Algorithm 1: Hybrid UCB-ACO for multi-tier task offloading.

Input: $N$ users, $T$ iterations, $\mathcal{J}$ tiers $\{L,E,F,C\}$, weights $w_k$ Output: Optimal Offloading Mapping ${\mathcal{X}}^{\ast }$ Initialize ${\tau }_{i,j}\left(0\right)={\tau }_{init}$ and $n_{i,j}\left(0\right)=0$ for all $i\in N,j\in J$ For $run=1$ to $num\_runs$ do    For $t=1$ to $T$ do      For each user $i\in \{1\dots N\}$ do        Calculate Exploration Bonus: $B_{i,j}\left(t\right)=\sqrt{{\displaystyle \frac{\ln t}{n_{i,j}\left(t\right)}}}$        Compute UCB Score: $U_{i,j}\left(t\right)={\overline{\mu }}_{i,j}\left(t\right)+c\cdot B_{i,j}\left(t\right)$ (where $c=2.0$)        Select target tier $j^{\ast }$ using decision rule: $j^{*}=\arg \underset{j\in J}{\max }\left({\tau }_{i,j}\left(t\right)\cdot U_{i,j}\left(t\right)\right)$        Execute task offloading and record $Dela{y}_{ij}$ and $Energ{y}_{ij}$      End For      Evaluate Global Fitness: $f\left(t\right)=w_{1}T+w_{2}E+\Psi$ (where $\Psi$ represents the inelastic constraint violation penalty)      Update Pheromones: ${\tau }_j\left(t+1\right)=\left(1-\rho \right){\tau }_j\left(t\right)+\Delta {\tau }_j^{best}$    End For End For Return Global Best Mapping ${\mathcal{X}}^{\ast }$