## 5 Simulation of Unmanned Delivery Vehicle Path Planning Based on the MSEChoA Algorithm  
To validate the effectiveness of the MSEChoA algorithm in actual unmanned delivery vehicle path planning, a simulation test was conducted using the grid method in MATLAB. The experiments were performed on 30 \(\times\) 30 scale maps with obstacle coverage rates of approximately 15% and 42%, representing simple and complex environmental maps, respectively, to simulate different real-world delivery scenarios. The experimental parameters were set as follows: a population size of 100 and a maximum iteration value of 1000. To ensure the reliability of the results, each scenario was repeated 10 times. In grid maps, it is usually necessary to convert between row-column indices and linear indices. Assuming the map size is rows \(\times\) cols, the conversion formula for rows and columns is as shown in Equation (15):  
\[\left\{ \begin{array}{l}index=(r-1)\times cols+c\\ r=\left[\frac{index-1}{cols}\right]+1\\ c=index-(r-1)\times cols\end{array} \right. \tag{15}\]  
The starting and ending points of the delivery unmanned vehicle are marked with green and red dots, respectively, and obstacles are represented by black squares. Different colored paths represent the path planning results of each algorithm. By comparing and analyzing these results, the differences in obstacle avoidance capability, path length, and operational efficiency of the algorithms can be observed. The MSEChoA algorithm was compared with other metaheuristic algorithms and various improved Chimp Optimization Algorithms. A randomly selected experimental result is shown in Figure 7:  
Figure 7A,B shows the path planning results of the MSEChoA algorithm compared to other metaheuristic algorithms and various improved Chimp Optimization Algorithms in a simple environment. The paths generated by MSEChoA are shorter and smoother, significantly outperforming the other algorithms. Compared to other improved chimp algorithms, MSEChoA still shows advantages, excelling in both path length and planning efficiency. Figure 7C,D present the comparison of path planning in a complex environment. MSEChoA still demonstrates excellent obstacle avoidance capabilities when faced with complex obstacles, generating paths that are superior in both length and smoothness compared to other algorithms. Even though algorithms like I  
Figure 6: Comparison of execution times among different algorithms. optimality in some cases, MSECHOA's overall performance is more stable, validating its superiority in complex scenarios. Table 6 presents the data on average path length, average standard deviation, and average runtimes for each algorithm in both simple and complex environments. The following is a detailed analysis of the data in the table:  
In a simple environment, the MSECHOA algorithm demonstrates the best path planning capability among all algorithms, with an average path length of 45.6985, indicating that this algorithm can effectively find the shortest path in simple environments. In contrast, traditional algorithms like ALO and MSGWO have relatively longer average path lengths, revealing their performance disadvantages in such environments. In a complex environment, MSECHOA also performs excellently, with an average path length of 45.6985, significantly better than other algorithms, especially