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180 Chapter 6 Plant leaf disease classification based on feature selection
The lowest level of gray wolf is omega. These wolves play the
role of scapegoat. They have to submit to all the other dominant
wolves. The omega also has the least right in the pack.
Those wolves that are not belong to those groups above will be
called delta. These wolves have a variety of roles such as watching
the boundaries of the territory and warning the pack, helping the
other wolves in hunting, or even caring the weak, ill, and
wounded wolves in the pack. To develop the mathematically
model, first, the fittest solution is considered as alpha, and the
beta and delta are considered to the second and the third fittest
solution, respectively. The next step of GWO is encircling prey,
which is calculated by proposed equations:
! ! ! !
(6.5)
D ¼ C $ X p ðtÞ X ðtÞ
X ðt þ 1Þ¼ X p ðtÞ A $D (6.6)
! ! ! !
where t indicates the current iteration, A and C are coefficient
!
!
vectors, X p is the position vector of the prey, and X is the position
!
!
vector of a gray wolf. The coefficient vectors are calculated by the
following equations:
A ¼ 2 a $ r 1 a (6.7)
! ! ! !
!
!
C ¼ 2 r 2 (6.8)
where a is linearly decreased from 2 to 0 and r 1 and r 2 are
!
!
!
random vector in [0, 1].
The following step is hunting, which defines the final position
!
of the wolf X ðt þ1Þ using these equations:
!
! ! !
D a ¼ C 1 $ X a X (6.9)
!
D b ¼ C 2 $ X b X (6.10)
!
! !
!
D d ¼ C 3 $ X d X (6.11)
! !
!
! ! ! !
X 1 ¼ X a A 1 $ D a (6.12)
! ! ! !
X 2 ¼ X b A 2 $ D b (6.13)
