The characteristics of objective functions have important impacts on the search process of the optimization algorithm. Many multimodal functions tend to make the algorithm fall into local optima, and the local search accuracy is usually affected by the coupling of the objective functions in different dimensions. A novel quantum-behaved particle swarm optimization algorithm with the flexible single-/multi-population strategy and the multi-stage perturbation strategy (QPSO_FM) is proposed in the present paper. This algorithm aims to adjust the optimization strategies based on the characteristics of the objective functions. The number of sub-populations is determined by the monotonicity variations of the objective functions, and two mechanisms are introduced to balance the diversity and the convergent speed for the multi-population case. The strategy of multi-stage perturbation is applied to enhance the search ability. At the first stage, the main target of the perturbation is to broaden the search range. The second stage applies the univariate perturbation (relying on the coupling degree of the objective function) to raise the local search accuracy. Performance comparisons between the proposed and existing algorithms are carried out through the experiments on the standard functions. The results show that the proposed algorithm can generally provide excellent global search ability and high local search accuracy.