This paper proposes an Improved Lemur Optimization algorithm (ILO), which combines the advantages of the Spider Monkey Optimization algorithm, Simulated Annealing algorithm, and Lemur Optimization algorithm. Through the use of an adaptive nonlinear decrement model, adaptive learning factors, and updated jump rates, the algorithm enhances its global exploration and local exploitation capabilities. A Gaussian function model is used to simulate the mountain environment, and a mathematical model for UAV flight is established based on constraints and objective functions. The fitness function is employed to determine the minimum cost for avoiding obstacles in a designated airspace, and cubic spline interpolation is used to smooth the flight path. The Improved Lemur Optimization algorithm was tested using the CEC2017 benchmark set, assessing its search capability, convergence speed, and accuracy. The simulation results show that ILO generates high-quality, smooth paths with fewer iterations, overcoming the issues of premature convergence and insufficient local search ability in traditional genetic algorithms. It adapts to complex terrain, providing an efficient and reliable solution.

This paper proposes an Improved Spider Wasp Optimizer (ISWO) to address inaccuracies in calculating the population $\left(N\right)$ during iterations of the SWO algorithm. By innovating the population iteration formula and integrating the advantages of Differential Evolution and the Crayfish Optimization Algorithm, along with introducing an opposition-based learning strategy, ISWO accelerates convergence. The adaptive parameters trade-off probability (TR) and crossover probability (Cr) are dynamically updated to balance the exploration and exploitation phases. In each generation, ISWO optimizes individual positions using Lévy flights, DE’s mutation, and crossover operations, and COA’s adaptive update mechanisms. The OBL strategy is applied every 10 generations to enhance population diversity. As the iterations progress, the population size gradually decreases, ultimately yielding the optimal solution and recording the convergence process. The algorithm’s performance is tested using the 2017 test set, modeling a mountainous environment with a Gaussian function model. Under constraint conditions, the objective function is updated to establish a mathematical model for UAV flight. The minimal cost for obstacle-avoiding flight within the specified airspace is obtained using the fitness function, and the flight path is smoothed through cubic spline interpolation. Overall, ISWO generates high-quality, smooth paths with fewer iterations, overcoming premature convergence and the insufficient local search capabilities of traditional genetic algorithms, adapting to complex terrains, and providing an efficient and reliable solution.

With the rapid development of both commercial and general aviation, the frequency assignment problem for aviation navigation stations has become increasingly important. This paper presents a general algorithm for frequency assignment at individual aviation navigation stations. Subsequently, a frequency assignment model for multiple civil aviation navigation stations is established to address large-scale frequency allocation challenges. To overcome the limitations of traditional multi-objective genetic algorithms, such as slow convergence speed and susceptibility to local optima, this study proposes several improved algorithms, including the multi-objective genetic algorithm with randomly assigned weights, the multi-objective genetic local search algorithm, and an improved multi-objective genetic local search algorithm, while optimizing key algorithm parameters. The problem involves multiple objectives, including minimizing interference in frequency assignment and reducing the total number of assigned frequencies. Experimental results demonstrate that the proposed improved multi-objective genetic algorithms—especially IMOGLSA-II—effectively address the frequency assignment problem for aviation navigation stations, achieving notable improvements in solution quality, convergence speed, and stability compared with other multi-objective genetic algorithms. In particular, although the time complexity of the proposed algorithm is slightly higher due to the incorporation of local search mechanisms, it exhibits clear advantages in reducing parameter sensitivity, simplifying algorithm structure, and enhancing engineering applicability. These characteristics make the proposed method not only well-suited to the static and constrained nature of aviation frequency assignment, but also more practical and effective than other mainstream multi-objective optimization algorithms in similar engineering scenarios. Furthermore, the proposed method offers a reliable approach that can be extended to other static frequency assignment problems and broader classes of multi-objective optimization tasks.