A Robust Optimization Procedure With Variations on Design Variables and Constraints

Sundaresan, Sivakumar; Ishii, Kosuke; Houser, Donald R.

doi:10.1080/03052159508941185

Cited by 117 publications

(62 citation statements)

References 3 publications

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“…3, wherein it is depicted that "Band-d" is located at the feasible region. Now, the robust solution from the proposed approach is compared with that of shifting constraint (SC) method (15) . SC reformulates the constraints in terms of the original constraints and their derivatives with respect to design variable within the design tolerance as follows: …”

Section: Mathematical Function Problemmentioning

confidence: 99%

DOE Based Robust Optimization Considering Tolerance Bands of Design Parameters

Lee

Ahn

2006

JSME Int. J., Ser. C

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The paper describes a robust optimization method to account for the tolerance of design variable and the variation in problem parameter. The proposed post-optimization effort is initiated from the deterministic optimum as a baseline. The successive process to find search directions and step sizes toward the robust optimum is conducted by determining the worst design that has the highest level in constraint violation. During the selection of the worst design, an orthogonal array table in the context of design of experiemtns (DOE) is used to reduce the constraint function evaluations especially for higher dimensionality problem. The analysis of means (ANOM) is adopted in a case where the variation in problem parameter is considered. The measurement criterion to select the worst design is based on the degree of cumulative constraint violation. A mathematical function problem is first conducted to examine the tolerance of design variable. A cantilever beam problem described by four design variables and a bracket problem with seven design variables are subsequently explored by considering both tolerance of design variable and variation in problem parameter.

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Section: Mathematical Function Problemmentioning

confidence: 99%

DOE Based Robust Optimization Considering Tolerance Bands of Design Parameters

Lee

Ahn

2006

JSME Int. J., Ser. C

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“…This methodology ensures that the design solution remains feasible and close to optimal even if there is a change in data. Different methodologies for robust design and optimization in mechanical systems have been extensively discussed in literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Most of these methods assume some kind of distribution for the uncertain variable to optimize the problem.…”

Section: Introductionmentioning

confidence: 99%

Robust design optimization using the price of robustness, robust least squares and regularization methods

Bukhari¹

2017

Int. J. Simul. Multidisci. Des. Optim.

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Abstract. In this paper a framework for robust optimization of mechanical design problems and process systems that have parametric uncertainty is presented using three different approaches. Robust optimization problems are formulated so that the optimal solution is robust which means it is minimally sensitive to any perturbations in parameters. The first method uses the price of robustness approach which assumes the uncertain parameters to be symmetric and bounded. The robustness for the design can be controlled by limiting the parameters that can perturb. The second method uses the robust least squares method to determine the optimal parameters when data itself is subjected to perturbations instead of the parameters. The last method manages uncertainty by restricting the perturbation on parameters to improve sensitivity similar to Tikhonov regularization. The methods are implemented on two sets of problems; one linear and the other non-linear. This methodology will be compared with a prior method using multiple Monte Carlo simulation runs which shows that the approach being presented in this paper results in better performance.Keywords: robust design / optimization / price of robustness / control of robustness / robust least square

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“…[11]. Other robust design alternatives are available, like the sensitivity-based formulations in [10,12]. An overview of still other robust design approaches such as the Taguchi method, physical programming approach, and robust design with an axiomatic approach are discussed in [13].…”

Section: Introductionmentioning

confidence: 99%

Minmax topology optimization

Brittain

Silva

Tortorelli

2011

Struct Multidisc Optim

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We describe a systematic approach for the robust optimal design of linear elastic structures subjected to unknown loading using minmax and topology optimization methods. Assuming only the loading region and norm, we distribute a given amount of material in the design domain to minimize the principal compliance, i.e. the maximum compliance that is produced by the worst-case loading scenario. We evaluate the principal compliance directly by satisfying the optimality conditions which take the form of a Steklov eigenvalue problem and thus we eliminate the need of an iterative nested optimization. To generate a well-posed topology optimization problem we use relaxation which requires homogenization theory. Examples are provided to demonstrate our algorithm.ii To Mom and Dad.iii

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A Robust Optimization Procedure With Variations on Design Variables and Constraints

Cited by 117 publications

References 3 publications

DOE Based Robust Optimization Considering Tolerance Bands of Design Parameters

DOE Based Robust Optimization Considering Tolerance Bands of Design Parameters

Robust design optimization using the price of robustness, robust least squares and regularization methods

Minmax topology optimization

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