Algorithm 2 Reproducible HHMAO Hyperparameter Search

Require:  Search bounds in Table 4, population size $M=40$, iterations $I=160$, switch iteration $t_s=96$, training set ${\mathcal{D}}_{\mathrm{tr}}$, validation set ${\mathcal{D}}_{\mathrm{val}}$, seed s Ensure:  Best hyperparameter vector ${\mathit{\theta }}^{*}$   1:Set random generators using seed s   2:Initialize M candidate vectors within the specified search bounds   3:Repair integer variables and project graph weights onto the unit simplex   4:Evaluate the initialized candidates using $\mathcal{F}$ and set ${\mathit{\theta }}^{*}$ to the best candidate   5:for $t=2$ to I do   6:   for $m=1$ to M do   7:     if $t\le t_s$ then   8:        Generate ${\mathit{\theta }}^{\prime }$ using the HHO exploration update   9:     else 10:        Generate ${\mathit{\theta }}^{\prime }$ using MRFO chain/cyclone refinement 11:     end if 12:     Clip continuous variables to their search bounds 13:     Round R and $L_g$ to the nearest admissible integers 14:     Project $({\omega }_s,{\omega }_c,{\omega }_a)$ onto the non-negative unit simplex 15:     Train STAG-GuardNet on ${\mathcal{D}}_{\mathrm{tr}}$ using Adam and evaluate $\mathcal{F}\left({\mathit{\theta }}^{\prime }\right)$ on ${\mathcal{D}}_{\mathrm{val}}$ 16:     if $\mathcal{F}\left({\mathit{\theta }}^{\prime }\right)<\mathcal{F}\left({\mathit{\theta }}^{\left(m\right)}\right)$ then 17:        ${\mathit{\theta }}^{\left(m\right)}\leftarrow {\mathit{\theta }}^{\prime }$ 18:     end if 19:     if $\mathcal{F}\left({\mathit{\theta }}^{\left(m\right)}\right)<\mathcal{F}\left({\mathit{\theta }}^{*}\right)$ then 20:        ${\mathit{\theta }}^{*}\leftarrow {\mathit{\theta }}^{\left(m\right)}$ 21:     end if 22:   end for 23:end for 24:return ${\mathit{\theta }}^{*}$