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Abstract: Magnetic field generators are a key component of Magnetic Particle Imaging (MPI) systems, and their power consumption is a major obstacle on the path to human-sized scanners. Despite their importance, a focused discussion of these generators is rare, and a comprehensive description of the design process is currently lacking. This work presents a methodology for the design and optimization of selection field generators operating with soft magnetic materials outside the linear regime in the context of MPI. Key elements are a mathematical model of magnetic field generators, a formalism for defining field sequences, and a relationship between power consumption and field sequence. These are used to define the design space of a field generator given its system requirements and constraints. The design process is then formulated as an optimization problem. Subsequently, this methodology is then utilized to design a new magnetic field generator specifically for cerebral imaging studies. The optimization result outperforms our existing MPI field generator in terms of power consumption and field of view size, providing a proof-of-concept for the entire methodology. As the approach is very general, it can be extended beyond the MPI context to other areas such as magnetic manipulation of medical devices and micro-robotics.