> 50 | cost [12.63]
87 --> 81 | cost [11.55]
88 --> 22 | cost [3.5700000000000003]
89 -->  8 | cost [12.48]
90 --> 63 | cost [11.22]
91 --> 23 | cost [5.76]
94 --> 16 | cost [4.83]
96 --> 52 | cost [3.18]
98 --> 45 | cost [6.42]
99 --> 38 | cost [9.39]

B = 100.36
i★ = 70
j★ = 66
k★ = 97