A OPEN PIT MINING AÇIK OCAK MADENCİLİĞİ

According to Storn and Price (1997,
2002), there are three operations in DE
including mutation, crossover, and selection.
The general idea behind DE is a scheme for
generating trial parameter vectors. Mutation
and crossover are used to generate new
vectors (trial vectors), and then selection
determines which of the vectors will survive
into the next generation.
A. Mutation
Mutation operation mutates a chromosome
into a new one by inverting randomly
selected genes of the chromosomes. For each
target vector x
i , G
, a mutant vector v is
generated according to equation 6.
r1 r2 r3 i
1,
NP
v x F x x
i , G 1 r1, G 1 r 2, G 1 r 3, G 1
(6)
In which the indexes r1, r2, r 3 are chosen
randomly. Note that these indexes are
different from each other and from the
running index i, therefore the number of the
population must be at least four ( NP 4). F
is a real number that controls the
amplification of the difference vector
x x .
r 2, G 1 r 3, G 1
B. Crossover
Crossover operation crosses two or more
chromosomes to create new chromosomes
for the population. The target vector is mixed
with the mutated vector, using the following
scheme, to yield the trial vector
ui , G 1 u1 i , G 1, u2 i , G 1 ,..., uDi , G 1
(7)
where
v
ji , G 1
if r j CR or j rn i
ui , G 1
, j 1,...,
D
v
ji , G
if r j CR or j rn i
r j 0,1
is the j th evaluation of a uniform
random generator number. CR is the
crossover constant, which has to be
determined by the user. rn j 1,...,
D is a
randomly chosen index which ensures that
ui , G 1
gets at least one element from v
i , G 1
.
Otherwise, no new parent vector would be
produced and the population would not alter.
C. Selection
Selection operation selects the best
chromosome from the population for the next
generation. In jDE a greedy selection scheme
is used as well. In dealing with a
minimization problem, the selection rule is
as follow
x
i , G 1
u if f u f x
x
i , G
otherwise
i , G 1 i , G 1 i , G
for i 1,..., D . f is the objective or fitness
function. If, and only if, the trial vector ui , G 1
yields a better cost function value (minimum
value in a minimization problem) than x
i , G
,
then x
i , G 1
is set to ui , G 1; otherwise, the old
value x
i , G
is retained.
In jDE, the control parameters that will be
adjusted by means of evolution are F and
CR. Both of them are applied at the
individual level. In means, the better values
of these control parameters lead to better
individuals, which, in turn, devise next
generations with better parameter values. In
each generation, new control parameters
Fi , G 1
and CRi , G 1
are calculated as
F
i , G 1
CR
i , G 1
F rand * F , if rand
l 1 u
2 1
Fi , G
, otherwise
rand
3,
if rand
4
2
(8)
CR , otherwise
i , G
and they produce factors F and CR in a new
parent vector. rand
j
, j 1,2,3,4
, are uniform
random values.
1
and
2
represent
probabilities to adjust factors F and CR,
respectively. According to Brest et al.
(2006), if 1
2
0.1, Fl
0.1 and f
u
0.9 then
the new F takes a value form [0.1,1.0] in a
random manner. The new CR takes a value
from [0,1]. Fi , G 1
and CRi , G 1
are calculated
before the mutation process. Therefore, these
new factors influence the mutation,
crossover, and selection operations in
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