Two kinds of optimal methods and test of their abilities for searching optimal solutions are presented in the paper. A 12 T high temperature superconducting (HTS) magnet by Bi-2223/Ag tape is designed according to the methods. A new configuration of the HTS magnet which can reduce the winding volume and improve the efficiency of superconductor utilization effectively is suggested with consideration of the constraints, such as central magnetic filed, field homogeneity, critical current characteristic and so on.
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