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Path planning for multiple unmanned aerial vehicles (UAVs) is crucial in collaborative operations and is commonly regarded as a complicated, multi-objective optimization problem. However, traditional approaches have difficulty balancing convergence and diversity, as well as effectively handling constraints. In this study, a directional evolutionary non-dominated sorting dung beetle optimizer with adaptive stochastic ranking (DENSDBO-ASR) is developed to address these issues in collaborative multi-UAV path planning. Two objectives are initially formulated: the first one represents the total cost of length and altitude, while the second represents the total cost of threat and time. Additionally, an improved multi-objective dung beetle optimizer is introduced, which integrates a directional evolutionary strategy including directional mutation and crossover, thereby accelerating convergence and enhancing global search capability. Furthermore, an adaptive stochastic ranking mechanism is proposed to successfully handle different constraints by dynamically adjusting the comparison probability. The effectiveness and superiority of DENSDBO-ASR are demonstrated by the constrained problem functions (CF) test, the Wilcoxon rank sum test, and the Friedman test. Finally, three sets of simulated tests are carried out, each including different numbers of UAVs. In the most challenging scenario, DENSDBO-ASR successfully identifies feasible paths with average values of the two objective functions as low as 637.26 and 0. The comparative results demonstrate that DENSDBO-ASR outperforms the other five algorithms in terms of convergence accuracy and population diversity, making it an exceptional optimization approach to path planning challenges.
Shen et al. (Sun,) studied this question.