Variable fidelity expected improvement for Cokriging

This thesis explores multi-fidelity, surrogate-based, Bayesian optimisation. These are a series of techniques that solve optimisation problems with a high cost for evaluating the objective function. A multi-fidelity approach allows for the incorporation of cheap approximations of the objective function. The multi-fidelity data allows us to fit a Cokriging surrogate model, this is a type of surrogate model designed for multi-fidelity data. A Cokriging model is a more accurate model than one that is fitted with only a small amount of high-fidelity data. A more accurate surrogate model allows for better points to be acquired by the Bayesian optimisation algorithm's acquisition function. In this regard, we have developed a variable fidelity acquisition function that works with the Cokriging model based on a similar approach developed for a hierarchical Kriging model. This new approach performs mor efficiently when compared with the traditional single fidelity acquisition function. Further, we demonstrated viable stopping criteria for a Bayesian optimisation algorithm, an area that is lacking in the literature. Finally, we derived a parallel variable fidelity acquisition function that performed as well as a sequential variable fidelity acquisition function allowing for the use of parallel computing.