## 3 Proposed Heterogeneous Algorithm for Efficient-Path Detection
### Heterogeneous ACO-PT Algorithm for Vehicle Management
Step 10 depicts the restarting of the ACO-PT algorithm. Step 11 determines whether an ant has arrived at the target vehicle and provides the most efficient path. Step 12 explains the process of creating heuristic and distance matrices, as well as the heuristic and distance matrices that were used to aid the ants' pathfinding. The pheromone-interpretation method is demonstrated in Step 13. As the ants proceed, they detect and analyze the termite-pheromone trails. This pheromone information may be utilized to direct ants to regions of the environment where termites have discovered food sources, indicating that these locations may be more efficient routes. Step 14 finds the most efficient path for all vehicles to reach the targeted vehicle using ACO, which is led by the pheromone information released by the termites. Step 15 determines the most efficient route for repetition, and the method is iterated several times to improve the path efficiency. When a good solution is found or the maximum number of iterations is achieved, the method is terminated. Figure 5: Heterogeneous algorithm for efficient-path detection. Each ant can build a vehicle route using ACO, in which each vehicle visits each point. To select the next point \(\delta\), the ant can use a probabilistic formula. Using ACO, each ant may construct a vehicle path in which each vehicle visits each location. The ant can apply probability formulas to choose the next location \(\delta\). \[\delta=\text{arg max}\bigg{\{}\Big{(}P_{A(\epsilon i)}\Big{)}\Big{(}\tilde{ \text{D}}_{(\epsilon i)}\Big{)}^{\text{G}}\bigg{\}} \tag{2}\]  
where \(P_{A}\) is the number of pheromones on the chosen path, \(\epsilon\) is the current location, \(i\) is the probable location, \(\tilde{\text{D}}_{(\epsilon i)}\) is the inverse distance between two vehicle locations, and \(G\) establishes the relevance of distance in contrast to pheromone quality. Locations previously visited by the vehicle are saved in working memory \(M\) and are not evaluated for selection. The value \(\hat{\text{R}}\) represents a random uniform variable [0.1], whereas the value \(\hat{\text{Ro}}\) represents a parameter. When each choice is made, the vehicle chooses the path with the highest rate selected from \(\delta\) unless \(\hat{\text{R}}\) is greater than \(\hat{\text{Ro}}\). In this case, the vehicle chooses a random variable \(\tilde{\text{C}}\), the next location to visit based on the probability distribution \(P_{di}\), which favors short pathways with high pheromone levels. \[P_{di}=\frac{\Big{(}P_{A(\epsilon i)}\Big{)}\Big{(}\tilde{\text{D}}_{(\epsilon i )}\Big{)}^{G}}{\sum_{i\
eq\hat{\text{R}}}\Big{(}P_{A(\epsilon i)}\Big{)}\Big{(} \tilde{\text{D}}_{(\epsilon i)}\Big{)}^{\text{G}}}\text{ {if }}\delta\
eq\hat{\text{R}},\text{ otherwise }0 \tag{3}\]  
Using \(\delta\) and \(P_{di}\), each vehicle may take the most advantageous path that has already been created or choose a course at random based on a probability distribution determined by distance and pheromone buildup. If the vehicle-capacity limit is reached, the vehicle returns to the depot before proceeding to the next site. This technique is repeated until each area has been visited and the destination has been reached. The pheromone trails of the vehicles must be updated to represent the vehicle performance and the caliber of the solutions discovered to enhance future solutions. This update is a crucial component of the adaptive-learning approach used by ACO and ensures that subsequent solutions will be better. After each individual solution has been created, a local update of the trail is performed, and after \(\hat{\text{Z}}\) solutions have been generated, a global update of the best route solution is performed. To imitate the natural evaporation of pheromones and prevent any one path from becoming overly dominant, local updating is performed by lowering the quantity of pheromones on all paths that have been visited.