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A Memetic Algorithm Using a Trust-Region Derivative-Free Optimization with Quadratic Modelling for Optimization of Expensive and Noisy Black-box Functions

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Evolutionary Computation in Dynamic and Uncertain Environments

Part of the book series: Studies in Computational Intelligence ((SCI,volume 51))

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References

  1. N. Alexandrov, J. Dennis, Jr, R. M. Lewis, and V. Torczon. A trust-region framework for managing the use of approximation models in optimization. Structural Optimization, 15(1):16-23, 1998.

    Article  Google Scholar 

  2. J.-F. Barthelemy and R. Haftka. Approximation concepts for optimum structural design—a review. Structural Optimization, 5:129-144, 1993.

    Article  Google Scholar 

  3. R. R. Barton. Metamodels for simulation input-output. In J. Swain, D. Goldsman, R. Crain, and J. Wilson, editors, Proceedings of the 1992 Winter Simulation Conference, pages 289-299, New York, NY, USA, 1992. ACM Press.

    Google Scholar 

  4. A. J. Booker, J. E. Dennis, Jr, P. D. Frank, D. B. Serafini, V. Torczon, and M. W. Trosset. A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization, 17(1):1-13, 1998.

    Article  Google Scholar 

  5. A. R. Conn, N. I. Gould, M. Lescrenier, and P. L. Toint. Performance of a multifrontal scheme for partially separable optimization. In S. Gomez and J. Hennart, editors, Advances in Optimization and Numerical Analysis, pages 79-96. Kluwer Academic Publishers, 1994.

    Google Scholar 

  6. A. R. Conn, N. I. Gould, and P. L. Toint. Trust-Region Methods. SIAM, Philadelphia, PA, 2000.

    MATH  Google Scholar 

  7. A. R. Conn, K. Scheinberg, and P. L. Toint. On the convergence of derivativefree methods for unconstrained optimization. In A. Iserles and M. Buhmann, editors, Approximation Theory and Optimization: Tributes to M.J.D. Powell, pages 83-108. Cambridge University Press, Cambridge; New York, 1997.

    Google Scholar 

  8. A. R. Conn, K. Scheinberg, and P. L. Toint. Recent progress in unconstrained nonlinear optimization without derivatives. Mathematical Programming, 79:397- 414,1997.

    MathSciNet  Google Scholar 

  9. A. R. Conn, K. Scheinberg, and P. L. Toint. A derivative free optimization algorithm in practice. In Proceedings of the Seventh AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St.Louis, MO. American Institute of Aeronautics and Astronautics, American Institute of Aeronautics and Astronautics, 1998.

    Google Scholar 

  10. A. R. Conn and P. L. Toint. An algorithm using quadratic interpolation for unconstrained derivative free optimization. In G. Di Pillo and F. Giannessi, editors, Nonlinear Optimization and Applications, pages 27-47. Plenum Press, New York, N.Y., 1996.

    Google Scholar 

  11. J. Dennis, Jr and V. Torczon. Managing approximation models in optimization. In N. M. Alexandrov and M. Y. Hussaini, editors, Multidisciplinary Design Optimization: State of the Art, pages 330-347. SIAM, Philadelphia, 1997.

    Google Scholar 

  12. P. D. Frank. Global modeling for optimization. SIAG/OPT Views-and-News, (7):9-12, 1995.

    Google Scholar 

  13. M. Gasca and T. Sauer. Polynomial interpolation in several variables. Advances in Computational Mathematics, 12:377-410, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  14. K. Giannakoglou. Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Progress in Aerospace Science, 38(1):43-76, 2002.

    Article  Google Scholar 

  15. A. A. Giunta and L. T. Watson. A comparison of approximation modeling techniques: polynomial versus interpolating models. In AIAA/USAF/NASA/ ISSMO Seventh Symposium on Multidisciplinary Analysis and Optimization, volume 1, St. Louis, MO, Sept. 2-4 1998. AIAA, AIAA. AIAA-1998-4758.

    Google Scholar 

  16. V. Hanagandi and M. Nikolaou. A hybrid approach to global optimization using a clustering algorithm in a genetic search framework. Computers and Chemical Engineering, 22(12):1913-1925, 1998.

    Article  Google Scholar 

  17. W. E. Hart and R. K. Belew. Optimization with genetic algorithm hybrids that use local search. In R. K. Belew and M. Mitchell, editors, Adaptive Individuals in Evolving Populations: Models and Algorithms, Santa Fe Institute Studies in the Sciences of Complexity, volume 26, chapter 27, pages 483-496. Addison-Wesley Publishing Company, Reading, MA, 1996.

    Google Scholar 

  18. R. L. Haupt and S. E. Haupt. Practical Genetic Algorithms. John Wiley and Sons, New York, 1998.

    MATH  Google Scholar 

  19. R. Jin, W. Chen, and T. Simpson. Comparative studies of metamodelling techniques under multiple modelling criteria. Structural and Multidisciplinary Optimization, 23:1-13, 2001.

    Article  Google Scholar 

  20. Y. Jin. A comprehensive survey of fitness approximation in evolutionary computation. Soft Computing, 9(1):3-12, 2005.

    Article  Google Scholar 

  21. Y. Jin, M. Olhofer, and B. Sendhoff. A framework for evolutionary optimization with approximate fitness functions. IEEE Transactions on evolutionary computation, 6(5):481-494, 2002.

    Article  Google Scholar 

  22. H.-S. Kim and S.-B. Cho. An efficient genetic algorithm with less fitness evaluation by clustering. In Proceedings of 2001 IEEE Congress on Evolutionary Computation, volume 2, pages 887-894. IEEE, IEEE, 2001.

    Article  Google Scholar 

  23. N. Krasnogor and J. Smith. A tutorial for competent memetic algorithms: Model, taxonomy and design issues. IEEE Transactions on Evolutionary Computation, 9(5):474-488, 2005.

    Article  Google Scholar 

  24. K.-H. Liang, X. Yao, and C. Newton. Evolutionary search of approximated n-dimensional landscapes. Journal of Knowledge-Based Intelligent Engineering Systems, 4(3):172-183, 2000.

    Google Scholar 

  25. Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin; New York, third edition, 1996.

    MATH  Google Scholar 

  26. J. J. Moré. Recent developments in algorithms and software for trust region methods. In A. Bachem, M. Grötschel, and B. Korte, editors, Mathematical Programming Bonn 1982 - The State of the Art, pages 258-287. Springer-Verlag, Berlin, 1983.

    Google Scholar 

  27. J. J. Moré, B. S. Garbow, and K. E. Hillstrom. Testing unconstrained optimization software. ACM Transactions on Mathematical Software, 7(1):17-41,1981.

    Article  MATH  Google Scholar 

  28. J. J. Moré and D. Sorensen. Computing a trust region step. SIAM Journal on Scientific and Statistical Computing, 4(3):553-572, 1983.

    Article  MATH  Google Scholar 

  29. Y. S. Ong and A. J. Keane. Meta-lamarckian learning in memetic algorithms. IEEE Transactions on Evolutionary Computation, 8(2):99-110, 2004.

    Article  Google Scholar 

  30. Y. S. Ong, P. B. Nair, and A. J. Keane. Evolutionary optimization of computationally expensive problems via surrogate modeling. American Institute of Aeronautics and Astronautics Journal, 41(4):687-696, 2003.

    Google Scholar 

  31. Y.-S. Ong, P. B. Nair, and K. Y. Lum. Max-min surrogate assisted evolutionary algorithms for robust aerodynamic design. IEEE Transactions on Evolutionary Computation, 10(4):392-404, 2006.

    Article  Google Scholar 

  32. M. J. Powell. Direct search algorithms for optimization calculations. Acta Numerica, pages 287-336, 1998.

    Google Scholar 

  33. M. J. Powell. UOBYQA: unconstrained optimization by quadratic approximation. Mathematical Programming, Series B, 92(3):555-582, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  34. M. J. Powell. On trust region methods for unconstrained minimization without derivatives. Mathematical Programming, Series B, 97(3):605-623, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  35. A. Ratle. Accelerating the convergence of evolutionary algorithms by fitness landscape approximations. In A. Eiben, B. Thomas, M. Schoenauer, and H.-P. Schwefel, editors, Proceedings of the 5th International Conference on Parallel Problem Solving from Nature - PPSN V, volume 1498 of Lecture Notes in Computer Science, pages 87-96, Berlin Heidelberg, 1998. Springer-Verlag.

    Google Scholar 

  36. J.-M. Renders and S. P. Flasse. Hybrid methods using genetic algorithms for global optimization. IEEE Transactions on Systems, Man and Cybernetics-Part B:Cybernetics, 26(2):243-258, 1996.

    Article  Google Scholar 

  37. A. Rinnooy Kan and G. Timmer. Stochastic global optimization methods part I: Clustering methods. Mathematical Programming, 39:27-56, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  38. T. Sauer. Computational aspects of multivariate polynomial interpolation. Advances in Computational Mathematics, 3(3):219-237, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  39. T. Sauer and Y. Xu. On multivariate Lagrange interpolation. Mathematics of Computation, 64(211):1147-1170, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  40. G. Seront and H. Bersini. A new GA-local search hybrid for continuous optimization based on multi level single linkage clustering. In H. Beyer, E. CantuPaz, D. Goldberg, I. Parmee, L. Spector, and D. Whitley, editors, Proceedings of GECCO-Genetic and Evolutionary Computation Conference 2000, pages 90-95. Morgan Kaufmann, 2000.

    Google Scholar 

  41. T. W. Simpson, J. J. Korte, T. M. Mauery, and F. Mistree. Comparison of response surface and Kriging models for multidisciplinary design optimization. In Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St.Louis, MO, volume 1, pages 381- 391. American Institute of Aeronautics and Astronautics, American Institute of Aeronautics and Astronautics, 1998. AIAA-1998-4755.

    Google Scholar 

  42. Y. Tenne and S. Armfield. Efficiently minimizing expensive black-box functions by a combination of an evolutionary algorithm, density cluster analysis and a trust-region derivative-free optimizer. Journal of Global Optimization, 2005. Accepted, To Appear.

    Google Scholar 

  43. Y. Tenne and S. Armfield. A novel evolutionary algorithm for efficient minimization of expensive black-box functions with assisted-modelling. In Proceedings of the IEEE World Congress on Computational Intelligence-WCCI 2006, 2006. Accepted, To Appear.

    Google Scholar 

  44. Y. Tenne and S. Armfield. Computational aspects and performance of a trustregion derivative-free algorithm for minimization of black-box functions. In Preparation.

    Google Scholar 

  45. P. L. Toint. Some numerical results using a sparse matrix updating formula in unconstrained optimization. Mathematics of Computation, 32(143):839-851,1978.

    Article  MATH  MathSciNet  Google Scholar 

  46. A. A. Törn. Cluster analysis using seed points and density-determined hyperspheres as an aid to global optimization. IEEE Transactions on Systems, Man and Cybernetics, 7(8):610-616, 1977.

    Article  MATH  Google Scholar 

  47. A. A. Törn. A search-clustering approach to global optimization. In L. Dixon and G. Szegö, editors, Towards Global Optimization 2, pages 49-62. North-Holland Publishing Company, Amsterdam; New York; Oxford, 1978.

    Google Scholar 

  48. A. A. Törn and A. Žilinskas. Global Optimization. Number 350 in Lecture Notes In Computer Science. Springer-Verlag, Berlin; Heidelberg; New York; London, 1989.

    Google Scholar 

  49. Y.-x. Yuan. A review of trust region algorithms for optimization. In J. Ball and J. C. Hunt, editors, ICIAM 99 : proceedings of the Fourth International Congress on Industrial and Applied Mathematics, Edinburgh, pages 271-282, New York; Oxford, 2000. Oxford University Press.

    Google Scholar 

  50. Z. Zhou, Y. S. Ong, P. B. Nair, A. J. Keane, and K. Y. Lum. Combining global and local surrogate models to accelerate evolutionary optimization. IEEE Transactions on Systems, Man and Cybernetics-Part C(Applications and Reviews), To Appear.

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, NSW 2006, Sydney, Australia

    Yoel Tenne

  2. School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, NSW 2006, Sydney, Australia

    Steven William Armfield

Authors
  1. Yoel Tenne
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  2. Steven William Armfield
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leiceste, UK

    Shengxiang Yang

  2. School of Computer Engineering, Nanyang Technological University, Blk N4, 2b-39, Nanyang Avenue, 639798, Singapore

    Yew-Soon Ong

  3. Honda Research Institute Europe, Carl-Legien-Str 30, 63073, Offenbach am Main, Germany

    Yaochu Jin

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Tenne, Y., Armfield, S.W. (2007). A Memetic Algorithm Using a Trust-Region Derivative-Free Optimization with Quadratic Modelling for Optimization of Expensive and Noisy Black-box Functions. In: Yang, S., Ong, YS., Jin, Y. (eds) Evolutionary Computation in Dynamic and Uncertain Environments. Studies in Computational Intelligence, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49774-5_17

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  • DOI: https://doi.org/10.1007/978-3-540-49774-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49772-1

  • Online ISBN: 978-3-540-49774-5

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