# UAV Formation Trajectory Planning Algorithms: A Review
## 4 Intelligent Algorithm
### Heuristic Algorithm
#### 4.1.5 Pigeon-Inspired Optimization
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Challenge** & **Optimization Criteria** & **Method** & **Dimension** \\ \hline P. [PERSON] et al. [63] & Trajectory, Environment & Tracking, Line of sight guidance law & PSO & 3D \\ G. [PERSON] et al. [64] & Trajectory, Environment & Cost analysis & PSO & 3D \\ [PERSON] et al. [65] & Time & Minimum boundary, Random optimization, & PSO & 4D \\ [PERSON] et al. [66] & UAV clustering & One-time strategy & PSO & 3D \\ Y.-[PERSON] et al. [67] & UAV clustering, & Two-stage optimization & PSO & 3D \\  & Multiple objectives & Binary value coding matrices, Adaptive inertia weights & IPSO & 2D \\ [PERSON] et al. [68] & Trajectory, UAV & VND & GPSO & 2D \\ [PERSON] et al. [69] & Environment, coverage problem & Minimizing cost function & \(\delta\)-PSO & 3D \\ Q.-[PERSON] et al. [70] & Environment & Reduction in dimension & Dubins + PSO & 2D \\ [PERSON] et al. [71] & Environment & Point sequence strategy, Inclined plane, Relative & ODPSO & 2D/3D \\ [PERSON] et al. [72] & Environment & Logical mapping, Adaptive linear change & CIIPSO & 3D \\ [PERSON] et al. [73] & Trajectory & Spatial refinement voting mechanism & PSO & 4D \\ [PERSON] et al. [74] & Environment, UAV & Tythgorean heat map, Coevolution & DCPSO & 3D \\ [PERSON] and [PERSON] [75] & UAV clustering & Constraint conversion & Dubins + & 2D \\ [PERSON] et al. [76] & Environment, UAV clustering & TSS, Multiple objective optimization & HIPSO-MSOS & 3D \\ [PERSON] et al. [77] & UAV clustering & Distributed full coverage, dynamic fitness & PSO & 3D \\ [PERSON] et al. [78] & Time, Trajectory & Evolutionary computation, Parallel recombination & PSO & 3D \\ [PERSON] et al. [79] & Trajectory & Adaptive, interference, Interactive coordination & MSROS & 3D \\ [PERSON] et al. [81] & Trajectory & GBPF, layered & HPSO & 3D \\ [PERSON] et al. [82] & Trajectory & Nonlinear time variation, adaptive, Distributed & NTVPSO-ADE & 3D \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A summary of Particle Swarm Optimization in our review. Figure 15: A PIO map and compass operator model and PIO trajectory map. (**a**) A PIO map compass operator model (arrows: the direction of attraction); (**b**) A Pigeon-Inspired Optimization (PIO) trajectory diagram (diamonds: starting points; Pentagrams: the end points; black areas: obstacles). traditional pigeon swarm algorithm optimization process that has optimization bias and is easy to fall into local optimization. [PERSON] et al. [87] proposed a mutational pigeon swarm optimization algorithm (MGLPIO) based on swarm learning strategy, which introduces the swarm learning strategy, triple mutation strategy, timestamp segmentation mechanism and coordination cost function into the swarm optimization algorithm (PIO). They used it to solve the optimal trajectory, which solves the problems of low population diversity, weak global search ability and weak convergence of traditional PIO. [PERSON] et al. [88] proposed an improved Pigeon-Inspired Optimization algorithm (IPIO) based on natural selection and Gauss-Cauchy mutation, established an environment-aware map, and designed an integer encoding method. A discrete compass operator, discrete landmark operators, Gaussian mutation and Cauchy mutation operators are introduced to break away from local optimum. Finally, natural selection is used to accelerate convergence, which solves the problem of collaborative dynamic target search and area coverage of UAV formations in uncertain environments. [PERSON] et al. [89] proposed a collaborative search decision-making method based on improved Pigeon-Inspired Optimization, which established a target probability information graph model with a normal distribution, an information graph of the search environment determinism, and a digital information graph. By adding the speed update and correction mechanism and the elite generation mechanism, they improve the traditional Pigeon-Inspired Optimization algorithm.