Information Technology Reference
In-Depth Information
[
L, U
]=[1
,
100]
,
w
i
∈
[1
,
50]
and
n
∈
Ta b l e 3 .
Randomly generated instances with
{
1400
,
1500
,
1600
,
1700
}
Number Maximal
Relative
Average
Relative
Number
Average
Maximal CPU
of jobs error of
p
i
arc number dimension volume of
of exact
error
error
time
n
δ
%
|A|
(in
%
)
|N
t
|
S
(
π
t
,T
)
solutions
ΔΔ
(in s)
1
2
3
4
5
6
7
8
9
1400
0.25%
100
1400
1
100
0
0
24.92
1400
0.4%
100
1400
1
100
0
0
24.8
1400
0.5%
99.997556
1377.21
0.078809
1
≈
0
0.000001 24.97
1400
0.75%
99.539142
575.2
≈
0
0
0.000023 0.000029 25.67
1400
1%
99.198461
422.65
≈
0
0
0.000042 0.00005 25.63
1400
2.5%
97.594897
154.9
0.000001
0
0.000157 0.000178 25.1
1400
5%
94.869044
70.36
0.002356
0
0.000533 0.000615 25.29
1400
15%
84.364242
14.35
0.029338
0
0.004339 0.004841 24.72
1400
25%
74.096446
5.18
0.14077
0
0.011998 0.013041 24.27
1500
0.25%
100
1500
1
100
0
0
31.44
1500
0.4%
100
1500
1
100
0
0
31.08
1500
0.5%
99.997493
1474.09
0.070241
0
≈
0
0.000001 31.64
1500
0.75%
99.544441
607.5
≈
0
0
0.000042 0.000052 32.39
1500
1%
99.193199
444.29
≈
0
0
0.000042 0.000052 32.39
1500
2.5%
97.61593
167.25
0.000005
0
0.000155 0.000171 31.43
1500
5%
94.861654
71.34
0.00282
0
0.000533 0.000582 31.36
1500
15%
84.409904
14.93
0.05372
0
0.004394 0.00492 30.46
1500
25%
74.281235
5.46
0.148403
0
0.011936 0.013685 30.33
1600
0.25%
100
1600
1
100
0
0
38.63
1600
0.4%
100
1600
1
100
0
0
38.67
1600
0.5%
99.997452
1569.35
0.046151
0
≈
0
0.000001 38.8
1600
0.75%
99.54273
638.18
≈
0
0
0.000023 0.00003 39.76
1600
1%
99.192323
464.89
≈
0
0
0.000042 0.000048 40.04
1600
2.5%
97.601128
174.91
0.000004
0
0.000157 0.000177 38.71
1600
5%
94.861356 76.990000
0.003505
0
0.000532 0.000581 38.46
1600
15%
84.343239
14.75
0.036278
0
0.004341 0.004811 37.34
1600
25%
74.123830
5.75
0.087651
0
0.011899 0.013192 36.34
1700
0.25%
100
1700
1
100
0
0
47.29
1700
0.4%
100
1700
1
100
0
0
47.18
1700
0.5%
99.997432
1665.41
0.034556
1
≈
0
0.000001 47.12
1700
0.75%
99.544993
671.09
≈
0
0
0.000023 0.000027 48.25
1700
1%
99.203930
495.13
≈
0
0
0.000041 0.000049 48.47
1700
2.5%
97.598734
180.99
0.000072
0
0.000156 0.000172 46.88
1700
5%
94.852439
80.53
0.001601
0
0.000533 0.000585 46.33
1700
15%
84.358524
17.27
0.028854
0
0.004379
0.0049
45.26
1700
25%
74.030579
6.03
0.082325
0
0.012069 0.013255 44.24
For all series presented in Tables 2 - 4, the average (maximum) error
Δ
of the value
γ
p
∗
of the objective function
γ
=
i
=1
w
i
C
i
obtained for the permutation
π
t
∈ S
max
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