# Improved Hybrid A* Algorithm Based on Lemming Optimization for Path Planning of Autonomous Vehicles
## 1 Introduction
[PERSON] [14] employed the Ramer-Douglas-Peucker (RDP) algorithm [15] to compress the path waypoints and then used polynomial fitting between adjacent waypoints to ensure smooth vehicle motion. Critical collision-prone segments were subsequently refined through interpolation. [PERSON] [16] proposed an effective trajectory generation algorithm to shorten and smooth jerky paths obtained from sampling-based planners in cluttered environments. This method utilizes cubic B-splines to represent collision-free trajectories with strict continuity while respecting velocity/acceleration constraints. [PERSON] [17] developed an autonomous vehicle trajectory planning algorithm combining quartic Bezier curves with risk potential fields. A potential field function evaluates the collision risk for candidate paths to generate collision-free trajectories. These algorithms depend heavily on the distribution and quality of known data points. Sparse or unevenly distributed data may cause significant errors, posing challenges for high-dimensional or nonlinear complex problems. Numerical optimization-based planning algorithms [18] obtain optimal paths or strategies by numerical optimization. There are various types of numerical optimization-based planning algorithms, with the most commonly used including dynamic programming (DP), model predictive control (MPC), genetic algorithms (GAs), and particle swarm optimization (PSO). [PERSON] [19] proposed an event-triggered model predictive adaptive dynamic programming (MPADP) algorithm to plan the path of an unmanned ground vehicle (UGV) at road intersections. The actor-critic scheme of adaptive dynamic programming (ADP) combined cost function approximation and control policy generation to formulate MPADP. [PERSON] [20] introduced a path planning and tracking framework to ensure collision-free trajectories for autonomous vehicles. For the path planning method, a 3D virtual danger potential field was constructed by superimposing trigonometric functions for roads and exponential functions for obstacles, generating the desired collision avoidance trajectories when potential collisions are detected. [PERSON] [21] proposed an AGV path planning method based on an artificial potential field-ant colony algorithm, which improves the performance of the algorithm by incorporating the artificial potential field for the construction of a potential field heuristic function and dynamically adjusting the pheromone fluctuation coefficients, introducing multiple parameters to dynamically adjust the pheromone increment, and optimizing the paths with the pruning method. Despite their advantages, numerical optimization-based planning algorithms are highly sensitive to the initial values, prone to local optima, and suffer from high computational complexity in high-dimensional or nonlinear problems, which influences their real-time performance and global optimality. Machine learning-based planning algorithms train models to learn environmental features and decision-making strategies from data. The trained models are then used to predict or generate optimal paths or actions in order to achieve adaptive and intelligent path planning. Machine learning methods that have been applied in the planning domain include neural networks [22], reinforcement learning [23], deep learning [24], and end-to-end learning [25]. The limitations of machine learning-based planning algorithms lie in their strong dependence on training data, limited generalization capabilities, high computational complexity, and potential challenges in interpretability and safety assurance in practical applications. A mixed-integer programming algorithm is an algorithm that combines multiple optimization techniques and methods to solve complex optimization problems. It typically combines classical mathematical programming methods (such as linear programming and integer programming) with modern heuristic algorithms (such as genetic algorithms and particle swarm optimization) or other artificial intelligence technologies.