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A novel method for the design of open configuration magnets for Magnetic Resonance Imaging (MRI) has been recently set up. The method is based on an innovative approach to the genetic optimization algorithms, described in some detail in an accompanying paper. The method has been applied to the design of open magnet configurations for MRI of parts of the human body. The configurations are optimally designed not only by taking into account field strength and homogeneity, but also looking for the most effective current density distribution in terms of superconductor performance, and looking for the most compact assembly. The need for optimal design in terms of superconductor performance is due to the severe working conditions in split coil configurations because of the field map in the windings, which presents values much higher than the central field.