## 3 Proposed Heterogeneous Algorithm for Efficient-Path Detection
### Heterogeneous ACO-PT Algorithm for Vehicle Management  
The proposed heterogeneous ACO-PT algorithm is more efficient in pathfinding due to the combination of two cutting-edge algorithms. It is based on the behavior of real ants and on real termites in nature. At the beginning, the proposed algorithm starts, thanks to the features of PT, by selecting vehicles and assigning values to them. Then, it checks whether an ant has arrived at the target vehicle; if not, it restarts. Otherwise, it assigns an efficient path. Next, it assigns initial parameters, sets heuristic and distance matrices, locates the path for ACO, and determines the most efficient route for iteration. The algorithm also takes into account the congestion-avoidance module and automatic-vehicle-detection module to find the most efficient path. This progression assumes that ants use the most efficient path for food. Hence, ants are considered numbers and pheromones values in this model. The values are changed based on the usage of the path by ants. Subsequently, when ants discover the empty entrance on the road suggested by the PT algorithm, they initiate optimization according to specific procedures. ACO begins by initializing its provided specifications, which are the vehicle and ant counts. The pheromone creates the starting route. The ACO forms the distances between matrices and vehicles. When all the parameters are complete, then an ant that is \(\beta\) is assigned a value of 1 and given to the initial vehicle that is at the entrance used by the vehicle. The ant begins from the first vehicle and provides random numbers from 0 to 1. The assigned random number is illustrated as 0.5. If this given random number is less than the initial path, then \(\rho_{0}\). This illustration proves that there is a path available that will be followed by the ant. The heterogeneous algorithm for efficient-path detection is depicted in Figure 5. Algorithm 1 gives the pseudocode of the proposed heterogeneous ACO-PT algorithm, which consists of the following steps:  
1. **Initialization:** {\(V\): vehicles; \(S\): system; \(E_{n}\): efficient route for iteration; \(V_{I}\): target vehicle; \(P_{c}\): efficient path; \(An\): ant; \(P\): assign priority; \(t_{c}\): time constraints; \(fu\): fuel consumption; \(V_{tp}\): vehicle type; \(An_{a}\): artificial ant; \(L_{s}\): location start; \(\Psi\): initial parameters; \(An_{t}\): total number of ants; \(\gamma\): pheromone evaporation rate; \(\Upsilon\): pheromone deposit rate; \(\sigma\): heuristic matrix; \(\omega\): distance matric; \(\hat{\Upsilon}\phi\): pheromone interpretation; \(\mu\): most efficient path reaching the targeted vehicle using ACO
2. **Input:** { \(V\), \(V_{I}\)}
3. **Output:** { \(P_{e}\)}
4. **Set**\(V\)
5. **Identify**\(V\to S\in V_{I}\)
6. Assign \(P\leftarrow\left(t_{c}+fu+V_{tp}\right)\)
7. Place \(An_{a}\forall\leftrightarrow L_{s}\)
8. _If \(An\
eq V_{I}\)_ then
9. _Set_\(\Psi=\left(An_{t}+\gamma+\Upsilon\right)\)
10. _Restart_\(\Psi\)
11. _If \(An\cong V_{I}\)_ then
12. **Set**\(\sigma\) &&& \(\omega\)
13. **Set**\(\hat{\Upsilon}\phi\)
14. **Locate**\(\mu\to\mathcal{ACO}\)
15. **Assign**\(P_{e}\)
16. **endif**
17. **endif**Algorithm 1 uses ACO-PT to discover paths efficiently. The variable-initialization method for this algorithm is shown in Step 1. Steps 2 and 3 provide the input and output, respectively. Steps 4 and 5 begin the vehicle-selection process by identifying all vehicles in the system that must reach the target vehicle. Each vehicle is allocated a value and a priority depending on parameters such as time limits, fuel usage, and vehicle type. Step 7 depicts the arrival of the desired automobile. Each vehicle's starting point is marked with the number of fake ants. The ants are utilized to create solutions to problems by constructing a trail across the surroundings. Steps 8 and 9 show that, if no ants arrive at the target vehicle, initial parameters for the ACO algorithm, such as the number of ants, the pheromone evaporation rate, and the pheromone deposit rate, are assigned.