The representation of a design influences the success of any kind of optimization significantly. The perfect trade-off between the number of parameters which define the search space and the achievable design flexibility is very crucial since it influences the convergence speed of the chosen optimization algorithm as well as the possibility to find the design which provides the best performance. Classical methods mostly define the design directly, e.g. via spline surfaces or by representations which are specialized to one design task. In the present chapter, the so-called deformation methods are focused which follow a different approach. Instead of describing the shape directly, deformation terms are used to morph an initial design into newones. This decouples a complex design from an expensive shape description while relying purely on mapping terms which are responsible for the geometry transformations. Thus, the designer is encouraged to determine the optimal relation between parameter set and design flexibility according to the given task. With respect to the optimization, these mapping terms are considered as parameters. In this chapter, the combination of two state of the art deformation algorithms with evolutionary optimization is focused. After an introduction of these techniques, a framework for an autonomous design optimization is sketched in more detail. By means of two optimizations, which feature a stator blade of a jet turbine the workability is shown and the advantages of such representations are highlighted.
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
Preview
Unable to display preview. Download preview PDF.
References
Arima, T., Sonoda, T., Shirotori, M., Tamura, A., and Kikuchi, K. (1999). A numerical investigation of transonic axial compressor rotor flow using a low-Reynolds-number k-ε turbulence model. ASME Journal of Turbomachinery, 121(1), pp. 44–58.
Bihrer, T. (2006). Direct Manipulation of Free-Form Deformation in Evolutionary Optimisation. Diploma Thesis. Computer Science Department/ Simulation, Systems Optimization and Robotics Group (SIM), TU Darmstadt, Germany
Coquillart, S. (1990). Extended Free-Form Deformation: A Sculpturing Tool for 3D Geometric Modeling. Computer Graphics, 24(4):187–196.
Fogel, D.B. (1995). Evolutionary Computation: toward a new philosophy of machine learning New York, NY: IEEE Press.
Foli, K., Okabe, T., Olhofer, M., and Sendhoff, B. (2006). Optimization of Micro Heat Exchanger: CFD, Analytical Approach and Multi-Objective Evolutionary Algorithms. International Journal of Heat and Mass Transfer, 49(5-6), pp. 1090–1099.
Geist, A. et al. (1995). PVM: Parallel Virtual Machine – A Users’ Guide and Tutorial for Networked Parallel Computing. Cambridge, Ma: The MIT Press.
Hansen, N., and Ostermeier, A. (2001). Completely Derandomized Self- adaptation in Evolution Strategies. In: Evolutionary Computation, vol. 9, no. 2, pp. 159–196.
Hasenjäger, M., Sendhoff, B., Sonoda, T., and Arima, T. (2005). Three dimensional evolutionary aerodynamic design optimization with CMA-ES. In: GECCO 2005: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, edited by H.-G. ∼Beyer et al. ACM Press, New York, NY, pp. 2173–2180.
Hasenjäger, M., Sendhoff, B., Sonoda, T., and Arima, T. (2005). Single and Multi-Objective Approaches to 3D Evolutionary Aerodynamic Design Optimisation. In: Proceedings of the 6th World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil.
Hsu, W.M., Hughes, J.F., and Kaufman, H. (1992). Direct Manipulations of Free-Form Deformations. Computer Graphics, 26:177–184.
Kanazaki, M., Obayashi, S., Morikawa, M., and Nakahash, K. (2002). Multiobjective Design Optimization of Merging Configuration for an Exhaust Manifold of a Car Engine. In: Parallel Problem Solving from Nature - PPSN VII, Guervos, Admidis, Beyer, Fernandez-Villacanas and Schwefel (Eds.), Lecture Notes in Computer Science, 2439, pp. 281–287.
Lépine, J., Guibault, F., Trépanier, J.Y., and Pépin, F. (2001). Optimized Nonuniform Rational B-spline Geometrical Representation for Aerodynamic Design of Wings. AIAA Journal, Vol. 39, No. 11.
Menzel, S., Olhofer, M., and Sendhoff, B. (2005). Evolutionary Design Optimisation of Complex Systems integrating Fluent for parallel Flow Evaluation. In: Proceedings of European Automotive CFD Conference, pp. 279–289.
Olhofer, M., Jin, Y., and Sendhoff, B. (2001). Adaptive encoding for aerodynamic shape optimization using Evolution Strategies. In: Congress on Evolutionary Computation (CEC). IEEE Press, Seoul, Korea, pp. 576–583.
Ong, Y.S., Nair, P.B., and Lum, K.Y. (2006). Max-Min Surrogate Assisted Evolutionary Algorithm for Robust Aerodynamic Design. IEEE Transactions on Evolutionary Computation, 10(4), pp. 392–404.
Oyama, A., Obayashi, S., and Nakamura, T. (2000). Real-coded Adaptive Range Genetic Algorithm Applied to Transonic Wing Optimization. Proceedings of  the 6th International Conference on Parallel Problem Solving from Nature. Springer, pp. 712–721.
Perry, E.C., Benzley, S.E., Landon, M., and Johnson, R. (2000). Shape Optimization of Fluid Flow Systems. In: Proceedings of ASME FEDSM’00. ASME Fluids Engineering Summer Conference, Boston.
Piegl, L., and Tiller, W. (1997). The NURBS Book. Springer-Verlag Berlin Heidelberg.
PVM: Parallel Virtual Machine. http://www.csm.ornl.gov/pvm/pvm_home.html.
Rechenberg, I. (1994). Evolutionsstrategie ’94. Friedrich Frommann Verlag⋅ Günther Holzboog, Stuttgart-Bad Cannstatt.
Requicha, A.A.G. (1980). Representations for Rigid Solids: Theory, Methods, and Systems. In: Computing Surveys 12, pp. 437–464.
Schwefel, H.P. (1995). Evolution and Optimum Seeking. John Wiley & sons. New York.
Sederberg, T.W., and Parry, S.R. (1986). Free-Form Deformation of Solid Geometric Models. Computer Graphics, 20(4):151–160.
Sendhoff, B., Kreuz, M., and von Seelen, W. (1997). A condition for the genotype-phenotype mapping: Causality. In: Thomas Bäck, editor, Proceedings of the Seventh International Conference on Genetic Algorithms (ICGA’97), Morgan Kauffmann, pp. 73–80.
Sonoda, T., Yamaguchi, Y., Arima, T., Olhofer, M., Sendhoff, B., and Schreiber, H-A. (2004). Advanced High Turning Compressor Airfoils for Low Reynolds Number Condition, Part 1: Design and Optimization. Journal of Turbomachinery, 126: 350–359.
Terzopoulos, D., and Qin, H. (1994). Dynamic NURBS with geometric constraints for interactive sculpting. In: ACM Transactions on Graphics 13, Nr. 2, pp. 103–136.
Ugail, H., and Wilson, M.J. (2003). Efficient shape parameterisation for automatic design optimisation using a partial differential equation formulation. In: Computers & Structures 81, pp. 2601–2609.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Menzel, S., Sendhoff, B. (2008). Representing the Change - Free Form Deformation for Evolutionary Design Optimization. In: Yu, T., Davis, L., Baydar, C., Roy, R. (eds) Evolutionary Computation in Practice. Studies in Computational Intelligence, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75771-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-75771-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75770-2
Online ISBN: 978-3-540-75771-9
eBook Packages: EngineeringEngineering (R0)