Abstract
In this paper, we present a multi-surrogates assisted memetic algorithm for solving optimization problems with computationally expensive fitness functions. The essential backbone of our framework is an evolutionary algorithm coupled with a local search solver that employs multi-surrogate in the spirit of Lamarckian learning. Inspired by the notion of ‘blessing and curse of uncertainty’ in approximation models, we combine regression and exact interpolating surrogate models in the evolutionary search. Empirical results are presented for a series of commonly used benchmark problems to demonstrate that the proposed framework converges to good solution quality more efficiently than the standard genetic algorithm, memetic algorithm and surrogate-assisted memetic algorithms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bishop C (1995) Neural networks for pattern recognition. Oxford University Press, Oxford
Büche D, Schraudolph NN, Koumoutsakos P (2005) Accelerating evolutionary algorithms with gaussian process fitness function models. IEEE Trans Syst Man Cybern Part C Special Issue Knowl Extraction Incorporat Evol Comput 35:183–194
Daberkow DD, Marvis DN (1998) New approaches to conceptual and preliminary aircraft design: a comparative assessment of a neural network formulation and a response surface methodology. In: Proceedings of 1998 World aviation conference, AIAA, Anaheim, Sept. 1998, AIAA-98-5509
Edwards AL (1976) An introduction to linear regression and correlation. W. H. Freeman, San Franisco
El-Beltagy MA, Nair PB, Keane AJ (1999) Metamodelling techniques for evolutionary optimization of computationally expensive problems: Promise and limitations. In: Procedings of IEEE genetic and evolutionary computation conference (GECCO’99) Florida, July 1999, pp 196–203
Emmerich M, Giotis A, Ozdemir M, Back T, Giannakoglou K (2002) Metamodel-assisted evolution strategies. In: Proceedings of the 7th international conference on parallel problem solving from nature (PPSN 2002), Granada, Spain, Sept. 2002, pp 361–370
Giannakoglou KC (2002) Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Int Rev J Progress Aerospace Sci 38(5):43–76
Guinta AA, Watson L (1998) A comparison of approximation modelling techniques: polynomial versus interpolating . In: Proceedings of the 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization vol. 1, St. Louis, Sept. 1998, pp 392–404, AIAA–98–4758
Herrera F, Lozano M, S´nchez A (2005) Hybrid crossover operators for real-coded genetic algorithms: an experimental study. Soft Comput 9(4):280–298
Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9(1):3–12
Jin Y, Sendhoff B (2004) Reducing fitness evaluations using clustering techniques and neural networks ensembles. In: Proceedings of the genetic and evolutionary computation conference, ser. LNCS, vol 3102. Springer, Berlin Heidelberg New~York, pp 688–699
Jin Y, Olhofer M, Sendhoff B (2002) A framework for evolutionary optimization with approximate fitness functions.IEEE Trans Evol Comput 6(5):481–494
Knowles J (2006) ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans Evol Comput 10(1):50–66
Lesh FH (1959) Multi-dimensional least-square polynomial curve fitting. Commun ACM 2(9):29–30
Lee J, Hajela P (2001) A computationally efficient feasible sequential quadratic programming algorithm. Soc Ind Appl Math 11(4):1092–1118
Nain P, Deb K (2003) Computationally effective search and optimization procedure using coarse to fine approximation. In: Proceedings of Congress on evolutionary computation (CEC’03), Canberra, Australia, Dec. 2003, pp 2081–2088
Ng H, Lim D, Ong YS, Lee BS, Freund L, Parvez S, Sendhoff B (2005) A multi-cluster grid enabled evolution framework for aerodynamic airfoil design optimization. In: International conference on natural computing (ICNC), ser. Lecture Notes in Computer Science, vol 3611. Springer, Berlin Heidelberg New York, pp 1112–1121
Ong YS, Keane AJ (2002) A domain knowledge based search advisor for design problem solving environments. Eng Appl Artif Intell 15(1):105–116
Ong YS, Keane AJ (2004) Meta-lamarckian in memetic algorithm. IEEE Trans Evol Comput 8(2):99–110
Ong YS, Nair PB, Keane AJ (2003) Evolutionary optimization of computationally expensive problems via surrogate modeling. Am Inst Aeronaut Astron J 41(4):687–696
Ong YS, Nair PB, Keane AJ, Wong KW (2004) Surrogate-assisted evolutionary optimization frameworks for high-fidelity engineering design problems. In: Jin Y (eds) Knowledge incorporation in evolutionary computation, studies in fuzziness and soft computing. Springer, Berlin Heidelbery New York, pp 307–332
Ong YS, Nair PB, Lum KY (2006a) Max-min surrogate-assisted evolutionary algorithm for robust aerodynamic design. IEEE Trans Evol Comput 10(4):392–404
Ong YS, Nair PB, Lum KY (2006b) Evolutionary algorithm with hermite radial basis function interpolants for computationally expensive adjoint solvers. Comput Optim Appl (in press)
Ong YS, Zhou Z, Lim D (2006c) Curse and blessing of uncertainty in evolutionary algorithm using approximation. In: Proceedings of the 2006 IEEE world congress on computational intelligence (WCCI2006), British Columbia, Canada, July 2006, pp 2928–2935
Powell M (1987) Radial basis functions for multi-variable interpolation: a review. In: Mason C, Cox MG (eds) Algorithms for approximation. Oxford University Press, Oxford, pp 143–167
Ratle A (2001) Kriging as a surrogate fitness landscape in evolutionary optimization. Artif Intell Eng Design Anal Manufacturing 15(1):37–49
Regis RG, Shoemaker CA (2004) Local function approximation in evolutionary algorithms for the optimization of costly functions. IEEE Trans Evol Comput 8(5):490–505
Ulmer H, Streichert F, Zell A (2003) Evolution startegies assisted by gaussian processes with improved pre-selection criterion. In: Proceedings IEEE congress on evolutionary computation CEC’03, Canberra, Australia, Dec. 2003, pp 1741– 1751
Xuan J, Chafekar D, Rasheed K (2003) Constrained multi- objective ga optimization using reduced models. In: Proceedings of the genetic and evolutionary computation conference (GECCO’03), Chicago, July 2003, pp. 174–177
Zhou Z, Ong YS, Nair PB, Keane AJ, Lum KY (2007) Combining global and local surrogate models to accelerate evolutionary optimization. IEEE Trans Syst Man Cybern Part C (TSMCC) 37(1):66–76
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhou, Z., Ong, Y.S., Lim, M.H. et al. Memetic algorithm using multi-surrogates for computationally expensive optimization problems. Soft Comput 11, 957–971 (2007). https://doi.org/10.1007/s00500-006-0145-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-006-0145-8