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TECHNICAL PAPERS

An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions

[+] Author and Article Information
Songqing Shan

Department of Mechanical and Manufacturing Engineering,  University of Manitoba, Winnipeg MB R3T 5V6, Canada

G. Gary Wang1

Department of Mechanical and Manufacturing Engineering,  University of Manitoba, Winnipeg MB R3T 5V6, Canadagary̱wang@umanitoba.ca

1

Corresponding author.

J. Mech. Des 127(5), 866-874 (Nov 26, 2004) (9 pages) doi:10.1115/1.1904639 History: Received February 13, 2004; Revised November 26, 2004

Both multiple objectives and computation-intensive black-box functions often exist simultaneously in engineering design problems. Few of existing multiobjective optimization approaches addresses problems with expensive black-box functions. In this paper, a new method called the Pareto set pursuing (PSP) method is developed. By developing sampling guidance functions based on approximation models, this approach progressively provides a designer with a rich and evenly distributed set of Pareto optimal points. This work describes PSP procedures in detail. From testing and design application, PSP demonstrates considerable promises in efficiency, accuracy, and robustness. Properties of PSP and differences between PSP and other approximation-based methods are also discussed. It is believed that PSP has a great potential to be a practical tool for multiobjective optimization problems.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

An illustration of the desired sampling scheme for PSP

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Figure 2

Flowchart of the Pareto-Set-Pursuing approach

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Figure 3

Initial points generated for the example problem with identified current frontier points

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Figure 4

Sample points at the end of the first iteration for the example problem

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Figure 5

Performance space, evaluated points, and Pareto set points for the example problem

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Figure 6

Performance space, evaluated points, and Pareto set points for Problem 1

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Figure 7

Performance space, evaluated points, and Pareto set points for Problem 3

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Figure 8

A section of the multiple function panel with design variables

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Figure 9

Performance space, evaluated points, Pareto set points for the panel design

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Figure 10

Sample points in the design space at the first iteration

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Figure 11

Sample points in the performance space at the first iteration

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Figure 12

Comparison of PSP with the method in Wilson (16): (a) The procedure of the method in Ref. 16; (b) a simplified illustration of PSP procedure

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