# Optimization Dubins Path of Multiple UAVs for Post-Earthquake Rapid-Assessment
Therefore, it is widely adopted to combine two powerful meta-heuristics algorithms into one hybrid procedure to take advantage of their respective strengths [32; 33; 34]. According to the characteristics of the MURARP,we design a hybrid genetic simulated annealing (HGSA) algorithm to solve it and the flyable path of each UAV can be obtained quickly. The main innovations of this paper are as follows:  
1. The MURARP proposed in this paper can be regarded as a variant of the TOP in the real application of multi-UAV for post-earthquake rapid assessment task, in which UAVs equipped with sensors access a group of potential targets, such that the total expected profit can be maximized. In the optimization process of the MURARP, various factors, such as the UAV endurance, dynamic constraints, multi-depot, the weight of potential targets, the heterogeneity of the UAV swarm and sensor errors, are considered. In this paper, the MURARP is modeled as a multi-depot revisit-allowed Dubins TOP with variable profit (MD-RDTOP-VP). The similarity between this model and the TOP model is that it is necessary to select the appropriate potential targets and determine the sequence of access. The differences are reflected as follows: (i) Multiple depots--In the classic TOP, all UAVs depart from the same start depot and return to the same end depot after completing the task. However, a UAV carrying out the rapid-assessment task in MD-RDTOP-VP needs to start from one of multiple depots and return to its departure depot after completing the task. (ii) The objective function--The optimization objective of the classic TOP is to maximize the total profit, while the optimization objective of MD-RDTOP-VP is to maximize the expected profit, which is calculated by multiplying the potential target's weight by the probability that valid information about that target was successfully collected. (iii) Target revisit-allowed strategy--The classic TOP model stipulates that each potential target can only be accessed at most once. However, in MD-RDTOP-VP, to increase the probability that valid information about a target was successfully collected, a UAV is allowed to visit a potential target more than once. 2. In this paper, the influence of the minimum turning radius of the UAV and heading angle discretization on the completion quality of the rapid assessment is studied. The instances of MD-RDTOP-VP are generated by modifying the classic benchmark instances of the TOP model. The numerical experiments are used to prove the influence of the minimum turning radius of the UAV on the completion quality. Then, the influence of the heading angle discretization is analyzed through simulation experiments. The results show that the high-quality MD-RDTOP-VP solution can be accelerated by selecting the appropriate heading angle discretization. In previous reports on the UAV path planning using the Dubins curve, most studies have assumed that the initial heading angle of the UAV is specified, but we also optimize that parameter. 3. This paper designs an HGSA algorithm for solving the MD-RDTOP-VP model. Since the MURARP proposed in this paper is a novel problem, the existing algorithms cannot be directly applied here. Therefore, a hybrid algorithm is developed to solve this problem. The performance of the algorithm is shown through numerical and simulation experiments. Finally, a case study based on real-world data of the 2017 Jiuzhaigou earthquake in China shows how to use our method in a post-earthquake scenario. The results show that the HGSA algorithm can obtain a high-quality feasible solution of the MD-RDTOP-VP model in a short time, which can meet the actual demand of quick path planning for each UAV in a post-earthquake scenario. The remainder of this paper is structured as follows. In Section 2, the mathematical model of the MURARP is given. The HGSA algorithm for solving the MURARP mathematical model is discussed in Section 3.