###### Abstract
Given that wireless sensor networks integrate knowledge from multiple disciplines, including wireless communication technology, computing, and sensor technology [25; 26; 27; 28], they have become a unique mode for data acquisition and information processing. In the actual deployment and application of wireless sensor networks, two core issues urgently need to be addressed. First, we need to delve into the hardware and physical components of sensor nodes, which involve innovations in sensor technology, the development of low-power chips, and the optimization of wireless communication technologies. Second, we must focus on the network layer, requiring innovations in communication protocols and optimization of algorithm design, covering key technologies such as routing selection, topology control, and deployment reconfiguration [29; 30; 31; 32]. Node deployment is a critical research direction in the field of wireless sensor networks, primarily focusing on how to effectively position sensor nodes to accomplish specific monitoring, control, or communication tasks. Efficient node deployment is essential for optimizing network performance, enhancing energy efficiency, and ensuring reliable data reception and transmission in wireless sensor networks. There has been much research work addressing the problem in different scenarios [33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47]. In paper [33], the authors statistically analyzed the convergence and deployment effect of the virtual spring force algorithm and present an optimized strategy where sensor deployment begins from the center of the target region by adding an external central force to derive the question of whether the algorithm can still cause holes or twisted structures in a small region of the final network distribution. In reference [34], the authors propose an algorithm to optimize sensor coverage using particle swarm optimization (PSO) and Voronoi diagrams. PSO is used to find the optimal deployment of the sensors that gives the best coverage while the Voronoi diagram is used to evaluate the fitness of the solution. In article [35], six metaheuristics algorithms are mentioned to show the superiority of each algorithm based on the value of optimized energy, and the simulation outcomes confirm that the whale optimization algorithm (WOA) gives optimized energy with improved network coverage with the lowest number of nodes. The paper [36] presents a hybrid metaheuristic algorithm-based clustering with multi-hop routing (HMA-CMHR) protocol for wireless sensor networks. The presented model incorporates different phases such as node initialization, clustering, routing, and energy-efficient data transmission sensors. In reference [37], the researchers recommend the creation of each sensor's specs and radius of influence based on a particular geographical location, which will contribute to better network planning and design. By using the ARIMA model for time series forecasting and the Al-Biruni Earth Radius algorithm for optimization, the approach bridges the gap between successive terrains while seeking the equilibrium between exploration and exploitation. In paper [38], a procedure is proposed to develop a proper circuit model for the injection clamp, and the obtained circuit is introduced into the global one representing the overall cable to address the coverage optimization problem in heterogeneous sensor networks but does not take into account the issue of connectivity between nodes. In reference [39], the conflicting objectives of coverage and network lifetime in wireless sensor networks are addressed, and two improved hybrid multi-objective evolutionary algorithms are proposed. However, this study overlooked the total cost of sensor nodes and their connectivity. In [40], based on the probabilistic sensing model and the dependency relationship between sensor nodes and target nodes, a solution was proposed to address the deviation error that occurs when a sensor node simultaneously covers multiple target nodes.