Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amoignon, O., Hradil, J., Navratil, J.: A numerical study of adaptive FFD in aerodynamic shape optimization. In: Proceedings of 52nd Aerospace Sciences Meeting (2014)
Amoignon, O., Navrátil, J., Hradil, J.: Study of parameterizations in the project CEDESA. In: Proceedings of 52nd Aerospace Sciences Meeting (2014)
Becker, G., Schäfer, M., Jameson, A.: An advanced NURBS fitting procedure for post-processing of grid-based shape optimizations. In: Proceedings of 49th Aerospace Sciences Meeting (2011)
Chen, S., Billings, S.A., Luo, W.: Orthogonal least squares methods and their application to non-linear system identification. Int. J. Control 50(5), 1873–1896 (1989)
Costa, E., Biancolini, M.E., Groth, C., Cella, U., Veble, G., Andrejasic, M.: RBF-based aerodynamic optimization of an industrial glider. In: Proceedings of International CAE Conference (2014)
Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (2012)
Gomm, J.B., Yu, D.L.: Selecting radial basis function network centers with recursive orthogonal least squares training. IEEE Trans. Neural Netw. 11(2), 306–314 (2000)
Hsu, W.M., Hughes, J.F., Kaufman, H.: Direct manipulation of free-form deformations. In: Proceedings of ACM SIGGRAPH, pp. 177–184 (1992)
Igel, C., Heidrich-Meisner, V., Glasmachers, T.: Shark. J. Mach. Learn. Res. 9, 993–996 (2008)
Lloyd, S.P.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)
MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)
Menzel, S., Olhofer, M., Sendhoff, B.: Direct manipulation of free form deformation in evolutionary design optimisation. In: Proceedings of the International Conference on Parallel Problem Solving From Nature, pp. 352–361 (2006)
Mina, A.A., Braha, D., Bar-Yam, Y.: Complex engineered systems: a new paradigm. In: Complex Engineered Systems: Science Meets Technology. Understanding Complex Systems, pp. 1–21. Springer, Heidelberg (2006)
Ohtake, Y., Belyaev, A., Seidel, H.P.: 3D scattered data approximation with adaptive compactly supported radial basis functions. In: Proceedings of IEEE International Conference on Shape Modeling Applications, pp. 31–39 (2004)
Olhofer, M., Jin, Y., Sendhoff, B.: Adaptive encoding for aerodynamic shape optimization using evolution strategies. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 576–583 (2001)
Richter, A., Achenbach, J., Menzel, S., Botsch, M.: Evolvability as a quality criterion for linear deformation representations in evolutionary optimization. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 901–910 (2016)
Richter, A., Botsch, M., Menzel, S.: Evolvability of representations in complex system engineering: a survey. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1327–1335 (2015)
Sieger, D., Gaulik, S., Achenbach, J., Menzel, S., Botsch, M.: Constrained space deformation techniques for design optimization. Comput. Aided Des. 73, 40–51 (2016)
Sieger, D., Menzel, S., Botsch, M.: A comprehensive comparison of shape deformation methods in evolutionary design optimization. In: Proceedings of the International Conference on Engineering Optimization (2012)
Simões, L.F., Izzo, D., Haasdijk, E., Eiben, A.E.: Self-adaptive genotype-phenotype maps: neural networks as a meta-representation. In: International Conference on Parallel Problem Solving from Nature, pp. 110–119 (2014)
Sterelny, K.: Symbiosis, evolvability and modularity. In: Modularity in Development and Evolution, pp. 490–516. University of Chicago Press (2004)
Vuong, A.V., Giannelli, C., Jüttler, B., Simeon, B.: A hierarchical approach to adaptive local refinement in isogeometric analysis. Comput. Methods Appl. Mech. Eng. 200(49), 3554–3567 (2011)
Wagner, G.P., Altenberg, L.: Perspectives: complex adaptations and the evolution of evolvability. Evolution 50(3), 967–976 (1996)
Webb, A.R., Shannon, S.: Shape-adaptive radial basis functions. IEEE Trans. Neural Netw. 9(6), 1155–1166 (1998)
Wendland, H.: Scattered Data Approximation. Cambridge University Press, Cambridge (2004)
Yang, Z., Sendhoff, B., Tang, K., Yao, X.: Target shape design optimization by evolving B-splines with cooperative coevolution. Appl. Soft Comput. 48, 672–682 (2016)
Zheng, J., Wang, Y., Seah, H.S.: Adaptive T-spline surface fitting to z-map models. In: Proceedings of the 3rd International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia, pp. 405–411 (2005)
Acknowledgments
Andreas Richter gratefully acknowledges the financial support from Honda Research Institute Europe (HRI-EU). Mario Botsch is supported by the Cluster of Excellence Cognitive Interaction Technology “CITEC” (EXC 277) at Bielefeld University, funded by the German Research Foundation (DFG).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Richter, A., Achenbach, J., Menzel, S., Botsch, M. (2017). Multi-objective Representation Setups for Deformation-Based Design Optimization. In: Trautmann, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2017. Lecture Notes in Computer Science(), vol 10173. Springer, Cham. https://doi.org/10.1007/978-3-319-54157-0_35
Download citation
DOI: https://doi.org/10.1007/978-3-319-54157-0_35
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54156-3
Online ISBN: 978-3-319-54157-0
eBook Packages: Computer ScienceComputer Science (R0)