Abstract
This chapter is concerned with the efficient use of metamodel-assisted evolutionary algorithms built in multilevel or hierarchical schemes for the solution of computationally expensive optimization problems. Existing methods developed by other researchers or the authors’ group are overviewed and a new enhancement based on fitness inheritance is proposed. Whereas conventional evolutionary algorithms require a great number of calls to the evaluation software, the use of low cost surrogates or metamodels, trained on the fly on previously evaluated individuals for pre-evaluating the evolving populations, reduce noticeably the CPU cost of an optimization. Since, themetamodel training requires a minimum amount of previous evaluations, the starting population is evaluated on the problem-specific model. Fitness inheritance is introduced in this context so as to approximate the objective function values in place of metamodels. In addition, to profit of the availability of evaluation or parameterization models of lower fidelity and CPU cost and/or refinement methods, a multilevel search algorithm relying also on the use of metamodels is presented. The algorithm may optionally operate as hierarchical-distributed (many levels performing distributed optimization) or distributed-hierarchical (more than one sub-populations undergoing their own hierarchical optimizations) to further reduce the design cycle time. The proposed algorithms are generic and can be used to solve any kind of optimization problems. Here, aerodynamic shape optimization problems, including turbomachinery applications, are used to demonstrate the efficiency of the proposed methods. A new computationally demanding application, namely the optimization of a 3D compressor blade is also shown.
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
Alba, E., Tomassini, M.: Parallelism and evolutionary algorithms. IEEE Trans. on Evolutionary Computation 6(5) (2002)
Asouti, V., Zymaris, A., Papadimitriou, D., Giannakoglou, K.: Continuous and discrete adjoint approaches for aerodynamic shape optimization with low Mach number preconditioning. Int. J. for Numerical Methods in Fluids 57(10), 1485–1504 (2008)
Auger, A., Hansen, N.: A restart cma evolution strategy with increasing population size. In: CEC 2005, UK, vol. 2, pp. 1769–1776 (2005)
Bäck, T.: Evolutionary Algorithms in Theory and Practice. Evolution Strategies. Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)
Benoudjit, N., Archambeau, C., Lendasse, A., Lee, J., Verleysen, M.: Width optimization of the Gaussian kernels in radial basis function networks. In: ESANN 2002, Bruges, pp. 425–432 (2002)
Branke, J., Schmidt, C.: Faster convergence by means of fitness estimation. Soft Computing — A Fusion of Foundations, Methodologies & Applications 9(1), 13–20 (2005)
Büche, D., Schraudolph, N., Koumoutsakos, P.: Accelerating evolutionary algorithms with Gaussian process fitness function models. Trans. on Systems, Man & Cybernetics — Part C: Applications & Reviews 35(2), 183–194 (2005)
Bull, L.: On model-based evolutionary computation. Soft Computing — A Fusion of Foundations, Methodologies & Applications 3(2), 76–82 (1999)
Cantu-Paz, E.: A survey of parallel genetic algorithms. Calculateurs Paralleles, Reseaux et Systemes Repartis 10(2), 141–171 (1998)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. Trans. on Evolutionary Computation 6(2), 182–197 (2002)
Désidéri, J., Janka, A.: Hierarchical parameterization for multilevel evolutionary shape optimization with application to aerodynamics. In: EUROGEN 2003, Barcelona (2003)
Doorly, D.J., PeirĂł, J.: Supervised parallel genetic algorithms in aerodynamic optimisation. AIAA Paper 1997-1852 (1997)
Drela, M., Giles, M.: Viscous-inviscid analysis of transonic and low Reynolds number airfoils. AIAA J. 25(10), 1347–1355 (1987)
Ducheyne, E., De Baets, B., De Wulf, R.: Fitness inheritance in multiple objective evolutionary algorithms: A test bench and real-world evaluation. Applied Soft Computing 8(1), 337–349 (2008)
Duvigneau, R., Chaigne, B., Désidéri, J.: Multi-level parameterization for shape optimization in aerodynamics and electromagnetics using a particle swarm optimization algorithm. Tech. Rep. RR-6003, INRIA, France (2006)
Eby, D., Averill, R., Punch III, W., Goodman, E.: Evaluation of injection island GA performance on flywheel design optimization. In: Proceedings of the 3rd Conf. on Adaptive Computing in Design & Manufacturing, pp. 121–136. Springer, Heidelberg (1998)
Emmerich, M.T.M., Giotis, A., Özdemir, M., Bäck, T., Giannakoglou, K.: Metamodel-assisted evolution strategies. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 361–370. Springer, Heidelberg (2002)
Emmerich, M., Giannakoglou, K., Naujoks, B.: Single- and multi-objective evolutionary optimization assisted by Gaussian random field metamodels. IEEE Trans. on Evolutionary Computation 10(4), 421–439 (2006)
Farina, M.: A neural network based generalized response surface multiobjective evolutionary algorithm. In: CEC 2002, Honolulu, HI, vol. 1, pp. 956–961 (2002)
Foster, I.: Globus toolkit version 4: Software for service-oriented systems. In: Jin, H., Reed, D., Jiang, W. (eds.) NPC 2005. LNCS, vol. 3779, pp. 2–13. Springer, Heidelberg (2005)
Fritzke, B.: Fast learning with incremental RBF networks. Neural Processing Letters, 2–5 (1994)
Fritzke, B.: Growing cell structures — A self-organizing network for unsupervised and supervised learning. Neural Networks 7(9), 1441–1460 (1994)
Georgopoulou, C., Giannakoglou, K.: A multi-objective metamodel-assisted memetic algorithm with strength-based local refinement. Engineering Optimization Accepted for publication (to appear, 2009)
Giannakoglou, K.: Designing turbomachinery blades using evolutionary methods. ASME Paper 99-GT-181 (1999)
Giannakoglou, K.: Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Progress in Aerospace Sciences 38(1), 43–76 (2002)
Giannakoglou, K.: The EASY (Evolutionary Algorithms System) software (2008), http://velos0.ltt.mech.ntua.gr/EASY
Giannakoglou, K., Georgopoulou, C.: Multiobjective metamodel-assisted memetic algorithms. In: Multiobjective Memetic Algorithms. Studies in Computational Intelligence. Springer, Heidelberg (2009)
Giannakoglou, K., Giotis, A., Karakasis, M.: Low-cost genetic optimization based on inexact pre-evaluations and the sensitivity analysis of design parameters. Inverse Problems in Engineering 9, 389–412 (2001)
Giannakoglou, K., Papadimitriou, D., Kampolis, I.: Aerodynamic shape design using evolutionary algorithms and new gradient-assisted metamodels. Computer Methods in Applied Mechanics & Engineering 195, 6312–6329 (2006)
Giannakoglou, K., Kampolis, I., Georgopoulou, C.: Metamodel-assisted evolutionary algorithms (MAEAs). In: Introduction to Optimization and Multidisciplinary Design in Aeronautics and Turbomachinery, Lecture Series, von Karman Institute, Rhodes–Saint Genése (2008)
Giotis, A., Giannakoglou, K.: Single- and multi-objective airfoil design using genetic algorithms and artificial intelligence. In: EUROGEN 1999, Jyväskylä (1999)
Giotis, A., Giannakoglou, K., PĂ©riaux, J.: A reduced-cost multi-objective optimization method based on the Pareto front technique, neural networks and PVM. In: ECCOMAS 2000, Barcelona (2000)
Goldberg, D.: Genetic Algorithms in Search, Optimization & Machine Learning. Addison-Wesley, Reading (1989)
Greenman, R., Roth, K.: Minimizing computational data requirements for multi-element airfoils using neural networks. AIAA Paper 1999-0258 (1999)
Haykin, S.: Neural Networks - A Comprehensive Foundation, 2nd edn. Prentice Hall, Englewood Cliffs (1999)
Herrera, F., Lozano, M., Moraga, C.: Hierarchical distributed genetic algorithms. Int. J. of Intelligent Systems 14(9), 1099–1121 (1999)
Jin, Y., Olhofer, M., Sendhoff, B.: A framework for evolutionary optimization with approximate fitness functions. IEEE Trans. on Evolutionary Computation 6(5), 481–494 (2002)
Kampolis, I., Giannakoglou, K.: A multilevel approach to single- and multiobjective aerodynamic optimization. Computer Methods in Applied Mechanics & Engineering 197, 2963–2975 (2008)
Kampolis, I., Giannakoglou, K.: Distributed evolutionary algorithms with hierarchical evaluation. Engineering Optimization Accepted for publication (to appear, 2009)
Kampolis, I., Karangelos, E., Giannakoglou, K.: Gradient-assisted radial basis function networks: theory and applications. Applied Mathematical Modelling 28(13), 197–209 (2004)
Kampolis, I., Papadimitriou, D., Giannakoglou, K.: Evolutionary optimization using a new radial basis function network and the adjoint formulation. Inverse Problems in Science & Engineering 14(4), 397–410 (2006)
Kampolis, I., Zymaris, A., Asouti, V., Giannakoglou, K.: Multilevel optimization strategies based on metamodel-assisted evolutionary algorithms, for computationally expensive problems. In: CEC 2007, Singapore (2007)
Karakasis, M., Giannakoglou, K.: On the use of metamodel-assisted, multi-objective evolutionary algorithms. Engineering Optimization 38(8), 941–957 (2006)
Karakasis, M., Giotis, A., Giannakoglou, K.: Inexact information aided, low-cost, distributed genetic algorithms for aerodynamic shape optimization. Int. J. for Numerical Methods in Fluids 43(10-11), 1149–1166 (2003)
Karakasis, M., Koubogiannis, D., Giannakoglou, K.: Hierarchical distributed evolutionary algorithms in shape optimization. Int. J. for Numerical Methods in Fluids 53(3), 455–469 (2007)
Karayiannis, N., Mi, G.: Growing radial basis neural networks: Merging supervised and unsupervised learning with network growth techniques. IEEE Trans. on Neural Networks 8(6), 1492–1506 (1997)
Keane, A., Nair, P.: Computational Approaches for Aerospace Design – The Pursuit of Excellence. John Wiley & Sons, Ltd., Chichester (2005)
Knowles, J., Corne, D.: M-PAES: A memetic algorithm for multiobjective optimization. In: CEC 2000, pp. 325–332. IEEE Press, Los Alamitos (2000)
Lambropoulos, N., Koubogiannis, D., Giannakoglou, K.: Acceleration of a Navier-Stokes equation solver for unstructured grids using agglomeration multigrid and parallel processing. Computer Methods in Applied Mechanics & Engineering 193, 781–803 (2004)
Langdo, W., Poli, R.: Evolving problems to learn about particle swarm and other optimisers. In: CEC 2005, UK, pp. 81–88 (2005)
Liakopoulos, P., Kampolis, I., Giannakoglou, K.: Grid-enabled, hierarchical distributed metamodel-assisted evolutionary algorithms for aerodynamic shape optimization. Future Generation Computer Systems 24, 701–708 (2008)
Lim, D., Ong, Y.S., Jin, Y., Sendhoff, B., Lee, B.S.: Efficient hierarchical parallel genetic algorithms using grid computing. Future Generation Computer Systems 23(4), 658–670 (2007)
Lin, S.C., Punch, W., Goodman, E.: Coarse-grain parallel genetic algorithms: categorization and new approach. In: 6th IEEE Symposium on Parallel & Distributed Processing, Dallas, pp. 28–37 (1994)
Massie, M., Chun, B., Culler, D.: The Ganglia distributed monitoring system: Design, implementation, and experience. Parallel Computing 30(7) (2004)
Mathioudakis, K., Papailiou, K., Neris, N., Bonhommet, C., Albrand, G., Wenger, U.: An annular cascade facility for studying tip clearance effects in high speed flows. In: XIII ISABE Conf., Chattanooga, TN (1997)
Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. Springer, Heidelberg (1996)
Michalewicz, Z., Fogel, D.: How to Solve it: Modern Heuristics, 2nd edn. Springer, Heidelberg (2004)
Montero, R., Huedo, E., Llorente, I.: A framework for adaptive execution on grids. J. of Software - Practice & Experience 34, 631–651 (2004)
Moody, J., Darken, C.: Fast learning in networks of locally-tuned processing units. Neural Computation 1(2), 281–294 (1989)
Muyl, F., Dumas, L., Herbert, V.: Hybrid method for aerodynamic shape optimization in automotive industry. Computers & Fluids 33(5-6), 849–858 (2004)
Nakayama, H., Inoue, K., Yoshimori, Y.: Approximate optimization using computational intelligence and its application to reinforcement of cable-stayed bridges. In: ECCOMAS 2004, Jyväskylä (2004)
Nocedal, J., Wright, S.: Numerical Optimization. Springer, Heidelberg (1999)
Nowostawski, M., Poli, R.: Parallel genetic algorithm taxonomy. In: KES 1999, pp. 88–92 (1999)
Ong, Y., Lum, K., Nair, P.: Hybrid evolutionary algorithm with Hermite radial basis function interpolants for computationally expensive adjoint solvers. Computational Optimization & Applications 39(1), 97–119 (2008)
Ong, Y.S., Lum, K.Y., Nair, P., Shi, D., Zhang, Z.K.: Global convergence of unconstrained and bound constrained surrogate-assisted evolutionary search in aerodynamic shape design. In: CEC 2003, Canberra, vol. 3, pp. 1856–1863 (2003)
Ong, Y.S., Nair, P., Keane, A.: Evolutionary optimization of computationally expensive problems via surrogate modeling. AIAA J. 41(4), 687–696 (2003)
Ong, Y.S., Lim, M., Zhu, N., Wong, K.: Classification of adaptive memetic algorithms: A comparative study. IEEE Trans. on Systems Man & Cybernetics - Part B 36, 141–152 (2006)
Papadimitriou, D., Giannakoglou, K.: A continuous adjoint method with objective function derivatives based on boundary integrals for inviscid and viscous flows. Computers & Fluids 36, 325–341 (2007)
Papadimitriou, D., Giannakoglou, K.: Total pressure loss minimization in turbomachinery cascades using a new continuous adjoint formulation. J. of Power & Energy (Part A) 221, 865–872 (2007)
Papadrakakis, M., Lagaros, N.D., Tsompanakis, Y.: Structural optimization using evolution strategies and neural networks. Computer Methods in Applied Mechanics & Engineering 156(1-4), 309–333 (1998)
Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, Heidelberg (1997)
Pierret, S., Van den Braembussche, R.: Turbomachinery blade design using a Navier-Stokes solver and artificial neural network. ASME J. of Turbomachinery 121(2), 326–332 (1999)
Poggio, T., Girosi, F.: Networks for approximation and learning. Proceedings of the IEEE 78(9), 1481–1497 (1990)
Politis, E., Giannakoglou, K., Papailiou, K.: High–speed flow in an annular cascade with tip clearance: Numerical investigation. ASME Paper 98-GT-247 (1998)
Poloni, C., Giurgevich, A., Onesti, L., Pediroda, V.: Hybridization of a multiobjective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics. Computer Methods in Applied Mechanics & Engineering 186(2), 403–420 (2000)
Ratle, A.: Optimal sampling strategies for learning a fitness model. In: CEC 1999, Washington, DC, vol. 3, pp. 2078–2085 (1999)
Sefrioui, M., Périaux, J.: A hierarchical genetic algorithm using multiple models for optimization. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 879–888. Springer, Heidelberg (2000)
Smith, R., Dike, B., Stegmann, S.: Fitness inheritance in genetic algorithms. In: SAC 1995, pp. 345–350. ACM, New York (1995)
Spalart, P., Allmaras, S.: A one-equation turbulence model for aerodynamic flows. AIAA Paper 92-0439 (1992)
Thain, D., Tannenbaum, T., Livny, M.: Distributed computing in practice: the Condor experience. Concurrency - Practice and Experience 17(2-4), 323–356 (2005)
Thévenin, D., Janiga, G.: Optimization and Computational Fluid Dynamics. Springer, Heidelberg (2008)
Ulmer, H., Streichert, F., Zell, A.: Evolution strategies assisted by Gaussian processes with improved pre-selection criterion. In: CEC 2003, Canberra, vol. 1, pp. 692–699 (2003)
Zhou, Z., Ong, Y.S., Lim, M., Lee, B.: Memetic algorithm using multi–surrogates for computational expensive optimization problems. Soft Computing 11(10), 957–971 (2007)
Zitzler, E., Laumans, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm. Tech. Rep. 103, ETH, Computer Engineering & Communication Networks Lab. (TIK), Zurich (2001)
Zitzler, E., Laumans, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: EUROGEN 2001, CIMNE, Barcelona, pp. 19–26 (2001)
Zitzler, E., Brockhoff, D., Thiele, L.: The hypervolume indicator revisited: On the design of pareto-compliant indicators via weighted integration. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 862–876. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Giannakoglou, K.C., Kampolis, I.C. (2010). Multilevel Optimization Algorithms Based on Metamodel- and Fitness Inheritance-Assisted Evolutionary Algorithms. In: Tenne, Y., Goh, CK. (eds) Computational Intelligence in Expensive Optimization Problems. Adaptation Learning and Optimization, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10701-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-10701-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10700-9
Online ISBN: 978-3-642-10701-6
eBook Packages: EngineeringEngineering (R0)