## 3 Materials and Methods
### Working Mechanism of the Method
### Simulation Setting

In the simulation, large-scale, agricultural land was considered. The size of the environment was 1000 m \(*\) 1000 m \(*\) 1000 m. In addition, 150 obstacles were also placed in this area. Three UAVs with different start and endpoints were considered in each simulation of the used methods. The map boundaries, UAVs, and obstacle positions were assumed based on Figure 3. Each used algorithm was run 15 times. Furthermore, simulation parameters are presented in Table 1. The best, worst, and average costs (distance traveled in meters), execution times and complexity, and finally, convergence curve analysis for each UAV in each algorithm was applied by different population sizes and iteration numbers. ### Analysis and Evaluation (Cost of Paths)

In this section, the proposed path planning methods are analyzed based on the cost function, introduced in Equation (3). The results obtained are presented in Table 2. The starting and ending points of UAVs are assumed to be different from each other. In this table, the costs for these autonomous robots were obtained from a set of various populations and iterations. This process was evaluated for all algorithms used. According to the results obtained, the Ex-GWO-based method achieved the best result compared to other used path planning methods. The Ex-GWO-based method gave the best solution in five of the assumed nine scenarios and ranked first among the three methods with a 55.56% success rate. In the ranking, the I-GWO-based method was second with 38.88% and the GWO-based method was third with 5.56%. These results are presented in Table 3. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Population size & 30, 50, 100 \\ \hline Maximum iteration & 50, 100, 200 \\ \hline Farmland Square & 1000 m \(*\) 1000 m \(*\) 1000 m \\ \hline r\({}_{1}\), r\({}_{2}\) & Rand [0,1] \\ \hline a & linearly decreased from 2 to 0 over \\ \hline A & [\(-\)2a, 2a] \\ \hline C & Rand [0, 2] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The simulation parameters. Based on the obtained results, it is determined that the Ex-GWO-based method exhibits good performance in large-scale and complex farmland with a high number of obstacles. This is because the Ex-GWO-based method finds the best solution according to the alpha, beta, delta wolves, and whole pack. The wolves use the whole pack's location knowledge to update their positions, so for experiments with larger population sizes and more iterations, the Ex-GWO-based method has a better chance of reaching the best solution. Therefore, the wolves in the pack minimize the escape paths of the hunt (prey), and hence, the prey can be caught faster. The fact that this mechanism can be better than other methods can be seen more clearly in large and crowded environments. On the other hand, another method proposed in this study, the I-GWO-based path planning method, outperforms good results in smaller and less populated environments. The basic update process in this method is very dependent on the alpha setup. Therefore, the speed of growth and the selection of the right places for the first wolf is of great importance. In this method, there is the possibility of finding problem solutions (prey) much faster in fewer iterations. For this reason, our proposed methods may be the most appropriate choices in various real-life application areas of mobile autonomous systems such as the use of UAVs for different and varied purposes and environments. In general, the GWO-based method has good performance in medium, small-sized, and not too crowded environments. In fact, the usage capacity of it may be between our two methods, but its success rate is not considered good according to the results. Briefly, the Ex-GWO-based path planning method may be performed more successfully in larger and crowded environments with larger populations and more iterations, and the I-GWO-based path planning method may give good results in medium and smaller, less populated environments.