# Optimizing Rule Weights to Improve FRBS Clustering in Wireless Sensor Networks
## 3 Results  
In order to check whether the optimization process presented in Section 2.5 was adequate for improving the performance of the proposed clustering method for the three types of scenarios described in Section 2.4, this section will detail the results for our approach CFC3 PSO in comparison with three other well-known clustering methods and a recent one: (i) Low-Energy Adaptive Clustering Hierarchy (LEACH) [12], (ii) Cluster Head Election mechanism using Fuzzy logic (CHEF) [20], (iii) Clustering Routing protocol for WSN based on type-2 fuzzy logic and ant colony optimization (CRT2 FLACO) [45], and (iv) Intelligent Clustering Under Uncertainty (ICUU) [33], which is the newest method. Although LEACH is an old distributed method, it is still used as a pattern for comparisons because it represents a simple mechanism for clustering that only employs stochastic methods to form the cluster. Thus, in LEACH, each node can independently become a CH based on an initial probability and the number of rounds. In CHEF, the authors used a fuzzy system to select the CHs. This fuzzy system has two input variables: the residual energy of each node, and the addition of the distance to every node that is within a predefined range. The third algorithm, CRT2 FLACO, uses a centralized Type-2 fuzzy controller with three input variables: the residual energy of each node, the distance between the node and the BS, and the number of neighbors of a node. In addition, it employs ant colony optimization (ACO) to decrease the transmission energy from the CH to the BS. The last method in the comparison was ICUU, which proposes an intelligent clustering mechanism using the silhouette index (SI) score, which is later used as a benchmark for optimized clustering conducted with the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The results were obtained by simulating the five methods (CFC3 PSO, LEACH, CHEF, CRT2 FLACO, and ICUU) for thirty WSNs generated for each scenario detailed in Section 2.4 that we call a \(map\). A \(map\) contains the records of the locations of the 100 randomly deployed nodes, the position of the BS, and the value of the parameters of the energy model (Section 2.3. We then ran each method for the 30 different maps to obtain the FND, HND, and LND metrics, and finally obtained the mean of each of these metrics for the scenario under test. The simulations were performed in Matlab. The results for each scenario can be seen in Table 4 for scenario 1, where BS was located in a corner of the deployment area; Table 5, with the BS placed outside the area at coordinates (150, 50); and Table 6, with the BS in the center of the area. As can be seen in Table 4, the proposed method CFC3 PSO achieved better results than any of the compared methods for all metrics. Due to the optimization of FND, this metric for CFC3 PSO was much better than the others, which suggests that the WSN could operate with all its nodes for longer than any of the other presented approaches. In addition, there was an increment in the value for HND, which was even higher than the LND of two other methods and very similar to the LND of CRT2 FLACO and ICUU. Thus, these results show that the optimization performed clearly outperformed the other methods. Finally, the value obtained by CFC3 PSO for LND was higher than any other approach. However, it was close to the HND, which means that the nodes had a very low energy after maximizing the HND and consequently they could not live much longer. In Table 5, we can again see that CFC3 PSO outperformed all the other methods compared, with a better value for FND, which was even higher than the LND values of the other approaches. In this case, the values obtained by CFC3 PSO for HND and LND were slightly lower than those in scenario 1, due to the distance to the BS, which was located outside the deployment area of the nodes. For this last scenario (Table 6), the improvement in the metrics caused by CFC3 PSO was clearly significant.