Orthogonalization of linear representations for efficient evolutionary design optimization.

Real-world evolutionary design optimizations of complex shapes can efficiently be solved using linear deformation representations, but the optimization performance crucially depends on the initial deformation setup. For instance, when modeling the deformation by radial basis functions (RBF) the convergence speed depends on the condition number of the involved kernel matrix, which previous work therefore tried to optimize through careful placement of RBF kernels. We show that such representation-specific techniques are inherently limited and propose a generic, representation-agnostic optimization based on orthogonalization of the deformation matrix. This straightforward black-box optimization projects any given linear deformation setup to optimal condition number without changing its design space, which, as we show through extensive numerical experiments, can boost the convergence speed of evolutionary optimizations by up to an order of magnitude.