Algorithm 2 The CTWRBMO
1:	Begin
2:	$\mathrm{Initialize} \mathrm{the} \mathrm{relevant} \mathrm{parameters} (\mathrm{T}, \mathrm{N}, \mathsf{\epsilon }$, $\mathit{wd}$, etc.)
3:	Initialize population using Circle chaotic map (Equation (7))
4:	Evaluate initial fitness of all individuals
5:	$\mathrm{Set} \mathrm{global} \mathrm{best} X_{\mathit{best}}$← best initial solution
6:	while t < T
7:	Calculate the fitness of each search agent
8:	$\mathrm{Update} \mathrm{global} \mathrm{best} \mathrm{solution} X_{\mathit{best}}$ if improved
9:	Dynamically update ε by (8)
10:	Dynamically updated wd by (9)
11:	Exploration:
12:	if rand < ε
13:	Generate candidate $X^{\mathit{food}\mathit{\_}i}$ using Equation (10)
14:	Else
15:	Generate candidate $X^{\mathit{food}\mathit{\_}i}$ using Equation (11)
16:	end if
17:	Exploitation:
18:	if rand < ε
19:	Update red-billed blue magpie position using Equation (13)
20:	Else
21:	Update red-billed blue magpie position using Equation (14)
22:	end if
23:	Apply greedy selection by Equation (12)
24:	$\mathrm{Update} X_{\mathit{best}}$ if new solution is better
25:	end while
26:	Return global best solution ${\mathbf{X}}_{\mathit{best}}$
27:	end