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Previous work on optimisation has primarily focused on the applications of genetic algorithms in conjunction with problem-specific or semi-analytic tools. Recent developments in fast algorithms now offer the possibility of designs and moreover allow for full flexibility in material specification across three dimensions. As an example, the paper combines genetic algorithms with fast hybrid finite-element/boundary-integral simulations to conduct shape optimisation of frequency selective surfaces (FSSs). Optimal shapes for FSS geometries subject to given performance criteria are demonstrated.