# A Novel Hybrid Harris Hawk-Arithmetic Optimization Algorithm for Industrial Wireless Mesh Networks
## 4 Results and Discussion
### Performance Analysis on Benchmark Functions
#### 4.1.2 Convergence Analysis  
The benchmark procedures were evaluated through 300 iterations, with 100 for the loop condition, to determine their convergence properties. Convergence, in this context,  
Figure 6: Benchmark functions search space plots.  
indicates the point at which an algorithm locates the smallest possible fitness value within the specified number of maximum iterations. Figure 7 illustrates the convergence analysis plot for all the benchmark functions in the presence of all the optimization algorithms.  
In the unimodal functions (F1-F4), the conventional HHO had the fastest convergence in reaching the global minima. However, in the remaining functions, the proposed HHAOA relocated the positions faster, reaching the objective function in the first place. In this  
Figure 7: Convergence performance of all the benchmark functions.  
performance, the MFO had the major setback of exploring desired search regions, leading to inadequate performance and securing the last position. In the multimodal functions (F8-F13), using the hawk's population effectively, the proposed HHAOA had a better transition phase from exploration to exploitation while noticing the convergence speed, which has a more significant speed of reaching the global minima with fewer iterations. In addition, the amplitude reduction rate is directly proportional to its convergence speed in the HHAOA performance in these functions. These results, in turn, illustrate the ability of HHAOA to focus more on the desired search locations during the iterations.  
It is important to note that, in F9, many algorithms were unable to reach the desired value because of the existence of multiple minimum values. (see Figure 6). Still, the HHAOA explicitly performed well and had the best and faster convergence near the global minima. SCA and MFO had the least convergence speed in these functions, followed by GWO, WOA, and AOA, respectively. Notably, the conventional HHO had performance comparable to that of the proposed HHAOA but could not outperform it because of the premature convergence towards reaching the objective function. In the fixed-dimension multimodal functions (F14-F21), the proposed HHAOA continued the first position by effectively finding the best minimum value. In these functions, AOA has the slowest convergence rate. Surprisingly, the HHO had the least performance and lost the ability to relocate the position to find the desired search regions within the desired number of iterations.  
As the number of dimensions increases, the quality of outcomes and the efficiency of alternative approaches deteriorate noticeably. This indicates that HHO can effectively uphold a favorable equilibrium between exploration and exploitation behaviors in scenarios involving multiple variables. The performances in the hybrid functions (F22-F30) have a similar results trend. Notably, in F24, MFO has the best convergence performance, followed by the HHAOA. The proposed HHAOA performs best in non-zero global minima functions by converging nearer to the global minima with fewer iterations, even at less than 50 iterations in most of the functions. Lastly, the proposed HHAOA can deliver exceptional outcomes across all dimensions and consistently outperforms other methods when dealing with problems involving many variables.