Abstract: The fruit fly optimization algorithm (FOA) suffers from low solution precision and failure with respect to position optimization in the negative interval. We propose a dynamic grouping and multi-strategy fruit fly optimization algorithm that divides the population into the subgroups to find the optimal solution by the use of adaptive grouping strategies. It also improves the optimization behavior of the optimal individual using a differential mutation operator and the elite pool individual. In later iterations, we evolve dominant subgroups by the particle swarm optimization algorithm to enhance the accuracy of the solution, and evolve the extended subgroups by an inverse chaos operator to avoid a local optimal solution. We select two representative test functions to verify the performance of the algorithm and compare the optimization results of the discrete gradient method-FOA (DGM-FOA) with the gravitational search algorithm (GSA), the FOA and two improved FOAs. The results show that the proposed algorithm has good convergence accuracy and computation speed.