# Improved Hybrid A* Algorithm Based on Lemming Optimization for Path Planning of Autonomous Vehicles
## 5 Simulation Experiments
### Simulation Result Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Optimization** & **LOA** & **SCA** & **GWO** \\
**Algorithm** & **Fitness Value** & **Fitness Value** & **Fitness Value** \\ \hline Number of tests 1 & 1,008.63 & 1,009.30 & 1,009.00 \\ Number of tests 2 & 1,008.58 & 1,009.31 & 1,009.01 \\ Number of tests 3 & 1,008.59 & 1,009.38 & 1,009.31 \\ Number of tests 4 & 1,008.62 & 1,009.34 & 1,009.31 \\ Number of tests 5 & 1,006.26 & 1,008.59 & 1,006.27 \\ Number of tests 6 & 1,006.24 & 1,009.02 & 1,008.59 \\ Number of tests 7 & 1,006.29 & 1,009.30 & 1,008.65 \\ Number of tests 8 & 1,006.25 & 1,008.60 & 1,007.96 \\ Number of tests 9 & 1,005.37 & 1,008.60 & 1,006.28 \\ Number of tests 10 & 1,005.36 & 1,008.85 & 1,006.25 \\ Average optimal & 1,007.02 & 1,009.09 & 1,008.06 \\ fitness value & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison chart of algorithm convergence for simple scenario. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Optimization** & **LOA** & **SCA** & **GWO** \\
**Algorithm** & **Fitness Value** & **Fitness Value** & **Fitness Value** \\ \hline Number of tests 1 & 1,007.22 & 1,010.42 & 1,009.24 \\ Number of tests 2 & 1,005.68 & 1,010.43 & 1,007.06 \\ Number of tests 3 & 1,007.59 & 1,010.43 & 1,009.24 \\ Number of tests 4 & 1,006.54 & 1,010.43 & 1,007.24 \\ Number of tests 5 & 1,007.07 & 1,011.35 & 1,009.24 \\ Number of tests 6 & 1,006.54 & 1,010.43 & 1,007.72 \\ Number of tests 7 & 1,007.07 & 1,009.25 & 1,007.07 \\ Number of tests 8 & 1,006.55 & 1,009.23 & 1,007.26 \\ Number of tests 9 Figure 14: Comparison of path search before and after optimization. Figure 13: Comparison of path search parameters. As shown in Table 10, the traditional hybrid A* algorithm has the highest average planning time and average path length values in both the simple and complex scenarios, with average times of 7.39 s and 14.79 s and average lengths of 15,730.5 mm and 16,421.2 mm. This is because the traditional hybrid A* algorithm has high computational complexity and poor real-time performance. Next, for the SCA optimization algorithm, in the simple scenario, the average planning time was 6.74 s and the average path length was 14,422.9 mm. Compared with the traditional hybrid A* algorithm, the average search time was reduced by 8.7% and the average path length was reduced by 8.3%. Meanwhile, in the complex scenario, the average planning time was 14.01 s and the average path length was 15,700.0 mm. Compared with the traditional hybrid A* algorithm, the average search time was reduced by 8.7% and the average path length was reduced by 8.3%. For the GWO optimization algorithm, in the simple scenario, the average planning time was 6.38 s and the average path length was 14,175.6 mm. Compared with the traditional hybrid A* algorithm, the average search time was reduced by 13.6% and the average path length was reduced by 9.8%. Meanwhile, in the complex scenario, the average planning time was 11.86 s, and the average path length was 14,433.5 mm. Compared with the traditional hybrid A* algorithm, the average search time was reduced by 19.8% and the average path length was reduced by 12.1%. Finally, for the LOA, in the simple scenario, the average planning time was 4.93 s, and the average path length was 13,980.6 mm. Compared with the traditional hybrid A* algorithm, the average search time was reduced by 33.2% and the average path length was reduced by 11.1%. Meanwhile, in the complex scenario, the average planning time was 11.31 s, and the average path length was 14,188.2 mm. Compared with the traditional hybrid A* algorithm, the average search time was reduced by 23.5% and the average path length was reduced by 13.6%. Based on the overall simulation results, the improved hybrid A* algorithm based on lemming optimization demonstrates more efficient path searching and smoother path curves.