Evolvability As A Quality Criterion For Linear Deformation Representations In Evolutionary Optimization

Industrial product design is characterized by increasing complexity due to the high number of involved parameters, objectives, and boundary conditions, all typically changing over time. Population-based evolutionary design optimization targets to solve these kinds of application problems, offering efficient algorithms striving for high-quality solutions. An important factor in the optimization setup is the representation, which defines the encoding of the design and the mapping from parameter space to design space. Being able to numerically quantify the quality of different representation settings would strengthen the optimal choice of encoding. Motivated by the biological concept of evolvability, we propose three criteria, namely variability, regularity, and improvement potential, to evaluate linear deformation representations for their use in shape optimization problems. The first aspect characterizes the exploration potential of the design space, the second measures the expected convergence speed, and the third determines the expected improvement of the quality of a design. We propose and experimentally analyze mathematical definitions for each of the three criteria. We demonstrate the successful application of our model to two evolutionary optimization scenarios: fitting of 1D height fields and fitting of 3D face scans, both based on RBF deformations. Due to the general character of our definition we expect the transferability of our concepts to alternative deformation methods.