Information Technology Reference
In-Depth Information
between the pre-speci
ed lower initial parameter bound x
j
;
low
and the upper initial
parameter bound x
j
;
high
as follows:
x
j
;
i
;
t
¼
x
j
;
low
þ
ð
;
Þð
x
j
;
high
x
j
;
low
Þ;
rand
0
1
ð
1
Þ
j
¼
1
;
2
; ...;
D
;
i
¼
1
;
2
; ...;
N
p
;
t
¼
0
:
The subscript t is the generation index, while j and i are the parameter and
particle indexes respectively. Hence, x
j,i,t
is the jth parameter of the ith particle in
generation t. In order to generate a trial solution, DE algorithm
rst mutates the best
solution vector x
best
;
t
from the current population by adding the scaled difference of
two vectors from the current population.
v
i
;
t
¼
x
best
;
t
þ
F
ð
x
r
1
;
t
x
r
2
;
t
Þ;
r
1
;
r
2
2
ð
2
Þ
1
;
2
; ...;
N
p
with V
i,t
being the mutant vector. Indices r
1
and r
2
are randomly selected with the
condition that they are different and have no relation to the particle index i iwhatsoever
(i.e. r
1
6¼
i). The mutation scale factor F is a positive real number, typically less
than one. Figure
1
illustrates the vector-generation process de
r
2
6¼
ned by Eq. (
2
).
In order to increase the diversity of the parameter vector, the crossover operation is
applied between the mutant vector v
i
;
t
and the original individuals X
i,t
. The result is
the trial vector u
i,t
which is computed by considering element to element as follows:
v
j
;
i
;
t
;
if rand(0,1)
CR or j
¼
j
rand
;
u
j
;
i
;
t
¼
ð
3
Þ
x
j
;
i
;
t
;
otherwise
:
with j
rand
2
f
1
;
2
; ...;
D
g
. The crossover parameter (0.0
≤
CR
≤
1.0) controls the
fraction of parameters that the mutant vector is contributing to the
final trial vector.
x
x
rt rt
1,
2,
x
2
x
1
rt
(
)
rt rt
F
x
x
1,
2,
x
x
2
rt
best t
,
v
it
x
Fig. 1 Two-dimensional example of an objective function showing its contour lines and the
process for generating v in scheme DE/best/l/exp from vectors of the current generation
Search WWH ::
Custom Search