Algorithm 1. AREGWO
Input: Number of wolves MW; maximum iteration number τmax, lower bound bmin; upper bound bmax; search dimension D; fitness function 𝒥(⋅). Output: Best solution ξ[1]; best fitness 𝒥(ξ[1]).
1.	Compute the search range: ρ = bmax − bmin.
2.	Randomly initialize MW wolves ${\xi }_m^{(0)}$, m = 1, 2, …, MW, within [bmin,bmax].
3.	Generate the opposite population: ${\xi }_m^{\mathit{opp}}=b^{\min }+b^{\max }-{\xi }_m^{(0)}.$
4.	Evaluate all original and opposite wolves using 𝒥(⋅).
5.	Select the best MW wolves to form the initial population.
6.	Sort the population and determine the best three wolves $({\xi }_{[1]}^{(\tau )},{\xi }_{[2]}^{(\tau )},{\xi }_{[3]}^{(\tau )}).$
7.	Set 𝒮stg = 0, and set the stagnation threshold as 𝒮max = max(5, round(0.1τmax)).
8.	for  τ = 1 to τmax do
9.	Save the current population as 𝒫(τ).
10.	Calculate the adaptive convergence factor: χ(τ) = 1 + cos(πτ/τmax).
11.	for m = 1 to Mω do
12.	for r = 1 to 3 do
13.	Generate coefficient vectors: $m_r^{(\tau )}=2\chi (\tau )r_{r,1}^{(\tau )}-\chi (\tau ),\begin{array}{c}\end{array}{n}_r^{(\tau )}=2r_{r,2}^{(\tau )}.$
14.	Generate the elite-guided candidate: $z_{m,r}^{(\tau )}={\xi }_{\left|r\right|}^{(\tau )}-m_r^{(\tau )}\odot \left|n_r^{(\tau )}\odot {\xi }_{\left|r\right|}^{(\tau )}-{\xi }_m^{(\tau )}\right|.$
15.	end for
16.	Generate the reinforced elite candidate: ${\tilde{\xi }}_m^{(\tau )}=0.5z_{m,1}^{(\tau )}+0.3z_{m,2}^{(\tau )}+0.2z_{m,3}^{(\tau )}.$
17.	end for
18.	Calculate the perturbation probability: μ(τ) = 0.2(1 − τ/τmax).
19.	Generate binary perturbation mask $I_m^{(\tau )}$ according to μ(τ).
20.	Apply adaptive weak perturbation: ${\tilde{\xi }}_m^{(\tau )}={\tilde{\xi }}_m^{(\tau )}+I_m^{(\tau )}\odot [0.05\chi (\tau )g_m^{(\tau )}\odot \rho ].$
21.	if 𝒮stg ≥ 𝒮max
22.	Select the worst 20% wolves as 𝒲poor.
23.	Regenerate wolves in 𝒲poor around the best wolf: ${\widehat{\xi }}_m^{(\tau )}={\xi }_{[1]}^{(\tau )}+0.1h_m^{(\tau )}\odot \rho .$
24.	Set 𝒮stg = 0.
25.	end if
26.	Apply boundary control: ${\overline{\xi }}_m^{(\tau )}=\min [\max ({\widehat{\xi }}_m^{(\tau )},b^{\min }),b^{\max }].$
27.	Evaluate the corrected new population ${\overline{\mathcal{P}}}^{(\tau )}$ using 𝒥(⋅).
28.	Apply greedy elite inheritance: ${\mathcal{P}}^{(\tau +1)}=\mathit{Bes}{t}_{M_W}({\mathcal{P}}^{(\tau )}\cup {\overline{\mathcal{P}}}^{(\tau )})$
29.	Update $({\xi }_{[1]}^{(\tau )},{\xi }_{[2]}^{(\tau )},{\xi }_{[3]}^{(\tau )})$
30.	if the best fitness is improved then set 𝒮stg = 0; else 𝒮stg = 𝒮stg + 1.
31.	Record the current best fitness in the convergence curve.
32.	end for
33.	Return ξ[1], 𝒥(ξ[1]).