## 1 Introduction  
Unmanned aerial vehicles (UAVs) have gained significant momentum in recent years, and their extensive uses have induced rapid growth in related research areas [1, 2, 3]. Currently, UAVs are used in a wide range of applications, both in civil and military fields. In particular, the use of UAVs in urban environments will increase significantly in the near future, forming the core component of urban air mobility (UAM), as described in smart cities [4, 5, 6]. For this reason, it will be mandatory to enhance the safety of flight operations, especially in urban inhabited areas with the lowest flying costs. However, the increase in UAV operations in urban low-altitude airspace will inevitably lead to a high likelihood of crashes on the ground because of unexpected UAV accidents in the air, which pose significant risks to people on the ground. Therefore, how to plan an optimal flying path for UAVs with the lowest ground risk and flying cost possible is an important and indispensable problem in UAM. Path planning is a key element in providing autonomy to UAVs in the execution of UAM missions by defining a set of waypoints to reach a destination while satisfying some optimality criteria and minimizing risk for people on the ground. The topic has been widely studied, and a large number of methods have been proposed. One popular family of path-planning methods includes sample-based techniques, which are used to explore the search space through a sampling scheme. Widely diffused approaches include probabilistic roadmaps (PRM) [7, 8], rapidly exploring random trees (RRT) [9, 10], and other RRT-basedmethods [11; 12]. Another popular kind of path-planning algorithm is based on graph-searching algorithms, which usually include the Voronoi diagram searching method [13], the Dijkstra algorithm [14], and the A* algorithm [15]. All of these methods use [PERSON]'s \(k\)-best algorithm to find the optimal UAV path. The third group of optimization techniques, which are also called population-based evolutionary algorithms, are now widely accepted and used to solve the UAV path-planning problem, including particle swarm optimization (PSO) [16; 17], genetic algorithm (GA) [18; 19], firefly algorithm (FA) [20; 21], beetle antennae search (BAS) [22; 23], and related improved methods [24; 25]. When using graph-searching-based algorithms, such as the Dijkstra algorithm, their expansion in every direction and blind recalculation of each direction is computationally expensive. Additionally, the Dijkstra algorithm cannot handle negative transition costs, which means that the calculated path is not necessarily the shortest. For the A* algorithm, the memory requirements are high because the algorithm needs to save the complete list of open nodes, which makes the space for memory limited. In this way, the use of heuristic algorithms is becoming an effective and popular way to optimize UAV path planning in complicated situations with high efficiency and accuracy, and only a few parameters are needed. Currently, it is difficult for these UAV path-planning algorithms to take ground risk distributions into account, which leads to unsafe operations for people on the ground. The risk caused by UAV operations in UAM is difficult to quantify. Therefore, some research has been conducted in an attempt to solve this problem with qualitative methods instead. For example, [PERSON] et al. [26] proposed two algorithms for UAV path planning based on risk awareness to tackle dynamic risks and threats within UAVs' operational environments. The authors also studied the possible risk factors in UAM for UAV operations [5]. [PERSON] et al. [27] proposed a 4D path-planning method for UAVs based on the risk-cost map to enable UAVs to fly along a cost-effective path. However, all the proposed algorithms only focus on UAV operation rules qualitatively instead of modeling the risk events related to urban characteristics.