## 3 The Proposed Sensor Deployment Algorithms
### The Particle Swarm/Genetic Hybrid Algorithm
This may be due to a larger number of monitored targets in scenario 2, which requires more iterations to assess perception probability and connectivity, leading to more computation time. Finally, when comparing the PSGH and FSWH algorithms, we find that, when the minimum perception probability requirements are met and the weights of various indicators are the same, the PSGH algorithm outperforms the FSWH algorithm in terms of both the optimization effect on the overall objective function \(F\) and the corresponding program runtime, whether in scenario 1 or scenario 2, or when satisfying different minimum perception probability requirements. ### Comparison of Comprehensive Optimization Metrics Under Different Weights

This section mainly studies the comprehensive optimization metrics under different weights for the four objective functions. The minimum perception probability is set to 50%, and the minimum connectivity is set to 2, with different objective function weights \(\phi_{1}\), \(\phi_{2}\), \(\phi_{3}\) being applied, where \(\phi_{1}=\{\alpha_{1}=0.25,\ \alpha_{2}=0.25,\ \alpha_{3}=0.25,\ \alpha_{4}=0.25\}\), \(\phi_{2}=\{\alpha_{1}=0.1,\ \alpha_{2}=0.2,\ \alpha_{3}=0.3,\ \alpha_{4}=0.4\}\), \(\phi_{3}=\{\alpha_{1}=0.4,\ \alpha_{2}=0.3,\ \alpha_{3}=0.2,\ \alpha_{4}=0.1\}\). Independent simulations of 100 experiments are conducted under these three different weight distribution requirements. The results are compared for the comprehensive optimization objective function \(F\) and the program's runtime under two different scenarios. The results are shown in Figures 9 and 10. From the above figures, we can conclude that after the minimum coverage and minimum connectivity requirements are determined, adjusting the weights of the sub-functions in the comprehensive optimization function \(F\) reveals that when the set minimum perception probability, minimum connectivity requirements, and the weights of various indicators are the same, whether in scenario 1 or scenario 2, or under different minimum perception probability requirements, the PSGH algorithm still outperforms the FSWH algorithm in terms of optimizing the overall objective function F and the corresponding program runtime. Additionally, it can be observed that the value of the objective function \(F\) at \(\phi_{2}\) is significantly lower than at \(\phi_{1}\) and \(\phi_{3}\), indicating that the deployment cost has a greater impact on the objective function. Figure 8: Average runtime of the two algorithms under different scenarios and varying minimum connectivity requirements. ## 5 Conclusions

In this study, we addressed the critical issue of deployment strategy in wireless sensor networks, particularly within complex and dynamic industrial environments. We adopted a probabilistic sensing model that closely aligns with practical applications, recognizing the varying importance of multiple monitoring metrics. While many existing studies focus solely on optimizing energy consumption, they often overlook the interplay between cost and connectivity. In our approach, we not only normalized deployment cost, energy consumption, connectivity, and sensing probability to eliminate dimensional discrepancies but also assigned different weights to each metric. This comprehensive consideration allows for a more effective optimization strategy. Furthermore, we introduced larger

Figure 10: Average runtime of the two algorithms on the objective function under different scenarios and varying weights of the objective function. Figure 9: Average optimization performance of the two algorithms on the objective function under different scenarios and varying weights of the objective function. obstacles to better accommodate diverse deployment scenarios. Our proposed particle swarm/genetic hybrid algorithm effectively optimizes deployment costs while ensuring connectivity and meeting minimum sensing probability requirements, even in scenarios with uncertain sensor quantities.