Robust Multi-Objective TEAM 22 Problem: A Case Study of Uncertainties in Design Optimization

Soares, Gustavo Luís; Adriano, Ricardo; Maia, Carlos Andrey; Jaulin, Luc; Vasconcelos, J.A.

doi:10.1109/tmag.2009.2012563

Cited by 48 publications

(29 citation statements)

References 7 publications

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“…The WCO [1]- [3], [11] is a popular approach, which can predict the worst scenario considering uncertainties and constraints with respect to specific designs by performing…”

Section: B Worst Case Optimizationmentioning

confidence: 99%

Six Sigma Quality Approach to Robust Optimization

Xiao

Rotaru

et al. 2015

IEEE Trans. Magn.

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In electromagnetic design, uncertainties in design variables are inevitable, thus in addition to pursuing the theoretical optimum of the objective function the evaluation of robustness of the optimum solution is also critical. Several methodologies exist to tackle robust optimization, such as worst case optimization and gradient index; this paper investigates the use of standard deviation and mean value of objective function under uncertainty of variables. A modified Kriging model with the ability of balancing exploration and exploitation is employed to facilitate the objective function prediction. Two TEAM benchmark problems are solved using different methodologies to compare the advantages and disadvantages of different robust optimization approaches.Index Terms-Gradient index (GI), Kriging, six sigma quality (SSQ) approach, worst case optimization (WCO).

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“…The WCO [1]- [3], [11] is a popular approach, which can predict the worst scenario considering uncertainties and constraints with respect to specific designs by performing…”

Section: B Worst Case Optimizationmentioning

confidence: 99%

Six Sigma Quality Approach to Robust Optimization

Xiao

Rotaru

et al. 2015

IEEE Trans. Magn.

View full text Add to dashboard Cite

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“…5. We considered the three-parameter problem presented in [2,16,17]. For this problem, the shape of SMES can be defined using three design variables that are modeled by a vector x = {R 2 , H 2 , D 2 }.…”

Section: Electromagnetic Applicationmentioning

confidence: 99%

A Robust Optimization Method Utilizing the Variance Decomposition Method for Electromagnetic Devices

Wang¹,

Li²,

Chen³

2014

Journal of Magnetics

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Uncertainties in loads, materials and manufacturing quality must be considered during electromagnetic devices design. This paper presents an effective methodology for robust optimization design based on the variance decomposition in order to keep higher accuracy of the robustness prediction. Sobol' theory is employed to estimate the response variance under some specific tolerance in design variables. Then, an optimal design is obtained by adding a criterion of response variance upon typical optimization problems as a constraint of the optimization. The main contribution of this paper is that the proposed method applies the variance decomposition to obtain a more accurate variance of the response, as well save the computational cost. The performance and robustness of the proposed algorithms are investigated through a numerical experiment with both an analytic function and the TEAM 22 problem.

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“…Some recent work in multi-objective optimization defines the concept of solution robustness by considering stability of the optimal solution with respect to errors in the objective function parameters (see Soares et al (2009);Cromvik et al (2011) and references therein). Soares et al (2009) define the concept of absolute and relative robustness as the expected value of the difference of a given composite utility function to a utility value calculated at a reference point, where the expectation is taken with respect to random function parameters.…”

Section: Introductionmentioning

confidence: 99%

“…Soares et al (2009) define the concept of absolute and relative robustness as the expected value of the difference of a given composite utility function to a utility value calculated at a reference point, where the expectation is taken with respect to random function parameters. Cromvik et al (2011) take a min-max approach over function parameters in their definition.…”

Section: Introductionmentioning

confidence: 99%

Robust and Stochastically Weighted Multiobjective Optimization Models and Reformulations

Mehrotra

2012

Operations Research

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We introduce and study a family of models for multi-expert multi-objective/criteria decision making. These models use a concept of weight robustness to generate a risk averse decision. In particular, the multi-expert multi-criteria robust weighted sum approach (McRow) introduced in this paper identifies a (robust) Pareto optimum decision that minimizes the worst case weighted sum of objectives over a given weight region. The corresponding objective value, called the robust-value of a decision, is shown to be increasing and concave in the weight set. Compact reformulations of the models with polyhedral and conic descriptions of the weight regions. The McRow model is developed further for stochastic multi-expert multi-criteria decision making by allowing ambiguity or randomness in the weight region as well as the objective functions. The properties of the proposed approach is illustrated with a few examples. The usefulness of the stochastic (McRow) model is demonstrated using a disaster planning example and an agriculture revenue management example.

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Robust Multi-Objective TEAM 22 Problem: A Case Study of Uncertainties in Design Optimization

Cited by 48 publications

References 7 publications

Six Sigma Quality Approach to Robust Optimization

Six Sigma Quality Approach to Robust Optimization

A Robust Optimization Method Utilizing the Variance Decomposition Method for Electromagnetic Devices

Robust and Stochastically Weighted Multiobjective Optimization Models and Reformulations

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