This paper presents a new approach to solve multiobjective optimization problems under uncertainty. Unlike the existing state-of-the-art, where means/variances of the objectives are used to ensure optimality, we employ a distributional formulation. The proposed formulations are based on joint probability, i.e., probability that all objectives are simultaneously bound by certain design thresholds under uncertainty. For minimization problems, these thresholds can be viewed as the desired upper bounds on the individual objectives. The tradeoffs are illustrated using the so-called decision surface, which is the surface of maximized joint probabilities for a set of design thresholds. Two optimization formulations to generate the decision surface are proposed, which provide the designer with the distinguishing capability that is not available in the existing literature, namely, decision making under uncertainty, while ensuring joint objective performance: (1) Maximum probability design: Given a set of thresholds (preferences within each objective), find a design that maximizes the joint probability while using a probabilistic aggregation as against an ambiguous weight-based method. (2) Optimum threshold design: Given a designer-specified joint probability, find a set of thresholds that satisfy the joint probability specification while allowing for a specification of preferences among the objectives.
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Joint Probability Formulation for Multiobjective Optimization Under Uncertainty
Sirisha Rangavajhala,
Sirisha Rangavajhala
Civil and Environmental Engineering,
Vanderbilt University
, VU Station B # 351831,2301 Vanderbilt Place,Nashville, TN 37235-1831
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Sankaran Mahadevan
Sankaran Mahadevan
Civil and Environmental Engineering,
e-mail: sankaran.mahadevan@vanderbilt.edu
Vanderbilt University
, VU Station B # 351831,2301 Vanderbilt Place,Nashville, TN 37235-1831
Search for other works by this author on:
Sirisha Rangavajhala
Civil and Environmental Engineering,
Vanderbilt University
, VU Station B # 351831,2301 Vanderbilt Place,Nashville, TN 37235-1831
Sankaran Mahadevan
Civil and Environmental Engineering,
Vanderbilt University
, VU Station B # 351831,2301 Vanderbilt Place,Nashville, TN 37235-1831e-mail: sankaran.mahadevan@vanderbilt.edu
J. Mech. Des. May 2011, 133(5): 051007 (11 pages)
Published Online: June 8, 2011
Article history
Received:
September 7, 2010
Revised:
January 20, 2011
Online:
June 8, 2011
Published:
June 8, 2011
Citation
Rangavajhala, S., and Mahadevan, S. (June 8, 2011). "Joint Probability Formulation for Multiobjective Optimization Under Uncertainty." ASME. J. Mech. Des. May 2011; 133(5): 051007. https://doi.org/10.1115/1.4003540
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