# Optimization Dubins Path of Multiple UAVs for Post-Earthquake Rapid-Assessment
The optimization objective of the MURARP is to maximize the rapid assessment completion quality by planning a flyable path for each UAV while satisfying the following three constraints: (i) the UAV endurance, i.e., the maximum safe UAV flight duration; (ii) the UAV dynamic constraints, that is, the curvature constraint of the minimum turning radius of UAV; (iii) uncertainty during the process, which is represented by the error of the sensors carried by heterogeneous UAVs. According to the above analysis, the MURARP can be transformed into a multi-UAV path planning problem, which can be defined as follows: to find a collision-free path between the initial configuration and the final configuration in a specific scenario [13]. The main objective of UAV path planning is to design a flyable path that UAV can fly to the destination with minimal comprehensive costs, i.e., maximize the probability of task completion while meeting the UAV performance requirements [14]. For multi-UAV path planning problems, extensive research has been conducted. To date, there are several notable surveys that outline the previous contributions performed in the field of UAV path planning [8; 13; 14; 15; 16; 17; 18]. The vehicle routing problem (VRP) model [19] was used to realize load balancing of the task allocation of multi-UAVs, with the optimization objective of minimizing the longest UAV path length. [PERSON] et al. [20] modeled multi-depot UAV path planning problems as resource allocation problems and introduced the minimum spanning tree method to obtain the shortest path of each UAV. [PERSON] [21] divided the potential targets into different communities according to different characteristics and developed a target sampling method to select multiple potential targets in the community for access. Then, a routing strategy to maximize the minimum coverage ratio was proposed. A TOP extended model, called the drone scheduling problem (DSP) [22], was modeled as a mixed integer linear programming (MILP) model that can design flight paths for drones to obtain as much benefit as possible under the constraint of the weight of the target and the task execution time. The total UAV arrival time can be minimized by a continuous approximate method [4]. The literature on UAV path planning using the Dubins path is very common. The DOP is a generalization of the existing OP [23]. Although the optimization objective of the DOP is similar to that of the OP, maximizing the collected profits in a given travel budget, the computational complexity of the DOP far exceeds that of the EOP because the DOP also needs to determine the heading angle when the drone accesses each target [24]. Because of the consideration of the UAV turning radius and heading angle, the EOP solution in a certain scenario may not match the DOP solution. The multi-UAV simultaneous arrival problem of path planning is formulated based on the Dubins path [25], to produce feasible paths. The path planning problem has proven to be an NP-hard problem [26]. Currently, the use of meta-heuristics algorithms has received more attention than deterministic algorithms. Because metaheuristics algorithms are problem-independent and there is no need to adapt a solution to a specific problem. Therefore, they approximately solve a wide range of path planning problems [18]. The genetic algorithm (GA) and hybrid algorithms based on GA represent state-of-the-art metaheuristics algorithms for solving VRP and its variants [27; 28], and they have been widely used in engineering practice. [PERSON] et al. [29] used an improved GA algorithm to plan a continuous UAV curve path for considering the constraints of a minimum UAV curvature angle. In addition, due to the specifics of the UAV path planning problem, careful adjustment of the GA relative parameter can improve the optimization performance of algorithm [30]. According to the research of scholars, it is much more efficient to perform a local search in the area found by the GA than a direct search [31].