## 1 Introduction  
Unmanned aerial vehicles (UAVs) are widely used in various fields such as military operations, agriculture, disaster relief, environmental monitoring, and communications due to their low cost, high maneuverability, and adaptability [1, 2, 3]. However, path planning in complex and dynamic environments remains a significant challenge, as it must ensure obstacle avoidance, flight safety, and energy efficiency. Finding the optimal path has become a key issue in UAV applications [4]. Traditional path planning methods such as the A* algorithm [5, 6], ant colony optimization (ACO) [7], and particle swarm optimization (PSO) [8] have been widely used but often struggle to balance real-time performance, global optimality, and obstacle avoidance. Therefore, researchers have worked to refine or integrate these methods with new approaches to improve their performance. For instance, [PERSON], [PERSON], and [PERSON] proposed a UAV trajectory planning strategy that leverages the rapid optimization capabilities of ant colony optimization (ACO), though it did not account for complex factors like flight angles [9]. [PERSON], [PERSON], and [PERSON] optimized the cost function weights of the A* algorithm and introduced virtual target points in the artificial potential field (APF) method, improving both path smoothness and obstacle avoidance [10]. [PERSON], [PERSON], and their team combined enhanced particle swarm optimization (EPSO) with genetic algorithms, adaptively tuning the acceleration coefficients of EPSO based on fitness values, which enhanced global search [11]. [PERSON], [PERSON], and [PERSON] applied Q-learning to dynamically adjust factors such as step size and cost function in the A* algorithm, creating a hybrid method that effectively balances global and local search [12]. [PERSON], [PERSON], and [PERSON] incorporated the Metropolis criterion from simulated annealing into ACO, reducing the likelihood of getting trapped in local optima. They also employed an inscribed circle smoothing method to optimize trajectories, enhancing both feasibility and effectiveness [13]. In recent years, the rapid development of artificial intelligence and intelligent optimization algorithms has led to the increasing application of advanced algorithms and deep learning methods in UAV path planning. [PERSON], [PERSON], and [PERSON] proposed a coupling degree-based heuristic priority planning method (CDH-PP), which enhances the efficiency of cooperative path planning for UAV swarms through coupling degree heuristics [14]. [PERSON], [PERSON], and [PERSON] addressed path planning challenges in complex dynamic environments using deep learning, introducing the RQ method and an adaptive sampling mechanism to improve obstacle avoidance capabilities [15]. [PERSON], [PERSON], and [PERSON] combined the rapidly-exploring random tree (RRT) algorithm with driver visual behavior to propose an RRT path planning method that simulates driver vision. They optimized the path using a greedy algorithm; however, while this method is effective in complex scenarios, it exhibits high computational complexity [16]. [PERSON], [PERSON], and [PERSON] introduced an improved mayfly algorithm (modMA), which optimizes UAV layout and reduces overall costs through exponentially decreasing inertia weights (EDIW), adaptive Cauchy mutations, and enhanced crossover operators [17]. [PERSON], [PERSON], and [PERSON] improved the global optimization capability of the elastic rope algorithm by enhancing the node update mechanism and introducing paths composed of m-dimensional nodes to increase its applicability [18]. Additionally, other studies have proposed innovative strategies for algorithm improvement. [PERSON], [PERSON], and [PERSON] effectively addressed two-point and multi-point path planning problems by employing a chaotic initialization method combined with genetic algorithms (GA) and simulated annealing (SA) [19].