Neutron/Gamma pulse shape discrimination (PSD) was measured using stilbene and EJ-299-34 plastic scintillators with readout by silicon photomultipliers (SiPMs). The SiPM pulses were digitized and processed for energy and pulse shape information using a digital technique performing numerical weighted integrations on each pulse. A genetic algorithm (GA) was developed to optimize the weighting vectors used for the pulse shape discrimination. Efficient PSD was obtained down to an electron-equivalent energy of 127 keV with stilbene and 391 keV with the EJ-299-34 PSD plastic. Separation at lower energies was possible at reduced detection efficiency, down to 78 keV and 186 keV at 50% efficiency. The detectors were used to measure separated gamma and neutron spectra from an Americium-Beryllium neutron source and from a Na-22 gamma source. The GA-optimized weighted integration was compared with digital charge comparison (DCC). The GA exhibited slightly improved performance with a 400 MSps digitization rate and showed a significant advantage at sample rates below 100 MSps.