Optimisation of electromagnetic problems with uncertain parameters and tolerances in the design variables

The common approach to continuous and discrete optimisation problems in electromagnetics does not take into account uncertainties and variations of the design variables. Local sensitivity analysis is usually performed only after the optimisation run to study the behaviour of the objective function in the neighbourhood of the optimum. However, this procedure may prove inefficient if the optimum has to be rejected due to sensitivity considerations and a new run has then to be performed. In this paper an alternative approach, which takes into account uncertainties in the design variables and physical data, is presented, and an analytical function is used to highlight the features of the proposed method. The essence of the technique is to couple the optimisation with a series of worst case analyses which are embedded in the optimisation loop. The method is fully general and can be applied to any optimisation method. The additional computational costs associated with the procedure maybe relatively high, but in the authors’ opinion the obtained gains in user confidence in the solution and the computational savings in some cases far offset the possible drawbacks of the method.