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for
each dimension
d
do
generate random value
rand ∼ U
(0
,
1).
if
v
d
=0and
rand ≥ w
then
v
d
←
0.
v
d
=0
then
generate random value
rand ∼ U
(0
,
1).
if
if
rand ≤ C
1
then
if
pbest
d
≥ x
d
then
v
d
←
1.
else
v
d
←−
1.
generate random value
rand
2
∼ U
(0
,
1).
x
d
← pbest
d
+
rand
2
−
0
.
5.
if
C
1
<rand≤ C
1
+
C
2
then
if
gbest
d
≥ x
d
then
v
d
←
1.
else
v
d
←−
1.
generate random value
rand
2
∼ U
(0
,
1).
x
d
← gbest
d
+
rand
2
−
0
.
5.
else
x
d
← x
d
+
v
d
.
Alg.
3: Particle movement
to simplify, dimension
d
), if
v
d
=0,
v
d
w
,
meaning that if
x
d
was either increasing or decreasing,
x
d
stops at this iteration
with probability 1
will be set to 0 with probability 1
−
w
.Otherwise,if
v
d
= 0, with probability
C
1
,
v
d
and
x
d
will
be updated depending on
pbest
d
and with probability
C
2
they will be updated
depending on
gbest
d
, always introducing an element of randomness and where
C
1
and
C
2
are constants between 0 and 1 such that
C
1
+
C
2
≤
−
1. The details on
how the updating of particle
k
takes place are given in Algorithm 3.
Position mutation.
After a particle moves to a new position, we randomly choose
an operation and then mutate its priority value
x
d
disregarding
v
d
.Asin [23],
m
,if
x
d
<
(
nm/
2),
x
d
for a problem of size
n
×
will take a random value in
n, mn
], and
v
d
=1.Otherwise,if
x
d
>
(
nm/
2),
x
d
[
mn
−
will take a random
value in [0
,n
]and
v
d
=
−
1.
Diversification strategy.
If all particles have the same
pbest
solutions, they will
be trapped into local optima. To prevent such situation, a diversification strategy
is proposed in [23] that keeps the
pbest
solutions different. In this strategy, the
pbest
solution of each particle is not the best solution found by the particle itself,
but one of the best
N
solutions found by the swarm so far, where
N
is the size
of the swarm. Once any particle generates a new solution, the
pbest
solutions
will be updated in these situations:
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