Stochastic Multiobjective Optimization on a Budget: Application to Multipass Wire Drawing With Quantified Uncertainties

Abstract

Design optimization of engineering systems with multiple competing objectives is a painstakingly tedious process especially when the objective functions are expensiveto-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 multi-objective 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.

Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions

“…Each pass reduces the cross section of the incoming wire. The authors refer the reader to Section 3.4 in [50] to gain further information about the modeling of the wire drawing process using finite element method. The wire drawing process here is represented by an expensive computer code of which only a small number of evaluations are possible.…”

Industrial Applications of Intelligent Adaptive Sampling Methods for Multi-Objective Optimization

“…Many approaches exist for running IDACE with multiple objectives [31][32][33][34][35][36][37][38][39]. Here, consider the two-dimensional case and the so-called centroid method which shares a similar intuition as its one-dimensional counterpart Eq.…”

Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning

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