## 3 Related Work  
A wide variety of meta-heuristic methods have been applied to the placement problem, ranging from the genetic algorithm (GA) [23], evolution algorithm with specialized operators [24], particle  
Figure 3: The sensing area of sensor in terms of square.  
Figure 2: Perception model of sensor node.  
swarm optimization algorithm (PSO) [25], simulated annealing algorithm (SA) [12; 13; 14; 15], virtual force algorithm (VF) [26], and the virtual force oriented particles algorithm [27]. Other algorithms are analyzed in [16] like the artificial bee colony algorithm (ABC), ant colony optimization algorithm (ACO), and PSO for the sensor deployment problem with the target coverage. An efficient sensor placement optimization model using the Gradient Descent method (GD) was developed in [8]. To evaluate its performance, the proposed method was compared with two optimization methods that were already applied to the sensor placement problem, namely SA and the covariance matrix adaptation evolution strategy (CMA-ES). The results show that GD performed significantly better on larger maps, with much less processing time, while the CMA-ES performed slightly better on smaller maps [8]. SA provides very good and stable results close to GD results on larger maps, and close to CMA-ES performance on smaller maps. These algorithms are adequate only for off-line applications where the sensor nodes need no adaptation after deployment. Based on [10], only the authors in [28], have presented a Corona-based deployment approach using optimum sensor nodes to achieve balanced energy consumption, and to maximize the area coverage and the network lifetime.  
As mentioned in [10], each and every approach has its limitations and considers the coverage and connectivity problem to be solved under certain circumstances. Only a few have considered solving the issue of the optimal number of nodes while optimizing coverage and connectivity. Based on [29], estimating the number of nodes can be done basically by dividing firstly the network area into a number of subsets of nodes, called cover sets, as shown in Figure 4. If the cover sets are disjointed, one sensor node can be present in only one cover set. As demonstrated in Figure 3, the diagonal is the diameter of the circular area of the sensor \(=2\ \times\) the radius of coverage. Since this diagonal divides the square into two isosceles triangles, then the sides of the square can be easily calculated using trigonometric functions. Sin \(\theta\)= perpendicular/hypotenuse \(=\mathrm{L}/\mathrm{d}\); where \(\theta=45^{\circ}\). So, the side of the square is \(\mathrm{L}=\mathrm{d}\times\sin 45^{\circ}\). Assuming the area to supervise is a square with sides A and B. Thus, the number of nodes is decided N = \(\frac{\Delta}{\mathrm{L}}\ \times\ \frac{\beta}{\mathrm{L}}\).  
Generally, this method is used to determine the initial number of sensor nodes, and based on the results obtained by the sensor deployment method, we can choose to increase or to decrease the number of nodes to deploy. In Figure 4, the area to supervise was divided into six cover sets, which means that six nodes are needed to cover the area. However, this method is far from providing the optimal coverage, connectivity, and network cost. Node deployment is simply a matter of choosing the best locations for the optimal number of nodes to cover the RoI. In addition, to calculate the node placement, composite factors, which are combinations of environmental factors, should be considered such as the relationship between the sensing range, the communication range, and the node deployment type [30]. Our approach is based on the SA algorithm, because, based on [12; 13; 14; 15], it provides a good and implementable response for network design and better energy efficiency by organizing the sensor nodes.  
Figure 4: Graph scenario of dividing an area into cover sets.