Multi-objective Representation Setups for Deformation-Based Design Optimization.

The increase of complexity in virtual product design requires high-quality optimization algorithms capable to find the global parameter solution for a given problem. The representation, which defines the encoding of the design and the mapping from parameter space to design space, is a key aspect for the performance of the optimization process. To initialize representations for a high performing optimization we utilize the concept of evolvability. Our interpretation of this concept consists of three performance criteria, namely variability, regularity, and improvement potential, where regularity and improvement potential characterize conflicting goals. In this article we address the generation of initial representation setups trading off between these two conflicting criteria for design optimization. We analyze Pareto-optimal compromises for deformation representations with radial basis functions in two test scenarios: fitting of 1D height fields and fitting of 3D face scans. We use the Pareto front as a ground-truth to show the feasibility of a single-objective optimization targeting one preference-based trade-off. Based on the results of both optimization approaches we propose two heuristic methods, Lloyd sampling and orthogonal least squares sampling, targeting representations with high regularity and high improvement potential at the two ends of the Pareto front. Thereby, we overcome the time consuming process of an evolutionary optimization to set up high-performing representations for these two cases.