## 4 Proposed Snake Optimizer
### Pseudocode and Operational Flow
### Statistical Significance Analysis Across Iterations and Scenarios

To validate the significance of performance differences observed across different iteration settings (30, 50, 100) and scenarios (1-4), we conducted a one-way ANOVA followed by [PERSON]'s Honest Significant Difference (HSD) post hoc tests on the final fitness values [33]. This statistical analysis was performed on SO results to assess whether the observed improvements are statistically meaningful. Table 5 summarizes the pairwise comparison results, showing the _p_-values and whether the differences are statistically significant at the 0.05 level. The analysis confirms that, in most cases, differences in performance across iterations and scenarios are statistically significant. In particular, longer iteration counts (e.g., 100) lead to significantly better optimization performance in complex scenarios such as Scenario 4. This statistical evidence supports the robustness and scalability of the SO in increasingly complex environments. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Metric** & **SO (Proposed)** & **PSO** & **GA** & **ABC** & **Q-Learning** \\ \hline Mean Final Fitness & **11.20** & 10.50 & 10.10 & 10.40 & 9.80 \\ Convergence Iterations & **14.00** & 18.30 & 21.70 & 19.40 & 25.80 \\ Spectrum Utilization Efficiency (\%) & **95.50** & 93.20 & 92.70 & 93.00 & 91.50 \\ Collision Rate & **0.06** & 0.08 & 0.09 & 0.08 & 0.12 \\ Spectral Capacity (bps/Hz) & **11.20** & 10.50 & 10.10 & 10.40 & 9.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of optimization algorithms in Scenario 4 (30 Bands). \begin{table}
\begin{tabular}{l c c} \hline \hline
**Comparison** & _p_**-Value** & **Significant (_p_ \textless{} 0.05)** \\ \hline Scenario 1: 30 vs. 100 iterations & 0.031 & Yes \\ Scenario 2: 30 vs. 50 iterations & 0.087 & No \\ Scenario 3: 50 vs. 100 iterations & 0.044 & Yes \\ Scenario 4: 30 vs. 100 iterations & 0.028 & Yes \\ Scenario 1 vs. Scenario 4 (100 iterations) & 0.015 & Yes \\ Scenario 2 vs. Scenario 3 (50 iterations) & 0.059 & No \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ANOVA and Tukey HSD test results on final fitness. ### Integration and Computational Complexity

The SO is integrated into an RL framework as a deterministic policy agent that interacts with the cognitive radio environment. At each iteration, SO receives the current state (e.g., channel occupancy, PU/SU activity), selects an action (channel allocation), and updates its population based on a reward signal combining spectrum efficiency, collision rate, and capacity. This forms a closed-loop learning process without relying on value functions or neural networks. The computational complexity per iteration of the proposed method is approximately \(\mathcal{O}(N\cdot D)\), where \(N\) is the population size and \(D\) is the number of decision variables (e.g., total SUs \(\times\) channels). This results from evaluating and updating each individual in the population. In contrast, deep reinforcement learning methods such as DQN or A3C involve training deep neural networks, which introduces additional computational burdens, including forward and backward passes through multiple layers, gradient computations, and memory-intensive experience replay buffers. These models often require hardware acceleration (e.g., GPUs) and longer training times, especially for high-dimensional or continuous action/state spaces. Given these differences, the SO-based RL framework is more computationally efficient and interpretable. It is particularly well-suited for real-time, embedded, or resource-constrained scenarios, such as dynamic spectrum management in CRNs, where fast decision-making and low power consumption are critical. The meta-heuristic nature of SO also allows it to handle discrete action spaces without the need for complex architectural tuning or convergence guarantees associated with deep learning models.