------------------------------------------------------------
                          α=7.0 —— rd100 —— 100 nodes       
------------------------------------------------------------

——————— Mon, 22 Jan 2024 07:53:51 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 27 hubs —— 1—86—21—9—78—33—10—27—50—46—77—95—6—99—47—94—98—45—100—39—43—7—22—48—90—60—101
total time           3634.98 (TL 3600)    gap                  0.302                
blossom time         0                    nb blossom           0.0                  
LB <= UB             37323.64<=53458.93   subtour              453.0                
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       1                    n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—86—21—9—78—33—10—27—50—46—77—95—6—99—47—94—98—45—100—39—43—7—22—48—90—60—101

RING
1  --- 86 | cost [1211.0]
6  --- 95 | cost [1183.0]
6  --- 99 | cost [637.0]
7  --- 22 | cost [1057.0]
7  --- 43 | cost [945.0]
9  --- 21 | cost [1757.0]
9  --- 78 | cost [693.0]
10 --- 27 | cost [833.0]
10 --- 33 | cost [287.0]
21 --- 86 | cost [609.0]
22 --- 48 | cost [1554.0]
27 --- 50 | cost [665.0]
33 --- 78 | cost [805.0]
39 --- 43 | cost [2107.0]
39 --- 100 | cost [1134.0]
45 --- 98 | cost [1533.0]
45 --- 100 | cost [1176.0]
46 --- 50 | cost [35.0]
46 --- 77 | cost [1554.0]
47 --- 94 | cost [1085.0]
47 --- 99 | cost [644.0]
48 --- 90 | cost [1225.0]
60 --- 90 | cost [1386.0]
60 --- 101 | cost [154.0]
77 --- 95 | cost [364.0]
94 --- 98 | cost [532.0]

STAR
2  --> 45 | cost [1065.0]
3  --> 33 | cost [345.0]
4  --> 10 | cost [675.0]
5  --> 22 | cost [279.0]
8  --> 60 | cost [102.0]
11 --> 22 | cost [588.0]
12 --> 21 | cost [351.0]
13 --> 21 | cost [354.0]
14 --> 21 | cost [306.0]
15 --> 21 | cost [387.0]
16 --> 45 | cost [306.0]
17 --> 50 | cost [483.0]
18 -->  1 | cost [264.0]
19 --> 46 | cost [252.0]
20 --> 10 | cost [474.0]
23 --> 45 | cost [804.0]
24 --> 43 | cost [135.0]
25 --> 43 | cost [126.0]
26 --> 10 | cost [630.0]
28 --> 77 | cost [222.0]
29 --> 100 | cost [282.0]
30 --> 48 | cost [237.0]
31 --> 98 | cost [429.0]
32 --> 21 | cost [405.0]
34 --> 22 | cost [378.0]
35 --> 100 | cost [417.0]
36 --> 47 | cost [492.0]
37 --> 77 | cost [318.0]
38 --> 50 | cost [411.0]
40 -->  7 | cost [213.0]
41 --> 22 | cost [150.0]
42 --> 43 | cost [198.0]
44 --> 100 | cost [219.0]
49 --> 21 | cost [105.0]
51 --> 90 | cost [126.0]
52 --> 100 | cost [429.0]
53 --> 99 | cost [144.0]
54 --> 46 | cost [300.0]
55 --> 39 | cost [336.0]
56 --> 46 | cost [75.0]
57 --> 47 | cost [300.0]
58 --> 98 | cost [618.0]
59 --> 95 | cost [57.0]
61 --> 22 | cost [345.0]
62 -->  1 | cost [282.0]
63 --> 21 | cost [306.0]
64 --> 47 | cost [606.0]
65 --> 90 | cost [288.0]
66 --> 98 | cost [216.0]
67 --> 21 | cost [306.0]
68 --> 90 | cost [399.0]
69 --> 60 | cost [249.0]
70 --> 50 | cost [672.0]
71 -->  1 | cost [393.0]
72 --> 50 | cost [579.0]
73 --> 50 | cost [81.0]
74 --> 10 | cost [525.0]
75 --> 21 | cost [75.0]
76 --> 98 | cost [354.0]
79 -->  6 | cost [138.0]
80 --> 48 | cost [231.0]
81 --> 48 | cost [429.0]
82 --> 21 | cost [126.0]
83 --> 90 | cost [216.0]
84 --> 98 | cost [540.0]
85 --> 21 | cost [228.0]
87 --> 21 | cost [477.0]
88 --> 98 | cost [507.0]
89 --> 98 | cost [1191.0]
91 --> 90 | cost [396.0]
92 --> 27 | cost [111.0]
93 --> 77 | cost [132.0]
96 --> 39 | cost [120.0]
97 --> 21 | cost [291.0]

BACKUP RING
1  --- 21 | cost [17.990000000000002]
6  --- 47 | cost [11.06]
6  --- 77 | cost [14.07]
7  --- 39 | cost [16.17]
7  --- 48 | cost [25.830000000000002]
9  --- 33 | cost [14.77]
9  --- 86 | cost [23.52]
10 --- 50 | cost [14.98]
10 --- 78 | cost [10.92]
21 --- 78 | cost [15.47]
22 --- 43 | cost [17.22]
22 --- 90 | cost [23.240000000000002]
27 --- 33 | cost [9.59]
27 --- 46 | cost [6.86]
39 --- 45 | cost [22.89]
43 --- 100 | cost [30.94]
45 --- 94 | cost [17.36]
46 --- 95 | cost [17.71]
47 --- 98 | cost [15.540000000000001]
48 --- 60 | cost [24.990000000000002]
50 --- 77 | cost [15.82]
90 --- 101 | cost [15.33]
94 --- 99 | cost [11.200000000000001]
95 --- 99 | cost [17.990000000000002]
98 --- 100 | cost [27.02]

BACKUP STAR
2  --> 100 | cost [12.42]
3  --> 10 | cost [3.9]
4  --> 21 | cost [3.06]
5  -->  7 | cost [5.7]
8  -->  1 | cost [1.6500000000000001]
11 -->  7 | cost [6.42]
12 -->  9 | cost [5.49]
13 --> 86 | cost [2.88]
14 --> 86 | cost [4.44]
15 --> 86 | cost [1.29]
16 --> 98 | cost [3.54]
17 --> 46 | cost [4.95]
19 --> 50 | cost [2.67]
20 --> 78 | cost [1.17]
23 --> 100 | cost [9.99]
24 -->  7 | cost [4.2]
25 -->  7 | cost [5.34]
26 -->  9 | cost [1.26]
28 --> 95 | cost [3.45]
29 --> 39 | cost [5.1000000000000005]
30 --> 22 | cost [4.41]
31 --> 45 | cost [5.1000000000000005]
32 --> 78 | cost [2.82]
34 -->  7 | cost [1.71]
35 --> 39 | cost [6.78]
36 --> 99 | cost [7.44]
37 --> 46 | cost [3.84]
38 --> 46 | cost [4.17]
40 --> 43 | cost [3.63]
41 -->  7 | cost [3.18]
42 -->  7 | cost [2.19]
44 --> 45 | cost [4.17]
49 --> 86 | cost [2.64]
51 --> 48 | cost [4.2]
52 --> 45 | cost [3.7800000000000002]
53 -->  6 | cost [1.77]
54 --> 50 | cost [3.0300000000000002]
55 -->  7 | cost [5.58]
56 --> 50 | cost [0.84]
57 --> 99 | cost [5.76]
58 --> 95 | cost [6.63]
59 --> 77 | cost [1.44]
61 -->  7 | cost [4.92]
63 --> 86 | cost [0.45]
64 --> 99 | cost [7.38]
65 --> 48 | cost [3.09]
66 --> 94 | cost [4.41]
67 --> 86 | cost [1.2]
68 --> 48 | cost [5.79]
69 -->  1 | cost [3.09]
70 --> 46 | cost [6.78]
72 --> 46 | cost [5.88]
73 --> 46 | cost [0.87]
74 --> 78 | cost [1.62]
75 --> 86 | cost [3.3000000000000003]
76 --> 95 | cost [4.2]
79 --> 99 | cost [2.07]
80 --> 90 | cost [4.68]
81 --> 22 | cost [4.53]
82 --> 86 | cost [3.72]
83 --> 48 | cost [3.99]
84 --> 45 | cost [6.54]
85 --> 86 | cost [4.32]
87 --> 86 | cost [3.81]
88 --> 45 | cost [6.84]
89 --> 45 | cost [11.91]
91 --> 48 | cost [6.6000000000000005]
92 --> 50 | cost [2.46]
93 --> 95 | cost [2.67]
96 --> 100 | cost [5.25]
97 --> 86 | cost [0.39]

B = 62.989999999999995
i★ = 45
j★ = 98
k★ = 94

       
——————— Mon, 22 Jan 2024 08:55:28 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 46 hubs —— 1-60-8-83-51-65-80-81-5-61-34-7-42-40-55-39-100-52-57-47-53-94-98-66-84-88-76-59-77-28-56-46-73-92-33-20-78-32-82-21-75-86-97-63-15-101-1
total time           3606.66 (TL 3600)    gap                  0.096                
blossom time         0                    nb blossom           0.0                  
LB <= UB             38372.5<=42440.88    Master/SP costs      41341/1099.88        
Master time          3592.7               SP time              13.95                
subtour              31383.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            46.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       35878                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—60—8—83—51—65—80—81—5—61—34—7—42—40—55—39—100—52—57—47—53—94—98—66—84—88—76—59—77—28—56—46—73—92—33—20—78—32—82—21—75—86—97—63—15—101

RING
1  --- 60 | cost [154.0]
5  --- 61 | cost [350.0]
5  --- 81 | cost [896.0]
7  --- 34 | cost [399.0]
7  --- 42 | cost [511.0]
8  --- 60 | cost [238.0]
8  --- 83 | cost [1337.0]
15 --- 63 | cost [210.0]
15 --- 101 | cost [910.0]
20 --- 33 | cost [847.0]
20 --- 78 | cost [273.0]
21 --- 75 | cost [175.0]
21 --- 82 | cost [294.0]
28 --- 56 | cost [896.0]
28 --- 77 | cost [518.0]
32 --- 78 | cost [658.0]
32 --- 82 | cost [728.0]
33 --- 92 | cost [1092.0]
34 --- 61 | cost [756.0]
39 --- 55 | cost [784.0]
39 --- 100 | cost [1134.0]
40 --- 42 | cost [616.0]
40 --- 55 | cost [833.0]
46 --- 56 | cost [175.0]
46 --- 73 | cost [203.0]
47 --- 53 | cost [693.0]
47 --- 57 | cost [700.0]
51 --- 65 | cost [581.0]
51 --- 83 | cost [238.0]
52 --- 57 | cost [1141.0]
52 --- 100 | cost [1001.0]
53 --- 94 | cost [798.0]
59 --- 76 | cost [910.0]
59 --- 77 | cost [336.0]
63 --- 97 | cost [56.0]
65 --- 80 | cost [420.0]
66 --- 84 | cost [812.0]
66 --- 98 | cost [504.0]
73 --- 92 | cost [609.0]
75 --- 86 | cost [770.0]
76 --- 88 | cost [875.0]
80 --- 81 | cost [469.0]
84 --- 88 | cost [133.0]
86 --- 97 | cost [91.0]
94 --- 98 | cost [532.0]

STAR
2  --> 84 | cost [711.0]
3  --> 33 | cost [345.0]
4  --> 32 | cost [126.0]
6  --> 53 | cost [177.0]
9  --> 20 | cost [279.0]
10 --> 33 | cost [123.0]
11 --> 61 | cost [243.0]
12 --> 82 | cost [237.0]
13 --> 97 | cost [270.0]
14 --> 82 | cost [231.0]
16 --> 98 | cost [354.0]
17 --> 73 | cost [414.0]
18 -->  1 | cost [264.0]
19 --> 46 | cost [252.0]
22 -->  5 | cost [279.0]
23 --> 84 | cost [546.0]
24 --> 42 | cost [204.0]
25 --> 42 | cost [327.0]
26 --> 20 | cost [156.0]
27 --> 92 | cost [111.0]
29 --> 100 | cost [282.0]
30 --> 80 | cost [252.0]
31 --> 84 | cost [162.0]
35 --> 100 | cost [417.0]
36 --> 57 | cost [300.0]
37 --> 28 | cost [108.0]
38 --> 73 | cost [333.0]
41 --> 34 | cost [291.0]
43 --> 42 | cost [198.0]
44 --> 100 | cost [219.0]
45 --> 52 | cost [378.0]
48 --> 80 | cost [231.0]
49 --> 21 | cost [105.0]
50 --> 46 | cost [15.0]
54 --> 73 | cost [240.0]
58 --> 76 | cost [288.0]
62 -->  1 | cost [282.0]
64 --> 47 | cost [606.0]
67 --> 97 | cost [96.0]
68 --> 83 | cost [243.0]
69 -->  8 | cost [183.0]
70 --> 73 | cost [591.0]
71 -->  8 | cost [378.0]
72 --> 73 | cost [501.0]
74 --> 20 | cost [57.0]
79 --> 53 | cost [195.0]
85 --> 82 | cost [123.0]
87 --> 15 | cost [360.0]
89 --> 84 | cost [663.0]
90 --> 51 | cost [126.0]
91 --> 65 | cost [360.0]
93 --> 77 | cost [132.0]
95 --> 59 | cost [57.0]
96 --> 39 | cost [120.0]
99 --> 53 | cost [144.0]

BACKUP RING
1  ---  8 | cost [3.85]
5  --- 34 | cost [9.8]
5  --- 80 | cost [13.09]
7  --- 40 | cost [4.97]
7  --- 61 | cost [11.48]
8  --- 51 | cost [13.02]
15 --- 97 | cost [2.66]
20 --- 32 | cost [9.03]
20 --- 92 | cost [12.530000000000001]
21 --- 32 | cost [9.450000000000001]
21 --- 86 | cost [6.09]
28 --- 46 | cost [10.43]
28 --- 59 | cost [8.33]
33 --- 73 | cost [16.94]
33 --- 78 | cost [8.05]
34 --- 42 | cost [8.96]
39 --- 40 | cost [13.09]
39 --- 52 | cost [18.41]
42 --- 55 | cost [14.07]
46 --- 92 | cost [6.0200000000000005]
47 --- 52 | cost [18.13]
47 --- 94 | cost [10.85]
51 --- 80 | cost [9.59]
53 --- 57 | cost [13.370000000000001]
53 --- 98 | cost [13.23]
55 --- 100 | cost [19.04]
56 --- 73 | cost [3.7800000000000002]
56 --- 77 | cost [13.93]
57 --- 100 | cost [21.42]
59 --- 88 | cost [17.78]
60 --- 83 | cost [15.68]
61 --- 81 | cost [12.46]
63 --- 86 | cost [1.05]
63 --- 101 | cost [11.13]
65 --- 81 | cost [6.86]
65 --- 83 | cost [7.21]
66 --- 88 | cost [7.140000000000001]
66 --- 94 | cost [10.290000000000001]
75 --- 82 | cost [2.52]
75 --- 97 | cost [8.33]
76 --- 77 | cost [12.11]
76 --- 84 | cost [10.01]
78 --- 82 | cost [13.65]
84 --- 98 | cost [12.6]

BACKUP STAR
2  --> 88 | cost [7.53]
3  --> 78 | cost [4.86]
4  --> 75 | cost [2.34]
6  --> 94 | cost [3.63]
9  --> 78 | cost [2.97]
10 --> 92 | cost [4.41]
11 -->  5 | cost [3.54]
12 --> 32 | cost [3.42]
13 --> 86 | cost [2.88]
14 --> 21 | cost [3.06]
16 --> 66 | cost [4.2]
17 --> 92 | cost [4.5]
19 --> 56 | cost [2.64]
22 --> 61 | cost [3.45]
23 --> 88 | cost [5.97]
24 -->  7 | cost [4.2]
25 --> 40 | cost [4.71]
26 --> 78 | cost [2.04]
27 --> 56 | cost [2.73]
29 --> 39 | cost [5.1000000000000005]
30 --> 81 | cost [3.6]
31 --> 88 | cost [1.77]
35 --> 39 | cost [6.78]
36 --> 47 | cost [4.92]
37 --> 77 | cost [3.18]
38 --> 46 | cost [4.17]
41 -->  7 | cost [3.18]
43 --> 40 | cost [3.63]
44 --> 52 | cost [5.19]
45 --> 100 | cost [5.04]
48 --> 65 | cost [3.09]
49 --> 75 | cost [1.1400000000000001]
50 --> 73 | cost [0.81]
54 --> 46 | cost [3.0]
58 --> 88 | cost [3.45]
64 --> 57 | cost [6.15]
67 --> 63 | cost [1.1400000000000001]
68 --> 51 | cost [3.27]
69 --> 60 | cost [2.49]
70 --> 46 | cost [6.78]
71 --> 60 | cost [3.84]
72 --> 46 | cost [5.88]
74 --> 78 | cost [1.62]
79 --> 47 | cost [4.65]
85 --> 21 | cost [2.2800000000000002]
87 --> 86 | cost [3.81]
89 --> 88 | cost [6.87]
90 --> 83 | cost [2.16]
91 --> 81 | cost [3.87]
93 --> 59 | cost [2.31]
95 --> 77 | cost [1.56]
96 --> 55 | cost [3.48]
99 --> 47 | cost [2.7600000000000002]

B = 35.480000000000004
i★ = 39
j★ = 100
k★ = 52