Egret Swarm Optimization

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File:Snowy egret (12033).jpg

A Snowy Egret

The Egret Swarm Optimization Algorithm (ESOA) is a meta-heuristic optimization algorithm that combines the predatory behavior of Snowy Egrets (Sit-And-Wait Strategy) and Great Egrets (Aggressive Strategy).

Inspiration

Among the egret family, the Snowy Egret and the Great Egret are two species that differ considerably in their feeding behavior. The Snowy Egret applies the least energy-intensive sit-and-wait strategy: it stands still and waits patiently, watching for prey until it appears and then darting to grab it with its beak. Snowy egrets that use the sit-and-wait strategy tend to retrieve relatively steady gains with very low energy consumption. Great egrets, on the other hand, are aggressive, and once they have spotted their prey, they will chase it until it is caught. The aggressive strategy is energy-intensive, but it also allows the Great Egret to potentially achieve higher returns. Inspired by the predatory behavior of snowy egrets and great egrets, an algorithm, ESOA, that combines the advantageous characteristics of both is proposed.

Mathematical model

The ESOA consists of three main components: a sit-and-wait strategy, an aggressive strategy, and a discriminant condition. Each egret swarm can consist of n egret squads, each of which in turn contains three egrets, with Egret A implementing the sit-and-wait strategy and Egret B and Egret C using the random walking and encircling mechanisms of the aggressive strategy, respectively.

Sit-And-Wait Strategy

The observation equation of the i-th Egret A can be described as ${\hat{y}}_i=A({\mathbf{𝐱}}_i)$, the retrieved real fitness of each iteration is $y_i$, then the pseudo gradient of the observation equation is ${\mathbf{𝐠}}_i,$ hence the new position of Egret A is as below:

${\mathbf{𝐱}}_{a,i}={\mathbf{𝐱}}_i+\exp (-t/(0.1\cdot t_{max}))\cdot 0.1\cdot hop\cdot {\mathbf{𝐠}}_i$,

where $t$ is the current iteration, $t_{max}$ is the maximum iteration, $hop$ is the gap between the low bound and upper bound of solution space.

Aggressive Strategy

Egret B applies random walking and the position update method is:

${\mathbf{𝐱}}_{b,i}={\mathbf{𝐱}}_i+\tan ({\mathbf{𝐫}}_{b,i})\cdot hop/(1+t)$,

where ${\mathbf{𝐫}}_{b,i}$ is the stochastic value in $(-\pi /2,\pi /2)$.

Egret C uses encircling mechanisms,

$\begin{array}{rl}{\mathbf{𝐃}}_h& ={\mathbf{𝐱}}_{ibest}-{\mathbf{𝐱}}_i,\\ {\mathbf{𝐃}}_g& ={\mathbf{𝐱}}_{gbest}-{\mathbf{𝐱}}_i,\\ {\mathbf{𝐱}}_{c,i}& =(1-{\mathbf{𝐫}}_i-{\mathbf{𝐫}}_g)\cdot {\mathbf{𝐱}}_i+{\mathbf{𝐫}}_h\cdot {\mathbf{𝐃}}_h+{\mathbf{𝐫}}_g\cdot {\mathbf{𝐃}}_g,\end{array}$

where ${\mathbf{𝐱}}_{ibest}$ and ${\mathbf{𝐱}}_{gbest}$ represent the best position of Egret Squad and Egret Swarm respectively. ${\mathbf{𝐫}}_i$ and ${\mathbf{𝐫}}_g$ are the random values in $[0,1]$.

Discriminant Condition

After each egret in the egret squad has calculated the updated position, it will jointly decide the updated position of the egret squad in the following form:

${\mathbf{𝐱}}_{s,i}=\left[{\mathbf{𝐱}}_{a,i}{\mathbf{𝐱}}_{b,i}{\mathbf{𝐱}}_{c,i}\right]$,

${\mathbf{𝐲}}_{s,i}=\left[y_{a,i}{y}_{b,i}{y}_{c,i}\right]$,

$c_i=argmin({\mathbf{𝐲}}_{s,i})$,

${\mathbf{𝐱}}_i=\{\begin{array}{l}{\mathbf{𝐱}}_{s,i}{|}_{c_i}if{\mathbf{𝐲}}_{s,i}{|}_{c_i}<y_{i}orr<0.3,\\ {\mathbf{𝐱}}_{i}else\end{array}.$

The egret squad compares the updated position and fitness of the three egrets with the fitness of the previous iteration, and adopts the update if one egret's updated position is better than that of the previous iteration. If each egret's updated position is worse than the previous one, there is a 30% probability of adopting the solution with the best-updated position.

Source Code

Python Code：https://github.com/Knightsll/Egret_Swarm_Optimization_Algorithm

MATLAB Code：https://ww2.mathworks.cn/matlabcentral/fileexchange/115595-egret-swarm-optimization-algorithm-esoa

Website: https://knightsll.github.io/about

References

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