# Development of a Multifunctional Unmanned Boat Platform for Aquaculture Automation
## 3 Experimental Verification
### Cruise Function Verification  
Based on the idea of the Monte Carlo simulation, for the feeding points given by the user, the shortest route is generated to complete the cruising and feeding to the fishing area. To briefly illustrate the principle, the following mathematical model is developed:  
Since the fishing area is a rectangular area:  
\[R=W\times H, \tag{3}\]  
where \(W\) and \(H\) are the width and height of the rectangle, respectively.  
There are \(N\) feeding points distributed in the following area:  
\[P_{\text{i}}=(x_{i},y_{i}), \tag{4}\]  
where \(i=1,2,\ldots,N\).  
The goal is to find a shortest path from the origin through all feeding points and back to the origin.  
Define the path \(p\) as the order of the feeding points \(P=\left\{P_{i_{1}},P_{i_{2}},\ldots,P_{i_{N}}\right\}\), where \(i_{1},i_{2},\ldots,i_{N}\) is an arrangement of \(1,2,\ldots,N\) and the total length of the cruise path \(L(P)\) can be expressed as follows:  
\[L(P)=\sum_{j-1}^{N-1}d(P_{i_{j}},P_{i_{j+1}})+d((0,0),P_{i_{1}})+d(P_{i_{N}}, (0,0)), \tag{5}\]  
where \(d(P,Q)\) denotes the Euclidean distance between point P and point Q.  
Next, Monte Carlo simulations were performed as follows:  
1. Use a random number generator to disrupt the feeding point order \(P=\left\{P_{i_{1}},P_{i_{2}},\ldots,P_{i_{N}}\right\}\) to obtain a randomized feeding point order arrangement \(P^{\prime}\).
2. Calculate the total cruise path length \(L(P^{\prime})\) based on the disorganized feeding point order \(P^{\prime}\).
3. Compare the obtained \(L(P^{\prime})\) and record the shortest cruise path.  
Repeat (1)-(3) until the number of simulations is reached.  
As shown in Figure 11, the figure illustrates the optimal cruise paths and their corresponding path lengths obtained after 300 iterations using the Monte Carlo algorithm, the simulated annealing algorithm, and The genetic algorithm, following the selection of 10 feeding points by farmers. From this comparison chart, it is clear that the cruise path length generated by the Monte Carlo algorithm is the shortest, with the most evenly distributed spatial distribution, and a clearer path. The other algorithms generate optimal paths with issues such as crossing and overlapping within a short time frame, indicating slower optimization speeds.  
Subsequently, we conducted a quantitative analysis based on the number of iterations and path lengths. Figure 12 presents the iterations-best path length graph for the three algorithms. Compared to the simulated annealing algorithm and The genetic algorithm, the Monte Carlo method demonstrates an extremely high convergence speed in the initial phase. It only requires approximately 50 iterations to quickly find a path length close to the optimal solution and stabilizes around 400. The rapid convergence of the Monte Carlo method not only conserves computational resources but also enhances overall optimization efficiency.  
In contrast to the genetic algorithm, which continuously explores throughout the iteration process and may find better solutions, its significant fluctuations and longer convergence time can introduce unnecessary complexity and delays in practical applications. The cruise path generation algorithm based on the Monte Carlo simulation can rapidly find  
Figure 11: Optimal path after generation.  
Figure 12: Iteration number–path length graph.  
the optimal path within a short period. This showcases the characteristics of fast generation speed and high generation efficiency.