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RESEARCH PAPERS

A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization

[+] Author and Article Information
Mian Li

Mechanical Engineering, University of Maryland, College Park, MD 20742

Shapour Azarm

Mechanical Engineering, University of Maryland, College Park, MD 20742azarm@umd.edu

Art Boyars

Code 4330C, Indian Head Division, Naval Surface Warfare Center, Indian Head, MD 20640

J. Mech. Des 128(4), 874-883 (Dec 20, 2005) (10 pages) doi:10.1115/1.2202884 History: Received March 08, 2005; Revised December 20, 2005

We present a deterministic non-gradient based approach that uses robustness measures in multi-objective optimization problems where uncontrollable parameter variations cause variation in the objective and constraint values. The approach is applicable for cases that have discontinuous objective and constraint functions with respect to uncontrollable parameters, and can be used for objective or feasibility robust optimization, or both together. In our approach, the known parameter tolerance region maps into sensitivity regions in the objective and constraint spaces. The robustness measures are indices calculated, using an optimizer, from the sizes of the acceptable objective and constraint variation regions and from worst-case estimates of the sensitivity regions’ sizes, resulting in an outer-inner structure. Two examples provide comparisons of the new approach with a similar published approach that is applicable only with continuous functions. Both approaches work well with continuous functions. For discontinuous functions the new approach gives solutions near the nominal Pareto front; the earlier approach does not.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 2

AOVR in normalized Δf-space

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Figure 3

(a) Worst-case estimate of the OSR in normalized Δf-space, and (b) robustness criterion

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Figure 4

The outer-inner structure of problem

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Figure 5

(a) Original constraint sensitivity region obtained for the combined g1 and g2, and (b) CSR used in calculation of feasibility robustness of design x0 in normalized Δg-space

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Figure 6

(a) AOVR and (b) corresponding PSR in Gunawan’s approach

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Figure 7

Condition causing rejection of robust designs in Gunawan’s approach

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Figure 8

Condition causing rejection of robust designs in our approach

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Figure 9

Cases where Gunawan’s method fails

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Figure 10

(a) Nominal and robust Pareto optimum solutions and (b) robust optimum solutions for the two approaches

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Figure 11

(a) Nominal and robust optimum solutions for the two approaches, and (b) robust optimum solutions for two approaches zoomed in for numerical problem

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Figure 12

Robust solutions when (Δf0,1,Δf0,2)=(0.016,0.1)

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Figure 13

Robust solutions when (Δf0,1,Δf0,2)=(0.014,0.12)

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Figure 1

(a) Tolerance region and (b) corresponding OSR of a design alternative

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