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A Joint Probability Approach to Multiobjective Optimization Under Uncertainty

[+] Author Affiliations
Sirisha Rangavajhala, Sankaran Mahadevan

Vanderbilt University, Nashville, TN

Paper No. DETC2010-28266, pp. 985-996; 12 pages
doi:10.1115/DETC2010-28266
From:
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 36th Design Automation Conference, Parts A and B
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4409-0 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME

abstract

In this paper, we present a new approach to solve optimization problems with multiple objectives under uncertainty. Optimality is considered in terms of the risk that the overall system performance, as defined by all of the multiple objectives exceeding their desired thresholds, remains acceptable. Unlike the existing state-of-the-art, where first-order moments of the system level objectives are used to ensure optimality, we employ a joint probability formulation in our research. The Pareto optimality criterion under uncertainty is defined in terms of joint probability, i.e., probability that all system objectives are less than the desired thresholds. These thresholds can be viewed as the desired upper/lower bounds on the individual system objectives. The higher the joint probability, the more reliably the thresholds bound the system performance, hence the lower the overall system performance risk. However, a desirable high joint probability may necessitate undesirably high/low thresholds, and hence the tradeoff. In this context, the proposed method provides two decision-making capabilities: (1) Maximum probability design: given a set of threshold values for system objectives, find the design that yields the maximum joint probability (2) Optimum threshold design: Given a desired joint probability, find the set of thresholds that yield this probability. In this paper, optimization formulations are presented to solve the above two decision-making problems. A two-bar truss example and the conceptual design of a two-stage-to-orbit launch vehicle are presented to illustrate the proposed methods. The numerical results show that optimizing the mean values of the objectives individually does not necessarily guarantee the desired performance of all objectives jointly under uncertainty, which is of ultimate interest in multiobjective optimization.

Copyright © 2010 by ASME

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