An experimental data set for the papers
The following data are used for experiments in the following papers.The data are presented for benchmarking purpose.
(1) Balancing and sequencing mixed-model U-lines with a co-evolutionary algorithm, Production Planning & Control, 2000, 11(8), 754-764.
(2) A coevolutionary algorithm for balancing and sequencing in mixed model assembly lines,Applied Intelligence 13, 247-258, 2000.
(3)An endosymbiotic evolutionary algorithm for the integration of balancing and sequencing in mixed-model U-lines, to appear in EJOR
Yeo Keun Kim
Department of Industrial Engineering
Chonnam National University
300 Yongbongdong, Pukku
Gwangju, 500-757
Republic of Korea
Tel: (82) (62) 530-1783, Fax: (82) (62) 530-1789
E-mail:
Thomopoulos 19 tasks Problem
Number of tasks = 19
Number of models = 3
0 1 /* MPS start */
1 1
2 1 /* MPS end */
/* Task Time of Thomopoulos 19*/
( task #) (task times of 3 models)
1, 0.5, 0.0, 1.0,
2, 0.4, 0.8, 1.2,
3, 0.0, 0.2, 0.4,
4, 0.4, 0.0, 0.0,
5, 0.2, 0.2, 0.2,
6, 0.2, 0.0, 0.0,
7, 0.4, 0.5, 0.6,
8, 0.0, 0.5, 0.5,
9, 0.4, 0.3, 0.2,
10, 0.0, 0.0, 0.2,
11, 0.3, 0.3, 0.3,
12, 0.1, 0.3, 0.5,
13, 0.1, 0.0, 0.1,
14, 0.2, 0.2, 0.2,
15, 0.7, 1.0, 1.5,
16, 0.0, 0.1, 0.0,
17, 0.5, 0.5, 0.0,
18, 0.3, 0.5, 0.3,
19, 0.4, 0.3, 0.0,
/* Precedence Relationof Thomopoulos 19*/
task # (no. of successors) immediate successors
0 (5) 1, 2, 3, 4, 5
1 (2) 6, 7
2 (3) 7, 8, 9
3 (3) 9, 10, 16
4 (1) 11
5 (1) 11
6 (1) 20
7 (1) 12
8 (1) 12
9 (1) 15
10 (1) 20
11 (3) 13, 14, 16
12 (1) 15
13 (1) 17
14 (2) 18, 19
15 (1) 20
16 (1) 20
17 (1) 19
18 (1) 20
19 (1) 20
20 (0)
Kim 61 tasks Problem
Number of tasks = 61
Number of models = 4
0 1 /* MPS start */
1 1
2 1
3 1 /* MPS end */
/* Task Time of Kim 61*/
task # (task times of 4 models)
1, 1.2, 0.5, 1.6, 1.6,
2, 2.5, 0.0, 3.0, 0.0,
3, 0.0, 2.6, 1.6, 1.6,
4, 0.7, 0.0, 0.0, 2.0,
5, 1.4, 1.9, 3.4, 2.4,
6, 1.8, 0.9, 0.0, 0.0,
7, 0.0, 0.7, 2.7, 1.7,
8, 0.0, 1.5, 0.5, 2.5,
9, 1.5, 0.0, 0.6, 0.6,
10, 1.5, 0.9, 0.0, 1.8,
11, 0.0, 1.1, 2.9, 2.9,
12, 1.1, 0.0, 3.0, 3.0,
13, 2.5, 1.7, 0.6, 1.7,
14, 0.9, 0.0, 1.5, 1.5,
15, 1.0, 2.5, 0.7, 2.5,
16, 2.6, 1.5, 1.3, 2.6,
17, 1.8, 0.5, 0.0, 0.5,
18, 1.8, 0.5, 0.0, 0.5,
19, 1.1, 1.2, 1.2, 1.2,
20, 1.4, 2.4, 3.3, 2.3,
21, 0.0, 0.4, 0.6, 1.6,
22, 2.2, 3.1, 0.9, 2.9,
23, 3.3, 2.3, 3.0, 2.0,
24, 2.3, 3.2, 3.0, 2.0,
25, 2.5, 0.0, 2.7, 2.7,
26, 3.2, 0.8, 0.8, 0.0,
27, 1.4, 1.0, 2.0, 2.0,
28, 0.0, 1.3, 2.3, 2.3,
29, 1.8, 0.0, 1.9, 0.0,
30, 3.0, 1.2, 1.4, 1.4,
31, 1.2, 2.3, 2.8, 2.8,
32, 2.1, 1.3, 1.1, 2.1,
33, 0.0, 2.0, 0.8, 2.8,
34, 1.2, 0.0, 2.2, 1.2,
35, 0.8, 0.0, 2.5, 0.8,
36, 1.2, 0.0, 2.0, 0.0,
37, 0.0, 1.8, 1.6, 1.6,
38, 1.3, 3.1, 1.4, 1.3,
39, 2.5, 1.6, 3.3, 3.3,
40, 2.5, 1.8, 1.2, 1.2,
41, 0.8, 0.6, 1.8, 0.0,
42, 0.4, 1.6, 1.2, 1.2,
43, 1.4, 0.8, 3.2, 3.2,
44, 0.4, 2.0, 0.0, 0.0,
45, 0.0, 2.6, 0.7, 2.7,
46, 2.6, 0.0, 1.8, 2.6,
47, 0.7, 2.1, 1.2, 0.4,
48, 1.1, 0.9, 3.2, 3.2,
49, 0.0, 0.8, 0.0, 0.0,
50, 0.7, 0.5, 1.5, 1.5,
51, 2.1, 2.9, 0.3, 0.3,
52, 0.0, 0.0, 0.9, 0.9,
53, 1.5, 0.0, 3.1, 3.1,
54, 0.5, 0.9, 0.7, 0.7,
55, 1.6, 1.5, 0.0, 0.0,
56, 2.6, 0.0, 1.8, 1.8,
57, 0.8, 2.1, 2.9, 1.9,
58, 2.2, 0.7, 0.0, 3.0,
59, 1.5, 1.3, 3.2, 3.2,
60, 3.3, 2.9, 0.9, 1.9,
61, 0.0, 2.6, 0.7, 2.7,
/* Precedence Relationof Kim 61*/
task # (no. of successors) immediate successors
0 (7) 1, 4, 18, 28, 39, 35, 51
1 (1) 2
2 (1) 3
3 (1) 7
4 (1) 5
5 (1) 6
6 (1) 7
7 (4) 8, 10, 13, 16
8 (1) 9
9 (1) 17
10 (1) 11
11 (1) 12
12 (1) 17
13 (1) 14
14 (1) 15
15 (1) 62
16 (1) 62
17 (1) 61
18 (1) 19
19 (1) 20
20 (3)21, 24, 26
21 (1) 22
22 (1) 23
23 (1) 27
24 (1) 25
25 (1) 27
26 (1) 62
27 (1) 53
28 (1) 29
29 (1) 30
30 (2) 31,34
31 (1) 32
32 (1) 33
33 (1) 49
34 (1) 49
35 (1) 36
36 (1) 37
37 (1) 38
38 (1)42
39 (1)40
40 (1)41
41 (1)42
42 (1)43
43 (1)44
44 (3)45, 47, 48
45 (2)46, 49
46 (1) 62
47 (1) 49
48 (1) 49
49 (1) 50
50 (1) 53
51 (1) 52
52 (1) 53
53 (1) 54
54 (3) 55,57,59
55 (1) 56
56 (1) 61
57 (1) 58
58 (1) 61
59 (1) 60
60 (1) 61
61 (1) 62
62 (0)
Arcus 111 tasks Problem
Number of tasks = 111
Number of models = 5
0 1 /* MPS start */
1 1
2 1
3 1
4 1 /* MPS end */
/* Task Time of Arcus's 111 */
task # (task times of 5 models)
1, 1960, 1960, 1960, 1960, 1960,
2, 1715, 1715, 1715, 1715, 1715,
3, 735, 735, 735, 735, 735,
4, 1715, 1715, 1715, 1715, 1715,
5, 490, 490, 490, 490, 490,
6, 1225, 1225, 1225, 1225, 1225,
7, 169, 169, 169, 169, 169,
8, 2252, 2252, 2252, 2252, 2252,
9, 1225, 1225, 1225, 1225, 1225,
10, 0, 2319, 0, 0, 0,
11, 1715, 1715, 1715, 1715, 1715,
12, 980, 980, 980, 980, 980,
13, 735, 735, 735, 735, 735,
14, 2281, 2281, 2281, 2281, 2281,
15, 2750, 2750, 2750, 2750, 2750,
16, 0, 0, 77, 0, 0,
17, 0, 0, 0, 89, 0,
18, 0, 0, 0, 0, 51,
19, 0, 364, 0, 0, 0,
20, 405, 0, 0, 0, 0,
21, 3060, 3060, 3060, 3060, 3060,
22, 125, 125, 125, 125, 125,
23, 3429, 3429, 3429, 3429, 3429,
24, 0, 0, 0, 43, 0,
25, 3430, 3430, 3430, 3430, 3430,
26, 1960, 1960, 1960, 1960, 1960,
27, 0, 0, 0, 29, 0,
28, 0, 0, 0, 27, 0,
29, 0, 0, 0, 0, 15,
30, 121, 0, 0, 0, 0,
31, 1715, 1715, 1715, 1715, 1715,
32, 2127, 2127, 2127, 2127, 2127,
33, 1470, 1470, 1470, 1470, 1470,
34, 4037, 4037, 4037, 4037, 4037,
35, 0, 0, 0, 68, 0,
36, 0, 0, 0, 62, 0,
37, 0, 0, 0, 0, 42,
38, 0, 364, 0, 0, 0,
39, 4998, 4998, 4998, 4998, 4998,
40, 1470, 1470, 1470, 1470, 1470,
41, 2963, 2963, 2963, 2963, 2963,
42, 5689, 5689, 5689, 5689, 5689,
43, 0, 0, 0, 68, 0,
44, 0, 0, 0, 18, 0,
45, 0, 0, 0, 0, 10,
46, 0, 0, 81, 0, 0,
47, 5200, 5200, 5200, 5200, 5200,
48, 0, 0, 39, 0, 0,
49, 0, 0, 67, 0, 0,
50, 0, 0, 0, 0, 27,
51, 0, 0, 0, 0, 15,
52, 121, 0, 0, 0, 0,
53, 0, 0, 58, 0, 0,
54, 1715, 1715, 1715, 1715, 1715,
55, 125, 125, 125, 125, 125,
56, 4010, 4010, 4010, 4010, 4010,
57, 1470, 1470, 1470, 1470, 1470,
58, 1470, 1470, 1470, 1470, 1470,
59, 2303, 2303, 2303, 2303, 2303,
60, 1960, 1960, 1960, 1960, 1960,
61, 2205, 2205, 2205, 2205, 2205,
62, 4018, 4018, 4018, 4018, 4018,
63, 2744, 2744, 2744, 2744, 2744,
64, 2999, 2999, 2999, 2999, 2999,
65, 735, 735, 735, 735, 735,
66, 735, 735, 735, 735, 735,
67, 735, 735, 735, 735, 735,
68, 735, 735, 735, 735, 735,
69, 0, 545, 0, 0, 0,
70, 3386, 3386, 3386, 3386, 3386,
71, 3234, 3234, 3234, 3234, 3234,
72, 2205, 2205, 2205, 2205, 2205,
73, 2206, 2206, 2206, 2206, 2206,
74, 490, 490, 490, 490, 490,
75, 825, 825, 825, 825, 825,
76, 3528, 3528, 3528, 3528, 3528,
77, 3568, 3568, 3568, 3568, 3568,
78, 1200, 1200, 1200, 1200, 1200,
79, 618, 618, 618, 618, 618,
80, 1470, 1470, 1470, 1470, 1470,
81, 1715, 1715, 1715, 1715, 1715,
82, 735, 735, 735, 735, 735,
83, 1960, 1960, 1960, 1960, 1960,
84, 2989, 2989, 2989, 2989, 2989,
85, 618, 618, 618, 618, 618,
86, 490, 490, 490, 490, 490,
87, 735, 735, 735, 735, 735,
88, 490, 490, 490, 490, 490,
89, 921, 921, 921, 921, 921,
90, 326, 326, 326, 326, 326,
91, 5390, 5390, 5390, 5390, 5390,
92, 243, 243, 243, 243, 243,
93, 371, 371, 371, 371, 371,
94, 58, 58, 58, 58, 58,
95, 6615, 6615, 6615, 6615, 6615,
96, 1225, 1225, 1225, 1225, 1225,
97, 769, 0, 0, 0, 0,
98, 768, 0, 0, 0, 0,
99, 1670, 1670, 1670, 1670, 1670,
100, 1670, 1670, 1670, 1670, 1670,
101, 490, 490, 490, 490, 490,
102, 0, 202, 0, 0, 0,
103, 0, 203, 0, 0, 0,
104, 202, 202, 202, 202, 202,
105, 2744, 2744, 2744, 2744, 2744,
106, 162, 0, 0, 0, 0,
107, 324, 0, 0, 0, 0,
108, 162, 0, 0, 0, 0,
109, 0, 121, 0, 0, 0,
110, 0, 162, 0, 0, 0,
111, 91, 91, 91, 91, 91,
/* Precedence Relationof Arcus 111 */
task # (no. of successors) immediate successors
0 ( 1) 1
1 ( 1) 2
2 ( 1) 3
3 ( 1) 4
4 ( 6) 5,6,7,8,9,10
5 ( 1) 39
6 ( 1) 39
7 ( 1) 83
8 ( 1) 71
9 ( 1) 32
10 ( 2) 11,12
11 ( 9) 13,14,15,16,17,18,19,20,21
12 ( 9) 13,14,15,16,17,18,19,20,21
13 ( 1) 71
14 ( 4) 22,23,24,25
15 ( 1) 26
16 ( 1) 27
17 ( 1) 28
18 ( 1) 29
19 ( 1) 30
20 ( 1) 91
21 ( 1) 111
22 ( 2) 31,83
23 ( 2) 32,33
24 ( 2) 69,70
25 ( 1) 34
26 ( 1) 82
27 ( 1) 35
28 ( 1) 36
29 ( 1) 37
30 ( 1) 38
31 ( 1) 39
32 ( 1) 41
33 ( 1) 111
34 ( 1) 42
35 ( 1) 43
36 ( 2) 44,91
37 ( 2) 45,91
38 ( 2) 46,91
39 ( 1) 40
40 ( 1) 111
41 ( 2) 69,70
42 ( 1) 47
43 ( 3) 48,49,91
44 ( 1) 50
45 ( 1) 51
46 ( 1) 52
47 ( 7) 54,55,56,57,58,59,60
48 ( 1) 53
49 ( 1) 91
50 ( 1) 111
51 ( 1) 111
52 ( 1) 111
53 ( 1) 111
54 ( 2) 69,70
55 ( 3) 61,62,63
56 ( 2) 63,64
57 ( 2) 65,91
58 ( 2) 66,91
59 ( 2) 67,91
60 ( 2) 68,91
61 ( 2) 69,70
62 ( 1) 71
63 ( 1) 111
64 ( 1) 72
65 ( 1) 111
66 ( 1) 111
67 ( 1) 111
68 ( 1) 111
69 ( 2) 77,78
70 ( 1) 73
71 ( 1) 91
72 ( 2) 74,91
73 ( 1) 75
74 ( 1) 76
75 ( 4) 77,78,91,79
76 ( 3) 80,81,82
77 ( 1) 83
78 ( 1) 84
79 ( 1) 85
80 ( 2) 86,91
81 ( 2) 87,91
82 ( 1) 111
83 ( 1) 91
84 ( 3) 88,89,91
85 ( 1) 111
86 ( 1) 111
87 ( 1) 90
88 ( 1) 105
89 ( 1) 105
90 ( 1) 111
91 ( 3) 92,93,94
92 ( 1) 95
93 ( 1) 95
94 ( 1) 95
95 ( 6) 96,97,98,99,100,104
96 ( 1) 101
97 ( 1) 102
98 ( 1) 103
99 ( 1) 111
100 ( 1) 111
101 ( 1) 105
102 ( 2) 106,107
103 ( 2) 107,108
104 ( 1) 111
105 ( 1) 111
106 ( 1) 109
107 ( 1) 111
108 ( 1) 110
109 ( 1) 111
110 ( 1) 111
111 ( 1) 112
112 ( 0)
1