------------------------------------------------------------
                        α=5.0 —— kroD100 —— 100 nodes       
------------------------------------------------------------

——————— Mon, 22 Jan 2024 01:16:38 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 23 hubs —— 1—49—94—8—38—23—61—72—58—75—67—68—96—40—2—10—56—26—39—77—73—79—101
total time           3638.32 (TL 3600)    gap                  0.823                
blossom time         0                    nb blossom           0.0                  
LB <= UB             97764.68<=551254.75  subtour              2695.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       734                  n lazycuts edges     0.0                  
F                    31.0                 post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—49—94—8—38—23—61—72—58—75—67—68—96—40—2—10—56—26—39—77—73—79—101

RING
1  --- 49 | cost [4900.0]
2  --- 10 | cost [5505.0]
2  --- 40 | cost [5480.0]
8  --- 38 | cost [925.0]
8  --- 94 | cost [4155.0]
10 --- 56 | cost [2270.0]
23 --- 38 | cost [1910.0]
23 --- 61 | cost [3400.0]
26 --- 39 | cost [8505.0]
26 --- 56 | cost [2840.0]
39 --- 77 | cost [1680.0]
40 --- 96 | cost [3560.0]
49 --- 94 | cost [2470.0]
58 --- 72 | cost [7335.0]
58 --- 75 | cost [3350.0]
61 --- 72 | cost [3155.0]
67 --- 68 | cost [8120.0]
67 --- 75 | cost [240.0]
68 --- 96 | cost [2530.0]
73 --- 77 | cost [2390.0]
73 --- 79 | cost [3375.0]
79 --- 101 | cost [2190.0]

STAR
3  --> 77 | cost [3195.0]
4  -->  1 | cost [8275.0]
5  -->  1 | cost [11255.0]
6  --> 77 | cost [3320.0]
7  -->  1 | cost [7575.0]
9  --> 73 | cost [7930.0]
11 -->  1 | cost [2950.0]
12 -->  1 | cost [14855.0]
13 -->  1 | cost [1825.0]
14 --> 77 | cost [5085.0]
15 -->  1 | cost [5115.0]
16 -->  1 | cost [7165.0]
17 --> 49 | cost [1725.0]
18 --> 73 | cost [5870.0]
19 --> 77 | cost [6455.0]
20 -->  8 | cost [11145.0]
21 --> 77 | cost [7600.0]
22 --> 49 | cost [3385.0]
24 -->  1 | cost [2035.0]
25 -->  1 | cost [12075.0]
27 -->  1 | cost [1750.0]
28 -->  1 | cost [15480.0]
29 --> 49 | cost [6650.0]
30 --> 77 | cost [7490.0]
31 -->  1 | cost [9160.0]
32 -->  1 | cost [2805.0]
33 --> 77 | cost [5560.0]
34 -->  1 | cost [1800.0]
35 --> 79 | cost [10180.0]
36 --> 49 | cost [7365.0]
37 --> 79 | cost [10630.0]
41 -->  1 | cost [3300.0]
42 -->  8 | cost [2885.0]
43 --> 73 | cost [2370.0]
44 -->  1 | cost [8980.0]
45 -->  8 | cost [7640.0]
46 -->  8 | cost [1430.0]
47 -->  1 | cost [14290.0]
48 --> 77 | cost [7970.0]
50 -->  1 | cost [465.0]
51 --> 77 | cost [6590.0]
52 -->  1 | cost [3315.0]
53 -->  1 | cost [10395.0]
54 --> 73 | cost [1805.0]
55 --> 77 | cost [6170.0]
57 -->  8 | cost [6415.0]
59 --> 77 | cost [2500.0]
60 -->  1 | cost [9895.0]
62 -->  1 | cost [11805.0]
63 --> 73 | cost [2240.0]
64 -->  1 | cost [8545.0]
65 --> 73 | cost [6025.0]
66 -->  8 | cost [440.0]
69 -->  1 | cost [5300.0]
70 --> 49 | cost [855.0]
71 -->  1 | cost [7285.0]
74 -->  1 | cost [6300.0]
76 -->  8 | cost [4400.0]
78 -->  1 | cost [8805.0]
80 -->  1 | cost [7625.0]
81 -->  1 | cost [1860.0]
82 -->  1 | cost [11555.0]
83 --> 77 | cost [3255.0]
84 -->  1 | cost [3550.0]
85 -->  1 | cost [9590.0]
86 --> 96 | cost [300.0]
87 --> 26 | cost [60.0]
88 -->  1 | cost [2015.0]
89 -->  1 | cost [3900.0]
90 -->  1 | cost [3270.0]
91 --> 73 | cost [1745.0]
92 -->  1 | cost [13890.0]
93 -->  1 | cost [8615.0]
95 --> 77 | cost [8670.0]
97 -->  1 | cost [3895.0]
98 --> 49 | cost [410.0]
99 -->  1 | cost [9385.0]
100 --> 77 | cost [7160.0]

BACKUP RING
1  --- 94 | cost [25.45]
2  --- 56 | cost [69.85000000000001]
2  --- 96 | cost [89.25]
8  --- 23 | cost [18.2]
8  --- 49 | cost [51.85]
10 --- 26 | cost [16.15]
10 --- 40 | cost [32.65]
23 --- 72 | cost [65.55]
26 --- 77 | cost [70.55]
38 --- 61 | cost [38.25]
38 --- 94 | cost [32.65]
39 --- 56 | cost [102.4]
39 --- 73 | cost [7.5]
40 --- 68 | cost [49.550000000000004]
58 --- 61 | cost [48.85]
58 --- 67 | cost [31.35]
67 --- 96 | cost [85.35000000000001]
68 --- 75 | cost [80.05]
72 --- 75 | cost [42.300000000000004]
73 --- 101 | cost [52.050000000000004]
77 --- 79 | cost [56.95]

BACKUP STAR
3  --> 40 | cost [6.05]
6  --> 40 | cost [2.05]
9  --> 10 | cost [10.15]
14 --> 68 | cost [1.05]
17 --> 94 | cost [9.25]
18 --> 40 | cost [12.5]
19 -->  2 | cost [9.75]
20 --> 10 | cost [15.75]
21 --> 56 | cost [11.85]
22 --> 58 | cost [20.900000000000002]
29 --> 58 | cost [12.200000000000001]
30 -->  2 | cost [10.35]
33 --> 68 | cost [3.8000000000000003]
35 -->  2 | cost [20.150000000000002]
36 --> 67 | cost [6.25]
37 -->  2 | cost [13.0]
42 --> 23 | cost [10.65]
43 --> 77 | cost [7.3]
45 --> 68 | cost [11.15]
46 --> 61 | cost [21.1]
48 -->  2 | cost [10.1]
51 -->  2 | cost [9.4]
54 --> 77 | cost [8.15]
55 --> 26 | cost [9.15]
57 --> 72 | cost [8.15]
59 --> 40 | cost [7.9]
63 --> 77 | cost [12.05]
65 --> 68 | cost [10.65]
66 --> 38 | cost [4.8500000000000005]
70 --> 94 | cost [26.95]
76 --> 72 | cost [18.8]
83 --> 40 | cost [1.55]
86 --> 68 | cost [22.650000000000002]
87 --> 10 | cost [16.7]
91 --> 77 | cost [8.2]
95 --> 56 | cost [5.9]
98 --> 94 | cost [23.5]
100 -->  2 | cost [5.1000000000000005]

B = 125.95000000000002
i★ = 77
j★ = 73
k★ = 79

       
——————— Mon, 22 Jan 2024 02:17:54 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 85 hubs —— 1-98-49-70-90-94-97-32-11-23-42-22-58-36-67-75-7-61-80-76-57-31-99-78-33-68-14-86-65-96-64-59-40-83-6-85-18-25-20-28-12-47-21-56-95-10-55-26-87-92-48-2-19-100-30-51-37-62-53-60-44-4-71-39-73-63-16-77-54-91-15-84-41-79-88-24-27-81-52-8-66-38-34-50-101-1
total time           3609.88 (TL 3600)    gap                  0.206                
blossom time         0                    nb blossom           0.0                  
LB <= UB             96005<=120859.5      Master/SP costs      118860/1999.5        
Master time          3605.72              SP time              4.16                 
subtour              40653.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            15.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       21434                
F                    31.0                 
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—98—49—70—90—94—97—32—11—23—42—22—58—36—67—75—7—61—80—76—57—31—99—78—33—68—14—86—65—96—64—59—40—83—6—85—18—25—20—28—12—47—21—56—95—10—55—26—87—92—48—2—19—100—30—51—37—62—53—60—44—4—71—39—73—63—16—77—54—91—15—84—41—79—88—24—27—81—52—8—66—38—34—50—101

RING
1  --- 98 | cost [4855.0]
2  --- 19 | cost [975.0]
2  --- 48 | cost [1010.0]
4  --- 44 | cost [725.0]
4  --- 71 | cost [1010.0]
6  --- 83 | cost [300.0]
6  --- 85 | cost [1350.0]
7  --- 61 | cost [1405.0]
7  --- 75 | cost [1690.0]
8  --- 52 | cost [430.0]
8  --- 66 | cost [440.0]
10 --- 55 | cost [1640.0]
10 --- 95 | cost [2240.0]
11 --- 23 | cost [2145.0]
11 --- 32 | cost [2595.0]
12 --- 28 | cost [905.0]
12 --- 47 | cost [1150.0]
14 --- 68 | cost [105.0]
14 --- 86 | cost [2180.0]
15 --- 84 | cost [1585.0]
15 --- 91 | cost [1505.0]
16 --- 63 | cost [735.0]
16 --- 77 | cost [1260.0]
18 --- 25 | cost [1570.0]
18 --- 85 | cost [940.0]
19 --- 100 | cost [975.0]
20 --- 25 | cost [175.0]
20 --- 28 | cost [3825.0]
21 --- 47 | cost [1090.0]
21 --- 56 | cost [1185.0]
22 --- 42 | cost [1985.0]
22 --- 58 | cost [2090.0]
23 --- 42 | cost [1065.0]
24 --- 27 | cost [310.0]
24 --- 88 | cost [505.0]
26 --- 55 | cost [915.0]
26 --- 87 | cost [60.0]
27 --- 81 | cost [1975.0]
30 --- 51 | cost [1020.0]
30 --- 100 | cost [650.0]
31 --- 57 | cost [1090.0]
31 --- 99 | cost [295.0]
32 --- 97 | cost [1150.0]
33 --- 68 | cost [380.0]
33 --- 78 | cost [1950.0]
34 --- 38 | cost [855.0]
34 --- 50 | cost [1515.0]
36 --- 58 | cost [2580.0]
36 --- 67 | cost [625.0]
37 --- 51 | cost [500.0]
37 --- 62 | cost [880.0]
38 --- 66 | cost [485.0]
39 --- 71 | cost [1525.0]
39 --- 73 | cost [750.0]
40 --- 59 | cost [790.0]
40 --- 83 | cost [155.0]
41 --- 79 | cost [1775.0]
41 --- 84 | cost [680.0]
44 --- 60 | cost [965.0]
48 --- 92 | cost [1605.0]
49 --- 70 | cost [855.0]
49 --- 98 | cost [410.0]
50 --- 101 | cost [465.0]
52 --- 81 | cost [1455.0]
53 --- 60 | cost [995.0]
53 --- 62 | cost [1840.0]
54 --- 77 | cost [815.0]
54 --- 91 | cost [70.0]
56 --- 95 | cost [590.0]
57 --- 76 | cost [2165.0]
59 --- 64 | cost [1205.0]
61 --- 80 | cost [3085.0]
63 --- 73 | cost [2240.0]
64 --- 96 | cost [2370.0]
65 --- 86 | cost [1460.0]
65 --- 96 | cost [1760.0]
67 --- 75 | cost [240.0]
70 --- 90 | cost [1625.0]
76 --- 80 | cost [675.0]
78 --- 99 | cost [605.0]
79 --- 88 | cost [635.0]
87 --- 92 | cost [2200.0]
90 --- 94 | cost [1170.0]
94 --- 97 | cost [1505.0]

STAR
3  --> 83 | cost [475.0]
5  --> 53 | cost [1090.0]
9  --> 10 | cost [1015.0]
13 --> 79 | cost [375.0]
17 --> 90 | cost [275.0]
29 --> 58 | cost [1220.0]
35 --> 51 | cost [1180.0]
43 --> 77 | cost [730.0]
45 --> 33 | cost [825.0]
46 --> 52 | cost [1210.0]
69 --> 15 | cost [1675.0]
72 --> 57 | cost [815.0]
74 --> 61 | cost [865.0]
82 --> 18 | cost [1830.0]
89 --> 90 | cost [950.0]
93 --> 44 | cost [775.0]

BACKUP RING
1  --- 49 | cost [49.0]
2  --- 92 | cost [19.400000000000002]
2  --- 100 | cost [5.1000000000000005]
4  --- 39 | cost [24.2]
4  --- 60 | cost [16.85]
6  --- 18 | cost [10.950000000000001]
6  --- 40 | cost [2.05]
7  --- 67 | cost [17.3]
7  --- 80 | cost [36.7]
8  --- 38 | cost [9.25]
8  --- 81 | cost [15.950000000000001]
10 --- 26 | cost [16.15]
10 --- 56 | cost [22.7]
11 --- 42 | cost [24.1]
11 --- 97 | cost [28.8]
12 --- 20 | cost [36.5]
12 --- 21 | cost [20.5]
14 --- 33 | cost [4.8500000000000005]
14 --- 65 | cost [10.25]
15 --- 41 | cost [20.75]
15 --- 54 | cost [15.05]
16 --- 54 | cost [11.950000000000001]
16 --- 73 | cost [29.400000000000002]
18 --- 20 | cost [17.1]
19 --- 30 | cost [16.0]
19 --- 48 | cost [16.0]
21 --- 95 | cost [15.85]
22 --- 23 | cost [30.5]
22 --- 36 | cost [43.75]
23 --- 32 | cost [47.35]
24 --- 79 | cost [11.450000000000001]
24 --- 81 | cost [22.400000000000002]
25 --- 28 | cost [38.550000000000004]
25 --- 85 | cost [24.85]
26 --- 92 | cost [22.5]
27 --- 52 | cost [30.5]
27 --- 88 | cost [6.5]
28 --- 47 | cost [12.5]
30 --- 37 | cost [15.15]
31 --- 76 | cost [20.25]
31 --- 78 | cost [4.95]
32 --- 94 | cost [8.950000000000001]
33 --- 99 | cost [17.5]
34 --- 66 | cost [12.450000000000001]
34 --- 101 | cost [18.0]
36 --- 75 | cost [7.95]
37 --- 53 | cost [26.55]
38 --- 50 | cost [22.6]
39 --- 63 | cost [17.900000000000002]
40 --- 64 | cost [19.3]
41 --- 88 | cost [14.1]
42 --- 58 | cost [28.7]
44 --- 53 | cost [15.0]
44 --- 71 | cost [16.95]
47 --- 56 | cost [21.25]
48 --- 87 | cost [36.050000000000004]
49 --- 90 | cost [16.85]
51 --- 62 | cost [13.25]
51 --- 100 | cost [5.7]
52 --- 66 | cost [6.55]
55 --- 87 | cost [9.200000000000001]
55 --- 95 | cost [31.95]
57 --- 80 | cost [19.95]
57 --- 99 | cost [12.65]
58 --- 67 | cost [31.35]
59 --- 83 | cost [9.200000000000001]
59 --- 96 | cost [28.3]
60 --- 62 | cost [19.25]
61 --- 75 | cost [29.0]
61 --- 76 | cost [24.05]
63 --- 77 | cost [12.05]
64 --- 65 | cost [40.550000000000004]
68 --- 78 | cost [19.8]
68 --- 86 | cost [22.650000000000002]
70 --- 94 | cost [26.95]
70 --- 98 | cost [12.5]
71 --- 73 | cost [21.1]
77 --- 91 | cost [8.2]
79 --- 84 | cost [23.6]
83 --- 85 | cost [15.25]
84 --- 91 | cost [29.45]
86 --- 96 | cost [3.0]
90 --- 97 | cost [19.85]

BACKUP STAR
3  --> 40 | cost [6.05]
5  --> 83 | cost [17.35]
9  --> 55 | cost [10.450000000000001]
13 --> 88 | cost [6.8]
17 --> 94 | cost [9.25]
29 --> 36 | cost [20.75]
35 --> 37 | cost [12.85]
43 --> 71 | cost [11.35]
45 --> 99 | cost [10.65]
46 -->  8 | cost [14.3]
69 --> 63 | cost [22.05]
72 --> 31 | cost [17.1]
74 -->  7 | cost [13.25]
82 --> 25 | cost [19.0]
89 --> 11 | cost [10.0]
93 -->  4 | cost [8.9]

B = 64.5
i★ = 22
j★ = 58
k★ = 36