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Research Papers

β-Pareto Set Prediction for Bi-Objective Reliability-Based Design Optimization

[+] Author and Article Information
Dong-Shin Lin

 National Cheng Kung University Tainan, 70101, Taiwanlinds@solab.me.ncku.edu.tw

Chun-Min Ho

 National Cheng Kung University Tainan, 70101, Taiwanhocm@solab.me.ncku.edu.tw

Kuei-Yuan Chan1

 National Cheng Kung University Tainan, 70101, Taiwanchanky@mail.ncku.edu.tw

1

Corresponding author.

J. Mech. Des 133(8), 081003 (Jul 27, 2011) (11 pages) doi:10.1115/1.4004442 History: Received July 07, 2010; Revised May 19, 2011; Accepted June 17, 2011; Published July 27, 2011; Online July 27, 2011

In this research, we investigate design optimization under uncertainties for problems with two objectives. Reliability-based design optimization (RBDO) that considers uncertainties as random variables and/or parameters and formulates constraints probabilistically has received extensive attention. However, research to date has focused primarily on single-objective problems only. We extend RBDO to problems for which multiple objectives are optimized simultaneously. Each constraint reliability value results in a Pareto set. The set of all Pareto frontiers at the various reliability values is denoted as the β-Pareto set. We study the relations between the deterministic Pareto set and the β-Pareto set and then develop a method to systematically determine the exact β-Pareto set of bi-objective linear programming problems. The method is also extended to predict the β-Pareto set of nonlinear problems using the sandwich technique. As a result, we are able to accurately predict the β-Pareto set in the objective space without solving multiple multi-objective optimization problems at various reliability levels. In the early stage of the product design process, the proposed approach can help decision-makers efficiently to determine how product performance varies with reliability level.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Existing approach for generating β-Pareto set

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Figure 2

Constructing the β-Pareto set of a BOLP under uncertainty

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Figure 3

Constructing the Pareto frontier of a BOLP

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Figure 4

Cone of a Pareto frame

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Figure 5

β-Pareto set of Eq. 16

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Figure 6

Flowchart for predicting β-Pareto set for BONLP

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Figure 7

Sandwich approach in Pareto approximation

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Figure 8

Linear segmentation of Eq. 18

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Figure 9

β-Pareto set approximation of Eq. 18

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Figure 10

β-Pareto set approximation of vehicle crashworthiness example

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