A comparative study of Loney's solenoid by different techniques of global optimization

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.