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The optimal shape design of Loney’s solenoid is carried out by different techniques of global optimization. The underlying inverse problem, which is numerically ill-conditioned with a gorge behavior, shows an outstanding potential as benchmark for magnetostatic inverse problems. In the paper four minimization methods have been compared: two of them are deterministic (Simplex and Quasi-Newton methods), two are stochastic (Evolution Strategy (1+1) formulation and Filled Function method combined with the Evolution Strategy method). The results have been discussed and compared.
Borghi et al. (1999) studied this question.