## 4 Proposed Snake Optimizer
### Pseudocode and Operational Flow
Figure 5 presents a histogram of the final fitness values obtained after 30 iterations. The histogram reveals a distribution where most runs resulted in a fitness value close to 14.4, with a few outliers reaching up to 15.4. This suggests that while the optimizer generally converges to similar solutions, there is some variability in the outcomes. Figure 6 shows the performance metrics across different runs in the first scenario with 30 iterations. The spectrum utilization efficiency is consistently high across all runs, close to 100%. The collision rate remains low, indicating effective avoidance of interference among secondary users. Spectral capacity fluctuates slightly across runs but generally stays within a similar range, demonstrating the optimizer's ability to maintain efficient use of available channels. Figure 7 displays the mean best fitness value over 50 iterations. The fitness value increases more gradually compared to the 30-iteration case, eventually stabilizing at around 14.3, similar to the previous result. This suggests that additional iterations do not significantly improve the solution's quality beyond a certain point. Figure 4: Mean best fitness value of SO for Scenario 1 with 30 iterations. Figure 8's histogram of final fitness values for 50 iterations shows a similar distribution to Figure 5, with most values clustering around 14.4 and a few reaching higher fitness levels. This consistency across different iteration counts indicates the robustness of the SO. In Figure 9, the performance metrics for 50 iterations are plotted. The results are consistent with those observed in Figure 6, with high spectrum utilization efficiency, low collision rates, and stable spectral capacity across all runs. This further supports the optimizer's effectiveness across different settings. Figure 5: Histogram of final fitness values for SO in Scenario 1 after 30 iterations. Figure 6: Spectrum utilization efficiency, collision rate, and spectral capacity across 10 runs for Scenario 1 with 30 iterations. Figure 10 depicts the mean best fitness value over 100 iterations. The fitness value again follows a steep rise in the early iterations, leveling off around the 30 th iteration and stabilizing at approximately 14.5. The slight increase in the final fitness value compared to the shorter iteration counts suggests that more iterations can lead to marginal improvements. Figure 11 shows the histogram of final fitness values after 100 iterations. The distribution is narrower compared to the previous histograms, with most runs resulting in a fitness value of around 14.4 to 14.6. This indicates a higher degree of convergence consistency when more iterations are allowed. Figure 8: Histogram of final fitness values for SO in Scenario 1 after 50 iterations. Figure 7: Mean best fitness value of SO for Scenario 1 with 50 iterations. Finally, Figure 12 presents the performance metrics for 100 iterations. The spectrum utilization efficiency remains high, the collision rate is low, and the spectral capacity is consistent across all runs. These results confirm the stability and reliability of SO in maintaining optimal performance even as the number of iterations increases. Figure 10: Mean best fitness value of SO for Scenario 1 with 100 iterations. Figure 9: Spectrum utilization efficiency, collision rate, and spectral capacity across 10 runs for Scenario 1 with 50 iterations. ### Experiment Result for Second Scenario

Figure 13 depicts the progression of the best fitness value (mean) for Scenario 2 across 30 iterations. The fitness value starts at approximately 10.6 and gradually increases, showing consistent improvement as the iterations proceed. The optimizer shows significant jumps in fitness around the 10 th and 15 th iterations, finally stabilizing at a peak fitness value of around 11.6, indicating the convergence of SO towards an optimal solution within this iteration count. Figure 11: Histogram of final fitness values for SO in Scenario 1 after 100 iterations.