# A Two-Stage Co-Evolution Multi-Objective Evolutionary Algorithm for UAV Trajectory Planning
###### Abstract  
With the increasing complexity of unmanned aerial vehicle (UAV) missions, single-objective optimization for UAV trajectory planning proves inadequate in handling multiple conflicting objectives. There is a notable absence of research on multi-objective optimization for UAV trajectory planning. This study introduces a novel two-stage co-evolutionary multi-objective evolutionary algorithm for UAV trajectory planning (TSCEA). Firstly, two primary optimization objectives were defined: minimizing total UAV flight distance and obstacle threats. Five constraints were defined: safe distances between UAV trajectory and obstacles, maximum flight altitude, speed, flight slope, and flight corner limitations. In order to effectively cope with UAV constraints on object space limitations, the evolution of the TSCEA algorithm is divided into an exploration phase and an exploitation phase. The exploration phase employs a two-population strategy where the main population ignores UAV constraints while an auxiliary population treats them as an additional objective. This approach enhances the algorithm's ability to explore constrained solutions. In contrast, the exploitation phase aims to converge towards the Pareto frontier by leveraging effective population information, resulting in multiple sets of key UAV trajectory points. Three experimental scenarios were designed to validate the effectiveness of TSCEA. Results demonstrate that the proposed algorithm not only successfully navigates UAVs around obstacles but also generates multiple sets of Pareto-optimal solutions that are well-distributed across objectives. Therefore, compared to single-objective optimization, TSCEA integrates the UAV mathematical model comprehensively and delivers multiple high-quality, non-dominated trajectory planning solutions. U  
A 2024 2  
for UAV trajectory planning usually focuses on only one of these aspects, ignoring other important optimization requirements, resulting in poor overall planning results. Multi-objective optimization for UAV trajectory planning (MOUTP) simultaneously considers the performance of multiple optimization objectives. Through multi-objective optimization algorithms and constraint processing techniques, it yields a set of planning solutions that satisfy different optimization objectives as much as possible. Not only can it satisfy the shortest flight distance, but it also can satisfy constraints such as the flight speed of the UAV, which makes the solution more flexible and the decision-making more comprehensive. At present, MOUTP algorithms are roughly divided into the following three categories. The first category is MOUTP based on node algorithms, which are characterized by short response times and high robustness and universality. This type of MOUTP is suitable for a variety of complex scenarios where obstacle avoidance is the main optimization objective. [PERSON] et al. [4] extended the obstacle grid in a map in order to maintain a safe distance between the UAV and obstacles. [PERSON] et al. [5] proposed MOUTP based on the PF-RRT* algorithm in complex environments, introduced a target weight bias strategy to simplify the search space near the obstacles by using a dichotomous method, and proposed an improved artificial potential field. [PERSON] et al. [6] proposed a new algorithm for fixed-wing UAV trajectory planning based on a genetic algorithm and the theory of the Dobbins curve. This method uses an initial circle node, a target circle node, a threat circle node, and key trajectory points to jointly construct a coding scheme. The second category is MOUTP based on intelligent optimization algorithms, which can extend multiple optimization objectives according to the decision maker's needs for meeting the various constraints and requirements of UAV trajectories. This type is suitable for balancing multiple optimization objectives. [PERSON] et al.