Intelligent optimization algorithm: Gannet optimization algorithm

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Intelligent optimization algorithm: Gannet optimization algorithm

Abstract: Gannet Optimization Algorithm (GOA) is a swarm optimization algorithm proposed by Pan et al. in March 2022 based on the predation behavior of ponds. It has the characteristics of strong optimization ability and fast convergence speed.

1. Gannet optimization algorithm

1.1 Population initialization

In GOA, the initial population has $N$ only pond my body, the second $i$ pond my island $X_i$ 的位置, 如公式 (1) 所示:
$X_i=\left(x_{i 1}, x_{i 2}, \cdots, x_{i D}\right), i=1,2, \cdots, N,\tag{1}$
其中 $x_{i j}=r_1 \times\left(U B_j-L B_j\right)+L B_j, i=1,2, \cdots, N, j=$ $\cdots, D$ , means the $i$ gannet atposition in dimension $j$ $D$ is the dimension of each pond, $r_1$ is $[0, 1]$ random number, $U B_j$ and $L B_j$ found in each pondThe upper and lower bounds of dimension $j .$
In addition, define a storage matrix $MX$ , used to store the position of individual gannets during each iteration. In the iterative process, if this $M X_i$ The value is better than the current $X_i$ value, then individual $X_i$ The value of $M X_i$ Replaced by the value of . Next, take a $[0, 1]$ random number $r$ , 当 $r < 0.5$ , the gannet is in the exploration stage; when $\geqslant 0.5$ , Tang I was in the development stage.

1.2 Exploration stage

When gannets find their prey in the air, they use $\mathrm{U} according to the depth of the prey in the water$ -shaped diving pattern and $\mathrm{V}$ -shaped diving is used to catch prey. When the prey is at a relatively deep position, the gannet dives in a U-shaped diving manner, as shown in the formula (2):
$\times \cos \left(2 \times \pi \times r_2\right) \times t_1,\tag{2}$
When the prey is at a relatively shallow position, the gannet moves with $\mathrm{V}$ -type diving mode diving, as shown in formula (3): where
V
$V(x)=\left\{\begin{array}{l}-\frac{1}{\ pi} \cdot x+1, x \in(0, \pi) \\ \frac{1}{\pi} \times x-1, x \in(\pi, 2 \pi)\end{array}, t_1=1-\frac{t}{T_{\text {max }}}\right.\tag{3}$
, where $t$ is the current iteration number, $T_{\text {max }}$ is the maximum number of iterations, $r_2$ and $r_3$ Both are $[0, 1]$ random number.
Introduce a random variable $q$ randomly selects a kind of gannet to update its position, and the position update method of gannet is as follows:
$X_i(t+1)=\left\{\begin{array}{l} X_i(t)+u_1+u _2, q \geqslant 0.5 \\ X_i(t)+v_1+v_2, q<0.5 \end{array}\right.\tag{4}$
式 (4) 中 $u_2=A \times\left(X_i(t)-X_r(t)\right), v_2=B \times$ $\left(X_i(t)-X_m(t)\right), \quad A=\left(2 \times r_4-1\right) \times a, \quad B=(2 \times$ $\left.r_5-1\right) \times b$ , where $r_4$ and $r_5$ Both are $[0, 1]$ random number, $u_1$ Is $[- a, a$ random number between $]$ $v_1$ is $[- b, b]$ random number between $X_i(t)$ is the $i$ pond i bird individual atPosition at iteration $t$ $X_i(t)$ is the position of the randomly selected individual bird in the current iteration, $X_m(t)$ refers to the average value of all individual positions in the current iteration, and its calculation formula is: $X_m(t)=$ $\frac{1}{N} \sum_{i=1}^N X_i(t)$

1.3 Development stage

When I enter the water in the pond, its catching ability $C$ greater than or equal to $c$ , it will suddenly rotate to catch fish; its catching ability $C$ is less than $c$ , 则会放弃捕鱼随机游行, 采用Levy 飞行模型模拟塘鹅游行, 其位置更新如下:
$\begin{aligned} & M X_i(t+1)= \\ & \begin{cases}t_1 \times \delta \times\left(X_i(t)-X_{\text {Best }}(t)\right)+X_i(t), & C \geqslant c \\ X_{\text {Best }}(t)-\left(X_i(t)-X_{\text {Best }}(t)\right) \times P \times t_1, & C<c\end{cases} \\ & \end{aligned}\tag{5}$
式 (5) 中, $t_1=1-\frac{t}{T_{\max }}, C=\frac{1}{R \times t_2}, t_2=1+\frac{t}{T_{\max }}$ ,
$R=\frac{M \times v_{\mathrm{e}} l^2}{L}, \quad L=0.2+(2-0.2) \times r_6, \quad \delta=C \times$
$\left|X_i(t)-X_{\text {Best }}(t)\right|, P=\operatorname{Levy}(D), \operatorname{Levy}(D)=0.01 \times$
$\frac{\mu \times \sigma}{|v|^{\frac{1}{\beta}}}, \sigma=\left(\frac{\Gamma(1+\beta)\times \sin \left(\frac{\pi \beta}{2}\right)}{\Gamma\left(\frac{1+\beta}{2}\right) \times \beta \times 2^{\left(\frac{\beta-1}{2}\right)}}\right)^{\frac{1}{\beta}}$ , where, $r_6$ for
$[0, 1]$ random number, $\mathrm{~kg}$ is the mass of Tang I, $\mathrm{~m} / \mathrm{s}$ is the speed of the gannet, $c$ is a constant, after many experiments, $\beta=1.5, X_{\text {Best }}(t)$ refers to the best performing individual in the current population, $\mu$ 和 $\sigma$ 是 $[0, 1]$ random number within.

2. Experimental results

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3. References

[1] Qi Huiling, Hu Hongping, Bai Yanping, etc. Prediction of COVID-19 Epidemic Based on Improved Gannet Algorithm Optimizing BP Neural Network [J/OL]. Journal of Shanxi University (Natural Science Edition): 1-10 [2023-07-23]. DOI: 10.13451/j.sxu.ns.2023025.