A fuzzy adaptive particle swarm optimization algorithm with Gaussian mutation for constrained engineering problems

Particle swarm optimization (PSO) has been successfully applied to solve some simple optimization tasks. However, the standard PSO algorithm cannot effectively handle multimodal and high-dimensional problems. Although numerous variants have been developed, they still have some limitations. In this study, a fuzzy inference-based adaptive PSO with Gaussian mutation (FAPSO-GM) is proposed. On the one hand, the fuzzy inference-based adaptive PSO (FAPSO) algorithm is first introduced, which realizes the dynamic tuning of parameters in the velocity updating formula through a two-input fuzzy system. In addition to taking the current number of iterations as the fuzzy input, a new variable, the maximum dimension difference weight, is considered, which can characterize whether a particle is far away from or close to the current global optimum. The fuzzy inference rules formulated based on these two variables achieve an appropriate balance between the global and local search capabilities of the algorithm. On the other hand, two single-example learning strategies integrating Gaussian mutation are constructed to speed up convergence and avoid falling into local optima, so as to enhance the search capability of the algorithm in the early iterations. The combination of these two aspects ensures that the FAPSO-GM algorithm can effectively find near-optimal solutions. The results on the CEC-2017 benchmark test set show that the proposed FAPSO-GM algorithm outperforms seven PSO variants and five other metaheuristic algorithms on 16 out of 29 functions. The Wilcoxon signed-rank test further confirms its significant superiority. In addition, 14 classical engineering design problems are considered, and the comparisons reveal that the FAPSO-GM algorithm provides better solutions for the majority of the problems (11 out of 14), demonstrating its excellent ability in solving practical engineering problems.