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Numerical optimization techniques are widely used for the design of electromagnetic devices. In practical implementations of such devices, the problem parameters may be subject to tolerances and uncertainties. Optimal designs should be insensitive to parameter variations. The demand for robustness is often neglected during the optimization process. A formulation of robust nonlinear design problems is proposed in this paper. The influence of uncertainties on the target performance and the feasibility of a solution is assessed and incorporated into the optimization strategy. Methods for the solution of robust problems are introduced. Special emphasis is put on keeping the computational effort as small as possible. The proposed robust optimization method is applied to a standard benchmark optimization problem.Index Terms-Electromagnetic design, robust optimization, TEAM problem, worst case design.

This paper gives an overview of some stochastic optimization strategies, namely, evolution strategies, genetic algorithms, and simulated annealing, and how these methods can be applied to problems in electrical engineering. Since these methods usually require a careful tuning of the parameters which control the behavior of the strategies (strategy parameters), significant features of the algorithms implemented by the authors are presented. An analytical comparison among them is performed. Finally, results are discussed on three optimization problems

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

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