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How to compare performance of robust design optimization algorithms, including a novel method

Published online by Cambridge University Press:  03 August 2017

Johan A. Persson  and
Johan Ölvander
Johan A. Persson*
Affiliation:
Department of Management and Engineering, Linköping University, Linköping, Sweden
Johan Ölvander
Affiliation:
Department of Management and Engineering, Linköping University, Linköping, Sweden
*
Reprint requests to: Johan A. Persson, Department of Management and Engineering, Linköping University, Linköping SE-581 83, Sweden. E-mail: johan.persson@liu.se
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Abstract

This paper proposes a method to compare the performances of different methods for robust design optimization of computationally demanding models. Its intended usage is to help the engineer to choose the optimization approach when faced with a robust optimization problem. This paper demonstrates the usage of the method to find the most appropriate robust design optimization method to solve an engineering problem. Five robust design optimization methods, including a novel method, are compared in the demonstration of the comparison method. Four of the five compared methods involve surrogate models to reduce the computational cost of performing robust design optimization. The five methods are used to optimize several mathematical functions that should be similar to the engineering problem. The methods are then used to optimize the engineering problem to confirm that the most suitable optimization method was identified. The performance metrics used are the mean value and standard deviation of the robust optimum as well as an index that combines the required number of simulations of the original model with the accuracy of the obtained solution. These measures represent the accuracy, robustness, and efficiency of the compared methods. The results of the comparison show that sequential robust optimization is the method with the best balance between accuracy and number of function evaluations. This is confirmed by the optimizations of the engineering problem. The comparison also shows that the novel method is better than its predecessor is.

Keywords

OptimizationRobust Design OptimizationSurrogate ModelsSurrogate-Based Optimization
Type
Special Issue Articles
Information
AI EDAM , Volume 31 , Special Issue 3: Uncertainty Quantification for Engineering Design , August 2017 , pp. 286 - 297
Copyright
Copyright © Cambridge University Press 2017 

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References

REFERENCES

Aspenberg, D., Jergeus, J., & Nilsson, L. (2013). Robust optimization of front members in a full frontal car impact. Engineering Optimization 45(3), 245–264.Google Scholar
Beyer, H.G., & Sendhoff, B. (2007). Robust optimization—a comprehensive survey. Computer Methods in Applied Mechanics and Engineering 196(33), 3190–3218.Google Scholar
Box, M.J. (1965). A new method of constrained optimization and a comparison with other methods. Computer Journal 8(1), 42–52.Google Scholar
Branke, J. (2001). Evolutionary Optimization in Dynamic Environments. Norwell, MA: Kluwer Academic.Google Scholar
Coelho, R.F. (2014). Metamodels for mixed variables based on moving least squares. Optimization and Engineering 15(2), 311–329.CrossRefGoogle Scholar
Eberhart, R.C., & Kennedy, J. (1995). A new optimizer using particle swarm theory. Proc. 6th Int. Symp. Micro Machine and Human Science, Vol. 1, pp. 39–43, Nagoya, Japan, October 4–6.Google Scholar
Forrester, A., Sobester, A., & Keane, A. (2008). Engineering Design Via Surrogate Modelling: A Practical Guide. Hoboken, NJ: Wiley.Google Scholar
Gobbi, M., Guarneri, P., Scala, L., & Scotti, L. (2014). A local approximation based multi-objective optimization algorithm with applications. Optimization and Engineering 15(3), 619–641.Google Scholar
Goldberg, D.E. (2006). Genetic Algorithms. Delhi: Pearson Education India.Google Scholar
Holland, J.H. (1975). Adaptation in Natural and Artificial Systems: An Introductory Analysis With Applications to Biology, Control, and Artificial Intelligence. Ann Arbor, MI: University of Michigan Press.Google Scholar
Jin, R., Du, X., & Chen, W. (2003). The use of metamodeling techniques for optimization under uncertainty. Structural and Multidisciplinary Optimization 25(2), 99–116.Google Scholar
Jones, D.R. (2001). A taxonomy of global optimization methods based on response surfaces. Journal of Global Optimization 21(4), 345–383.Google Scholar
Krus, P., & Ölvander, J. (2013). Performance index and meta-optimization of a direct search optimization method. Engineering Optimization 45(10), 1167–1185.Google Scholar
McKay, M.D., Beckman, R.J., & Conover, W.J. (1979). Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245.Google Scholar
Mercer, R.E., & Sampson, J.R. (1978). Adaptive search using a reproductive metaplan. Kybernetes 7(3), 215–228. doi:10.1108/eb005486 Google Scholar
Myers, R.H., Montgomery, D.C., & Anderson-Cook, C.M. (2009). Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Hoboken, NJ: Wiley.Google Scholar
Neculai, A. (2008). An unconstrained optimization test functions collection. Advanced Modeling and Optimization 10(1), 147–161.Google Scholar
Nelder, J.A., & Mead, R. (1965). A simplex method for function minimization. Computer Journal 7(4), 308–313.Google Scholar
Ölvander, J., & Krus, P. (2006). Optimizing the optimization—a method for comparison of optimization algorithms. Proc. AIAA Multidisciplinary Design Optimization Specialists Conf., Paper No. AIAA 2006-1915, Newport, RI, May 1–4. doi:10.2514/6.2006-1915 Google Scholar
Paenke, I., Branke, J., & Jin, Y. (2006). Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation. IEEE Transactions on Evolutionary Computation 10(4), 405–420.Google Scholar
Persson, J., & Ölvander, J. (2011). Comparison of sampling methods for a dynamic pressure regulator. Proc. 49th AIAA Aerospace Sciences Meeting, Paper No. AIAA 2011-1205, Orlando, FL, January 4–7. doi:10.2514/6.2011-1205 Google Scholar
Persson, J.A., & Ölvander, J. (2013). Comparison of different uses of metamodels for robust design optimization. Proc. 51th AIAA Aerospace Sciences Meeting, Paper No. AIAA 2013-1039, Grapevine, TX, January 7–10. doi:10.2514/6.2013-1039 Google Scholar
Persson, J.A., & Ölvander, J. (2015). Optimization of the complex-RFM optimization algorithm. Optimization and Engineering 16(1), 27–48.Google Scholar
Rehman, S., Langelaar, M., & van Keulen, F. (2014). Efficient kriging-based robust optimization of unconstrained problems. Journal of Computational Science. Advance online publication. doi:10.1016/j.jocs.2014.04.005 Google Scholar
Reisenthel, P.H., & Lesieutre, D. J. (2011). A numerical experiment on allocating resources between design of experiment samples and surrogate-based optimization infills. Proc. 52ndAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Paper No. AIAA 2011-2150, Denver, CO, April, 4–7.Google Scholar
Schutte, J.F., & Haftka, R.T. (2005). Improved global convergence probability using independent swarms. Proc. 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Structures, Structural Dynamics, and Materials and Co-located Conf., Austin, TX. doi:10.2514/6.2005-1896 Google Scholar
Tarkian, M., Persson, J., Ölvander, J., & Feng, X. (2012). Multidisciplinary design optimization of modular industrial robots by utilizing high level CAD templates. Journal of Mechanical Design 134(12), 124502.Google Scholar
Tenne, Y. (2015). An adaptive-topology ensemble algorithm for engineering optimization problems. Optimization and Engineering 16(2), 303–334.Google Scholar
Toal, D.J.J., & Keane, A.J. (2012). Non-stationary kriging for design optimization. Engineering Optimization 44(6), 741–765.Google Scholar
Wang, G.G., & Shan, S. (2007). Review of metamodeling techniques in support of engineering design optimization. Journal of Mechanical Design 129(4), 370–380.Google Scholar
Wiebenga, J.H., Van Den Boogaard, A.H., & Klaseboer, G. (2012). Sequential robust optimization of a V-bending process using numerical simulations. Structural and Multidisciplinary Optimization 46(1), 137–153.Google Scholar