Information Technology Reference
In-Depth Information
Mutant population:
V
k
is the set of
NP
individuals in the mutant population at gener-
ation
t
,i.e.,
V
k
=
V
1
,
V
2
,...,
V
NP
.
Trial population:
U
k
is the set of
NP
individuals in the trial population at generation
t
,
i.e.,
U
k
=
U
1
,
U
2
,...,
U
NP
.
Mutant constant:
F
(0
,
2) is a real number constant which affects the differential
variation between two individuals.
∈
Crossover constant:
CR
(0
,
1) is a real number constant which affects the diversity
of population for the next generation.
Fitness function:
In a minimization problem, the objective function is given by
f
i
X
i
,
for the individual
X
i
∈
.
Traditional DEs explained above are designed for continuous optimization problems
where chromosomes are floating-point numbers. To cope with discrete spaces, a sim-
ple and novel discrete DE (DDE) algorithm is presented in [36, 20], where solutions are
based on discrete/binary values. In the DDE algorithm, each target individual belonging
to the
NP
number of individuals is represented by a solution as
X
i
=
x
i
1
,
x
i
2
,...,
x
im
,
consisting of discrete values of a permutation of clusters as well as a tour of nodes
visited, at the generation
k
. The mutant individual is obtained by perturbing the gener-
ation best solution in the target population. So the differential variation is achieved in
the form of perturbations of the best solution from the generation best solution in the
target population. Perturbations are stochastically managed such that each individual in
the mutant population is expected to be distinctive. To obtain the mutant individual, the
following equation can be used:
V
i
=
DC
d
X
k
−
1
if r
<
P
m
insert
X
k
−
1
g
g
ot herwise
(6.1)
Where
X
k
−
g
is the best solution in the target population at the previous generation;
P
m
is
the perturbation probability;
DC
d
is the destruction and construction procedure with the
destruction size of
d
as a perturbation operator; and insert is a simple random insertion
move from a given node to another node in the same cluster. A uniform random number
r
is generated between [0, 1]. If
r
is less than then the
DC
d
operator is applied to generate
the mutant individual
V
i
=
DC
d
X
k
−
g
; otherwise, the best solution from the previous
generation is perturbed with a random insertion move resulting in the mutant individual
V
i
=
insert
X
k
−
1
g
. Equation 6.1 will be denoted as
V
i
DC
d
X
k
−
1
:=
P
m
⊕
to ease the
g
i
:=1
,
2
,..,
NP
understanding of pseudocodes. Following the perturbation phase, the trial individual is
obtained such that:
U
i
=
CR
V
i
,
X
k
−
1
if r
<
P
c
i
(6.2)
V
i
ot herwise
where
CR
is the crossover operator; and
P
c
is the crossover probability. In other words, if
a uniform random number
r
is less than the crossover probability
P
c
, then the crossover
operator is applied to generate the trial individual
U
i
=
CR
V
i
,
X
k
−
1
. Otherwise the
i
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