Algorithm 1: ESOA based on Gaussian Mutation.
Input: $lo{c}_{self\_i}$, $ste{p}_a$, $ste{p}_b$
Operation
/* Sit-and-wait step */
1.	Update the integrated gradient g via Equations (4)–(8)
2.	Update the weight of observation method w by Equations (9)–(11)
3.	Get the expected position $lo{c}_{anext\_i}$ of Egret A by Equation (13)
4.	Retrieve the Egret A’s fitness $fi{t}_{anext\_i}$
5.	Return $lo{c}_{anext\_i}$, $fi{t}_{anext\_i}$
/* Aggressive step */
6.	Get the expected position $lo{c}_{bnext\_i}$ of egret B by Equations (14) and (15)
7.	Get the expected position $lo{c}_{cnext\_i}$ of egret C by Equations (18) and (19)
8.	Retrieve the fitness of egret B $fi{t}_{bnext\_i}$ and egret C $fi{t}_{cnext\_i}$
9.	Return $lo{c}_{bnext\_i}$, $lo{c}_{cnext\_i}$, $fi{t}_{bnext\_i}$, $fi{t}_{cnext\_i}$
/* Search the global optimum based on Gaussian mutation-step */
10.   while $t<t_{\max }$ 11.    Implement Sit-and-wait step, Obtain $lo{c}_{anext\_i}^t$, $fi{t}_{anext\_i}^t$ 12.    Implement Aggressive step, Obtain $lo{c}_{bnext\_i}^t$, $fi{t}_{bnext\_i}^t$, $lo{c}_{cnext\_i}^t$, $fi{t}_{cnext\_i}^t$ 13.    Get next position via Equations (20)–(23) 14.    $lo{c}_{best}=Gauss(lo{c}_{self\_i}^{t+1},lo{c}_{best})$ 15.    Retrieve the fitness of best position $fi{t}_{best}$ 16.    Return $lo{c}_{best}$, $fi{t}_{best}$
/* Operation Ending */
Output: $lo{c}_{best}$, $fi{t}_{best}$