Algorithm 1 Dual-Strategy Enhanced Cuckoo Catfish Optimizer (DCCO)

Require: Objective f, bounds, N, D, budget $B\ge N$, initializer and original CCO settings

Ensure: Best evaluated point ${\mathbf{x}}_{\mathrm{best}}$

1:Set $n_{\mathrm{FE}}\leftarrow 0$; construct the clustering sample and centers   2:Generate $N_c\approx N/2$ Cauchy proposals and $N-N_c$ uniform proposals   3:for each initial candidate do   4:      Repair and evaluate it, checking the budget before every objective call   5:      Update $n_{\mathrm{FE}}$ and the best-so-far record   6:end for   7:Initialize the retained CCO state and cached objective values   8:while $n_{\mathrm{FE}}<B$ do   9:      Complete one CCO population sweep with a budget guard before every evaluation 10:      if the budget is exhausted then 11:            return ${\mathbf{x}}_{\mathrm{best}}$ 12:      end if 13:      Execute HCS once on the population 14:      if HCS reports budget exhaustion then 15:            return ${\mathbf{x}}_{\mathrm{best}}$ 16:      end if 17:      Attempt VCS once on the post-HCS population 18:      if VCS reports budget exhaustion then 19:            return ${\mathbf{x}}_{\mathrm{best}}$ 20:      end if 21:      Commit accepted vectors and cached values; refresh the retained CCO state 22:end while 23:return ${\mathbf{x}}_{\mathrm{best}}$

The budget includes any evaluated clustering samples and all rejected proposals. An exhaustion flag ends the complete execution immediately.