## 4 Proposed Snake Optimizer
### Pseudocode and Operational Flow
The top SU band allocations represent instances in which users were present across a range of bands, and thus indicates the optimizer's (more evenly) distributing a finite number of users over available spectrum. The mean final fitness value slightly increased to 19.30 as the iteration count went up to 50 but so did standard deviation (0.67). Their mean conversion time falls to 9.70 iterations and makes the optimization process faster, and the rate of spectrum utilization efficiency rises to 96.50%, while occupied collision probability is equal to 0.06 and the rate spectral capacity reaches about 19.30 \(\mathrm{bps}/\mathrm{Hz}\). SU band allocations with the best performance would be those that more non-overlapping allocation can offer, and by doing so over many available bands these users were better off distributed over separate SU bands than to all that share a single new secondary-user-assigned shared-licensed channel. For 100 iterations, as shown in Table 3, the mean of the final fitness value continued to increase to a mean \(\pm\) sd of 19.80 \(\pm\) 0.42 points of a fitness score at an equilibrium status. The optimizer needed 18.20 iterations to converge on average, meaning it was a more exhaustive search. The spectrum utilization efficiency was 99.00%, the collision rate in this case was 0.02, and the spectral capacitance equaled its theoretical limit, with a value of 19.80 \(\mathrm{bps}/\mathrm{Hz}\). In other words, optimal SU allocation is the allocation pattern that will maximally separate users to avoid as much overlapping as possible, hence obtaining potentially large degrees of different capacity bands. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Metric** & **Scenario 1** & **Scenario 2** & **Scenario 3** & **Scenario 4 (30 Bands)** \\ \hline Iterations & 30/50/100 & 30/50/100 & 30/50/100 & 30/50/100 \\ Mean Final Fitness & 14.40/14.30/14.50 & 11.60/11.70/11.80 & 19.20/19.30/19.80 & 10.80/11.20/11.60 \\ Std Dev of Final Fitness & 0.52/0.48/0.53 & 0.52/0.48/0.42 & 0.63/0.67/0.42 & 0.71/0.60/0.48 \\ Mean Convergence Time (iterations) & 8.00/58.0/12.80 & 7.00/11.60/11.70 & 11.61/0.79/10.82 & 12.0/14.00/15.50 \\ Spectrum Utilization Efficiency (\%) & 96.00/95.33/96.67 & 96.67/97.50/98.33 & 96.00/96.56/99.00 & 94.00/95.50/97.00 \\ Collision Rate & 0.06/0.07/0.05 & 0.05/0.04/0.03 & 0.07/0.06/0.02 & 0.08/0.06/0.04 \\ Spectral Capacity (\(\mathrm{bps}/\mathrm{Hz}\)) & 14.40/14.30/14.50 & 11.60/11.70/11.80 & 19.20/19.30/19.80 & 10.80/11.20/11.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of results across scenarios. At 100 iterations, the mean final fitness value further increased to 19.80, with a standard deviation of 0.42. The optimizer took longer to converge, with a mean convergence time of 18.20 iterations, suggesting a more exhaustive search. The spectrum utilization efficiency reached 99.00%, with a very low collision rate of 0.02 and a spectral capacity of 19.80 bps/Hz. The best SU band allocations reflected a highly efficient distribution of users across the bands, with minimal overlap and high spectral capacity. Across all scenarios, SO demonstrated consistent performance improvements with increasing iteration counts, achieving higher fitness values, better spectrum utilization efficiency, and lower collision rates. The results highlight the optimizer's capability to adapt to different scenarios, effectively balancing exploration and exploitation to achieve optimal band allocations. It is worth noting that the standard deviation of the final fitness values consistently decreases as the number of iterations increases to 100 across all scenarios. This trend suggests that SO becomes more stable and less sensitive to initial random conditions with extended iterations. As the optimization progresses, the algorithm increasingly converges toward similar high-quality solutions across different runs, leading to reduced variability. This behavior is a typical indication of improved convergence reliability and robustness in meta-heuristic optimization.