Abstract Differential evolution optimization is used to find the volume fraction that maximizes the first natural frequency for a functionally graded beam. A formulation using three parameters is used to describe volume fraction. Beams with different ratios of material properties are considered. Two methods are used to compute the natural frequencies, analytical and meshless numerical method. Results show that differential evolution is capable to find distributions for volume fraction that increase the natural frequency of beams. It was also found that the RBF numerical method can be used with differential evolution to solve problems related to maximization of natural frequencies in functionally graded beams.