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Inverse multi-objective robust evolutionary design

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Abstract

In this paper, we present an Inverse Multi-Objective Robust Evolutionary (IMORE) design methodology that handles the presence of uncertainty without making assumptions about the uncertainty structure. We model the clustering of uncertain events in families of nested sets using a multi-level optimization search. To reduce the high computational costs of the proposed methodology we proposed schemes for (1) adapting the step-size in estimating the uncertainty, and (2) trimming down the number of calls to the objective function in the nested search. Both offline and online adaptation strategies are considered in conjunction with the IMORE design algorithm. Design of Experiments (DOE) approaches further reduce the number of objective function calls in the online adaptive IMORE algorithm. Empirical studies conducted on a series of test functions having diverse complexities show that the proposed algorithms converge to a set of Pareto-optimal design solutions with non-dominated nominal and robustness performances efficiently.

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Notes

  1. There are two basic strategies for using Memetic Algorithms [15–17]:

    • Lamarckian learning forces the genotype to reflect the result of improvement in local search by placing the locally improved individual back into the population to compete for reproductive opportunities.

    • Baldwinian learning only alters the fitness of the individuals and the improved genotype is not encoded back into the population.

  2. Based on the central limit theorem, random samples from a given distribution with mean μ and variance σ 2 will approach a Gaussian/Normal distribution N(μ, σ 2) when the sample size increases.

  3. Note that x * represents the nominal global optimum (maximum).

  4. Note that x^ represents the robust global optimum (maximum).

References

  1. D. E. Goldberg, in Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, 1989.

  2. Y. Jin and J. Branke, “Evolutionary optimization in uncertain environment–A survey,” IEEE Transactions on Evolutionary Computation, vol. 9, pp. 303–317, 2005.

    Article  Google Scholar 

  3. Y. S. Ong, P. B. Nair, and K. Y. Lum, “Max-min surrogate assisted evolutionary algorithm for robust aerodynamic design,” IEEE Transactions on Evolutionary Computation, in press, expected August 2006.

  4. W. L. Oberkampf, et. al., “Estimation of total uncertainty in modeling and simulation,” Sandia Report SAND2000-0824, 2000.

  5. W. L. Oberkampf, J. Helton, and K. Sentz, “Mathematical representation of uncertainty”, in AIAA Proceedings of Non-Deterministic Approaches Forum, Paper no. 2001-1645, Reston, VA, 2001.

  6. Y. Ben-Haim, Information Gap Decision Theory, Academic Press: California, 2001.

    MATH  Google Scholar 

  7. Y. Ben-Haim, “Uncertainty, probability, and information-gaps,” Reliability Engineering and System Safety, vol. 85, pp. 249–266, 2004.

    Article  Google Scholar 

  8. Y. Ben-Haim, in Robust Reliability in Mechanical Sciences, Springer-Verlag: Berlin, 1996.

    MATH  Google Scholar 

  9. L. Huyse, “Solving problems of optimization under uncertainty as statistical decision problems”, AIAA-2002-1519, 2001.

  10. A. Ben-Tal and A. Nemirovski, “Robust convex optimization,” Mathematics of Operations Research, vol. 23, pp. 769–805, 1998.

    MathSciNet  MATH  Google Scholar 

  11. S. Tsutsui and A. Ghosh, “Genetic algorithms with a robust solution searching scheme,” IEEE Transaction on Evolutionary Computation, vol. 1, pp. 201–208, 1997.

    Article  Google Scholar 

  12. D. V. Arnold and H. G. Beyer, “Local performance of the (1+1)-ES in a noisy environment,” IEEE Transaction on Evolutionary Computation, vol. 6, pp 30–41, 2002.

    Article  MathSciNet  Google Scholar 

  13. Y. Jin and B. Sendhoff, “Trade-off between performance and robustness: An evolutionary multiobjective approach,” in Proceedings of Second International Conference on Evolutionary Multi-criteria Optimization, C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, and L. Thiele (eds.), LNCS 2632, Springer: Faro, 2003, pp. 237–251.

  14. I. Paenke, J. Branke, and Y. Jin, “Efficient search for robust solutions by means of evolutionary algorithm and fitness approximation,” IEEE Transactions on Evolutionary Computation, 2006, vol. 10, pp. 405–420.

    Article  Google Scholar 

  15. Y. S. Ong, M. H. Lim, N. Zhu, and K. W. Wong, “Classification of adaptive memetic algorithms: a comparative study,” IEEE Transactions on Systems, Man and Cybernetics—Part B, vol. 36, 2006.

  16. Y. S. Ong and A. J. Keane, “Meta-lamarckian learning in memetic algorithm,” IEEE Transactions On Evolutionary Computation, vol. 8, pp. 99–110, 2004.

    Article  Google Scholar 

  17. Z. 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, in press, 2006.

  18. L. Huyse and R. M. Lewis, “Aerodynamic shape optimization of two-dimensional airfoils under uncertain operating conditions,” Hampton, Virginia: ICASE NASA Langley Research Centre, 2001.

  19. D. K. Anthony and A. J. Keane, “Robust optimal design of a lightweight space structure using a genetic algorithm,” AIAA Journal, vol. 41, pp. 1601–1604, 2003.

    Google Scholar 

  20. D. Wiesmann, U. Hammel, and T. Back, “Robust design of multilayer optical coatings by means of evolutionary algorithms,” IEEE Transaction on Evolutionary Computation, vol. 2, pp 162–167, 1998.

    Article  Google Scholar 

  21. N. Srinivas and K. Deb, “Multi-objective optimization using non-dominated sorting in genetic algorithms,” Evolutionary Computation, vol. 2, pp 221–248, 1994.

    Google Scholar 

  22. K. Deb and S. Jain, “Running performance metrics for evolutionary multi-objective optimization,” in Proceeding of the Fourth Asia Pacific Conference on Simulated Evolution and Learning, L. Wang, K. C. Tan, T. Furuhashi, J.-H. Kim, and X. Yao (eds.), 2002, pp. 13–20.

  23. K. Deb and S. Jain, “Evaluating evolutionary multi-objective optimization algorithms using running performance metrics,” in K. C. Tan, M. H. Lim, X. Yao, and L. Wang (eds.), Recent Advances in Simulated Evolution and Learning, Singapore: World Scientific Publishers, 2004, pp. 307–326.

  24. K. T. Fang, C. X. Ma, and P. Winker, “Centered L2-discrepancy of random sampling and latin hypercube design, and construction of uniform designs,” Mathematics of Computation, vol. 71, pp. 275–296, 2000.

    Article  MathSciNet  Google Scholar 

  25. T. W. Simpson, D. K. J. Lin, and C. Wei, “Sampling strategies for computer experiments: design and analysis,” International Journal of Reliability and Applications, vol. 2, 209–240, 2001.

    Google Scholar 

  26. B. Tang, “Orthogonal array-based latin hypercubes,” Journal of the American Statistical Association, vol. 88, pp. 1392–1397, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  27. Y. S. Ong, P. B. Nair, and A. J. Keane, “Evolutionary optimization of computationally expensive problems via surrogate modeling,” AIAA Journal, vol. 41, pp. 687–696, 2003.

    Article  Google Scholar 

  28. Y. Jin, “A comprehensive survey of fitness approximation in evolutionary computation,” Soft Computing Journal, vol. 9, pp. 3–12, 2005.

    Article  Google Scholar 

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Acknowledgment

This work was funded by Honda Research Institute Germany. The authors would like to thank E. Körner at Honda Research Institute Europe, and the Parallel and Distributed Computing Centre of Nanyang Technological University for their support in this work.

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Authors and Affiliations

  1. School of Computer Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore

    Dudy Lim, Yew-Soon Ong & Bu Sung Lee

  2. Honda Research Institute Europe GmbH, Carl-Legien-Strasse 30, 63073, Offenbach, Germany

    Yaochu Jin & Bernhard Sendhoff

Authors
  1. Dudy Lim
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  2. Yew-Soon Ong
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  3. Yaochu Jin
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  4. Bernhard Sendhoff
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  5. Bu Sung Lee
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Correspondence to Dudy Lim.

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Lim, D., Ong, YS., Jin, Y. et al. Inverse multi-objective robust evolutionary design. Genet Program Evolvable Mach 7, 383–404 (2006). https://doi.org/10.1007/s10710-006-9013-7

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