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

——————— Thu, 18 Jan 2024 22:45:40 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 30 hubs —— 1—40—12—49—61—29—52—87—96—81—33—36—57—41—77—68—2—23—94—50—39—8—38—17—6—65—64—67—79—101
total time           3638.16 (TL 3600)    gap                  0.468                
blossom time         0                    nb blossom           0.0                  
LB <= UB             101569.53<=191049.42 subtour              742.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       351                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—40—12—49—61—29—52—87—96—81—33—36—57—41—77—68—2—23—94—50—39—8—38—17—6—65—64—67—79—101

RING
1  --- 40 | cost [2653.0]
2  --- 23 | cost [2443.0]
2  --- 68 | cost [1463.0]
6  --- 17 | cost [5740.0]
6  --- 65 | cost [3185.0]
8  --- 38 | cost [5929.0]
8  --- 39 | cost [5138.0]
12 --- 40 | cost [1568.0]
12 --- 49 | cost [2751.0]
17 --- 38 | cost [6223.0]
23 --- 94 | cost [3353.0]
29 --- 52 | cost [8057.0]
29 --- 61 | cost [2275.0]
33 --- 36 | cost [1155.0]
33 --- 81 | cost [819.0]
36 --- 57 | cost [294.0]
39 --- 50 | cost [3626.0]
41 --- 57 | cost [7126.0]
41 --- 77 | cost [4032.0]
49 --- 61 | cost [3710.0]
50 --- 94 | cost [2954.0]
52 --- 87 | cost [3136.0]
64 --- 65 | cost [3906.0]
64 --- 67 | cost [1960.0]
67 --- 79 | cost [2114.0]
68 --- 77 | cost [3171.0]
79 --- 101 | cost [5187.0]
81 --- 96 | cost [4158.0]
87 --- 96 | cost [1974.0]

STAR
3  --> 36 | cost [2547.0]
4  --> 40 | cost [1695.0]
5  --> 50 | cost [1593.0]
7  --> 49 | cost [3213.0]
9  --> 49 | cost [2145.0]
10 --> 36 | cost [717.0]
11 --> 36 | cost [2880.0]
13 --> 79 | cost [390.0]
14 --> 36 | cost [630.0]
15 --> 79 | cost [735.0]
16 --> 49 | cost [1806.0]
18 --> 29 | cost [321.0]
19 --> 36 | cost [1167.0]
20 --> 64 | cost [75.0]
21 --> 23 | cost [1062.0]
22 -->  8 | cost [384.0]
24 --> 61 | cost [966.0]
25 -->  8 | cost [1209.0]
26 --> 49 | cost [2103.0]
27 -->  1 | cost [1386.0]
28 --> 39 | cost [285.0]
30 --> 77 | cost [1152.0]
31 -->  6 | cost [942.0]
32 --> 61 | cost [717.0]
34 -->  8 | cost [1650.0]
35 --> 23 | cost [864.0]
37 --> 49 | cost [1083.0]
42 --> 64 | cost [705.0]
43 --> 50 | cost [2040.0]
44 --> 36 | cost [2691.0]
45 --> 36 | cost [648.0]
46 --> 29 | cost [804.0]
47 -->  6 | cost [840.0]
48 --> 36 | cost [2307.0]
51 --> 49 | cost [2271.0]
53 -->  1 | cost [96.0]
54 -->  6 | cost [327.0]
55 --> 64 | cost [522.0]
56 --> 38 | cost [531.0]
58 -->  8 | cost [2286.0]
59 --> 68 | cost [2343.0]
60 --> 36 | cost [2037.0]
62 --> 50 | cost [855.0]
63 --> 49 | cost [2016.0]
66 --> 36 | cost [2127.0]
69 --> 36 | cost [1311.0]
70 --> 94 | cost [921.0]
71 --> 50 | cost [1284.0]
72 --> 50 | cost [771.0]
73 --> 36 | cost [2583.0]
74 --> 57 | cost [186.0]
75 -->  8 | cost [789.0]
76 --> 94 | cost [762.0]
78 --> 49 | cost [2364.0]
80 --> 65 | cost [771.0]
82 --> 49 | cost [2682.0]
83 --> 50 | cost [879.0]
84 --> 36 | cost [2712.0]
85 -->  1 | cost [648.0]
86 --> 50 | cost [933.0]
88 --> 39 | cost [795.0]
89 --> 23 | cost [1770.0]
90 -->  8 | cost [1383.0]
91 --> 94 | cost [387.0]
92 --> 36 | cost [918.0]
93 --> 49 | cost [819.0]
95 --> 94 | cost [369.0]
97 --> 36 | cost [1167.0]
98 -->  8 | cost [1968.0]
99 --> 36 | cost [912.0]
100 --> 36 | cost [477.0]

BACKUP RING
1  --- 12 | cost [38.01]
2  --- 77 | cost [35.28]
2  --- 94 | cost [51.38]
6  --- 38 | cost [73.64]
6  --- 64 | cost [47.67]
8  --- 17 | cost [21.56]
8  --- 50 | cost [62.230000000000004]
12 --- 61 | cost [52.99]
17 --- 65 | cost [83.65]
23 --- 50 | cost [41.44]
23 --- 68 | cost [23.45]
29 --- 49 | cost [14.42]
29 --- 87 | cost [107.03]
33 --- 57 | cost [11.34]
33 --- 96 | cost [49.49]
36 --- 41 | cost [73.5]
36 --- 81 | cost [18.830000000000002]
38 --- 39 | cost [8.05]
39 --- 94 | cost [61.95]
40 --- 49 | cost [42.980000000000004]
41 --- 68 | cost [35.7]
52 --- 61 | cost [86.45]
52 --- 96 | cost [21.490000000000002]
57 --- 77 | cost [89.04]
64 --- 79 | cost [20.44]
65 --- 67 | cost [21.35]
67 --- 101 | cost [72.8]
81 --- 87 | cost [57.4]

BACKUP STAR
3  --> 41 | cost [12.42]
4  --> 12 | cost [13.35]
5  --> 38 | cost [10.53]
7  --> 61 | cost [16.26]
9  --> 61 | cost [8.4]
10 --> 57 | cost [8.43]
11 --> 52 | cost [0.81]
13 --> 65 | cost [9.42]
14 --> 57 | cost [6.75]
15 -->  1 | cost [15.33]
16 --> 29 | cost [15.9]
18 --> 49 | cost [3.21]
19 --> 57 | cost [12.9]
20 --> 79 | cost [9.06]
21 --> 68 | cost [14.25]
22 --> 17 | cost [12.42]
24 --> 29 | cost [12.870000000000001]
25 --> 17 | cost [3.06]
26 --> 61 | cost [5.13]
28 --> 38 | cost [3.27]
30 --> 68 | cost [4.17]
31 --> 67 | cost [3.9]
32 --> 29 | cost [13.89]
34 --> 17 | cost [8.19]
35 -->  2 | cost [2.2800000000000002]
37 --> 29 | cost [6.48]
42 --> 67 | cost [9.6]
43 --> 38 | cost [15.030000000000001]
44 --> 52 | cost [14.67]
45 --> 81 | cost [2.37]
46 --> 12 | cost [9.75]
47 --> 67 | cost [5.01]
48 --> 52 | cost [7.86]
51 --> 52 | cost [18.45]
54 -->  8 | cost [14.94]
55 --> 67 | cost [6.48]
56 --> 39 | cost [8.73]
58 --> 17 | cost [16.95]
59 --> 41 | cost [8.55]
60 --> 12 | cost [19.2]
62 --> 39 | cost [14.22]
63 --> 52 | cost [17.34]
66 --> 52 | cost [16.05]
69 --> 57 | cost [11.94]
70 --> 23 | cost [10.11]
71 --> 38 | cost [2.58]
72 --> 39 | cost [8.46]
73 --> 41 | cost [12.72]
74 --> 36 | cost [3.09]
75 -->  6 | cost [8.040000000000001]
76 --> 23 | cost [13.23]
78 --> 61 | cost [9.57]
80 --> 77 | cost [5.82]
82 --> 61 | cost [13.05]
83 --> 39 | cost [12.93]
84 --> 52 | cost [3.54]
86 --> 38 | cost [12.870000000000001]
88 --> 38 | cost [9.33]
89 --> 41 | cost [6.390000000000001]
90 --> 17 | cost [5.55]
91 --> 23 | cost [10.5]
92 --> 57 | cost [10.47]
93 --> 12 | cost [11.49]
95 --> 50 | cost [9.27]
97 --> 81 | cost [3.6]
98 --> 39 | cost [11.46]
99 --> 57 | cost [10.32]
100 --> 33 | cost [1.47]

B = 175.06000000000003
i★ = 12
j★ = 49
k★ = 61

       
——————— Thu, 18 Jan 2024 23:47:06 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 50 hubs —— 1-40-12-18-37-61-26-9-16-63-44-84-48-19-10-14-57-74-69-73-41-30-89-21-94-91-95-28-38-39-34-90-25-72-75-8-20-64-55-22-6-31-65-35-83-54-67-79-15-101-1
total time           3608.05 (TL 3600)    gap                  0.353                
blossom time         0                    nb blossom           0.0                  
LB <= UB             103885<=160617.47    Master/SP costs      159944/673.47        
Master time          3598.49              SP time              9.56                 
subtour              32490.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            35.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       23165                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—40—12—18—37—61—26—9—16—63—44—84—48—19—10—14—57—74—69—73—41—30—89—21—94—91—95—28—38—39—34—90—25—72—75—8—20—64—55—22—6—31—65—35—83—54—67—79—15—101

RING
1  --- 40 | cost [2653.0]
6  --- 22 | cost [3038.0]
6  --- 31 | cost [2198.0]
8  --- 20 | cost [5803.0]
8  --- 75 | cost [1841.0]
9  --- 16 | cost [2989.0]
9  --- 26 | cost [1547.0]
10 --- 14 | cost [1841.0]
10 --- 19 | cost [1106.0]
12 --- 18 | cost [3206.0]
12 --- 40 | cost [1568.0]
14 --- 57 | cost [1575.0]
15 --- 79 | cost [1715.0]
15 --- 101 | cost [3577.0]
16 --- 63 | cost [847.0]
18 --- 37 | cost [1820.0]
19 --- 48 | cost [3997.0]
20 --- 64 | cost [175.0]
21 --- 89 | cost [2583.0]
21 --- 94 | cost [4893.0]
22 --- 55 | cost [4746.0]
25 --- 72 | cost [6223.0]
25 --- 90 | cost [672.0]
26 --- 61 | cost [1197.0]
28 --- 38 | cost [763.0]
28 --- 95 | cost [5740.0]
30 --- 41 | cost [2688.0]
30 --- 89 | cost [2632.0]
31 --- 65 | cost [1813.0]
34 --- 39 | cost [5159.0]
34 --- 90 | cost [630.0]
35 --- 65 | cost [5341.0]
35 --- 83 | cost [4753.0]
37 --- 61 | cost [1897.0]
38 --- 39 | cost [805.0]
41 --- 73 | cost [2968.0]
44 --- 63 | cost [763.0]
44 --- 84 | cost [2667.0]
48 --- 84 | cost [1057.0]
54 --- 67 | cost [3822.0]
54 --- 83 | cost [3388.0]
55 --- 64 | cost [1218.0]
57 --- 74 | cost [434.0]
67 --- 79 | cost [2114.0]
69 --- 73 | cost [2996.0]
69 --- 74 | cost [2506.0]
72 --- 75 | cost [4417.0]
91 --- 94 | cost [903.0]
91 --- 95 | cost [1344.0]

STAR
2  --> 35 | cost [228.0]
3  --> 73 | cost [54.0]
4  --> 14 | cost [1152.0]
5  --> 38 | cost [1053.0]
7  --> 26 | cost [1113.0]
11 --> 84 | cost [285.0]
13 --> 79 | cost [390.0]
17 --> 25 | cost [306.0]
23 --> 35 | cost [864.0]
24 --> 61 | cost [966.0]
27 --> 15 | cost [750.0]
29 --> 18 | cost [321.0]
32 --> 61 | cost [717.0]
33 --> 74 | cost [465.0]
36 --> 57 | cost [126.0]
42 --> 55 | cost [327.0]
43 --> 38 | cost [1503.0]
45 --> 57 | cost [696.0]
46 --> 18 | cost [939.0]
47 --> 31 | cost [261.0]
49 --> 18 | cost [321.0]
50 --> 72 | cost [771.0]
51 --> 63 | cost [366.0]
52 --> 84 | cost [354.0]
53 -->  1 | cost [96.0]
56 --> 83 | cost [1902.0]
58 --> 34 | cost [996.0]
59 --> 73 | cost [417.0]
60 --> 14 | cost [1494.0]
62 --> 83 | cost [132.0]
66 --> 44 | cost [570.0]
68 --> 35 | cost [459.0]
70 --> 91 | cost [708.0]
71 --> 38 | cost [258.0]
76 --> 91 | cost [708.0]
77 --> 30 | cost [1152.0]
78 -->  9 | cost [249.0]
80 --> 30 | cost [1473.0]
81 --> 57 | cost [825.0]
82 -->  9 | cost [537.0]
85 -->  1 | cost [648.0]
86 --> 95 | cost [975.0]
87 --> 84 | cost [1605.0]
88 --> 28 | cost [609.0]
92 --> 10 | cost [204.0]
93 --> 19 | cost [1086.0]
96 --> 84 | cost [1008.0]
97 --> 74 | cost [1155.0]
98 --> 28 | cost [1062.0]
99 --> 19 | cost [300.0]
100 --> 74 | cost [360.0]

BACKUP RING
1  --- 12 | cost [38.01]
6  --- 55 | cost [37.24]
6  --- 65 | cost [31.85]
8  --- 64 | cost [57.120000000000005]
8  --- 72 | cost [49.56]
9  --- 61 | cost [19.6]
9  --- 63 | cost [37.660000000000004]
10 --- 48 | cost [41.58]
10 --- 57 | cost [19.67]
12 --- 37 | cost [49.21]
14 --- 19 | cost [24.150000000000002]
14 --- 74 | cost [19.18]
15 --- 67 | cost [37.31]
16 --- 26 | cost [42.21]
16 --- 44 | cost [15.47]
18 --- 40 | cost [46.9]
18 --- 61 | cost [29.89]
19 --- 84 | cost [50.47]
20 --- 55 | cost [13.44]
20 --- 75 | cost [55.370000000000005]
21 --- 30 | cost [35.0]
21 --- 91 | cost [41.300000000000004]
22 --- 31 | cost [45.15]
22 --- 64 | cost [59.64]
25 --- 34 | cost [12.39]
25 --- 75 | cost [46.27]
26 --- 37 | cost [28.63]
28 --- 39 | cost [6.65]
28 --- 91 | cost [69.09]
30 --- 73 | cost [56.07]
31 --- 35 | cost [58.52]
34 --- 38 | cost [58.45]
35 --- 54 | cost [40.32]
38 --- 95 | cost [50.26]
39 --- 90 | cost [50.68]
41 --- 69 | cost [45.36]
41 --- 89 | cost [14.91]
44 --- 48 | cost [22.05]
54 --- 79 | cost [58.38]
57 --- 69 | cost [27.86]
63 --- 84 | cost [33.39]
65 --- 83 | cost [71.61]
67 --- 83 | cost [71.26]
72 --- 90 | cost [60.410000000000004]
73 --- 74 | cost [54.18]
79 --- 101 | cost [51.870000000000005]
89 --- 94 | cost [72.24]
94 --- 95 | cost [8.61]

BACKUP STAR
2  --> 30 | cost [9.93]
3  --> 41 | cost [12.42]
4  --> 12 | cost [13.35]
5  --> 28 | cost [13.47]
7  -->  9 | cost [13.17]
11 --> 48 | cost [7.08]
13 --> 15 | cost [7.0200000000000005]
17 --> 90 | cost [5.55]
23 --> 91 | cost [10.5]
24 --> 26 | cost [11.82]
27 --> 40 | cost [9.0]
29 --> 37 | cost [6.48]
32 --> 26 | cost [7.68]
33 --> 57 | cost [4.86]
36 --> 74 | cost [3.09]
42 --> 64 | cost [7.05]
43 --> 28 | cost [17.61]
45 --> 74 | cost [7.41]
46 --> 12 | cost [9.75]
47 --> 67 | cost [5.01]
49 --> 37 | cost [10.83]
50 --> 83 | cost [8.790000000000001]
51 --> 16 | cost [4.71]
52 --> 48 | cost [7.86]
56 --> 38 | cost [5.3100000000000005]
58 --> 90 | cost [11.82]
59 --> 41 | cost [8.55]
60 --> 69 | cost [17.16]
62 --> 72 | cost [6.69]
66 --> 63 | cost [8.07]
68 --> 30 | cost [4.17]
70 --> 94 | cost [9.21]
71 --> 39 | cost [4.68]
76 --> 94 | cost [7.62]
77 --> 65 | cost [12.0]
78 --> 26 | cost [6.36]
80 --> 65 | cost [7.71]
81 --> 74 | cost [8.16]
82 --> 26 | cost [9.48]
86 --> 72 | cost [11.73]
87 --> 48 | cost [18.48]
88 --> 39 | cost [7.95]
92 --> 19 | cost [3.18]
93 --> 18 | cost [11.370000000000001]
96 --> 48 | cost [10.950000000000001]
97 --> 57 | cost [11.790000000000001]
98 --> 39 | cost [11.46]
99 --> 10 | cost [3.24]
100 --> 57 | cost [4.32]

B = 96.21
i★ = 65
j★ = 35
k★ = 83