# Adaptive Path Planning for UAV-Based Pollution Sampling
## 4 Experiments and Results
### Results of Analysis of the Selected Optimization Methods
Please note that, unlike Figure 3, the colored lines represent different runs of the same algorithm rather than different algorithms. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Algorithm** & **CT [s]** & **CFEs** & **COST** & **SMOO** & **LEN [m]** & **NPTS** & **EE [kWh]** & **NCOL** \\ \hline I-GWO & 189.205 & 9300 & 7036.044 & 0.754 & 124,789 & 1251 & 1.064 & 0 \\ ACO\({}_{\mathbb{R}}\) & 109.428 & 25,850 & 648.173 & 0.817 & 93,424 & 938 & 0.600 & 0 \\ PSO & 124.214 & 16,800 & 3822.815 & 0.717 & 237,134 & 2373 & 4.258 & 0 \\ GA & 258.184 & 31,500 & 2607.089 & 0.726 & 195,170 & 1955 & 2.997 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Detailed metrics for the 1 st test case and 1 st run. Figure 3: Paths optimized in a single run by different algorithms (first case). The conclusions drawn from the first run (Table 4) generally apply to subsequent runs of the algorithms as well. Paths produced by \(\text{ACO}_{\mathbb{R}}\) consistently exhibit exceptional quality across metrics like LEN, NPTS, SMOO, and EEE. \(\text{ACO}_{\mathbb{R}}\) is outperformed by I-GWO and PSO only in terms of CFEs. However, it maintains the shortest CT, as previously discussed. Furthermore, the algorithm yields the most consistent results, showing the lowest standard deviation across several metrics, including COST, NPTS, LEN, and EEE. I-GWO achieves the lowest CFEs, but it produces paths with the highest COST and takes the longest CT to compute them. PSO and the GA produce similar results, while PSO is more efficient (lower CT and CFEs) and the GA demonstrates greater reliability (lower standard deviations across most metrics). The 1 st test case is thoroughly explained as a representative example. Analogous experiments were performed for the other test cases in order to evaluate the algorithms' performance. The summarized results can be found in Table 5.  
Interestingly, when examining the medians across all test cases, \(\text{ACO}_{\mathbb{R}}\) continues to lead. Despite its strong performance, \(\text{ACO}_{\mathbb{R}}\) exhibits the highest variability, with the largest standard deviations observed in CT, COST, CFEs, and SMOO. Nevertheless, 75% of the generated paths remain effective and consistent. In terms of repeatability, the GA excels, recording the lowest standard deviation in 4 out of 8 metrics, most notably COST and CFEs. However, its performance fallers in other areas, ranking second-to-last in CT, LEN, and EEE, with only I-GWO performing worse in these categories. Figure 4: Variability of the optimized paths in multiple runs (1 st case). Selecting the optimal algorithm from the metrics provided in Table 5 requires addressing a multi-criteria optimization problem. To tackle this, a point-based optimization method was applied. The median values from Table 5 were evaluated by assigning weighted scores based on their relevance to GPP. The metric with the lowest importance was assigned a weight of 1, followed by progressively higher weights for increasingly significant metrics. The NCOL metric was omitted from the evaluation as no collisions were observed during the experiment. Additionally, EEE showed a strong correlation with both LEN and NPTS (0.990 for each). Consequently, LEN and NPTS were excluded from the optimization process. Since NPTS is calculated by sampling the Dubins path at a constant step size, its correlation with LEN is 1, making these two metrics effectively identical in the information they provide. However, they were retained in the comparison tables to improve clarity and to emphasize both the actual path length and its associated complexity. COST is the primary metric due to its strong relationship with several critical mission parameters. Following this, EEE and SMOO were prioritized. EEE reflects the impact of minor altitude changes, while SMOO captures the complexity of horizontal maneuvers. After these, computational performance metrics--CT and CFEs--were evaluated.