Advances in Bayesian Optimization with Applications in Aerospace Engineering

Optimization requires the quantities of interest that define objective functions and constraints to be evaluated a large number of times. In aerospace engineering, these quantities of interest can be expensive to compute (e.g., numerically solving a set of partial differential equations), leading to a challenging optimization problem. Bayesian optimization (BO) is a class of algorithms for the global optimization of expensive-to-evaluate functions. BO leverages all past evaluations available to construct a surrogate model. This surrogate model is then used to select the next design to evaluate. This paper reviews two recent advances in BO that tackle the challenges of optimizing expensive functions and thus can enrich the optimization toolbox of the aerospace engineer. The first method addresses optimization problems subject to inequality constraints where a finite budget of evaluations is available, a common situation when dealing with expensive models (e.g., a limited time to conduct the optimization study or limited access to a supercomputer). This challenge is addressed via a lookahead BO algorithm that plans the sequence of designs to evaluate in order to maximize the improvement achieved, not only at the next iteration, but once the total budget is consumed. The second method demonstrates how sensitivity information, such as gradients computed with adjoint methods, can be incorporated into a BO algorithm. This algorithm exploits sensitivity information in two ways: first, to enhance the surrogate model, and second, to improve the selection of the next design to evaluate by accounting for future gradient evaluations. The benefits of the two methods are demonstrated on aerospace examples

On the Use of Upper Trust Bounds in Constrained Bayesian Optimization Infill Criterion

In order to handle constrained optimization problems with a large number of design variables, a new approach has been proposed to address constraints in a surrogate-based optimization framework. This approach focuses on sequential enrichment using adaptive surrogate models based on Bayesian optimization approach, and Gaussian process models. A constraints criterion using the uncertainty estimation of the Gaussian process models is introduced. Different evolutions of the algorithm, based on the accuracy of the constraints surrogate models, are used for selecting the infill sample points. The resulting algorithm has been tested on the well known modified Branin optimization problem