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Parameters Identification of Fractional Order Chapter | 18 539

18.4.2.2 Chaotic Grey Wolf Optimizer Strategy (CGWO)
From the previous controlling equations of the hunting mechanism of
wolves, it’s illustrated that there are two essential parameters A and C that
are trade-offs between the exploration and exploitation phases.
In GWO, parameter A changes according to the lineally decreasing of
vector a from 2 to 0. While in CGWO, the vector a is decreasing from the
same range chaotically, consequently A will be changed based on the chaos
maps as illustrated in Eq. (18.15).

ða f 2 a i Þ
a 5 a i 2 i: : ChaosðiÞ; ð18:15Þ
I
where a i ; a f are the initial and final values of the parameters a, they are
adjusted as 2 and 0.00001 respectively. i, I are the current iteration and the
-
maximum number of iterations respectively. Chaos is the chaotic map.
Additionally, parameters C in the GWO has random values between 0
and 2 with the uniform distribution. However, in CGWO, the parameter C
has a random values in the same interval over the course of iterations with
respect to the chaos maps. Therefore, the chaos maps are normalized to lie
in the same ranges [0 2] as follows in Eqs. (18.16) (18.23)

- Ch~ aos:ðd 2 eÞ
Norm Chaos 5 1 e ð18:16Þ
b 2 a
-
C 5 Norm ChaosðiÞ ð18:17Þ
where [ab] are the minimum and maximum ranges of chaotic maps. [ed]
are the range of the normalization. The [ed] interval is selected as [0.00001
-
2]. NormChaos is the normalized chaos map.

18.4.3 Chaotic Grasshopper Optimization Algorithm
18.4.3.1 Grasshopper Optimization Algorithm Overview
GOA algorithm has been recently introduced in Saremi et al. (2017)to
mimic the behavior of the grasshopper swarms in nature. The grasshoppers
are found in two phases of life. In the nymph phase, the movement of grass-
hopper is slow with small steps, however the long range and the abrupt
movement is the main feature of the swarm in the adulthood phase (Saremi
et al., 2017). In both of these phases, the main target of the grasshoppers is
searching for the sources of food (Saremi et al., 2017). These features can be
mathematically modeled to generate GOA technique (Saremi et al., 2017)as
in Eqs. (18.18) (18.19):

X i 5 S i 1 G i 1 A i ð18:18Þ