Obtaining high convergence and uniform distributions remains a major challenge in most metaheuristic multi-objective optimization problems. In this article, a novel multi-objective particle swarm optimization (PSO) algorithm is proposed based on Gaussian mutation and an improved learning strategy. The approach adopts a Gaussian mutation strategy to improve the uniformity of external archives and current populations. To improve the global optimal solution, different learning strategies are proposed for non-dominated and dominated solutions. An indicator is presented to measure the distribution width of the non-dominated solution set, which is produced by various algorithms. Experiments were performed using eight benchmark test functions. The results illustrate that the multi-objective improved PSO algorithm (MOIPSO) yields better convergence and distributions than the other two algorithms, and the distance width indicator is reasonable and effective.

It is generally known that the balance between convergence and diversity is a key issue for solving multi-objective optimization problems. Thus, a chaotic multi-objective particle swarm optimization approach incorporating clone immunity (CICMOPSO) is proposed in this paper. First, points in a non-dominated solution set are mapped to a parallel-cell coordinate system. Then, the status of the particles is evaluated by the Pareto entropy and difference entropy. At the same time, the algorithm parameters are adjusted by feedback information. At the late stage of the algorithm, the local-search ability of the particle swarm still needs to be improved. Logistic mapping and the neighboring immune operator are used to maintain and change the external archive. Experimental test results show that the convergence and diversity of the algorithm are improved.

In the last few decades, the particle swarm optimization (PSO) algorithm has been demonstrated to be an effective approach for solving real-world optimization problems. To improve the effectiveness of the PSO algorithm in finding the global best solution for constrained optimization problems, we proposed an improved composite particle swarm optimization algorithm (ICPSO). Based on the optimization principles of the PSO algorithm, in the ICPSO algorithm, we constructed an evolutionary update mechanism for the personal best position population. This mechanism incorporated composite concepts, specifically the integration of the $ \varepsilon $-constraint, differential evolution (DE) strategy, and feasibility rule. This approach could effectively balance the objective function and constraints, and could improve the ability of local exploitation and global exploration. Experiments on the CEC2006 and CEC2017 benchmark functions and real-world constraint optimization problems from the CEC2020 dataset showed that the ICPSO algorithm could effectively solve complex constrained optimization problems.

Safe, efficient, and feasible path planning for unmanned aerial vehicle (UAV) in complex three-dimensional environments remains a critical challenge in intelligent navigation. Although the traditional artificial potential field (APF) method offers high computational efficiency, it is prone to local minima and target inaccessibility in complex environments. To overcome these limitations, this paper proposes a novel 3D path planning approach that integrates an APF with particle swarm optimization (PSO). The method introduces a Gaussian repulsive function to improve obstacle boundary perception and ensure smooth potential field transitions. Combined with a PSO-based optimization of trajectory points, it effectively enhances the algorithm’s ability to escape local minima and improves global path accessibility. To validate the effectiveness of the proposed method, a comprehensive evaluation framework was developed, incorporating key performance metrics such as total path length, average safety distance, and minimum safety distance. Benchmark comparisons were conducted against several advanced path planning algorithms in static, dynamic, and more complex obstacle environments. In addition, a path executability verification framework was introduced, employing multiple flight controllers to perform trajectory tracking simulations and systematically assess control feasibility and adaptability in complex dynamic scenarios. Experimental results show that the proposed method exhibits clear advantages in both path planning quality and practical executability, particularly demonstrating strong adaptability and robustness in complex environments.

To solve the nonlinear constrained optimization problem, a particle swarm optimization algorithm based on the improved Deb criterion (CPSO) is proposed. Based on the Deb criterion, the algorithm retains the information of ‘excellent’ infeasible solutions. The algorithm uses this information to escape from the local best solution and quickly converge to the global best solution. Additionally, to further improve the global search ability of the algorithm, the DE strategy is used to optimize the personal best position of the particle, which speeds up the convergence speed of the algorithm. The performance of our method was tested on 24 benchmark problems from IEEE CEC2006 and three real-world constraint optimization problems from CEC2020. The simulation results show that the CPSO algorithm is effective.