Speaker
Description
Robust optimization is a crucial technique for enabling design optimization in safety-critical applications, such as those found in the aerospace industry. The objective is to identify an optimal design that is relatively insensitive to uncertainties arising from uncertain model parameters, the model form itself, or unknown environmental conditions. These uncertainties introduce randomness into the objective function, and quantiles serve as appropriate robustness measures, representing an effective optimization target.
The main challenge for quantile-based robust optimization problems is the computational burden, since each objective function evaluation requires solving an uncertainty forward problem. Surrogate-based optimization techniques can alleviate this computational burden, and in particular, Bayesian optimization techniques based on Gaussian processes (GP) have been proposed in the literature.
In this study, we propose a mono-level approach for quantile-based robust optimization. Mono-level approaches construct a global surrogate in the augmented design space consisting of the design and stochastic domains. Such mono-level approaches have been applied in the context of reliability-based design optimization (RBDO) and for robust optimization in the case of a linear robustness measure. Since the computation of a quantile is a nonlinear operation, we rely on sampling-based techniques to compute quantile estimates. We construct an error indicator of the quantile by propagating the epistemic uncertainty of the GP surrogate to the quantile estimate. The quantile estimate and the error indicator are then used within an acquisition policy to select the next infill point in the design space. Our investigation shows that the accuracy of the sampling-based quantile estimate is crucial for the success of the acquisition policy. To allow for large sample sizes, we therefore incorporate an efficient posterior sampling approach introduced in [1], which has the advantage of linear scaling with increasing sample size.
We compare our novel approach to a state of the art bi-level surrogate-based approach. The bi-level approach performs an outer-loop Bayesian optimization in the design space and requires a second-level inner-loop Bayesian optimization at each design point to compute the target quantiles. This approach has the disadvantage that a GP surrogate is built from scratch at each design point evaluation, neglecting the available information gained in previous iterations. For moderate dimensional stochastic domains, our proposed mono-level approach outperforms the bi-level approach in terms of model evaluations. We demonstrate the results on analytical models as well as on benchmarks from structural mechanics.
[1] Wilson et. al. Efficiently sampling functions from Gaussian process posteriors. PMLR, 2020.
