## 4 Fibonacci Tree Optimization Algorithm
Anything that can increase/decrease \(1-\mu/\sigma(\mathbb{E}[e]/1000)\) by increasing \(\bar{s}\) can also be achieved by decreasing \(\bar{w}\). Next, we set up a benchmark strategy: a fixed sleep time strategy, in which \(S_{k}=\bar{s}=W_{k}=\bar{w}=1\) s. The relationship between the number of nodes \(N\), the sensing radius \(r\) and the overall detection accuracy is studied. The results are shown in Figure 12. For both the proposed adaptive scheduling and fixed scheduling strategies, the detection accuracy will improve with the increase of the sensing radius and the number of nodes. However, the detection accuracy improvement of the proposed adaptive scheduling strategy is significantly higher than that of the fixed scheduling strategy. Figure 11: The detection accuracy and energy depletion against \(\theta\). (**a**) \(\bar{w}\) is fixed to 1 s, varying \(\bar{s}\); (**b**) \(\bar{s}\) is fixed to 1 s, varying \(\bar{w}\). #### 6.2.3 Optimization

By constructing a 3-D surface from the scattered data (see Figure 13), we found that \(J(\delta,\theta)\) is a bivariate multi-modal function, which favors the FTO algorithm. Figure 14 shows the optimization process of the FTO algorithm, and the values of the horizontal and vertical axis represent the values of \(\delta\) and \(\theta\), respectively. The darker the color of the contour map, the smaller the value of \(J\). The algorithm stops after 500 iterations, and Figure 15 provides the final comparison of the peak areas. We can see that the peak area in the lower-left corner is the largest, and is where the optimal point is most likely to appear. The central point of the aforementioned area was taken as the ultimate global optimization point with the coordinate pair \((\delta,\theta)=(0.175,0.175)\). Figure 12: Detection accuracy for the proposed adaptive scheduling and fixed scheduling (**a**) against the number of cognitive sensors \(N\) (\(r\) is fixed and \(r=3.15\) m); and (**b**) sensing radius \(r\) (\(N\) is fixed and \(N=100\)). Figure 13: 3-D surface graph for scattered data. Figure 14: The contour plots in iterations. Figure 15: The determination of the ultimate optimum point. As a comparison, we also implemented the particle swarm optimization (PSO) algorithm, genetic algorithm (GA), comprehensive learning PSO (CLPSO) algorithm, differential evolution (DE) algorithm, and the artificial bee colony (ABC) algorithm. Table 10 outlines the parameters, and Table 11 presents their optimization results. The FTO algorithm outperforms others in most iteration rounds. ### Test

Once the parameters of the strategy are determined, they remain unchanged in the coming hours. Figure 15(a) presents the optimal \(J\) for the first four runs, applying ABC, DE, GA, PSO, CLPSO and FTO; Figure 15(b) shows a statistical result from 100 runs. From the perspective of distribution, FTO demonstrates a better optimistic effect than the other algorithms for its lowest center \(J\) value 0.47. \begin{table}
\begin{tabular}{c c} \hline
**Algorithm** & **Parameter** & **Value** \\ \hline Population & 20 \\ Cognitive ratio & 2 \\ Social coefficient & 2 \\ Inertia weight & 0.4–0.9 \\ Population & 100 \\ Point mutation & 0.01 \\ Hoist mutation & 0.4 \\ Parsimony coefficient & 0.01 \\ Learning rate & 0.05–0.5 \\ Population & 20 \\ Cognitive ratio & 2 \\ Social coefficient & 2 \\ Inertia weight & 0.4–0.9 \\ Population & 20 \\ Scaling factor & 0.6 \\ Crossover rate & 0.8 \\ Followers & 50 \\ Scouters & 20 \\ Employed foragers & 1 \\ Nested branch depth & 2 \\ Total branch depth & 6 \\ Search space & [0,1] \\ Max iterations & 1000 \\ Precision & 0.001 \\ \hline \end{tabular}
\end{table} 
Table 10: The algorithm parameters adopted.