## 3 Simulation Analysis of Path Planning Algorithm Based on Improved Genetic Algorithm
### Simulation Experiment and Analysis  
In simulation, the weight coefficients of the fitness function (1) need to be determined. The initial values of the weight coefficients are set based on experience, with the main goal of improving coverage and reducing repetition rate. The weights of the smoothness of the path and the steering are assigned as 0.1, which improves the smoothness of the path and work efficiency. By observing the impact of different weight coefficients on simulation results, the weights are gradually adjusted to ensure that the weight coefficients fully reflect the importance of different performance indicators. The final weighting coefficients are work coverage rate weight \(w_{1}\) = 0.7, repetition rate weight \(w_{2}\) = 0.1, path smoothness weight \(w_{3}\) = 0.1, and number of turns weight \(w_{4}\) = 0.1. The simulation parameters set system are shown in Table 1.  
The coordinates of the boundary points of the work area in the simulation are A (33.42,107.4), B (33.4202,107.4), C (33.4202,107.4007), and D (33.42,107.4007). A total of 1400 grids were generated in this simulation, and all the above parameters were inputed into the full coverage path planning simulation platform.  
The path planning results are shown in the Figure 4a,b displays the optimal fitness values for each generation during the iteration process of TCGA and GA. In Figure 4b, it can be seen that the initial fitness value of TCGA is higher than that of GA, which is due to the guiding role of using Markov chains in the initial population generation process. By selecting initial individuals with high fitness values based on the transition probabilities between states, the quality of the solution set can be improved. Secondly, after 393 iterations, the fitness function value of TCGA reached the optimal value of 11.8  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Operation width & 1 m \\ \hline Length & 70 m \\ \hline Width & 20 m \\ \hline Minimum turning radius & 1.9 m \\ \hline Initial population size & 2500 \\ \hline Maximum number of iterations & 1000 \\ \hline Path point sampling rate & 0.01 m \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters of complete coverage path planning.  
Figure 3: GUI of complete coverage path planning. The * is the entrance, and the yellow line indicates the planned path. Black dots indicate the grid that has been traversed.  
and remained stable in subsequent iterations. The fitness function value of GA reached its optimal value of 11.63 after 980 iterations, thus proving that MCGA has significantly higher efficiency in finding the optimal solution over GA, and has a faster convergence speed and higher fitness level.  
The path planning for other field size regions has also been executed by GA and MCGA, and the important results of path planning for MCGA and GA algorithms are shown in Table 2. Compared to GA, the path length planned by MCGA is reduced by an average of 21.8%, the number of turns is reduced by an average of 6 times, the repetition rate is reduced by 83.8%, and the coverage rate is increased by 7.76%. These results show that the proposed approach significantly improves the quality of complete coverage path planning by combining Markov chains with genetic algorithms.