# A Bee Colony-Based Optimized Searching Mechanism in the Internet of Things
## 4 Results and Discussion
### Evaluation of Performance in Terms of finestLimit Parameter  
In this section, experiments are conducted with respect to the finestLimit parameter. In order to analyze the efficiency of the proposed E-ABC, numerous benchmark functions and their base functions are utilized in the experiments. The functions \(f1,\ f2\) are unimodal, while other functions, such as \(f3,\ f4,\ f5,\ f6\) and \(f7\), are multimodal functions. Furthermore, the colony size is taken as 20, and the maximum fitness values are taken as 500 and 1500 for 10 dimensions and 30 dimensions, respectively. The limit value is calculated as (colony size x dimensions)/2, and 20 independent runs are conducted with various seeds, as in [8].  
Convergence refers to a mathematical concept that can be defined as a series of components that ultimately reaches a single value, known as a limit. Convergence itself is not an algorithm; rather, it is a value that an algorithm manipulates or iterates on. The phrase \"fast convergence speed\" is used in this study; the term \"fast\" specifies the algorithm's convergence rate, and it demonstrates how quickly the ABC converges towards excellent-quality solutions. The value of the limit is calculated as \(Limit=\frac{CS\times D}{2}\), where CS denotes the colony size and D denotes the dimension [18].  
The convergence speed for the proposed E-ABC is examined on Rotated Bent Cigar function \(f1\), as shown in Figure 3a. It shows the dominance of the E-ABC in contrast to four well-known algorithms, namely the original ABC, quick ABC, global ABC and improved qABC algorithms. The graphical results present the mean objective value versus fitness evaluations. Considering an example where the fitness evaluation value is noted as 500,the mean value against 500 is observed as \(8\times 10^{3}\) for the standard ABC, \(7.5\times 10^{3}\) for the GABC, \(5\times 10^{3}\) for the qABC, \(5\times 10^{3}\) for the qABC, \(3\times 10^{3}\) for the iqABC and \(2.5\times 10^{3}\) for the E-ABC. The results reveal that the proposed E-ABC achieves a 45.83% better convergence rate as compared to the ABC. It provides 41.67%, 20.83% and 4.17% better results than the GABC, the qABC and the iqABC, respectively. Figure 3b elucidates the convergence speed with respect to Shifted and Rotated Schwefel function \(f4\). The results show that the E-ABC achieves the optimal solution, in contrast to the other base schemes. The convergence graph for Shifted and Rotated HappyCat function \(f6\) is shown in Figure 3c. The results show that when the mean objective function value is 1000, the proposed E-ABC reaches the optimal value, while the other schemes require more time to approach the optimal value. Figure 3d presents Shifted and Rotated HGBat function \(f7\) regarding the convergence rate. From the graph, it is clear that the E-ABC reaches the mean objective value of \(6\times 10^{2}\) when the value of the fitness evaluation is five hundred, while the iqABC achieves the same goal when the fitness evaluation value is 1000. The other base schemes require even more time to approach the optimal solution.