# A Two-Stage Co-Evolution Multi-Objective Evolutionary Algorithm for UAV Trajectory Planning
###### Abstract
[7] used the multi-objective optimization theory to model a UAV trajectory planning problem, designed multiple objective functions and weight-vector-adaptive combinations for the model, and proposed MOUTP with dimensional exploration as the main optimization objective. [PERSON] et al. [8] proposed an enhanced version of the chimpanzee optimization algorithm to solve MOUTP in 3D environments by combining differential variational operators and adaptive norms to enhance the algorithm's search capability and prevent key trajectory point solutions from falling into multiple local optima. [PERSON], [PERSON] et al. [9] proposed an improved version of the 3D Vector Field Histogram * (3 DVFH *) method for local trajectory planning of UAV in medical applications, in which a variant of weighted products, weighted Chebyshev distance, and factorial achievement scaling were investigated in addition to the classical weighted sum. The third category is MOUTP based on deep learning algorithms, which provide more flexible, intelligent, and adaptive multi-objective UAV trajectory-planning schemes. [PERSON] et al. [10] proposed MOUTP based on a deep reinforcement learning (DRL) algorithm, which introduced multiple target optimization allocation networks in a double-delay deterministic policy gradient algorithm while establishing task assignment weight coefficients to prioritize important tasks. [PERSON] et al. [11] used a deep deterministic policy gradient (DDPG)-based algorithm for set environments with 3D continuous actions, while a reward function based on inner product weights was proposed in order to balance features such as the UAV target tracking distance and UAV obstacle avoidance. [PERSON] et al. [12] proposed an information theoretical exploration algorithm for UAV platforms, called Entropy Explorer (EE), for determining UAV obstacle avoidance in MOUTP. Most of the above studies used weight vectors to balance multiple optimization objectives, but the parameters of weight vectors are easily affected by the decision maker's preferences. Meanwhile, the UAV constraint divides the target space into multiple infeasible domains, which makes solving for non-dominated critical waypoints quite difficult. At present, a small number of studies have regarded MOUTP as a constrained multi-objective optimization problem. By simulating the natural evolutionary process, multiple performance objectives are optimized while satisfying the constraints of the planningsystem. The basic working principle is as follows. First, a random initial population (a collection of candidate UAV solutions) is generated, and the optimal individuals are selected for crossover and mutation by evaluating their fitness and constraint satisfaction to generate a new generation of individuals (new candidate UAV solutions). Through repeated iterations, the fitness of individuals is continuously optimized to find multiple non-dominated solutions that satisfy the MOUTP constraints. However, they suffer from problems such as a long response time and high computational complexity during the planning process [13; 14; 15]. In order to further improve the performance of MOUTP, a novel multi-objective evolutionary algorithm with two-stage co-evolution for UAV trajectory planning (TSCEA) is proposed in this paper. The innovations and contributions of this research are summarized as follows. 1. A multi-objective optimization framework for UAV trajectory planning is proposed. Meanwhile, the distance of the UAV from an obstacle is regarded as a strong constraint, and the framework can be extended with multiple conflicting objectives and multiple constraints. 2. A two-phase co-evolutionary constraint-handling technique is proposed, where a two-population strategy is adopted in the exploration phase, the primary population is not restricted by the UAV constraints, and the secondary population treats the constraints as an additional objective.