Continuing advances, in the field of parallel computing have allowed nonlinear optimization techniques to be applied to many problems previously considered too computationally demanding. We describe a general magnet design software package, CamGASP, which uses Genetic Algorithms (GAs) for the design of large whole-body MRI systems. The method of GAs allows a population of many designs to evolve with a bias toward the fittest designs continuing to later generations. Central to all nonlinear optimization techniques is the cost function, which decreases for designs that match the required specifications and are hence deemed to be "fitter." Multiple evaluations of the cost function are necessary to complete a single generation and this task can readily be shared across a network of processors, working in parallel. Thus GAs are especially suited to running on parallel computer systems. We present results of the performance of the GA software and also discuss methods for rapid calculation of magnetic fields from circular coils. We also present specific superconducting MRI magnet designs including a split coil optimized for simultaneous PET and MRI.