Algorithm 1 SMA-WSN Cluster-Head Selection.

Input: alive nodes, residual energy, node positions, BS position, radio range r, weights $\alpha$, $\beta$, $\gamma$, M = 8 iterations. Output: selected cluster heads CH_set and cluster membership. Phase 1—Approach: For each alive node i, compute: $\mathrm{\Phi }$_E(i) = E_res(i)/E0 $\mathrm{\Phi }$_D(i) = 1/(1 + dist(i, BS)/max_dist) $\mathrm{\Phi }$_C(i) = |neighbors(i, r)|/(N_alive − 1) f(i) = $\alpha$·$\mathrm{\Phi }$_E(i) + $\beta$·$\mathrm{\Phi }$_D(i) + $\gamma$·$\mathrm{\Phi }$_C(i) Assign growth weight w(i) ∝ f(i); initialize archive A. Phase 2—Wrap: For M = 8 iterations, for each node i: r ← Uniform(0, 1) if r < p_scout (=0.03): scout perturbation (exploration) else if r < 0.5: oscillatory approach toward best in A else: contraction step Update f(i); update archive A. Phase 3—Selection: Rank nodes by archived fitness; elect the top k* = round(p* · N_alive) nodes as CH_set, with p* = 0.10 for rounds ≤ 300 and p* = 0.15 thereafter. The increase is timed to coincide with the onset of node attrition: at E0 = 0.2 J, fault-free networks typically register their first node death around round 300–330 (Section 6), after which the alive-node count begins to shrink. Raising the CH ratio from 10% to 15% at this point keeps the absolute number of cluster heads, and hence the per-CH relay load, roughly stable as N_alive declines, rather than concentrating an increasing aggregation burden onto a fixed, shrinking set of heads. Each non-CH node joins the CH with the highest f(i) within r. If no CH within r → node transmits directly to BS (orphan rule). Return CH_set and cluster membership.