## 3 Materials and Methods
### Working Mechanism of the Method
Additionally, in Figure 7, the movements of UAVs for each algorithm are also shown on the defined map based on the obtained simulation results in various population sizes and iterations. In this figure, the circles show the start state of each UAV, and the star symbols show the destination state of each UAV. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**Pop**} & \multirow{2}{*}{**Iter**} & \multicolumn{3}{c}{**UAV\({}_{1}\)**} & \multicolumn{3}{c}{**UAV\({}_{2}\)**} & \multicolumn{3}{c}{**UAV\({}_{3}\)**} \\  & & & \multicolumn{3}{c}{**(Cost-m)**} & \multicolumn{3}{c}{**(Cost-m)**} & \multicolumn{3}{c}{**(Cost-m)**} & \multicolumn{3}{c}{**(Cost-m)**} & \multicolumn{3}{c}{**Overall Simulation Time**} \\  & & & \multicolumn{1}{c}{_Best_} & _Ave_ & _Worst_ & _Best_ & _Ave_ & _Worst_ & _Best_ & _Ave_ & _Worst_ & **(s)** \\ \hline
**GWO** & 30 & 50 & **2199** & 2645 & 3385 & 2019 & 2328 & 2566 & 2148 & 2611 & 3526 & **8.416** \\ \hline
**I-GWO** & 30 & 50 & **2199** & 2736 & 3290 & 2087 & 2378 & 2579 & **2107** & 2446 & 2723 & 11.747 \\ \hline
**Ex-GWO** & 30 & 50 & 2250 & 2649 & 3205 & **1996** & 2314 & 2655 & 2156 & 2713 & 4195 & 9.910 \\ \hline
**GWO** & 50 & 100 & 2145 & 2573 & 3295 & 1955 & 2234 & 2497 & 2095 & 2526 & 3469 & **15.040** \\ \hline
**I-GWO** & 50 & 100 & 2181 & 2558 & 3119 & 1993 & 2321 & 2520 & **2090** & 2361 & 2662 & 17.654 \\ \hline
**EX-GWO** & 50 & 100 & **2128** & 2621 & 3121 & **1918** & 2238 & 2593 & 2102 & 2638 & 4139 & 16.686 \\ \hline
**GWO** & 100 & 200 & 2070 & 2522 & 3202 & 1870 & 2136 & 2403 & 2026 & 2453 & 3417 & **23.378** \\ \hline
**I-GWO** & 100 & 200 & **2045** & 2537 & 3047 & 1936 & 2223 & 2466 & 2016 & 2261 & 2588 & 26.659 \\ \hline
**EX-GWO** & 100 & 200 & 2088 & 2479 & 2983 & **1858** & 2186 & 2528 & **2007** & 2568 & 4065 & 24.794 \\ \hline \hline \end{tabular}

* The best values are bold.

\end{table} 
Table 2: Simulation results for each path planning algorithm on crowded large-scale map. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Algorithm** & **Success Rate (Percent)** & **Rank** \\ \hline
**GWO** & 5.56 & 3 \\ \hline
**I-GWO** & 38.88 & 2 \\ \hline
**Ex-GWO** & **55.56** & **1** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ranking summary of metaheuristic algorithms in cost parameter. ### Analysis and Evaluation (Taken Times and Complexity)

The execution times of the proposed methods are also taken into consideration. The best execution time analyses for each method are presented in Figure 8 for various population sizes and iterations. The GWO has the best overall-time performance, while Ex-GWO and I-GWO rank second and third, respectively. Indeed, the GWO-based path planning for three UAVs in the parallel periods consumes the minimum time to reach its destination. The reason for this may be due to the fact that it depends on the three first wolves. In the I-GWO, the incorrect position or the wrong movement of the alpha wolf can move the

Figure 7: The movement of UAVs on the generated paths in each method. (**a**) population of 30, 50 iterations; (**b**) population of 50, 100 iterations; (**c**) population of 100, 200 iterations. whole pack away from the target or cause them to catch the prey late. At the Ex-GWO, each pack member has more roles and contributions than the other two methods, which means that this algorithm may need a longer execution time. However, the Ex-GWO may not be the worst in terms of time, as seen with its better performance in crowded environments. The results show that in the crowded map scenarios with many barriers, the I-GWO-based method does not perform well with regard to the overall time and optimum path cost. The fact that the GWO had the best overall time does not mean that the other two methods were bad, because these two methods could be concluded in an acceptable time. In addition, the time complexity analysis of the proposed methods is O(n\({}^{2}\)).