# UAV Formation Trajectory Planning Algorithms: A Review
## 4 Intelligent Algorithm
### Heuristic Algorithm
#### 4.1.4 Particle Swarm Optimization  
Particle Swarm Optimization (PSO) is an adaptive stochastic optimization algorithm with a population search strategy developed by simulating the foraging behavior of birds, which is used to solve various problems in engineering and science. Particle Swarm Optimization initializes the trajectory planning problem into a group of random particles and then iterates to find the optimal solution. In each iteration, particles update their position and velocity by tracking individual and global extreme values, and then, they use the search space to complete the optimal trajectory planning. Figure 14 shows a particle motion diagram. [PERSON] et al. [63] proposed a random time algorithm based on the Particle Swarm Optimization algorithm. Tracking guidance law and line of sight guidance law are used to track the trajectory generated by the Particle Swarm Optimization algorithm at any time, which solves the problem of using a pop-up window when multiple UAV tracks may collide and trajectory planning when there are moving obstacles. [PERSON] et al. [64] proposed a collaborative trajectory planning method for multiple UAVs based on the Particle Swarm Optimization (PSO) algorithm, analyzed the main influencing factors of the cost function after modeling, and carried out collaborative dynamic analysis of multiple UAVs, including static three-dimensional trajectory planning, which solves the problems of unsatisfactory trajectory and poor real-time performance in multi-UAV collaborative trajectory planning. Figure 14: A particle motion diagram. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Challenge** & **Optimization Criteria** & **Method** & **Dimension** \\ \hline [PERSON] et al. [40] & Environment & Region division & MPC + GA & 2D \\ [PERSON] et al. [41] & UAV clustering & Subsequence crossover, Forward insertion mutation & GA & 2D \\ [PERSON] et al. [42] & Environment & B-Spline, DE & DE & 3D \\ [PERSON] et al. [63] & Environment & GVR, Parallel computing & MOEAs & 3D \\ [PERSON] and [PERSON] [44] & Trajectory & Task allocation & Voronoi + GA & 2D \\ [PERSON] and [PERSON] [45] & Trajectory & Height filtration, Fuzzy c-mean & Voronoi + GA & 3D \\ [PERSON] [46] & Trajectory & Curves & GA & 2D \\ [PERSON] and [PERSON] [47] & Environment & Level update & DE & 3D \\ [PERSON] et al. [48] & Time, Trajectory & Cluster and parallel computing & GA & 2D \\ [PERSON] et al. [49] & Environment, UAV & Coevolution & GA & 2D \\ [PERSON] et al. [50] & Trajectory & Parallel optimization & +ACO & 2D \\ [PERSON] et al. [51] & Trajectory, Multiple objectives & Evolutionary operator & GA + HS & 2D \\ [PERSON] et al. [52] & Time & Node scheduling & GA & 2D \\ [PERSON]. [PERSON] et al. [53] & Trajectory, Multiple objectives & Time conversion & GA & 2D \\ [PERSON] et al. [54] & Trajectory, coverage problem & Clustering, Task time & GA & 2D \\ [PERSON] et al. [55] & Trajectory, coverage problem & K-means, Multiple chromosome & GA & 2D \\ [PERSON] et al. [56] & Trajectory & Adaptive interference operator, Regionalization & GA & 3D \\ [PERSON] et al. [57] & coverage problem & Augmented random frame & GA & 3D \\ [PERSON] et al. [58] & Time, coverage problem & Iterative use & GA & 3D \\ [PERSON] et al. [59] & Environment & Decision variable, Adaptive & GA & 2D \\ [PERSON] et al. [60] & Environment, UAV & Variable population & GTPA-VP & 2D \\ [PERSON]. [PERSON] et al. [61] & Trajectory, Multiple objectives & Partially matched crossover, Secondary & GA + PSO & 2D \\ [PERSON]. [PERSON] et al. [62] & Multiple objectives, UAV & & Task analysis & GA & 2D \\  & clustering & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of evolutionary algorithms in our review. [PERSON] et al.