The trajectory planning of multiple unmanned aerial vehicles (UAVs) is the core of efficient UAV mission execution. Existing studies have mainly transformed this problem into a single-objective optimization problem using a single metric to evaluate multi-UAV trajectory planning methods. However, multi-UAV trajectory planning evolves into a many-objective optimization problem due to the complexity of the demand and the environment. Therefore, a multi-UAV cooperative trajectory planning model based on many-objective optimization is proposed to optimize trajectory distance, trajectory time, trajectory threat, and trajectory coordination distance costs of UAVs. The NSGA-III algorithm, which overcomes the problems of traditional trajectory planning, is used to solve the model. This paper also designs a segmented crossover strategy and introduces dynamic crossover probability in the crossover operator to improve the solving efficiency of the model and accelerate the convergence speed of the algorithm. Experimental results prove the effectiveness of the multi-UAV cooperative trajectory planning algorithm, thereby addressing different actual needs.

With the increase of problem dimensions, most solutions of existing many-objective optimization algorithms are non-dominant. Therefore, the selection of individuals and the retention of elite individuals are important. Existing algorithms cannot provide sufficient solution precision and guarantee the diversity and convergence of solution sets when solving practical many-objective industrial problems. Thus, this work proposes an improved many-objective pigeon-inspired optimization (ImMAPIO) algorithm with multiple selection strategies to solve many-objective optimization problems. Multiple selection strategies integrating hypervolume, knee point, and vector angles are utilized to increase selection pressure to the true Pareto Front. Thus, the accuracy, convergence, and diversity of solutions are improved. ImMAPIO is applied to the DTLZ and WFG test functions with four to fifteen objectives and compared against NSGA-III, GrEA, MOEA/D, RVEA, and many-objective Pigeon-inspired optimization algorithm. Experimental results indicate the superiority of ImMAPIO on these test functions.