## 4 Results and Discussion
Furthermore, when BTMACO is compared to its rivals, the VoI produced by it shows an effective value as BTMACO reaches the effective value. Although BTMACO requires a longer computation time (seconds) than other competitors, it makes the AUV achieve the target profit by reducing the time required to complete its journey while constructing the minimum tour distance, maximizing the VoI. Table 2 summarizes  
Figure 3: The optimal coverage path generated by the algorithm with 36 sensor nodes distributed within 0.6 km \(\times\) 0.6 km \(\times\) 0.6 km: (**a**) BTACO; (**b**) BTAACO; (**c**) BTMACO. the results of the three algorithms of the testing of four scenarios in the same situation. The best results were obtained for path length and VoI target scenarios with 13 and 36 sensor nodes, as indicated by bold red and bold yellow. ### Trajectory Planning for AUV  
To verify the effectiveness and performance of the proposed BTMACO for constructing the tour of the AUV, the proposed method was compared with previously published ones used in [24; 26]. The two methods were engaged in the same situations, including sensor node locations, event importance, and data length, as shown in Table 3. In addition, the same factors were used in the two methods, with \(SN=12\), \(\alpha=600\), and \(\beta=0.5\). The comparison of the proposed method and previously published methods is presented in Figure 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Objective** & **Distance** & & & & & \\ \hline Method & BTACO & & & BTAACO & & BTMACO & \\ No. of nodes & 13 & 36 & 13 & 36 & 13 & 36 \\ D (m) & 8671.9 & 14,705.5 & **8162.3** & 13,475.7 & 8488.2 & 12,847.7 \\ VoI & 28.2 & 79.2 & **28.4** & 79.3 & 28.3 & 79.4 \\ EC (k) & 2818.4 & 13,234.9 & **2652.7** & 12,128.1 & 2758.6 & 11,562.9 \\ CT(s) & 9.37 & **24** & 7.94 & 28.54 & 8.18 & 29.72 \\ \hline
**Objective** & **VoI** & & & & & \\ \hline Method & BTACO & & BTAACO & & BTMACO & \\ No. of nodes & 13 & 36 & 13 & 36 & 13 & 36 \\ D (m) & 8730.6 & 13,538.3 & **8157.3** & 13,066.2 & 8574.1 & 12,788.5 \\ VoI & 28.2 & 79.3 & **28.4** & 79.3 & 28.3 & 79.4 \\ EC (k) & 2837.4 & 12,184.4 & **2651.1** & 11,759.6 & 2786.6 & 11,509.6 \\ CT(s) & 7.74 & 26.67 & 10.05 & **39.07** & 10.21 & 45.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The simulation results of four scenarios. Figure 4: Performance of the three designed methods with generation. A sensor network deployed over a surface area of 0.5 km by 0.5 km was considered, as illustrated in Figure 5a. The comparison of the methods presented in [24; 26] with the proposed modified ACO method brings out several key points, especially with the focus on energy efficiency and the VoI. Both approaches presented in [24; 26] used path-planning algorithms in their design to attain the highest VoI. Neither of these methods places a strong emphasis on energy efficiency when determining the order in which sensor nodes are visited. As shown in Figure 5b, the AUV creates a tour based on the method presented in [24], visiting SNs 1 to 4 first because they have low event importance and SNs 10, 11, and 12 at the end. Similarly, the tour designed by the autonomous vehicle in [26] shows slight differences from that in [24], in line with the approach used in [24], as shown in Figure 5c. Moreover, the Vols of both methodologies are about 49.8378 in [24] and 49.9909 in [26], indicating a moderate ability to capture relevant information during AUV operation. Nonetheless, these approaches do not place significant emphasis on energy efficiency when determining the sequence in which sensor nodes are accessed. Additionally, an excessive focus on the  
Figure 5: Result of the constructed tour: (**a**) Sensor node deployment. (**b**) The resulting tour in [24]. (**c**) The resulting tour in [26]. (**d**) A tour built by using the suggested BTMACO.