Magnetic design optimization and objective function approximation

This paper addresses the problem of optimizing a device by using an interpolation of the objective function. Optimization by means of stochastic methods can explore the objective function and give reliable indications on its global extrema, but the number of function calls can be unacceptably large when numerically evaluated functions are used. An optimization procedure applied not directly on the objective function but on its interpolation can significantly reduce the cost of the optimization. An efficient coupling between interpolation technique and optimization method is needed both to explore features of the optimization algorithm and to exploit advantages of the interpolation. This paper analyzes the performance of a multiquadric interpolation procedure on analytical functions and on finite-element evaluations.