Page 177 - IJOCTA-15-1

Recent metaheuristics on control parameter determination
The mathematical expression of this behavior is local optimum and is formulated as the following
given in the following Eqs. (24-25). equation (30).

x (t + 1) =
x m (t + 1) = x m (t) − E. |rl.x m (t) − p (t)| (24)
(
x (t) + CF.[lb + R. (ub − lb) , if r ≤ PSR
x (t) + PSR (1 − r) + r]. (x r1 − x r2 ) , else
x fm (t + 1) = x f (t) − E. |rl.x f (t) − p (t)| (25)
(30)
where E is the energy function and is calculated where PSR indicates the rate of the hunter’s
as E = E 0 .E 1 .E 0 and E 1 are the diminishing and achievement. r 1 and r 2 indicate the randomly se-
starting energy of prey, respectively. lected numbers. ub and lb denotes the bounds of
the gazelles and U indicates the binary vector as
2.8. Gazelle optimization algorithm generated by Eq. (31):

The Gazelle Optimization Algorithm is one
0, if r < 0.34
of the population-based methods developed by U = (31)
Agushaka et al in 2023. 31 Gazelles’ survival skills 1, else
are used as inspiration for developing the algo- where r is a random number in [0,1].
rithm. It consists of two phases, which are explo-
ration and exploitation. In the exploitation stage,
the grazing gazelle is simulated while the predator 2.9. Pelican optimization algorithm
is absent and chasing it. During the exploration
Pelican Optimization Algorithm is one of the
phase, the gazelle notices the predator and moves
herd-based methods developed by observing and
towards a safe shelter. At the exploitation and
modeling the behavior of pelicans during the
exploration phase, the updated positions of the
hunting stage. It was proposed by Trojovsk´y et
gazelles are calculated with Eq. (26). 32
al in 2022. The hunting stage consists of two
stages: approaching the prey and flying over the
x (t + 1) = x (t) +s.R.R B .(E (t) − R B .x (t)) water. After the pelican determines the position
(26) of the prey, it approaches the determined place.
The behavior of the pelican is modeled mathe-
where x(t) is the current position of the gazelle.
s-parameter indicates the velocity of the gazelle. matically as in Eq. (32).
R and R B are random vectors represented by the
uniform distribution and the Brownian motion. x i,j (t + 1) =
When the gazelle spotted the hunter, the motion
x i,j (t) + r. (p j − I.x i,j (t)) , if f p < f i
of the gazelle was formulated by using Eq. (27).
x i,j (t) + r. (x i,j (t) − p j ) , else
(32)
x (t + 1) = x (t) +s.µ.R L . (E (t) − R L .x (t))
where x i,j (t), and x i,j (t + 1) indicate the current
(27)
and the next positions of the ith pelicans at the
where R L is a random integers vector with Levy jth dimension, respectively. r is a constant num-
distribution. If the hunter chases the gazelle, the ber, I is the randomly chosen number as 1 or 2.
next motion of the gazelle is formulated as in Eq. p j denotes the position of the prey at the jth di-
(28). mension. f p and f i indicate the cost values of the
prey and the i th pelican, respectively. When they
x (t + 1) = x (t) approach the water, pelicans stretch their wings,
(28) fly over it, and collect the captured fish in their
+s.µ.CF. R. R B . (E (t) − R L .x (t))
pouches. Thus, they can catch and collect more
where S denotes the upper level of the velocity. fish in their hunting area. This demonstrates that
CF is formulated using Eq. (29). the pelicans are quite effective at local search.
The mathematical modeling of this behavior is
2.it presented in Eq. (33):

it max it
C F = 1 − (29)
max it
x i,j (t) =
The hunter’s success affects the gazelle’s survival. it (33)
This behavior allows the method to get rid of the x i,j (t) +R 1 − max it . (2r − 1) .x i,j (t)
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