An optimization procedure for the shape design of morphing aircraft is presented. The process is coupled with a knowledge-based framework combining parametric geometry representation, multidisciplinary modelling, and genetic algorithm. The parameterization method exploits the implicit properties of the Bernstein polynomial least squares fitting to allow both local and global shape control. The framework is able to introduce morphing shape changes in a feasible way, taking into account the presence of structural parts, such as the wing-box, the physical behaviour of the morphing skins, and the effects that these modifications have on the aerodynamic performances. It inherits CAD capabilities of generating 3D deformed morphing shapes and it is able to automatically produce aerodynamic and structural models linked to the same parametric geometry. Dedicated crossover and mutation strategies are used to allow the parametric framework to be efficiently incorporated into the genetic algorithm. This procedure is applied to the shape design of Reference Aircraft (RA) and to the assessment of the potential benefits that morphing devices can bring in terms of aircraft performances. It is adopted for the design of a variable camber morphing wing to investigate the effect of conformal leading and trailing edge control surfaces. Results concerning four different morphing configurations are reported.