# Energy-Efficient Internet of Drones Path-Planning Study Using Meta-Heuristic Algorithms
## 4 Result Discussion and Analysis
### Results and Discussion
#### 4.2.5 Straight Line Rate (SLR) Evaluation  
For further investigation of the performance of the mentioned algorithms, we study straight line rate (SLR), which is defined by the length of the generated path over the shortest path. The shortest path is defined as the Euclidean distance from the starting point to the destination, regardless of existing obstacles. The straight line rate can be explained as follows:  
\[SLR=\frac{\sum_{i=1}^{N_{\omega}-1}\sqrt{(x_{i+1}-x_{i})^{2}+(y_{i+1}-y_{i})^{2 }+(z_{i+1}-z_{i})^{2}}}{\sqrt{(x_{N_{\omega}}-x_{1})^{2}+(y_{N_{\omega}}-y_{1} )^{2}+(z_{N_{\omega}}-z_{1})^{2}}}, \tag{22}\]  
where \((x_{1},y_{1},z_{1})\) and \((x_{N_{\omega}},y_{N_{\omega}},z_{N_{\omega}})\) are the coordinates of th starting and ending points of the path, respectively. The lower the value of SLR, the better the performance. We use a design of experiment tool to analyze the SLR, and Minitab software is utilized to run the ANOVA test. SLR shows the indicator of the shortest path length. It is defined as the ratio of the generated path to the shortest path, as explained in Equation (22). To further evaluate and compare the performance of algorithms, complete random design is applied to the generated data. The aim is to show if these algorithms are significantly different at a significance level of 0.05. We test the normality of data using the Anderson-Darling tool, and the results are illustrated in Figure 6. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Drone** & **Algorithm** & **Best** & **Worst** & **Mean** & **STD** \\ \hline \multirow{6}{*}{UAV2} & PSO & **2014.5** & 2591.82 & **2120.04** & 101.653 \\ \cline{2-6}  & IPSO & **2014.5** & **2487.12** & 2172.91 & **72.2923** \\ \cline{2-6}  & CIPSO & 2014.5 & 2529 & 2151.76 & 84.0366 \\ \cline{2-6}  & ABC & 2016.41 & 2977.13 & 2256.55 & 193.813 \\ \cline{2-6}  & GA & 2045.672 & 2455.225 & 2226.042 & 83.33722 \\ \hline \multirow{6}{*}{UAV3} & PSO & 2218.07 & 4356 & 2390.31 & 424.777 \\ \cline{2-6}  & IPSO & **2056.41** & **2642.45** & **2200.61** & **86.7288** \\ \cline{2-6}  & CIPSO & 2104.9 & 3156.52 & 2257.52 & 188.143 \\ \cline{2-6}  & ABC & 2061.43 & 2671.54 & 2309.05 & 135.134 \\ \cline{2-6}  & GA & 2096.605 & 2719.034 & 2428.615 & 169.0806 \\ \hline \multirow{6}{*}{UAV4} & PSO & 2042.52 & 3467.21 & 2117.91 & 256.92 \\ \cline{2-6}  & IPSO & 2011.98 & **2046.18** & 2023.54 & **10.3423** \\ \cline{2-6}  & CIPSO & **1818.57** & 2203.93 & **1845.25** & 72.1855 \\ \cline{2-6}  & ABC & 2030.07 & 2586.42 & 2154.89 & 161.564 \\ \cline{2-6}  & GA & 2071.561 & 3054.177 & 2384.51 & 264.2965 \\ \hline \multirow{6}{*}{UAV5} & PSO & 2050.73 & 2171.21 & 2067.81 & 26.4614 \\ \cline{2-6}  & IPSO & 2040.87 & **2148.3** & **2045.79** & **19.8377** \\ \cline{1-1} \cline{2-6}  & CIPSO & **2014.5** & 2518.53 & 2157.05 & 81.1005 \\ \cline{1-1} \cline{2-6}  & ABC & 2043.28 & 2241.74 & 2133.88 & 93.6581 \\ \cline{1-1} \cline{2-6}  & GA & 2051.807 & 2172.429 & 2094.52 & 38.80558 \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._The \(p\)-value is less than \(0.005<\alpha\), which indicates that the data are not normal. Hence, we apply a non-parametric test, Kruskal-Wallis, with a significance level of 0.05. To make the comparison more significant, we compare the 95% confidence intervals for all algorithms. Results are plotted in Figure 7 for all UAVs. The CIs illustrate that IPSO shows the smallest SLR, which provides the shortest path length. Thus, there is a difference between algorithms on SLR. This can be confirmed by applying the one-way ANOVA test to validate the results for different algorithms. We apply the Kruskal-Wallis test under two hypotheses. The null hypothesis assumes that there is no significant difference among algorithms, while the alternative hypothesis assumes that at least one algorithm differs from the others. The test statistic result has a \(p\)-value of zero for all UAVs, indicating that the null hypothesis is rejected at \(\alpha\) level higher than 0.05 in a favor of the alternative hypothesis.