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Addressing Limitations of Pareto Front in Design Under Uncertainty

[+] Author Affiliations
Vijitashwa Pandey, Zissimos P. Mourelatos

Oakland University, Rochester, MI

Efstratios Nikolaidis

University of Toledo, Toledo, OH

Paper No. DETC2011-47238, pp. 1099-1113; 15 pages
doi:10.1115/DETC2011-47238
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 37th Design Automation Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5482-2
  • Copyright © 2011 by ASME

abstract

Engineering design reconciles design constraints with decision maker preferences. The task of eliciting and encoding decision maker preferences is, however, extremely difficult. A Pareto front representing the locus of the non-dominated designs is therefore, often generated to help a decision maker select the best design. In this paper, we show that this method has a shortcoming. We show that when there is uncertainty in both the decision problem variables and in the decision maker’s preferences, this methodology is inconsistent with multi-attribute utility theory, unless the decision maker trades off attributes or some functions of them linearly. This is a strong restriction. To account for this, we propose a methodology that enables a decision maker to select the best design on a modified Pareto front which is acquired using envelopes of a set of certainty equivalent surfaces. This methodology does not require separability of the multi-attribute utility function into single attribute utilities, nor does it require the decision maker to trade the attributes (or any function of them) linearly. We demonstrate this methodology on a simple optimization problem and in design of a reduction gear.

Copyright © 2011 by ASME

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