The optimization of geometric boundaries and placement of conductors to achieve specific design goals is the principle activity in computational electromagnetics. However the heuristic determination of design variables soon leads to total confusion as the user attempts to wrestle with multiple choices. Even if there are just two states for n parameters there will be, 2n trials. The range of problems posed is vast. One such is the determination of magnet geometries needed to produce an unpolluted uniform field in Magnet Resonance Imaging (MRI) systems, and another application concerns the design of pole shapes in particle accelerators where the higher harmonic distortions must be minimized in dipoles and multipole magnets.