Non-separable fitness functions for evolutionary shape optimization benchmarking

Target shape matching can be used as a quick and easy surrogate task when evaluating optimization algorithms intended for computationally expensive tasks, such as turbine blade design using computational fluid dynamics. Many reasonable shape representations render the shape matching fitness landscape linearly separable, unlike that of the turbine design task. Optimization algorithms may exploit this property, so evaluations based on shape matching may be inappropriate for turbine design. To address this disparity, a method is proposed to generate a linearly non-separable shape matching fitness landscape: the test shape is compared to one or more distracter shapes as well as the target, and the individual fitness measures are combined non-linearly. A demonstration is given, using a simple polygon representation and exhaustively varying two parameters, to show that this method does indeed generate a fitness landscape that cannot be linearly decomposed.