# Navigation of Autonomous Tug via Evolutionary Algorithms with Radar Plot Fitness Evaluation
## 4 Results
### Situation 1  
The view of the water area at the beginning of the first situation is shown in Figure 4. The situation takes place in waters restricted to the northwest and east, and there are three small islands in the middle of the water area.  
The tug considered is located in the southern part of the water area and is represented by a green icon. The dashed line connects the initial position of the tug with the destination point and indicates its initial course. The three other ships present in the water area are represented by red icons and their initial course and destination points are also marked. Unlike the ship considered, the other ships do not maneuver, they are only moving navigational obstacles, moving at a constant speed. Figure 5 shows a graphical view of the solution to navigation situation no. 1.  
The navigation routes proposed by both versions of the evolutionary algorithm have a similar shape, but the route (a) obtained from the algorithm with the classic fitness assessment method has one less turning point and runs in the immediate vicinity of one of the islands. In comparison, the algorithm using the radar method found a shorter route, using only 1 turning point, placed in such a way as to pass one of the moving other ships behind its stern, which is considered a safer maneuver than passing in front of its bow. The route proposed by the postulated algorithm also requires 24.7% fewer course changes, compared to the classic algorithm.  
\begin{table}
\begin{tabular}{l c c c c} \hline \multirow{2}{*}{**Situation, Algorithm**} & \multirow{2}{*}{**Total Distance (nm)**} & \multicolumn{2}{c}{**Difference in Path**} & \multicolumn{2}{c}{**Difference in**} \\  & & **Length with Respect** & **Total Course** & **Course Change with** \\  & & **to Classic Fitness** & **Change (deg)** & **Respect to Classic** \\  & & **Method (\%)** & & **Fitness Method (\%)** \\ \hline Situation 1, classic fitness method & 9.03 & – & 38.99 & – \\ Situation 1, radar fitness method & 8.95 & 0.89 & 31.27 & 24.70 \\ Situation 2, classic fitness method & 8.99 & – & 48.69 & – \\ Situation 2, radar fitness method & 8.92 & 0.78 & 47.18 & 3.20 \\ Situation 3, classic fitness method & 7.31 & – & 18.30 & – \\ Situation 3, radar fitness method & 7.24 & 0.97 & 11.92 & 53.60 \\ Situation 4, classic fitness method & 11.15 & – & 122.15 & – \\ Situation 4, radar fitness method & 11.24 & \(-\)0.80 & 113.85 & 7.29 \\ \hline \end{tabular}
\end{table}
Table 2: Summary of each situation solution with total path distance, and total course change.  
The colored hexagons visible in Figure 5 symbolize the safety domains, the violation of which is considered to be the risk of collision. The blue domains show the initial position of other ships, while the red ones show the position of the other ship in the event of approaching or intersecting the proposed passage route with the predicted route of the other ship.  
Figure 4: Situation 1, a strait with 3 islands and 3 other ships.  
Figure 5: Situation 1 solutions. (**a**) Solution with a classic fitness method, and (**b**) solution with a radar fitness method.