Due to their unique offerings, bio-inspired algorithms have become popular in problem solving. Flower pollination algorithm (FPA), which is relatively a new member of this family, is shown to be one promising algorithm and this optimizer is still open to possible enhancements. One of the reasons that adds to the popularity of FPA is indeed the simplicity in implementation. It has two basic procedures, namely global and local pollination, which correspond to global and local search, respectively. Moreover, a single parameter, referred to as switching probability, puts control on these search procedures. Thus, the mentioned switching probability actually defines the search characteristics throughout generations, which directly affects the success of FPA. Accordingly, the present work analyses the effects of various switching probability characteristics, including exponentially, linearly and sawtooth changing patterns. This is the main motivation of the present study. Secondarily, a systematically intensifying step size procedure, which is commonly ignored by most of the stochastic search algorithms, is adopted along with these strategies. The aim of the proposed step size function is to encourage a more intensified search towards the end, while providing a more diversified search at the initialization stage to avoid local optima and premature convergence. Thus, more promising results might be obtained. All developed modifications are tested by using well-known unconstrained function minimization problems. As demonstrated by several nonparametric statistical tests, results point out significant improvements over the standard FPA.