------------------------------------------------------------
                        α=5.0 —— kroC100 —— 100 nodes       
------------------------------------------------------------

——————— Thu, 18 Jan 2024 20:43:08 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
ILP ——— 39 hubs —— 1—40—4—18—49—78—61—51—11—96—81—14—73—77—30—68—23—70—76—2—38—39—28—88—98—58—34—90—25—17—8—42—20—64—6—67—65—79—101
total time           3640.2 (TL 3600)     gap                  0.539                
blossom time         0                    nb blossom           0.0                  
LB <= UB             96029.24<=208181.95  subtour              2719.0               
connectivity cuts    0.0                  uc strategy          0                    
uc tolerance         0.01                 tildeV               2:100                
2-opt strategy       0                                                              
explored_nodes       853                  n lazycuts edges     0.0                  
F                    7.0                  post procedure       true                 
o_i                  0                                                                                                                                                  
Found solution
RING NODES
1—40—4—18—49—78—61—51—11—96—81—14—73—77—30—68—23—70—76—2—38—39—28—88—98—58—34—90—25—17—8—42—20—64—6—67—65—79—101

RING
1  --- 40 | cost [1895.0]
2  --- 38 | cost [5455.0]
2  --- 76 | cost [3865.0]
4  --- 18 | cost [3270.0]
4  --- 40 | cost [2825.0]
6  --- 64 | cost [3405.0]
6  --- 67 | cost [2185.0]
8  --- 17 | cost [1540.0]
8  --- 42 | cost [2955.0]
11 --- 51 | cost [3025.0]
11 --- 96 | cost [1485.0]
14 --- 73 | cost [4390.0]
14 --- 81 | cost [2360.0]
17 --- 25 | cost [510.0]
18 --- 49 | cost [535.0]
20 --- 42 | cost [1215.0]
20 --- 64 | cost [125.0]
23 --- 68 | cost [1675.0]
23 --- 70 | cost [1685.0]
25 --- 90 | cost [480.0]
28 --- 39 | cost [475.0]
28 --- 88 | cost [1015.0]
30 --- 68 | cost [695.0]
30 --- 77 | cost [1920.0]
34 --- 58 | cost [1660.0]
34 --- 90 | cost [450.0]
38 --- 39 | cost [575.0]
49 --- 78 | cost [3940.0]
51 --- 61 | cost [3285.0]
58 --- 98 | cost [1030.0]
61 --- 78 | cost [1595.0]
65 --- 67 | cost [1525.0]
65 --- 79 | cost [2040.0]
70 --- 76 | cost [580.0]
73 --- 77 | cost [4870.0]
79 --- 101 | cost [3705.0]
81 --- 96 | cost [2970.0]
88 --- 98 | cost [910.0]

STAR
3  --> 30 | cost [3965.0]
5  --> 39 | cost [2305.0]
7  --> 78 | cost [1800.0]
9  --> 78 | cost [415.0]
10 --> 49 | cost [2985.0]
12 --> 40 | cost [1120.0]
13 --> 79 | cost [650.0]
15 --> 79 | cost [1225.0]
16 --> 78 | cost [2505.0]
19 --> 49 | cost [2255.0]
21 --> 23 | cost [1770.0]
22 -->  6 | cost [2170.0]
24 --> 78 | cost [3010.0]
26 --> 61 | cost [855.0]
27 -->  1 | cost [2310.0]
29 --> 49 | cost [1030.0]
31 --> 67 | cost [650.0]
32 --> 61 | cost [1195.0]
33 --> 14 | cost [1870.0]
35 -->  2 | cost [380.0]
36 --> 81 | cost [1345.0]
37 --> 61 | cost [1355.0]
41 -->  2 | cost [3570.0]
43 --> 76 | cost [4805.0]
44 --> 11 | cost [2355.0]
45 --> 81 | cost [395.0]
46 -->  1 | cost [2885.0]
47 --> 67 | cost [835.0]
48 --> 49 | cost [4340.0]
50 -->  2 | cost [3140.0]
52 --> 96 | cost [1535.0]
53 -->  1 | cost [160.0]
54 -->  6 | cost [545.0]
55 --> 42 | cost [545.0]
56 --> 38 | cost [885.0]
57 --> 73 | cost [4105.0]
59 --> 23 | cost [4775.0]
60 -->  4 | cost [1290.0]
62 --> 38 | cost [2650.0]
63 --> 11 | cost [2815.0]
66 --> 61 | cost [3905.0]
69 --> 73 | cost [2140.0]
71 --> 38 | cost [430.0]
72 --> 38 | cost [1575.0]
74 --> 73 | cost [3870.0]
75 --> 67 | cost [2995.0]
80 --> 65 | cost [1285.0]
82 --> 78 | cost [580.0]
83 -->  6 | cost [2950.0]
84 --> 78 | cost [5375.0]
85 -->  1 | cost [1080.0]
86 --> 23 | cost [4040.0]
87 --> 96 | cost [1410.0]
89 --> 73 | cost [2430.0]
91 --> 76 | cost [1180.0]
92 --> 49 | cost [2785.0]
93 --> 49 | cost [1365.0]
94 --> 76 | cost [1270.0]
95 --> 76 | cost [1875.0]
97 --> 81 | cost [600.0]
99 --> 49 | cost [2485.0]
100 --> 11 | cost [4670.0]

BACKUP RING
1  ---  4 | cost [47.1]
2  --- 39 | cost [52.65]
2  --- 70 | cost [33.95]
4  --- 49 | cost [27.400000000000002]
6  --- 20 | cost [35.2]
6  --- 65 | cost [22.75]
8  --- 20 | cost [41.45]
8  --- 25 | cost [20.150000000000002]
11 --- 61 | cost [60.95]
11 --- 81 | cost [39.4]
14 --- 77 | cost [56.6]
14 --- 96 | cost [49.0]
17 --- 42 | cost [38.15]
17 --- 90 | cost [9.25]
18 --- 40 | cost [33.5]
18 --- 78 | cost [34.05]
23 --- 30 | cost [22.5]
23 --- 76 | cost [22.05]
25 --- 34 | cost [8.85]
28 --- 38 | cost [5.45]
28 --- 98 | cost [17.7]
30 --- 73 | cost [40.050000000000004]
34 --- 98 | cost [19.8]
38 --- 76 | cost [54.6]
39 --- 88 | cost [13.25]
42 --- 64 | cost [11.75]
49 --- 61 | cost [26.5]
51 --- 78 | cost [27.35]
51 --- 96 | cost [42.7]
58 --- 88 | cost [17.0]
58 --- 90 | cost [19.7]
64 --- 67 | cost [14.0]
65 --- 101 | cost [51.2]
67 --- 79 | cost [15.1]
68 --- 70 | cost [33.1]
68 --- 77 | cost [22.650000000000002]
73 --- 81 | cost [49.550000000000004]

BACKUP STAR
3  --> 73 | cost [0.9]
5  --> 38 | cost [17.55]
7  --> 61 | cost [27.1]
9  --> 61 | cost [14.0]
10 --> 14 | cost [13.15]
12 --> 49 | cost [19.650000000000002]
13 --> 65 | cost [15.700000000000001]
15 -->  1 | cost [25.55]
16 --> 51 | cost [7.8500000000000005]
19 --> 14 | cost [17.25]
21 --> 70 | cost [20.75]
22 -->  8 | cost [6.4]
24 --> 61 | cost [16.1]
26 --> 78 | cost [10.6]
29 --> 18 | cost [5.3500000000000005]
31 --> 65 | cost [12.950000000000001]
32 --> 78 | cost [23.400000000000002]
33 --> 81 | cost [5.8500000000000005]
35 --> 68 | cost [7.65]
36 --> 14 | cost [10.5]
37 --> 18 | cost [13.0]
41 --> 30 | cost [19.2]
43 --> 38 | cost [25.05]
44 --> 51 | cost [10.65]
45 --> 14 | cost [20.400000000000002]
47 -->  6 | cost [14.0]
48 --> 11 | cost [11.8]
50 --> 38 | cost [25.55]
52 --> 11 | cost [1.35]
54 -->  8 | cost [24.900000000000002]
55 --> 64 | cost [8.700000000000001]
56 --> 28 | cost [12.450000000000001]
57 --> 14 | cost [11.25]
59 --> 73 | cost [6.95]
60 --> 14 | cost [24.900000000000002]
62 --> 39 | cost [23.7]
63 --> 51 | cost [6.1000000000000005]
66 --> 51 | cost [19.5]
69 --> 14 | cost [22.95]
71 --> 39 | cost [7.8]
72 --> 39 | cost [14.1]
74 --> 81 | cost [13.6]
75 -->  8 | cost [13.15]
80 --> 77 | cost [9.700000000000001]
82 --> 61 | cost [21.75]
83 --> 39 | cost [21.55]
84 --> 11 | cost [4.75]
86 --> 38 | cost [21.45]
87 --> 11 | cost [22.8]
89 --> 30 | cost [18.8]
91 --> 70 | cost [11.8]
92 --> 14 | cost [15.85]
93 -->  4 | cost [14.5]
94 --> 70 | cost [15.35]
95 --> 70 | cost [20.650000000000002]
97 --> 96 | cost [25.45]
99 --> 14 | cost [12.25]
100 --> 81 | cost [7.9]

B = 124.19999999999997
i★ = 18
j★ = 49
k★ = 78

       
——————— Thu, 18 Jan 2024 21:44:32 ————————— seperate y_ij <= y_jj - x_ij on lazy constraints ————————— use blossom = false
BD  —— 77 hubs —— 1-15-65-13-67-42-20-64-55-6-22-75-8-17-25-90-58-98-88-28-39-38-56-5-86-95-94-91-76-70-23-83-72-62-2-30-68-80-41-3-69-49-18-46-32-24-4-19-36-33-57-99-10-16-63-48-37-61-26-9-78-82-51-44-45-81-97-84-52-11-66-92-93-40-27-85-101-1
total time           3609.12 (TL 3600)    gap                  0.371                
blossom time         0                    nb blossom           0.0                  
LB <= UB             91876.25<=146124.75  Master/SP costs      145570/554.75        
Master time          3602.33              SP time              6.79                 
subtour              42428.0              connectivity cuts    0.0                  
uc strategy          0                    uc tolerance         0.01                 
opt. cuts            20.0                 SP method            poly                 
tildeV               2:100                inst transformation  2                    
2-opt strategy       0                                                              
explored nodes       23761                
F                    7.0                  
                                          o_i                  0                                                              
                                          
Found solution
RING NODES
1—15—65—13—67—42—20—64—55—6—22—75—8—17—25—90—58—98—88—28—39—38—56—5—86—95—94—91—76—70—23—83—72—62—2—30—68—80—41—3—69—49—18—46—32—24—4—19—36—33—57—99—10—16—63—48—37—61—26—9—78—82—51—44—45—81—97—84—52—11—66—92—93—40—27—85—101

RING
1  --- 15 | cost [2555.0]
2  --- 30 | cost [1655.0]
2  --- 62 | cost [2930.0]
3  --- 41 | cost [2070.0]
3  --- 69 | cost [2075.0]
4  --- 19 | cost [2800.0]
4  --- 24 | cost [5200.0]
5  --- 56 | cost [1095.0]
5  --- 86 | cost [1260.0]
6  --- 22 | cost [2170.0]
6  --- 55 | cost [2660.0]
8  --- 17 | cost [1540.0]
8  --- 75 | cost [1315.0]
9  --- 26 | cost [1105.0]
9  --- 78 | cost [415.0]
10 --- 16 | cost [3870.0]
10 --- 99 | cost [540.0]
11 --- 52 | cost [135.0]
11 --- 66 | cost [2555.0]
13 --- 65 | cost [1570.0]
13 --- 67 | cost [1590.0]
15 --- 65 | cost [2660.0]
16 --- 63 | cost [605.0]
17 --- 25 | cost [510.0]
18 --- 46 | cost [1565.0]
18 --- 49 | cost [535.0]
19 --- 36 | cost [1945.0]
20 --- 42 | cost [1215.0]
20 --- 64 | cost [125.0]
22 --- 75 | cost [835.0]
23 --- 70 | cost [1685.0]
23 --- 83 | cost [3725.0]
24 --- 32 | cost [760.0]
25 --- 90 | cost [480.0]
26 --- 61 | cost [855.0]
27 --- 40 | cost [1500.0]
27 --- 85 | cost [1285.0]
28 --- 39 | cost [475.0]
28 --- 88 | cost [1015.0]
30 --- 68 | cost [695.0]
32 --- 46 | cost [2210.0]
33 --- 36 | cost [825.0]
33 --- 57 | cost [810.0]
37 --- 48 | cost [3950.0]
37 --- 61 | cost [1355.0]
38 --- 39 | cost [575.0]
38 --- 56 | cost [885.0]
40 --- 93 | cost [2945.0]
41 --- 80 | cost [3770.0]
42 --- 67 | cost [1600.0]
44 --- 45 | cost [4035.0]
44 --- 51 | cost [1065.0]
45 --- 81 | cost [395.0]
48 --- 63 | cost [2115.0]
49 --- 69 | cost [5445.0]
51 --- 82 | cost [2780.0]
52 --- 84 | cost [590.0]
55 --- 64 | cost [870.0]
57 --- 99 | cost [1720.0]
58 --- 90 | cost [1970.0]
58 --- 98 | cost [1030.0]
62 --- 72 | cost [1115.0]
66 --- 92 | cost [2080.0]
68 --- 80 | cost [2545.0]
70 --- 76 | cost [580.0]
72 --- 83 | cost [950.0]
76 --- 91 | cost [1180.0]
78 --- 82 | cost [580.0]
81 --- 97 | cost [600.0]
84 --- 97 | cost [3570.0]
85 --- 101 | cost [1080.0]
86 --- 95 | cost [1625.0]
88 --- 98 | cost [910.0]
91 --- 94 | cost [645.0]
92 --- 93 | cost [2220.0]
94 --- 95 | cost [615.0]

STAR
7  --> 82 | cost [1705.0]
12 --> 40 | cost [1120.0]
14 --> 36 | cost [1050.0]
21 --> 23 | cost [1770.0]
29 --> 18 | cost [535.0]
31 --> 67 | cost [650.0]
34 --> 90 | cost [450.0]
35 -->  2 | cost [380.0]
43 -->  5 | cost [850.0]
47 --> 67 | cost [835.0]
50 --> 72 | cost [1285.0]
53 -->  1 | cost [160.0]
54 -->  6 | cost [545.0]
59 -->  3 | cost [650.0]
60 -->  4 | cost [1290.0]
71 --> 38 | cost [430.0]
73 -->  3 | cost [90.0]
74 --> 57 | cost [310.0]
77 --> 80 | cost [970.0]
79 --> 13 | cost [650.0]
87 --> 52 | cost [2240.0]
89 --> 41 | cost [1065.0]
96 --> 11 | cost [1485.0]
100 --> 33 | cost [245.0]

BACKUP RING
1  --- 65 | cost [51.2]
2  --- 68 | cost [10.450000000000001]
2  --- 72 | cost [38.9]
3  --- 49 | cost [73.35000000000001]
3  --- 80 | cost [57.45]
4  --- 32 | cost [57.2]
4  --- 36 | cost [29.650000000000002]
5  --- 38 | cost [17.55]
5  --- 95 | cost [28.45]
6  --- 64 | cost [34.05]
6  --- 75 | cost [13.4]
8  --- 22 | cost [6.4]
8  --- 25 | cost [20.150000000000002]
9  --- 61 | cost [14.0]
9  --- 82 | cost [8.950000000000001]
10 --- 57 | cost [14.05]
10 --- 63 | cost [37.15]
11 --- 84 | cost [4.75]
11 --- 92 | cost [38.5]
13 --- 15 | cost [11.700000000000001]
13 --- 42 | cost [28.85]
16 --- 48 | cost [26.7]
16 --- 99 | cost [37.15]
17 --- 75 | cost [28.45]
17 --- 90 | cost [9.25]
18 --- 32 | cost [28.5]
18 --- 69 | cost [59.35]
19 --- 24 | cost [51.9]
19 --- 33 | cost [23.95]
20 --- 55 | cost [9.6]
20 --- 67 | cost [15.25]
22 --- 55 | cost [33.9]
23 --- 72 | cost [41.2]
23 --- 76 | cost [22.05]
24 --- 46 | cost [16.3]
25 --- 58 | cost [24.45]
26 --- 37 | cost [20.45]
26 --- 78 | cost [10.6]
27 --- 93 | cost [40.800000000000004]
27 --- 101 | cost [23.1]
28 --- 38 | cost [5.45]
28 --- 98 | cost [17.7]
30 --- 62 | cost [45.85]
30 --- 80 | cost [24.55]
33 --- 99 | cost [20.8]
36 --- 57 | cost [2.1]
37 --- 63 | cost [22.1]
39 --- 56 | cost [14.55]
39 --- 88 | cost [13.25]
40 --- 85 | cost [15.3]
40 --- 92 | cost [51.7]
41 --- 68 | cost [25.5]
41 --- 69 | cost [32.4]
42 --- 64 | cost [11.75]
44 --- 81 | cost [42.85]
44 --- 82 | cost [37.25]
45 --- 51 | cost [50.9]
45 --- 97 | cost [9.4]
46 --- 49 | cost [16.75]
48 --- 61 | cost [52.25]
51 --- 78 | cost [27.35]
52 --- 66 | cost [26.75]
52 --- 97 | cost [37.800000000000004]
56 --- 86 | cost [19.75]
58 --- 88 | cost [17.0]
62 --- 83 | cost [2.2]
65 --- 67 | cost [15.25]
66 --- 93 | cost [33.3]
70 --- 83 | cost [44.95]
70 --- 91 | cost [11.8]
76 --- 94 | cost [12.700000000000001]
81 --- 84 | cost [37.7]
86 --- 94 | cost [21.7]
90 --- 98 | cost [20.85]
91 --- 95 | cost [9.6]

BACKUP STAR
7  --> 78 | cost [18.0]
12 --> 46 | cost [16.25]
14 --> 57 | cost [11.25]
21 --> 70 | cost [20.75]
29 --> 49 | cost [10.3]
31 --> 65 | cost [12.950000000000001]
34 --> 25 | cost [8.85]
35 --> 68 | cost [7.65]
43 --> 56 | cost [16.95]
47 --> 55 | cost [13.5]
50 --> 62 | cost [14.25]
54 --> 75 | cost [11.8]
59 --> 41 | cost [14.25]
60 --> 93 | cost [27.35]
71 --> 39 | cost [7.8]
73 --> 41 | cost [21.2]
74 --> 36 | cost [5.15]
77 --> 30 | cost [19.2]
79 --> 15 | cost [12.25]
87 --> 11 | cost [22.8]
89 --> 30 | cost [18.8]
96 --> 52 | cost [15.35]
100 --> 57 | cost [7.2]

B = 79.25
i★ = 19
j★ = 4
k★ = 24