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International Journal for Uncertainty Quantification
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ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018021315
pages 233-249

STOCHASTIC MULTIOBJECTIVE OPTIMIZATION ON A BUDGET: APPLICATION TO MULTIPASS WIRE DRAWING WITH QUANTIFIED UNCERTAINTIES

Piyush Pandita
School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, 47907
Ilias Bilionis
School of Mechanical Engineering, Purdue University Mechanical Engineering Room 1069, 585 Purdue Mall West Lafayette, IN 47907-2088, USA
Jitesh Panchal
School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, 47907
B. P. Gautham
TATA Research Development and Design Centre, TATA Consultancy Services, Pune, India
Amol Joshi
TATA Research Development and Design Centre, TATA Consultancy Services, Pune, India
Pramod Zagade
TATA Research Development and Design Centre, TATA Consultancy Services, Pune, India

RÉSUMÉ

Design optimization of engineering systems with multiple competing objectives is a painstakingly tedious process especially when the objective functions are expensive-to-evaluate computer codes with parametric uncertainties. The effectiveness of the state-of-the-art techniques is greatly diminished because they require a large number of objective evaluations, which makes them impractical for problems of the above kind. Bayesian global optimization (BGO) has managed to deal with these challenges in solving single-objective optimization problems and has recently been extended to multiobjective optimization (MOO). BGO models the objectives via probabilistic surrogates and uses the epistemic uncertainty to define an information acquisition function (IAF) that quantifies the merit of evaluating the objective at new designs. This iterative data acquisition process continues until a stopping criterion is met. The most commonly used IAF for MOO is the expected improvement over the dominated hypervolume (EIHV) which in its original form is unable to deal with parametric uncertainties or measurement noise. In this work, we provide a systematic reformulation of EIHV to deal with stochastic MOO problems. The primary contribution of this paper lies in being able to filter out the noise and reformulate the EIHV without having to observe or estimate the stochastic parameters. An addendum of the probabilistic nature of our methodology is that it enables us to characterize our confidence about the predicted Pareto front. We verify and validate the proposed methodology by applying it to synthetic test problems with known solutions. We demonstrate our approach on an industrial problem of die pass design for a steel-wire drawing process.


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