The Fruit fly Optimization Algorithm (FOA) is easy to fall into premature convergence due to the decrease of population diversity in the process of optimization. In order to overcome the problem, a multiple subgroups fruit fly optimization algorithm based on sequential quadratic programming local search (MFOA-SQP) is proposed. The fruit flies are assigned to multiple subgroups and the mutual learning between subgroups adjusts the step by introducing the inertia weight and learning factors in particle swarm optimization algorithm. The subgroups are reclassified every a certain number of iterations, which can improve population diversity and avoid premature convergence. The best individual is searched by SQP to improve the local fruit fly depth search capability, improving the stability and accelerating the evolution of population in the late iterations. Experiments on 6 benchmark test functions are carried out and an application case that classifies banking customers by the optimized generalized regression neural network is adopted. The results show that the proposed algorithm has superior performance in terms of optimization accuracy and speed, and can effectively improve the classification accuracy of generalized regression neural networks.