# A Multilevel Adaptive Path-Planning Model in Off-Road Environments
## 4 Performance Evaluation of Improved ACA  
### Parameter Optimization  
Parameters that had considerable impacts on the performance of ACA included the pheromone heuristic factor (\(\alpha\)), expectation heuristic factor (\(\beta\)), pheromone volatility factor (\(\rho\)), pheromone intensity (\(Q\)), and the number of ants (\(m\)). In our algorithm, the concept of fuzzy grids was introduced, and therefore it was important to select the trafficability heuristic factor (\(\gamma\)). The selection of parameters substantially affects the convergence and quality of solutions. Up to now, parameter setting has lacked a strict theoretical basis, and no universal methods for parameter configuration are available. Thus, the parameters should be configured as per the requirements of tasks. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Level** & **Terrain** & **Characteristics** & **Speed Influence** \\  & & & **Coefficient of Terrain** \\ \hline
1 & Plain & Flatland, with an elevation difference & 1 \\  & & less than 50 m. & \\
2 & Grassland & Relatively flat land, with grass and & \\  & & shrubs as the major surface feature. & 0.8 \\
3 & Hill & Ground surface without distinct & \\  & & borderlines, and the elevation & 0.5 \\  & & difference is between 50 and 200 m. & \\
4 & Gobi Desert & Flat and broad ground surface, & \\  & & covered by gravel. & \\
5 & Mountain & Ground surface with large relief and & \\  & & an elevation difference above 200 m. & \\
6 & Residential area & Area with a certain concentration of & 0.2 \\  & & buildings. & \\
7 & Alpine plateau & Terrain that is a mixture of mountain, & \\  & & plateau, and basin, with an altitude & 0.2 \\  & & higher than 3000 m. & \\
8 & Coastal island & A narrow corridor that connects ocean & \\  & & and land. & \\
9 & Wooded mountain & Mountains with forest as the main & \\  & & ground object. & \\
10 & Watered paddy & Flatland with mild fluctuations and & \\  & & densely distributed water bodies. & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relationship between terrains and speed influence coefficient of terrains. Figure 3: Generalized barrier grid maps (**a-c**). As Figure 4a shows, on the three maps, when \(\alpha\) increased from 0 to 1, the average traveling time dropped considerably; when \(\alpha\) continued to increase, the average traveling time presented a trend of mild growth. As Figure 4b shows, when \(\alpha\) was between 0.1 and 0.5, the algorithm failed to converge after 100 iterations. This was because when the value of \(\alpha\) was small, the guiding effect of pheromone on the ant's foraging was weak, and the ant could not gain heuristic experience from the former ants; as a result, the algorithm diverged. The average traveling time in Figure 4a is the average value for the shortest route after 50 iterations. As \(\alpha\) continued to grow from 1.0 to 1.5, the average number of iterations significantly declined before leveling off. With the average traveling time and the average number of iterations taken into account, the pheromone heuristic factor was set at 1; that is, \(\alpha=1\). As Figure 5a shows, as \(\beta\) grew, the average traveling time on the three maps declined before leveling off. On map C, errors were reported in the algorithm when the value of \(\beta\) was small. This was because map C had a high barrier rate and complex environmental information, and the ant was unable to find a way with a small expectation heuristic factor. As Figure 5b shows, the average number of iterations presented a linear declining trend with the increase in \(\beta\). With the average traveling time and average number of iterations considered, the expectation heuristic factor was set at 4; that is, \(\beta=4\). As Figure 6a shows, when \(\gamma<3\), as the value of \(\gamma\) grew, the average traveling time on the maps presented a trend of mild decline; when \(\gamma>3\), the average traveling time slightly rose as the value of \(\gamma\) increased.