High-Dimensional Bayesian Optimisation with Large-Scale Constraints via Latent Space Gaussian Processes

Abstract

Design optimisation offers the potential to develop lightweight aircraft structures with reduced environmental impact. Due to the high number of design variables and constraints, these challenges are typically addressed using gradient-based optimisation methods to maintain efficiency. However, this approach often results in a local solution, overlooking the global design space. Moreover, gradients are frequently unavailable. Bayesian Optimisation presents a promising alternative, enabling sample-efficient global optimisation through probabilistic surrogate models that do not depend on gradients. Although Bayesian Optimisation has shown its effectiveness for problems with a small number of design variables, it struggles to scale to high-dimensional problems, particularly when incorporating large-scale constraints. This challenge is especially pronounced in aeroelastic tailoring, where directional stiffness properties are integrated into the structural design to manage aeroelastic deformations and enhance both aerodynamic and structural performance. Ensuring the safe operation of the system requires simultaneously addressing constraints from various analysis disciplines, making global design space exploration even more complex. This study seeks to address this issue by employing high-dimensional Bayesian Optimisation combined with a dimensionality reduction technique to tackle the optimisation challenges in aeroelastic tailoring. The proposed approach is validated through experiments on a well-known benchmark case with black-box constraints, as well as its application to the aeroelastic tailoring problem, demonstrating the feasibility of Bayesian Optimisation for high-dimensional problems with large-scale constraints.