Mean Apparent Propagator (MAP) MRI provides a robust analytical framework to estimate the diffusion probability density function (PDF). Several scalar metrics are calculated from the PDF, which might better characterize tissue microstructure compared to conventional diffusion methods. The downside of MAP MRI is the long acquisition times of over an hour. In this study we developed a genetic algorithm (GA) to determine optimal q-space subsampling scheme for MAP MRI that will keep total scan time under 10 minutes, while preserving accuracy. Results show that the metrics derived from the optimized schemes match those from the full set closely.