Optimal shape design problems are distributed parameter problems, typically requiring the solution of a partial differential equation over a domain whose shape is not known and which has to be determined as part of the problem. As such they are inherently nonlinear in nature and pose special (computational) difficulties. (They are similar in nature to moving boundary problems – such as modelling the melting of an iceberg.) In fact in these problems the solution of the partial differential equation takes place over a region whose shape has to be chosen to optimise some functional and hence numerical (approximate) solution methods are the only feasible ones.