# Improved Hybrid A* Algorithm Based on Lemming Optimization for Path Planning of Autonomous Vehicles
## 4 Hybrid Path Planning Algorithm  
### Framework of Integrated Algorithms  
First, the path planning system constructs a dual-layer nested optimization framework. The outer layer employs the LOA metaheuristic algorithm to form a collaborative optimization layer, while the inner layer utilizes the improved hybrid A* algorithm to build the path planning layer, establishing a hierarchical optimization architecture. During initialization, the system models the environment via grid-based mapping to create a planning scenario encompassing obstacles, start points, and goal points, with standardized parameters set as benchmark references. The pseudo-code for the construction of this dual-layer optimization framework is provided in Algorithm 1.  
```
1 Function initializePopulation()
2 initial_population \(\leftarrow\) zeros(SearchAgents, dim)
3 initial_population [0] \(\leftarrow\) standard_params
4 Fori \(\gets\) 1 to SearchAgents-1 do
5 Forj \(\gets\) 0 to dim-1 do
6 range-ub[j]-lb[j]
7 std_dev\(\leftarrow\)range*0.2
8 val\(\leftarrow\)standard_params[j]+randn(0*std_dev
9 initial_population [i,j] \(\leftarrow\) min(max(val, lb [j]), ub [j])
10 Endfor
11 Endfor
12 Return initial_population
13 EndFunction
```  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scene** & **Applicable** & **Reeds-Shepp** & **Limitations** \\  & **Algorithm** & **Advantage** & **J** \\ \hline Structured roads & Hybrid A* & Fast calculation & Path may not be \\  & & speed & smooth \\ Extremely confined & Reeds–Shepp + & Kinematic & Parameter \\ spaces & LOA & assurance and & adjustment \\ Highly dynamic & & global optimization & required \\ environments & & RRT & Quick obstacle & Low path quality \\ Off-road terrain & Reeds–Shepp + & Good terrain & Need to predict \\  & MPC & adaptability & coefficient of \\  & & & friction \\ \hline \hline \end{tabular}
\end{table}
Table 4: Specific applications of the Reeds–Shepp algorithm in different scenarios.  
During the optimization phase, the system innovatively adopts an \"elite retention\" strategy for population initialization. Here, the standard parameters serve as seed individuals, while the remaining individuals are generated around them via a normal distribution--ensuring both population diversity and the preservation of known feasible solutions. This architectural design enables the optimization algorithm to intelligently adjust the key parameters of the hybrid A* (e.g., minimum turning radius, step length, and steering penalty coefficients), striking a balance between avoiding purely random searches and preventing local optima stagnation. The pseudo-code for elite-retained population initialization is detailed in Algorithm 2.  
```
14 Function main()
15 Initialize parameters: startPose, goalPose, sign, row, col, ob_coo, safe_dis, standard_length
16 Robi \(\leftarrow\) Function(x)
17 Return evaluateParams(x, startPose, goalPose, sign, row, col, ob_coo, safe_dis, standard_length)
18[LOA_curve, optimized_params] \(\leftarrow\) improvedLOA(fobi)
19 Return LOA_curve, optimized_params
20 End Function
21 Function evaluateParams(params, startPose, goalPose, sign, row, col, ob_coo, safe_dis, standard_length)
22[route, path_length] \(\leftarrow\) runHybridAstar(params, startPose, goalPose, sign, row, col, ob_coo, safe_dis)
23 fitness \(\leftarrow\) path_length
24 Return fitness
25 End Function
26 Function runHybridAstar(params, start, goal, sign, rows, cols, obstacles, safety_dist)
27 Return route, length
28 End Function
29 Function improvedALA(objective_function)
30 Return optimization_curve, best_params
31 End Function
```  
**Algorithm 2** Initialization of elite reserved stock