Title: Stochastic Multi-objective Optimization on a Budget: Application to multi-pass 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
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 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.