------------------------------------------------------------
                         α=7.0 —— lin105 —— 105 nodes       
------------------------------------------------------------

——————— Fri, 26 Jan 2024 13:48:57 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 12 hubs —— 1—15—103—104—49—55—105—52—43—33—27—106
total time           3636.0 (TL 3600)     gap                  0.641                
blossom time         0                    nb blossom           0.0                  
LB <= UB             79434.42<=221555.28  subtour              241.0                
connectivity cuts    123.0                uc strategy          4                    
uc tolerance         0.01                 tildeV               2:105                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—15—103—104—49—55—105—52—43—33—27—106

RING
1  --- 15 | cost [3311.0]
15 --- 103 | cost [700.0]
27 --- 33 | cost [1365.0]
27 --- 106 | cost [5411.0]
33 --- 43 | cost [4053.0]
43 --- 52 | cost [882.0]
49 --- 55 | cost [1253.0]
49 --- 104 | cost [2240.0]
52 --- 105 | cost [2849.0]
55 --- 105 | cost [1694.0]
103 --- 104 | cost [4053.0]

STAR
2  -->  1 | cost [93.0]
3  -->  1 | cost [927.0]
4  -->  1 | cost [3630.0]
5  -->  1 | cost [3453.0]
6  -->  1 | cost [450.0]
7  -->  1 | cost [543.0]
8  -->  1 | cost [1794.0]
9  -->  1 | cost [2091.0]
10 -->  1 | cost [897.0]
11 -->  1 | cost [993.0]
12 -->  1 | cost [1464.0]
13 --> 52 | cost [3552.0]
14 --> 52 | cost [3375.0]
16 --> 52 | cost [2715.0]
17 -->  1 | cost [2538.0]
18 -->  1 | cost [2457.0]
19 -->  1 | cost [2145.0]
20 -->  1 | cost [1872.0]
21 -->  1 | cost [1737.0]
22 -->  1 | cost [1830.0]
23 -->  1 | cost [1983.0]
24 --> 52 | cost [2478.0]
25 --> 52 | cost [2433.0]
26 --> 52 | cost [2337.0]
28 -->  1 | cost [2073.0]
29 -->  1 | cost [1926.0]
30 -->  1 | cost [2151.0]
31 -->  1 | cost [2271.0]
32 -->  1 | cost [2361.0]
34 --> 52 | cost [2589.0]
35 --> 52 | cost [2388.0]
36 --> 52 | cost [1491.0]
37 --> 52 | cost [1482.0]
38 --> 52 | cost [2061.0]
39 --> 52 | cost [1851.0]
40 --> 52 | cost [1491.0]
41 --> 52 | cost [573.0]
42 --> 52 | cost [591.0]
44 --> 52 | cost [606.0]
45 --> 52 | cost [1152.0]
46 --> 52 | cost [189.0]
47 --> 52 | cost [510.0]
48 --> 105 | cost [1092.0]
50 --> 105 | cost [906.0]
51 --> 52 | cost [474.0]
53 --> 52 | cost [189.0]
54 --> 52 | cost [510.0]
56 --> 55 | cost [189.0]
57 --> 52 | cost [606.0]
58 --> 52 | cost [378.0]
59 --> 55 | cost [624.0]
60 --> 52 | cost [2103.0]
61 --> 52 | cost [1986.0]
62 --> 105 | cost [876.0]
63 --> 105 | cost [1164.0]
64 --> 105 | cost [921.0]
65 --> 52 | cost [2655.0]
66 --> 52 | cost [2598.0]
67 --> 105 | cost [1323.0]
68 --> 105 | cost [1428.0]
69 --> 105 | cost [1533.0]
70 --> 105 | cost [1728.0]
71 --> 105 | cost [1551.0]
72 --> 105 | cost [1497.0]
73 --> 105 | cost [1536.0]
74 --> 105 | cost [1716.0]
75 --> 105 | cost [1818.0]
76 --> 105 | cost [1650.0]
77 --> 105 | cost [1614.0]
78 --> 105 | cost [1788.0]
79 --> 105 | cost [1707.0]
80 --> 105 | cost [1740.0]
81 --> 105 | cost [1899.0]
82 --> 105 | cost [1875.0]
83 --> 105 | cost [1971.0]
84 --> 105 | cost [1920.0]
85 --> 105 | cost [2208.0]
86 --> 105 | cost [2148.0]
87 --> 105 | cost [3525.0]
88 --> 105 | cost [3444.0]
89 --> 105 | cost [2667.0]
90 --> 105 | cost [2793.0]
91 --> 105 | cost [3063.0]
92 --> 105 | cost [3153.0]
93 --> 105 | cost [3069.0]
94 --> 105 | cost [4173.0]
95 --> 105 | cost [4125.0]
96 --> 105 | cost [3498.0]
97 --> 105 | cost [3588.0]
98 --> 105 | cost [3558.0]
99 --> 105 | cost [3660.0]
100 --> 105 | cost [4596.0]
101 --> 105 | cost [3930.0]
102 --> 105 | cost [4023.0]

BACKUP RING
1  --- 103 | cost [39.410000000000004]
15 --- 104 | cost [47.04]
27 --- 43 | cost [47.04]
33 --- 52 | cost [48.370000000000005]
33 --- 106 | cost [59.43]
43 --- 105 | cost [35.35]
49 --- 103 | cost [56.84]
49 --- 105 | cost [28.91]
52 --- 55 | cost [25.76]
55 --- 104 | cost [27.580000000000002]

BACKUP STAR
13 --> 27 | cost [24.39]
14 --> 27 | cost [22.32]
16 --> 27 | cost [5.5200000000000005]
24 --> 27 | cost [0.96]
25 --> 27 | cost [4.83]
26 --> 27 | cost [4.74]
34 --> 43 | cost [23.43]
35 --> 43 | cost [21.36]
36 --> 33 | cost [8.76]
37 --> 43 | cost [11.1]
38 --> 43 | cost [19.32]
39 --> 43 | cost [17.25]
40 --> 49 | cost [4.3500000000000005]
41 --> 43 | cost [2.0100000000000002]
42 --> 43 | cost [2.85]
44 --> 43 | cost [4.74]
45 --> 49 | cost [3.9]
46 --> 43 | cost [1.8900000000000001]
47 --> 43 | cost [5.1000000000000005]
48 --> 49 | cost [3.54]
50 --> 55 | cost [1.8900000000000001]
51 --> 43 | cost [6.0600000000000005]
53 --> 43 | cost [5.67]
54 --> 55 | cost [6.15]
56 --> 105 | cost [5.5200000000000005]
57 --> 105 | cost [6.24]
58 --> 43 | cost [7.5600000000000005]
59 --> 105 | cost [5.61]
60 --> 43 | cost [23.01]
61 --> 43 | cost [22.11]
62 --> 52 | cost [12.780000000000001]
63 --> 52 | cost [13.200000000000001]
64 --> 55 | cost [16.26]
65 --> 105 | cost [29.01]
66 --> 105 | cost [27.63]
67 --> 55 | cost [19.32]
68 --> 55 | cost [20.31]
69 --> 52 | cost [21.96]
70 --> 52 | cost [22.32]
71 --> 55 | cost [21.27]
72 --> 55 | cost [21.75]
73 --> 55 | cost [22.59]
74 --> 52 | cost [23.64]
75 --> 52 | cost [24.810000000000002]
76 --> 55 | cost [23.73]
77 --> 55 | cost [22.92]
78 --> 55 | cost [23.82]
79 --> 55 | cost [23.85]
80 --> 55 | cost [24.63]
81 --> 52 | cost [25.740000000000002]
82 --> 55 | cost [24.75]
83 --> 55 | cost [25.830000000000002]
84 --> 55 | cost [25.62]
85 --> 55 | cost [28.23]
86 --> 55 | cost [28.44]
87 --> 52 | cost [36.36]
88 --> 52 | cost [36.24]
89 --> 55 | cost [33.93]
90 --> 52 | cost [34.59]
91 --> 55 | cost [36.75]
92 --> 55 | cost [37.68]
93 --> 55 | cost [37.62]
94 --> 52 | cost [44.52]
95 --> 52 | cost [44.61]
96 --> 55 | cost [41.19]
97 --> 55 | cost [42.12]
98 --> 55 | cost [42.81]
99 --> 52 | cost [43.77]
100 --> 52 | cost [49.5]
101 --> 55 | cost [45.6]
102 --> 55 | cost [46.56]

B = 1202.81
i★ = 52
j★ = 105
k★ = 55

       
——————— Fri, 26 Jan 2024 14:50:13 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 58 hubs —— 1-3-8-9-5-13-34-38-39-60-65-87-94-95-99-90-89-93-96-92-91-85-82-78-71-68-67-72-77-76-74-69-63-58-57-56-55-50-48-45-44-41-36-26-25-24-28-30-29-22-21-15-11-10-7-6-2-106-1
total time           3606.32 (TL 3600)    gap                  0.111                
blossom time         0                    nb blossom           0.0                  
LB <= UB             76636<=86171.3       Master/SP costs      85675/496.3          
Master time          3598.6               SP time              7.73                 
subtour              36402.0              connectivity cuts    2000.0               
uc strategy          4                    uc tolerance         0.01                 
opt. cuts            36.0                 SP method            poly                 
tildeV               2:105                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       36537                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—3—8—9—5—13—34—38—39—60—65—87—94—95—99—90—89—93—96—92—91—85—82—78—71—68—67—72—77—76—74—69—63—58—57—56—55—50—48—45—44—41—36—26—25—24—28—30—29—22—21—15—11—10—7—6—2—106

RING
1  ---  3 | cost [2163.0]
2  ---  6 | cost [833.0]
2  --- 106 | cost [217.0]
3  ---  8 | cost [2044.0]
5  ---  9 | cost [3409.0]
5  --- 13 | cost [1974.0]
6  ---  7 | cost [217.0]
7  --- 10 | cost [826.0]
8  ---  9 | cost [714.0]
10 --- 11 | cost [224.0]
11 --- 15 | cost [1120.0]
13 --- 34 | cost [2870.0]
15 --- 21 | cost [777.0]
21 --- 22 | cost [217.0]
22 --- 29 | cost [224.0]
24 --- 25 | cost [1106.0]
24 --- 28 | cost [1288.0]
25 --- 26 | cost [224.0]
26 --- 36 | cost [1988.0]
28 --- 30 | cost [770.0]
29 --- 30 | cost [700.0]
34 --- 38 | cost [2149.0]
36 --- 41 | cost [2149.0]
38 --- 39 | cost [490.0]
39 --- 60 | cost [4102.0]
41 --- 44 | cost [1036.0]
44 --- 45 | cost [1435.0]
45 --- 48 | cost [441.0]
48 --- 50 | cost [441.0]
50 --- 55 | cost [441.0]
55 --- 56 | cost [441.0]
56 --- 57 | cost [1435.0]
57 --- 58 | cost [1106.0]
58 --- 63 | cost [2219.0]
60 --- 65 | cost [2149.0]
63 --- 69 | cost [2212.0]
65 --- 87 | cost [2870.0]
67 --- 68 | cost [245.0]
67 --- 72 | cost [980.0]
68 --- 71 | cost [371.0]
69 --- 74 | cost [427.0]
71 --- 78 | cost [609.0]
72 --- 77 | cost [273.0]
74 --- 76 | cost [1141.0]
76 --- 77 | cost [1267.0]
78 --- 82 | cost [217.0]
82 --- 85 | cost [826.0]
85 --- 91 | cost [1995.0]
87 --- 94 | cost [2149.0]
89 --- 90 | cost [714.0]
89 --- 93 | cost [2184.0]
90 --- 99 | cost [2149.0]
91 --- 92 | cost [217.0]
92 --- 96 | cost [833.0]
93 --- 96 | cost [2226.0]
94 --- 95 | cost [490.0]
95 --- 99 | cost [3409.0]

STAR
4  -->  5 | cost [213.0]
12 --> 15 | cost [681.0]
14 --> 13 | cost [213.0]
16 --> 25 | cost [291.0]
17 --> 25 | cost [348.0]
18 --> 25 | cost [117.0]
19 --> 24 | cost [117.0]
20 --> 28 | cost [213.0]
23 --> 28 | cost [96.0]
27 --> 24 | cost [96.0]
31 --> 30 | cost [168.0]
32 --> 30 | cost [276.0]
33 --> 28 | cost [477.0]
35 --> 34 | cost [210.0]
37 --> 36 | cost [306.0]
40 --> 45 | cost [366.0]
42 --> 41 | cost [306.0]
43 --> 41 | cost [201.0]
46 --> 41 | cost [384.0]
47 --> 44 | cost [189.0]
49 --> 48 | cost [354.0]
51 --> 57 | cost [378.0]
52 --> 58 | cost [378.0]
53 --> 58 | cost [189.0]
54 --> 57 | cost [189.0]
59 --> 56 | cost [468.0]
61 --> 60 | cost [213.0]
62 --> 63 | cost [306.0]
64 --> 67 | cost [582.0]
66 --> 65 | cost [213.0]
70 --> 74 | cost [276.0]
73 --> 76 | cost [117.0]
75 --> 74 | cost [117.0]
79 --> 77 | cost [93.0]
80 --> 76 | cost [93.0]
81 --> 74 | cost [210.0]
83 --> 82 | cost [129.0]
84 --> 82 | cost [264.0]
86 --> 77 | cost [567.0]
88 --> 87 | cost [210.0]
97 --> 96 | cost [93.0]
98 --> 99 | cost [306.0]
100 --> 95 | cost [489.0]
101 --> 96 | cost [447.0]
102 --> 96 | cost [543.0]
103 --> 21 | cost [252.0]
104 --> 45 | cost [636.0]
105 --> 56 | cost [552.0]

BACKUP RING
1  ---  8 | cost [41.86]
2  ---  7 | cost [10.5]
3  ---  9 | cost [27.16]
5  ---  8 | cost [41.09]
5  --- 34 | cost [48.160000000000004]
6  --- 10 | cost [10.43]
6  --- 106 | cost [10.5]
7  --- 11 | cost [10.5]
9  --- 13 | cost [40.53]
10 --- 15 | cost [13.16]
11 --- 21 | cost [17.85]
13 --- 38 | cost [50.19]
15 --- 22 | cost [9.94]
21 --- 29 | cost [4.41]
22 --- 30 | cost [8.61]
24 --- 26 | cost [11.27]
24 --- 30 | cost [20.23]
25 --- 28 | cost [23.87]
25 --- 36 | cost [22.12]
26 --- 41 | cost [41.300000000000004]
28 --- 29 | cost [12.11]
34 --- 39 | cost [24.080000000000002]
36 --- 44 | cost [27.580000000000002]
38 --- 60 | cost [42.980000000000004]
39 --- 65 | cost [62.440000000000005]
41 --- 45 | cost [24.150000000000002]
44 --- 48 | cost [14.98]
45 --- 50 | cost [8.82]
48 --- 55 | cost [8.82]
50 --- 56 | cost [8.82]
55 --- 57 | cost [14.98]
56 --- 58 | cost [25.41]
57 --- 63 | cost [27.09]
58 --- 69 | cost [42.42]
60 --- 87 | cost [50.19]
63 --- 74 | cost [25.41]
65 --- 94 | cost [50.19]
67 --- 71 | cost [5.88]
67 --- 77 | cost [11.69]
68 --- 72 | cost [9.66]
68 --- 78 | cost [8.47]
69 --- 76 | cost [11.48]
71 --- 82 | cost [8.26]
72 --- 76 | cost [12.950000000000001]
74 --- 77 | cost [23.87]
78 --- 85 | cost [10.43]
82 --- 91 | cost [28.07]
85 --- 92 | cost [22.12]
87 --- 95 | cost [24.080000000000002]
89 --- 96 | cost [43.75]
89 --- 99 | cost [23.17]
90 --- 93 | cost [27.86]
90 --- 95 | cost [37.24]
91 --- 96 | cost [10.5]
92 --- 93 | cost [21.07]
94 --- 99 | cost [38.85]

BACKUP STAR
4  --> 13 | cost [9.21]
12 --> 24 | cost [7.8]
14 -->  5 | cost [9.21]
16 --> 26 | cost [3.84]
17 --> 26 | cost [4.23]
18 --> 26 | cost [2.13]
19 --> 25 | cost [4.89]
20 --> 30 | cost [4.71]
23 --> 30 | cost [3.87]
27 --> 26 | cost [4.74]
31 --> 29 | cost [3.6]
32 --> 29 | cost [4.3500000000000005]
33 --> 30 | cost [5.3100000000000005]
35 --> 38 | cost [8.49]
37 --> 26 | cost [9.03]
40 --> 48 | cost [5.16]
42 --> 44 | cost [7.26]
43 --> 44 | cost [4.74]
46 --> 44 | cost [5.1000000000000005]
47 --> 41 | cost [5.5200000000000005]
49 --> 45 | cost [3.9]
51 --> 44 | cost [3.7800000000000002]
52 --> 41 | cost [5.73]
53 --> 57 | cost [5.1000000000000005]
54 --> 58 | cost [5.1000000000000005]
59 --> 55 | cost [6.24]
61 --> 65 | cost [8.46]
62 --> 58 | cost [9.0]
64 --> 72 | cost [5.91]
66 --> 60 | cost [10.35]
70 --> 69 | cost [3.06]
73 --> 69 | cost [4.3500000000000005]
75 --> 69 | cost [2.94]
79 --> 72 | cost [2.1]
80 --> 74 | cost [5.19]
81 --> 69 | cost [3.84]
83 --> 78 | cost [2.19]
84 --> 78 | cost [3.15]
86 --> 76 | cost [6.63]
88 --> 94 | cost [8.49]
97 --> 92 | cost [4.5]
98 --> 93 | cost [8.76]
100 --> 94 | cost [5.43]
101 --> 92 | cost [8.040000000000001]
102 --> 92 | cost [9.0]
103 --> 15 | cost [3.0]
104 --> 44 | cost [7.0200000000000005]
105 --> 57 | cost [6.24]

B = 70.9
i★ = 39
j★ = 60
k★ = 65