Using an integrated processing methodology, an injection or compression moulded thermoplastic structure can be locally reinforced, for example, with textile structures or uni-directional fibre tows. Netshape components can be produced with cycle times typical for injection or compression moulding but with higher mechanical properties. As the inclusion of local reinforcements adds complexity to the design process, both in the terms of amounts and location, mathematical optimization techniques in conjunction with finite element simulations can be a useful tool to design weight and cost effective structures. This work evaluates approximation models used in conjunction with genetic algorithms by using a generic but industry relevant beam structure as an example problem. The underlying finite element model is based on layered shell elements with up to four different materials through the thickness and with nine design variables controlling the material thicknesses in different areas. Material non-linear behaviour is included for the over-moulding polymer and for the compressive response of one specific fabric material. The accuracy of four different approximation methods was assessed, polynomial models with and without term selection, radial basis functions and Kriging. Rather than solely examine the mean approximation error, a method is proposed of how to treat single large approximation errors. It is shown that a Multi-Island Genetic algorithm can be successfully used to optimize the structural weight under 64 constraints with continuous and mixed continuous-discrete design variables.