Page 176 - IJOCTA-15-1

Y. Olmez et al. / IJOCTA, Vol.15, No.1, pp.166-182 (2025)
is the random nonlinear weight in the range of where v i (t + 1) is the position value of the i th rab-
(0, ∞) and determined by the following equation bit at (t + 1) th iteration. x j (t) denotes the cur-
(13): rent solution of the j th rabbit. n 1 and r 1 denote
!
2.randn the parameter with normal distribution and the
it it
w = 1 − . rand. random parameter, respectively. The equations
max it max it
for the hiding stage are given in Eqs. (18-19):
(13)
v i (t + 1) = x i (t) + R. (r 4 .g − x i (t)) (18)
where randn denoted a random value in [(−1) −
(+1)]. max it is the number of the maximum iter-
ations. g (t) = x i (t) + H.g r .x i (t) (19)

2.5. Cheetah optimization algorithm Where r4 and H represent the random and the
hiding parameters, respectively. g is the chosen
Cheetah Optimizer is one of the methods inspired burrow for hiding. Finally, an energy factor is
by nature and was introduced by Akbari et al. in modeled the provide balance between the explo-
2022. 28 The algorithm is developed by taking in- ration and the exploitation phases using Eq. (10).
spiration from the behavior of the cheetahs during
the hunting stage. According to hunting behav-
it 1
iors, the optimization method consists of three A (t) = 4 1 − ln (20)
strategies, which are searching, sitting and wait- max it r
ing, and attacking. According to the search strat- where max it indicates the number of the itera-
egy, the new solutions are updated by using Eq. tions (it).
(14):

2.7. Golden jackal optimization algorithm
x i,j (t + 1) = x i,j (t) + r −1 .a i,j (t) (14) Golden Jackal Optimization was also developed
i,j
where x (i,j) (t) and x (i,j) (t + 1) demonstrate the inspired by nature and was introduced by Chopra
current and the next positions of the ith cheetah et al. in 2022. 30 It is based on the behavior of
on d-dimension. r −1 and a (t) denote random golden jackals during the hunting process. The
(i,j) (i,j)
parameters and the step length of the cheetah, re- hunting techniques of the jackals are modeled as
spectively. According to the second strategy, sit- three stages: searching, encircling, and attacking.
ting and waiting, the new solutions are calculated The male jackal leads the prey. The jackals’ posi-
as in Eq. (15): tions are updated via Eq. (21) corresponding to
the prey.

x i,j (t + 1) = x i,j (t) (15) x m (t + 1) + x fm (t + 1)
x (t + 1) = (21)
Finally, according to the third strategy, attack- 2
ing, the new positions are found via the following where x m (t + 1) and x fm (t + 1) demonstrate the
equation (16): male and female jackals obtained using Eqs. (22)-
(23)
x i,j (t + 1) = x β,j (t) + r i,j .β i,j (t) (16)
x m (t + 1) = x m (t) − E. |x m (t) − rl.p (t)| (22)
Where r i,j and x β,j (t) denote the turning param-
eter and position of the prey, respectively. β i,j (t)
is the interaction parameter.
x fm (t + 1) = x f (t) − E. |x f (t) − rl.p (t)| (23)
2.6. Artificial rabbit optimization where x m (t) and x m (t + 1) denote the current and
algorithm the next positions of the male jackal and x f (t)
and x f (t + 1) represent the current and the next
Artificial Rabbit Optimization is a nature-
value of the female jackal. p(t) is the prey posi-
inspired algorithm proposed by Wang et al. in
tion. E and rl indicate an energy function and
2022.
a random vector generated with Levy distribu-
tion, respectively. When a jackal pair attacks the
v i (t + 1) = x j (t) + R. (x i (t) − x j (t)) prey, its evading energy decreases, and the jackals
(17)
+round (0.5. (0.05 + r 1 )) .n 1 surround the prey identified in the previous step.
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