# Control of robust design in multiobjective optimization under uncertainties

- 554 Downloads
- 11 Citations

## Abstract

In design and optimization problems, a solution is called *robust* if it is stable enough with respect to perturbation of model input parameters. In engineering design optimization, the designer may prefer a use of robust solution to a more optimal one to set a stable system design. Although in literature there is a handful of methods for obtaining such solutions, they do not provide a designer with a direct and systematic control over a required robustness. In this paper, a new approach to robust design in multiobjective optimization is introduced, which is able to generate robust design with model uncertainties. In addition, it introduces an opportunity to control the extent of robustness by designer preferences. The presented method is different from its other counterparts. For keeping robust design feasible, it does not change any constraint. Conversely, only a special tunable objective function is constructed to incorporate the preferences of the designer related to the robustness. The effectiveness of the method is tested on well known engineering design problems.

### Keywords

Robust design optimization Multiobjective optimization Fuzzy uncertainty Directed search domain## Notes

### Acknowledgments

The first author gratefully acknowledges the research scholarship awarded by the School of MACE, the University of Manchester.

### References

- Amarchinta H, Grandhi R (2008) Multi-attribute structural optimization based on conjoint analysis. AIAA J 46(4):884CrossRefGoogle Scholar
- Box G, Fung C (1986) Studies in quality improvement: minimizing transmitted variation by parameter design. Center for Quality and Productivity Improvement Report No 8, University of Wisconsin-MadisonGoogle Scholar
- Bryne D (1987) Taguchi approach to parameter design. Quality Progress, pp 19–26Google Scholar
- Carlsson C, Fuller R (2001) On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst 122(2):315–326CrossRefMATHMathSciNetGoogle Scholar
- Chen W, Allen JK, Tsui KL, Mistree F (1996) A procedure for robust design: minimizing variations caused by noise factors and control factors. ASME J Mech Des 118:478–485CrossRefGoogle Scholar
- Cox N (1987) How to perform statistical tolerance analysis. NASA STI/Recon Technical Report N 87:24,582Google Scholar
- Deb K, Gupta H (2005) Searching for robust Pareto-optimal solutions in multi-objective optimization. In: Proceedings of the third evolutionary multi-criteria optimization (EMO-05) conference (Also Lecture Notes on Computer Science 3410). Springer, pp 150–164Google Scholar
- Erfani T, Utyuzhnikov S (2010a) Directed search domain: a method for even generation of the Pareto frontier in multiobjective optimization. Eng Optim 43(5):467–484. doi:10.1080/0305,215X.2010.497,185 CrossRefMathSciNetGoogle Scholar
- Erfani T, Utyuzhnikov SV (2010b) Handling uncertainty and finding robust pareto frontier in multiobjective optimization using fuzzy set theory. In: 51st AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference et al, Orlando, FloridaGoogle Scholar
- Gunawan S, Azarm S (2005) Multi-objective robust optimization using a sensitivity region concept. Struct Multidisc Optim 29(1):50–60CrossRefGoogle Scholar
- Kannan B, Kramer S (1994) An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des 116:405CrossRefGoogle Scholar
- Lu X, Li H (2009) Perturbation theory based robust design under model uncertainty. J Mech Des 131:111,006Google Scholar
- Messac A (1996) Physical programming: effective optimization for computational design. AIAA J 34(1):149–158CrossRefMATHGoogle Scholar
- Messac A, Ismail Yahaya A (2002) Multiobjective robust design using physical programming. Struct Multidisc Optim 23(5):357–371CrossRefGoogle Scholar
- Mohandas S (1989) Multiobjective optimization dealing with uncertainty. In: Advances in design automation, 1989: design optimization: presented at the 1989 ASME design technical conferences-15th design automation conference, Montreal, Quebec, Canada, 17–21 September 1989. Amer Society of Mechanical, p 241Google Scholar
- Parkinson A (1995) Robust mechanical design using engineering models. J Vib Acoust 117:48CrossRefGoogle Scholar
- Parkinson A, Sorensen C, Pourhassan N (1993) A general approach for robust optimal design. J Mech Des 115:74CrossRefGoogle Scholar
- Ramakrishnan B, Rao S (1991) A robust optimization approach using Taguchi’s Loss Function for solving nonlinear optimization problems. In: Advances in Design Automation, 1991: presented at the 1991 ASME design technical conferences–17th design automation conference, 22–25 September 1991. Miami, Florida, American Society of Mechanical Engineers, p 241Google Scholar
- Rao S (1983) Optimization theory and applications. 2nd ed., John Wiley & Sons, New York, NY, USAGoogle Scholar
- Rao S (1996) Engineering optimization: theory and practice. Wiley-InterscienceGoogle Scholar
- Ross P (1995) Taguchi techniques for quality engineering: loss function, orthogonal experiments, parameter and tolerance design. McGraw-Hill ProfessionalGoogle Scholar
- Shimoyama K, Lim J, Jeong S, Obayashi S, Koishi M et al (2009) Practical implementation of robust design assisted by response surface approximation and visual data-mining. J Mech Des 131:061,007CrossRefGoogle Scholar
- Su J, Renaud J (1996) Automatic differentiation in robust optimization. AIAA Journal 5(6):1072–1079Google Scholar
- Sundaresan S, Ishii K, Houser D (1991) A procedure using manufacturing variance to design gears with minimum transmission error. J Mech Des 113:318CrossRefGoogle Scholar
- Taguchi G, Elsayed E, Hsiang T (1989) Quality engineering in production systems. McGraw-Hill CompaniesGoogle Scholar
- Ting K, Long Y (1996) Performance quality and tolerance sensitivity of mechanisms. J Mech Des 118:144CrossRefGoogle Scholar
- Utyuzhnikov S, Fantini P, Guenov M (2005) Numerical method for generating the entire Pareto frontier in multiobjective optimization. In: Proceedings of Eurogen’2005, Munich, 12–14 SeptemberGoogle Scholar