# Improved Hybrid A* Algorithm Based on Lemming Optimization for Path Planning of Autonomous Vehicles
## 5 Simulation Experiments
### Simulation Result Analysis  
By comparing the multiple evaluation metrics involved in the comprehensive fitness function (including the path length, smoothness, and obstacle avoidance safety), a smaller fitness value indicates better overall path performance. To ensure the broad applicability and reliability of the experimental results, multiple repeated experiments were conducted in both simple and complex scenarios to thoroughly compare and analyze the average performance of the algorithm. The method of multiple repeated experiments not only helps to reduce random errors in a single experiment but also more accurately reflects the general performance of the algorithm. The experimental results are shown in Figures 11 and 12 and Tables 8 and 9. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter/Variable** & **Function** & **Expression Value** \\ \hline Max\_iter & Maximum number of iterations & Set by yourself (40) \\ progress & Iteration progress & Iter/Max\_iter \\ theta & Exploration angle adjustment & 2 \(\times\)atan(1 \(-\) progress\({}^{0,8}\)) \\ No\_improve\_count & Early stop counter & Threshold(10) \\ Exploration–exploitation & 2 \(\times\) log(1/(rand(0+1\times 10^{-10}))\) \(\times\) theta \\ N & Population size & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Convergence control parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Function** & **Expression Value** \\ \hline Local\_weight & Current optimal solution guidance & 0.5 + 0.5 \(\times\) progress \\ Learn\_rate & Historical optimal learning rate & Max(0.2, 1 \(-\) progress) \\ Parameters & Function & Expression value \\ Spiral\_coef & Spiral search coefficient & 1 \(-\)0.5 \(\times\) progress \\ G & Global jump strength & 2 \(\times\) (sign(rand\(-\)0.5)) \(\times\) (1 \(-\) progress\({}^{2}\)) \\ global\_mean & Population mean guidance & 0.1 \(\times\) rand \\ best\_history & Historical optimal solution guidance & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Location update weight parameters. Figure 11: Comparison of convergence curves for simple scenario. Figure 12: Comparison of convergence curves for complex scenario. The repeated experimental results indicate that, under the same number of iterations, the LOA algorithm achieved a final average best fitness value of 1,007.02, while the SCA and GWO algorithms yielded values of 1,009.09 and 1,008.06, respectively. Therefore, the overall simulation experiments demonstrate that the LOA exhibits superior local exploitation capabilities and optimization efficiency, delivering the best comprehensive optimization performance in this test. GWO ranks second, while SCA shows relatively poor effectiveness. The comparison of several algorithms in terms of path search parameters is shown in Figure 13 and Table 10, and the comparison of path trajectories before and after optimization is shown in Figure 14. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & **Algorithm** & **Path Length/mm** & **Planning Time/s** & **Number of Nodes** \\ \hline \multirow{4}{*}{Simple scenario} & Hybrid A* & 15,730.5 & 7.39 & 1150 \\  & SCA + Hybrid A* & 14,422.9 & 6.74 & 840 \\  & GWO + Hybrid A* & 14,175.6 & 6.38 & 820 \\  & LOA + Hybrid A* & 13,980.6 & 4.93 & 800 \\  & Hybrid A* & 16,421.2 & 14.79 & 1650 \\  & SCA + Hybrid A* & 15,700.0 & 14.01 & 1580 \\  & GWO + Hybrid A* & 14,433.5 & 11.86 & 1260 \\  & LOA + Hybrid A* & 14,188.2 & 11.31 & 1260 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Path performance metric comparison.