Constrained Bayesian Optimisation in High-Dimensional Spaces

Abstract

Optimisation is at the heart of modern engineering. From reducing aircraft emissions to designing safer cars or tailoring drugs for specific diseases, the goal is to find the best solution among countless possibilities. Yet real-world systems are complex, and every design must meet strict constraints related to safety, performance, and physical laws. A design that performs well but violates just one constraint, such as structural failure during flight or non-compliance, is not desirable.

To assess a design’s performance, engineers rely on complex computer simulations that capture physical processes like drag or structural deformation of an aircraft. These simulations often behave like black boxes, as they are expensive to run and the relationship between inputs and outputs is typically non-linear and opaque. This makes exhaustive search of the design space impossible and necessitates data-efficient optimisation strategies.

Bayesian Optimisation (BO) has emerged as a state-of-the-art method for optimising expensive black-box functions, offering a principled way to make the most of limited data. It builds a probabilistic model of the system to guide evaluations efficiently, balancing exploration of uncertain regions with exploitation of promising designs. Although BO has been widely adopted across scientific and engineering domains, it continues to face significant challenges in scenarios that involve both high-dimensional input spaces and complex feasibility constraints. These settings form the primary focus of this thesis.

The first contribution of this work is to show why techniques that work in unconstrained settings, such as random subspace embeddings or simple model priors, often fail under constraints. To address this, the thesis introduces supervised subspace methods and revisits dimensionality-scaled priors that improve both robustness and feasibility discovery in constrained problems.

Second, it proposes scalable strategies to model thousands of constraints, which arise, for example, in structural or aerospace design. Rather than modelling each constraint separately, the thesis uses dimensionality reduction to reduce input and output dimensionality, making constrained optimisation tractable at scale.

Finally, it develops methods for multi-source optimisation, where both accurate and approximate models are available. A modelling framework captures their discrepancies and a novel acquisition strategy balances information gain, cost, and constraint satisfaction, accelerating convergence under tight budgets.

Together, these contributions extend the reach of BO to realistic, simulation-based engineering problems. The resulting tools are broadly applicable and help bridge the gap between theoretical advances in optimisation and the practical demands of high-stakes engineering design.