## 4 Fibonacci Tree Optimization Algorithm

Table 5: The comparison between FTO and other optimization algorithms. ### Why Do We Claim FTOS Strategy Is Superior to Other Scheduling Strategies? 1. Some of the latest scheduling strategies, such as LEACH, work under strict assumptions; for example, the network structure is flat, nodes are densely distributed, time is synchronized, and so forth. The FTOS strategy does not require time synchronization (centralized scheduling); each node independently determines the duty cycle; node density is not important; the location and distance information is not needed. 2. The FTOS strategy determines the scheduling parameters as per the occurrence of events from the previous period, which is very scalable. 3. Once the parameters are determined, they remain unchanged in the coming hours; you can easily deploy them. Table 6 enlists the above-mentioned points. ## 6 Experiment

### Experimental Setup

We set up a wireless sensor network comprising three nodes (\(N=3\)), covering a 5 m \(\times\) 5 m lawn area (see Figure 7). Each node owns a single-chip microcomputer with a STM32F103 ZET6 processor and a diffuse reflection photoelectric infrared proximity sensor. The technical parameters of the sensor are presented in Table 7.

We randomly throw objects into the area to simulate the event. The diffuse reflection photoelectric infrared proximity sensor with a sensing radius of \(r=3\)-5 m (\(r_{min}=3,r_{max}=5\)) opens the switch when there is an object to block; the processor then issues a command to pull the buzzer. Since the working voltage of the single-chip microcomputer is fixed to 5 V, the power formula is \(P=UI\), so that the current reflects the size of the power consumption. Consequently, the energy is measured by the reading of the ammeter placed on each microcontroller. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **FTOS** & **Other Scheduling Strategies** \\ \hline \multirow{4}{*}{Assumptions} & Time synchronization & no & yes \\  & Node density & no requirement & high \\  & Transmission radii & tunable & untunable \\  & Node location & movable & immovable \\  & Adaptability & strong & weak \\  & Deployment & easy & difficult \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The differences between FTOS and other scheduling strategies. Figure 7: The experimental scene. Now that we have determined the functional relations between \(\varepsilon_{S}\), \(\varepsilon_{W}\) and \(\delta\), \(\theta\), the explicit form of the objective function \(J\) can be obtained by putting the fitted functions in. #### 6.2.2 Univariate Analysis

Three sets of parameters, (0.175, 0.175), (0.65, 0.65), (0.5, 0.5), were used to test the sensing power dissipation against \(\alpha\) in base sleep duration \(\bar{s}\) and base working duration \(\bar{w}\). The result is shown in Figure 9. When the distance between the event and the sensor, and the base sleep duration and base working duration, are fixed (\(d=3.15\) m, \(\bar{w}=1\) s, \(\bar{s}=1\) s), the working power increases exponentially with \(\alpha\), and the sleeping power dissipation remains unchanged for \(\alpha\). With the increase of step-size parameter \(\delta\) and \(\theta\), both the working power dissipation \(\varepsilon_{\bar{w}}\) and the sleeping power dissipation \(\varepsilon_{\bar{w}}\) decrease. Figure 10 shows the variation of detection accuracy and expected energy depletion with \(\delta\). Figure 11 shows the variation of detection accuracy and expected energy depletion with \(\theta\). It can be seen that the two parts of the objective function \(J\), \(1-\mu\) grow with \(\delta\), while \(\sigma(\mathbb{E}[e]/1000)\) decreases with \(\delta\); the optima can only be obtained by jointly optimizing \(1-\mu\) and \(\sigma(\mathbb{E}[e]/1000)\). \(1-\mu\) and \(\sigma(\mathbb{E}[e]/1000)\) move in the opposite direction against

\(\theta\) and \(\bar{w}\) and \(\bar{s}\) impose opposite effects on \(1-\mu\) and \(\sigma(\mathbb{E}[e]/1000)\).