# Mobile Robot Path Planning Algorithm Based on NSGA-II
## 4 Experimental Simulation and Analysis
### Global Path Planning Experiment and Analysis  
To verify the effectiveness of the algorithms, each algorithm was independently run multiple times. Table 2 compares the results of multiple simulations on complex grid maps. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Population size \(M\) & 200 \\ Maximum iterations \(G_{max}\) & 50 \\ Crossover rate \(P_{c}\) & 0.9 \\ Mutation rate \(P_{m}\) & 0.1 \\ Calculation Parameters \(\lambda\) & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter setting. Figure 6: Two types of grid maps. (**a**) complex map; (**b**) simple map. From Table 2, it can be seen that the average length of the optimal path of our algorithm was shorter than the other two algorithms, the path smoothness was better, and the number of times the optimal solution was found was higher. The stability of the algorithm was improved, indicating that our algorithm has a better global search capability in path planning. To ensure the comprehensiveness of the simulation outcomes, the proposed algorithm, NSGA-II algorithm, and GA algorithm were each employed to address grid maps of differing complexity levels independently. The optimal paths and convergence curves derived by NSGA-II for the two maps are depicted in Figure 7. Similarly, the optimal paths and convergence curves yielded by GA for the two maps are illustrated in Figure 8. Additionally, the optimal paths and convergence curves attained by the proposed algorithm for the two maps are shown in Figure 9. The comparative experimental results of the simple map are detailed in Table 3, while those of the complex map are provided in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Algorithm** & **NSGA-II** & **GA** & **The Algorithm Proposed in This Paper** \\ \hline \multirow{2}{*}{1} & Length & 32.3848 & 32.1421 & **30.3848** \\  & Smoothness & 8.3767 & 7.4767 & 4.1104 \\ \hline \multirow{2}{*}{2} & Length & 31.7990 & 31.2132 & **30.3848** \\  & Smoothness & 5.4805 & 4.6584 & **3.5623** \\ \hline \multirow{2}{*}{3} & Length & 32.3848 & 31.7990 & **30.3848** \\  & Smoothness & 8.3767 & 5.7545 & **3.5623** \\ \hline \multirow{2}{*}{4} & Length & 31.2132 & 32.1421 & 31.2132 \\  & Smoothness & 4.3844 & 6.5766 & 3.8364 \\ \hline \multirow{2}{*}{5} & Length & 32.1421 & 32.3848 & **30.3848** \\  & Smoothness & 6.5766 & 8.3767 & **3.5623** \\ \hline \multirow{2}{*}{6} & Length & 31.2132 & 31.2132 & **30.3848** \\  & Smoothness & 4.3844 & 4.6584 & **3.5623** \\ \hline \multirow{2}{*}{7} & Length & 31.7990 & 31.7990 & **30.3848** \\  & Smoothness & 5.7545 & 5.4805 & 4.1104 \\ \hline \multirow{2}{*}{Mean} & Length & 31.84801 & 31.81334 & **30.50314** \\  & Smoothness & 6.19054 & 6.14026 & **3.75806** \\ \hline \multirow{2}{*}{Variance} & Length & 0.25 & 0.21 & **0.09** \\  & Smoothness & 2.82 & 1.99 & **0.07** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of effectiveness results. Figure 7: _Cont._  
Figure 8: Planned path and convergence curve of G.A. (**a**) Planned path of simple map; (**b**) convergence curve of simple map; (**c**) planned path of complex map; (**d**) convergence curve of complex map. Figure 7: Planned path and convergence curve of NSGA-II. (**a**) Planned path of simple map; (**b**) convergence curve of simple map; (**c**) planned path of complex map; (**d**) convergence curve of complex map. The experimental results indicated that when using simple maps, both the NSGA-II algorithm and our algorithm yielded favorable outcomes. However, our algorithm exhibited significantly fewer iterations compared to the other two algorithms, and it also had fewer inflection points in the optimal path. Moreover, when dealing with maps in complex environments, the advantage of our algorithm became more pronounced. The paths planned by our algorithm were noticeably shorter than those generated by the other algorithms.