# Improved Hybrid A* Algorithm Based on Lemming Optimization for Path Planning of Autonomous Vehicles
## 1 Introduction
Combining mathematical programming with heuristic algorithms effectively solves the computational complexity problem of traditional hybrid A* algorithms in high-dimensional state space searches by combining the accuracy of mathematical programming with the efficient search capabilities of heuristic algorithms [26]. Hybrid meta-heuristic algorithms significantly improve the performance of path planning problem solving by synergistically integrating the complementary advantages of multiple optimization mechanisms [27]. The integration of machine learning and planning algorithms has formed a new generation of intelligent path planning paradigms whose core goal is to enhance the adaptability and intelligence of traditional planning algorithms through data-driven methods [28]. Multi-objective mixed programming achieves a dynamic balance between safety, efficiency, and comfort by constructing a hierarchical optimization system [29]. The latest developments in the application of mixed-integer programming algorithms and optimization techniques in actual autonomous driving systems are listed in Table 1.  
By embedding natural group intelligence strategies into traditional path planning frameworks, this improvement not only enhances the algorithm performance but also sets new standards for the reliability of autonomous driving in extreme scenarios, demonstrating the cutting-edge value of the fusion of bionics and artificial intelligence. The development of optimization algorithms is one of the core drivers of the evolution of autonomous driving technology. Combining optimization algorithms not only improves the quality and efficiency of path planning but also pushes the whole system towards higher-order automation and intelligence [30]. Optimization algorithms can be classified into the following six categories: learning-enhanced optimization, distributed collaborative optimization, quantum-inspired optimization, bio-inspired intelligent optimization, robust stochastic optimization, and lightweight real-time optimization. Currently, the most popular application is bio-inspired intelligent optimization, which is achieved by simulating the intelligent behavior of biological populations or physical phenomena in nature [31]. Table 2 compares several optimization algorithms. In summary, the challenges faced by autonomous vehicle path planning include low efficiency during path searches, safety issues between vehicles and other objects, and the final insufficiently smooth path curve. Therefore, this paper proposes an improved hybrid A* algorithm based on lemming optimization. First, the distance function of the improved hybrid A* algorithm is enhanced to improve the efficiency. Second, the lemming optimization algorithm is integrated to improve the path curve smoothness and reduce the computational load. The main goals of this work are (1) to ensure the safety of the vehicle path by setting a safe distance from obstacles and to select the optimal node in the path search by choosing an appropriate distance heuristic function and increasing the angle penalty coefficient to improve the search efficiency; (2) to perform a global search \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm Type** & **Core Technology** &
\begin{tabular}{c} **Advantageous** \\ **Scenarios** \\ \end{tabular} & **Application** \\ \hline Layered planning & Hybrid A* + MPC & Structured roads & Benz DRIVEPILOT3.0 \\ Deep learning-driven & BEV-Transformer & Complex urban road & Huawei ADS 3.0 \\ Hybrid enhancement & RRT + reinforcement & Extreme obstacle & Waymo Driver 5 \\  & learning & scenarios & Tesla Dojo platform \\ End-to-end & Multimodal large & Adaptation to all & \\ architecture & model & scenarios & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Application of mixed programming algorithms in autonomous driving systems.