A GRS method for Pareto-optimal front identification in electromagnetic multiobjective synthesis

Generalized response surfaces (GRS) methods are a well established technique for single-objective optimization in the case of time consuming objective function evaluation. The essential idea is to consider throughout the optimization two different objective functions; the first one be evaluated in as few cases as possible due to its computational cost, the second one is the interpolation of the true objective function via some interpolation technique and it can be evaluated as many time as is needed. Evolutionary multiobjective optimization is a well established computational research area where several powerful methods are available for a fully convergent Pareto optimal front (POF) approximation. The computational cost of multiobjective optimization evolutionary algorithms (MOEAs) is relevant and it may be impractical when industrial design is concerned and the task of reducing objectives function calls is an open research topic. To this aim the link between GRS methods and MOEAs seems to be an appealing alternative. Though very appealing such linking is not straightforward due to the fact that when dealing with multiobjective problems the equivalent of the current optimum region of single-objective problems (an n-dimensional hypersphere centered on the current optimum) is a very complex and often non- connected area of design domain search space; the iterative update-search strategy is thus non-trivial in this case.