## 3 The Proposed Sensor Deployment Algorithms
### The Particle Swarm/Genetic Hybrid Algorithm
\begin{array}{l}O(N)=O(K)+O(M)\\ \qquad\qquad=N_{1}\times M_{2}\times N_{2}\times m+M_{1}\times M_{2}\times N_{ 2}\times m\\ \qquad\approx M_{1}\times N_{1}\times M_{2}\times N_{2}\times m\end{array}  \tag{16}\]

## 4 Simulation Results and Discussion

In this section, we further provide numerical results to validate our theoretical analysis. Without loss of generality, the simulation parameters were set as follows in MATLAB for WIN10. The computer configuration was as follows: the processor (CPU) was an Intel(R) Core(TM) i7-10750H CPU @ 2.60 GHz; the clock speed was 2.59 GHz; the memory (RAM) was 1024 GB with an NVIDIA GeForce GTX 1650 Ti. The monitoring area was set to \(200\times 200\), with 400 potential deployment positions, defined as follows: First, several points within the monitoring area are selected as potential deployment positions, arranged in a regular pattern. Specifically, each 10 \(\times\) 10 grid has a center point as a potential deployment location. Obstacles are also present within the area, where sensors cannot be deployed, and this information is known beforehand. Overall, the potential deployment locations are non-uniformly distributed, with deployment costs for each position \(d_{i}\) being

Figure 3: The flowchart of the PSGH algorithm. randomly set as an integer between 1 and 5. For the distribution of monitoring targets, we design two scenarios: the first has a uniform distribution, while the second has a concentration of targets in specific regions, as illustrated in Figure 4. Due to differing levels of importance, each monitoring target has a unique minimum coverage requirement, denoted by a minimum coverage rate \(k_{j}\), which is randomly set to values of 50 %, 60%, 80%, or 90%. The connectivity parameter \(c\) is set to three, meaning that each sensor node deployed within the monitoring area must be connected to at least three other sensor nodes. The perception model for the sensors is a probabilistic sensing model, and there are three types of sensors with specific parameters as shown in Table 1. The parameters \(\lambda\) and \(\beta\) in the sensing probability calculation formula are set to be 1. In order to compare the performance between different algorithms, this study also adopted a fish swarm/grey wolf hybrid (FSWH) algorithm to comprehensively evaluate the overall performance of the PSGH algorithm in sensor deployment. ### Comparison of Comprehensive Optimization Metrics Under Different Coverage Requirements

This section primarily studies the comprehensive optimization indicators under different minimum coverage rate requirements. In the simulation setup, we set the perception probabilities to 50%, 60%, and 70%; the minimum connectivity to 2; and the weight of the sub-functions to \(\alpha_{1}=0.25,\ \alpha_{2}=0.25,\ \alpha_{3}=0.25,\ \alpha_{4}=0.25\). Independent 100-simulation experiments were conducted under these three different coverage rate requirements, comparing the comprehensive optimization objective function \(F\) and the program runtime under two different scenarios. The results are shown in Figures 5 and 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Types** & **Sensor Cost per Unit** & **Sensor Coverage Range** \\ \hline A & 3 & \(R_{s}=15,R_{se}=5,R_{e}=30\) \\ \hline B & 8 & \(R_{s}=30,R_{se}=10,R_{e}=60\) \\ \hline C & 17 & \(R_{s}=45,R_{se}=15,R_{e}=90\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cost and Performance of Different Types of Sensors. Figure 4: Schematic diagram of obstacle deployment in two types of scenarios. First, we compare the optimization effect on the overall objective function \(F\). In scenario 1, where the monitored targets are uniformly distributed, both algorithms show that the objective function \(F\) increases as the required perception probability rises. This is because when the perception probability requirement increases, it leads to an increase in the number of deployed sensors or the use of higher-performance, more expensive sensors for deployment.