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A Self-adaptive Genetic Algorithm Applied to Multi-Objective Optimization of an Airfoil

  • Conference paper
EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 227))

Abstract

Genetic algorithms (GAs) have been used to tackle non-linear multi-objective optimization (MOO) problems successfully, but their success is governed by key parameters which have been shown to be sensitive to the nature of the particular problem, incorporating concerns such as the numbers of objectives and variables, and the size and topology of the search space, making it hard to determine the best settings in advance. This work describes a real-encoded multi-objective optimizing GA (MOGA) that uses self-adaptive mutation and crossover, and which is applied to optimization of an airfoil, for minimization of drag and maximization of lift coefficients. The MOGA is integrated with a Free-Form Deformation tool to manage the section geometry, and XFoil which evaluates each airfoil in terms of its aerodynamic efficiency. The performance is compared with those of the heuristic MOO algorithms, the Multi-Objective Tabu Search (MOTS) and NSGA-II, showing that this GA achieves better convergence.

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References

  1. Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, 2nd edn. MIT Press, Massachusetts (1992)

    Google Scholar 

  2. Goldberg, D.E.: Genetic Algorithms in Search, Optimization & Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  3. Schaffer, J.D.: Some experiments in machine learning using vector evaluated genetic algorithms (1984)

    Google Scholar 

  4. Jones, D.F., Mirrazavi, S.K., Tamiz, M.: Multi-objective meta-heuristics An overview of the current state-of-the-art. European Journal of Operational Research 137(1), 1–9 (2002)

    Article  MATH  Google Scholar 

  5. Coello Coello, C.A.: Evolutionary multi-objective optimization: a historical view of the field. IEEE Computational Intelligence Magazine 1(1), 28–36 (2006)

    Article  MathSciNet  Google Scholar 

  6. Fleming, P.J., Purshouse, R.C., Lygoe, R.J.: Many-objective optimization: An engineering design perspective. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 14–32. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms - part i: A unified formulation. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 28(1), 26 (1998)

    Article  Google Scholar 

  8. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley, Chichester (2001) ID: 2

    Google Scholar 

  9. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)

    Article  Google Scholar 

  10. Jong, K.A.D.: An analysis of the behavior of a class of genetic adaptive systems (1975) AAI7609381

    Google Scholar 

  11. Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems, 115–148 (1995)

    Google Scholar 

  12. Bäck, T.: Self-adaptation in genetic algorithms. In: Proceedings of the First European Conference on Artificial Life, pp. 263–271. MIT Press (1992)

    Google Scholar 

  13. Eiben, A.E., Schut, M.C., Wilde, A.R.D.: Boosting genetic algorithms with self-adaptive selection. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1584–1589 (2006)

    Google Scholar 

  14. Eiben, A.E., Schut, M.C., de Wilde, A.R.: Is self-adaptation of selection pressure and population size possible? a case study. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Darrell Whitley, L., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 900–909. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Zhang, J., Sanderson, A.C.: Self-adaptive multi-objective differential evolution with direction information provided by archived inferior solutions. In: IEEE Congress on Evolutionary Computation, CEC 2008 (IEEE World Congress on Computational Intelligence), pp. 2801–2810 (2008) ID: 1

    Google Scholar 

  16. Zhang, J., Sanderson, A.C.: Jade: Self-adaptive differential evolution with fast and reliable convergence performance. In: IEEE Congress on Evolutionary Computation, CEC 2007, pp. 2251–2258 (2007) ID: 1

    Google Scholar 

  17. Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4), 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tušar, T., Filipič, B.: Differential evolution versus genetic algorithms in multiobjective optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 257–271. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Sareni, B., Regnier, J., Roboam, X.: Recombination and self-adaptation in multi-objective genetic algorithms. In: Liardet, P., Collet, P., Fonlupt, C., Lutton, E., Schoenauer, M. (eds.) EA 2003. LNCS, vol. 2936, pp. 115–126. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  20. Tan, K.C., Goh, C.K., Yang, Y.J., Lee, T.H.: Evolving better population distribution and exploration in evolutionary multi-objective optimization. European Journal of Operational Research 171(2), 463–495 (2006)

    Article  MATH  Google Scholar 

  21. Tan, K.C., Chiam, S.C., Mamun, A.A., Goh, C.K.: Balancing exploration and exploitation with adaptive variation for evolutionary multi-objective optimization. European Journal of Operational Research 197(2), 701–713 (2009)

    Article  MATH  Google Scholar 

  22. Ho, C.W., Lee, K.H., Leung, K.S.: A genetic algorithm based on mutation and crossover with adaptive probabilities. In: Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol. 1, p. 775 (1999)

    Google Scholar 

  23. Li, M., Cai, Z., Sun, G.: An adaptive genetic algorithm with diversity-guided mutation and its global convergence property. Journal of Central South University of Technology 11(3), 323–327 (2004)

    Article  Google Scholar 

  24. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: Nsga-ii. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J., Schwefel, H.P. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  25. Deb, K., Goyal, M.: A combined genetic adaptive search (geneas) for engineering design. Computer Science and Informatics 26, 30–45 (1996)

    Google Scholar 

  26. Kukkonen, S., Deb, K.: Improved pruning of non-dominated solutions based on crowding distance for bi-objective optimization problems. In: IEEE Congress on Evolutionary Computation, CEC 2006, pp. 1179–1186 (2006) ID: 1

    Google Scholar 

  27. Bäck, T., Eiben, A.E., van der Vaart, N.A.L.: An emperical study on GAs “without parameters”. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J., Schwefel, H.P. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 315–324. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  28. Smith, J.E., Fogarty, T.C.: Self adaptation of mutation rates in a steady state genetic algorithm. In: Proceedings of the 1996 IEEE Conference on Evolutionary Computation, pp. 318–323. IEEE (1996)

    Google Scholar 

  29. Kipouros, T., Peachey, T., Abramson, D., Savill, M.: Enhancing and developing the practical optimisation capabilities and intelligence of automatic design software AIAA 2012-1677. In: 8th AIAA Multidisciplinary Design Optimization Specialist Conference (MDO). American Institute of Aeronautics and Astronautics (April 2012)

    Google Scholar 

  30. Jaeggi, D.M., Parks, G.T., Kipouros, T., Clarkson, P.J.: The development of a multi-objective tabu search algorithm for continuous optimisation problems. European Journal of Operational Research 185(3), 1192–1212 (2008) ID: 3

    Google Scholar 

  31. Abott, I., von Doenhoff, A.: Theory of wing sections: including a summary of airfoil data. Dover, New York (1959)

    Google Scholar 

  32. Sederberg, T.W., Parry, S.R.: Free-form deformation of solid geometric models. SIGGRAPH Comput. Graph. 20(4), 151–160 (1986)

    Article  Google Scholar 

  33. Drela, M.: Xfoil - an analysis and design system for low reynolds number airfoils. In: Low Reynolds Number Aerodynamics Conference, Germany, Notre Dame, pp. 1–12 (1989)

    Google Scholar 

  34. Inselberg, A.: Parallel Coordinates: Visual Multidimensional Geometry and Its Applications. Springer (2009)

    Google Scholar 

  35. Kipouros, T., Mleczko, M., Savill, M.: Use of parallel coordinates for post-analyses of multi-objective aerodynamic design optimisation in turbomachinery. AIAA-2008-2138. In: 4th AIAA Multi-Disciplinary Design Optimization Specialist Conference. Structures, Structural Dynamics, and Materials and Co-located Conferences, Schaumburg, Illinois. American Institute of Aeronautics and Astronautics (April 2008)

    Google Scholar 

  36. Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E.: Pisa - a platform and programming language independent interface for search algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 494–508. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  37. Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms - a comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  38. Epanechnikov, V.: Non-parametric estimation of a multivariate probability density. Theory of Probability & Its Applications 14(1), 153–158 (1969)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Engineering, Cranfield University, College Rd, Cranfield, MK43 0AL, UK

    John M. Oliver, Timoleon Kipouros & A. Mark Savill

Authors
  1. John M. Oliver
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  2. Timoleon Kipouros
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  3. A. Mark Savill
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Corresponding author

Correspondence to John M. Oliver .

Editor information

Editors and Affiliations

  1. , Leiden Institute of Advanced, Leiden University, Niels Bohrweg 1, Leiden, 2333CA, Netherlands

    Michael Emmerich

  2. , Leiden Institute of Advanced, Leiden University, Niels Bohrweg 1, Leiden, 2333CA, Netherlands

    Andre Deutz

  3. , Depto. de Computacion, CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, Mexico, 07360, Mexico

    Oliver Schuetze

  4. , Leiden Institute of Advanced, Leiden University, Niels Bohrweg 1, Leiden, 2333CA, Netherlands

    Thomas Bäck

  5. , Luxembourg Centre for, University of Luxembourg, Avenue des Hauts Fourneaux 7, Belval, 4362, Luxembourg

    Emilia Tantar

  6. , Computer Science and, University of Luxembourg, rue Richard Coudenhove-Kalergi 6, Luxembourg, 1359, Luxembourg

    Alexandru-Adrian Tantar

  7. , Bordeaux Mathematical Institute, Université Bordeaux I, cours de la Libération 351, Talence cedex, 33405, France

    Pierre Del Moral

  8. , UFR Sciences et Modélisation, Université Bordeaux Segalen, 3ter place de la Victoire, Bordeaux, 33076, France

    Pierrick Legrand

  9. Faculty of Sci., Tech. & Communication, Computer Science and, University of Luxembourg, rue Richard Coudenhove-Kalergi 6, Luxembourg, 1359, Luxembourg

    Pascal Bouvry

  10. , Depto. de Computatción, CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, Mexico, 07360, Mexico

    Carlos A. Coello

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Oliver, J.M., Kipouros, T., Savill, A.M. (2013). A Self-adaptive Genetic Algorithm Applied to Multi-Objective Optimization of an Airfoil. In: Emmerich, M., et al. EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV. Advances in Intelligent Systems and Computing, vol 227. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-01128-8_17

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  • DOI: https://doi.org/10.1007/978-3-319-01128-8_17

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-01127-1

  • Online ISBN: 978-3-319-01128-8

  • eBook Packages: EngineeringEngineering (R0)

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