Mitchell, C.E. Qiang, J. Sannibale, F. JACoW Geneva, Switzerland The next generation of X-ray free electron lasers requires beams with increasingly high peak current and low emittances at ~MHz repetition rates, placing increased demands on the performance of high-brightness electron photoinjector sources. To explore the high-dimensional parameter space associated with photoinjector design, global multiobjective optimization methods based on genetic algorithms or similar tools are playing an increasingly critical role. We review our experience with applying these tools both to understand and to optimize simulated injector beam performance for projects such as LCLS-II (at SLAC) and the Advanced Photoinjector EXperiment (at LBNL), including both challenges and successes.