Acquisition time is a major limitation in recovering brain white matter microstructure with diffusion magnetic resonance imaging. Finding a sampling scheme that maximizes signal quality and satisfies given time constraints is NP-hard. Therefore, we propose a heuristic method based on genetic algorithm that finds sub-optimal solutions in reasonable time. Our diffusion model is defined in the $$$q\tau$$$-space, so that it captures both spacial and temporal phenomena. The experiments on synthetic data and in-vivo diffusion images of the C57Bl6 wild-type mouse corpus callosum reveal superiority of our approach over random sampling and even distribution in the $$$q\tau$$$-space.